Total Internal Reflection Microscopy

Home , Objective (optics)

Dissertation zur Erlangung des Doktorgrades der Technischen Fakultät der Albert-Ludwigs-Universität Freiburg im Breisgau

Total internal reﬂection microscopy: super-resolution imaging of bacterial dynamics and dark ﬁeld imaging

Philipp von Olshausen

Dezember 2012

Albert-Ludwigs-Universität Freiburg im Breisgau Technische Fakultät Institut für Mikrosystemtechnik Dekan Prof. Dr. Yiannos Manoli

Referenten Prof. Dr. Alexander Rohrbach Jun.-Prof. Dr. Maximilian Ulbrich

Datum der Disputation 28. Februar 2013

Contents

Abstract 5

Zusammenfassung 7

Publications 9

Abbreviations 11

1. Introduction 13 1.1. High-resolution microscopy ...... 13 1.2. Super-resolution microscopy ...... 14 1.3. Label-free microscopy ...... 16 1.4. The bacterial cytoskeleton ...... 17 1.5. Outline ...... 18

2. Theoretical background 19 2.1. Basic optical concepts ...... 19 2.1.1. Fourier transformation ...... 19 2.1.2. Coherent and incoherent image formation ...... 20 2.1.3. Point spread function and optical transfer function ...... 23 2.1.4. Resolution ...... 24 2.2. Total internal reflection microscopy ...... 24 2.2.1. Total internal reflection ...... 25 2.3. Theory of structured illumination microscopy ...... 29 2.3.1. The moiré effect ...... 29 2.3.2. Illumination patterns in SIM ...... 30 2.3.3. Image formation in SIM ...... 30 2.3.4. Resolution enhancement ...... 32 2.4. Numerical image reconstruction in structured illumination microscopy . . 35 2.4.1. Preprocessing of the raw images ...... 36 2.4.2. Separation of spectral components ...... 37 2.4.3. Recombination of shifted spectral components ...... 39

3. Experimental TIRF-SIM set-up 43 3.1. Optical set-up ...... 44 3.1.1. Technical details of the illumination beam path ...... 47 3.1.2. Excitation patterns ...... 49

1 Contents

3.1.3. Epi-fluorescence ...... 50 3.2. Spatial light modulator ...... 51 3.2.1. Holograms ...... 52 3.2.2. Polarization effects of the SLM ...... 56 3.2.3. Correction of non-flatness ...... 57 3.3. Polarization in the illumination beam path ...... 58 3.3.1. Pellicle ...... 59 3.3.2. Dichroic mirror ...... 60 3.4. Drift ...... 61 3.5. Alignment of the optical set-up ...... 63 3.6. Image acquisition ...... 64 3.6.1. Speed ...... 65 3.7. Imaging results with TIRF-SIM ...... 65 3.7.1. Modulation contrast ...... 66 3.7.2. Polystyrene beads ...... 67 3.7.3. Biological samples ...... 70 3.8. Discussion ...... 74 3.8.1. Alternative experimental realizations ...... 74 3.8.2. Strengths and limits of the presented optical set-up ...... 76 3.8.3. Comparison with competitive techniques ...... 77

4. Dynamics of the actin-like protein MreB in Bacillus subtilis 81 4.1. Biological background ...... 81 4.1.1. MreB ...... 82 4.1.2. Cell wall ...... 83 4.2. Results ...... 84 4.2.1. 3D distribution of MreB ...... 84 4.2.2. Filamentous Structure of MreB ...... 84 4.2.3. Dynamics of MreB ...... 86 4.2.4. Tracks of MreB motion ...... 89 4.2.5. Transport velocities of MreB ...... 90 4.2.6. Stationary filaments in protoplasts ...... 93 4.3. Discussion ...... 94 4.3.1. Overexpression ...... 94 4.3.2. TIRF-SIM as the ideal super-resolution microscopy technique to study MreB in B. subtilis ...... 95 4.3.3. Structure and dynamics of MreB - a comparison with recent publications ...... 96 4.3.4. MreB filaments are transported by coupled molecular motors that likely belong to the cell wall synthesis machinery ...... 97 4.3.5. Reversal and orientational change of the filament transport direction 99 4.3.6. Coupled molecular motors might explain filament length dependent transport velocity ...... 99

2 Contents

4.3.7. MreB ﬁlaments organize the synthesis of the cell wall ...... 100 4.4. Outlook ...... 103

5. Total internal reflection dark field microscopy 105 5.1. Imaging Theory ...... 107 5.1.1. Coherent scattering of an evanescent wave ...... 107 5.1.2. 2D Coherent optical transfer function ...... 109 5.1.3. Image formation ...... 110 5.1.4. Two-point resolution in coherent imaging ...... 115 5.2. Experimental set-up ...... 117 5.2.1. Imaging modalities ...... 119 5.2.2. Corrections for an imperfect system ...... 120 5.2.3. Effects of image averaging on the background ...... 121 5.3. Results ...... 123 5.3.1. Images of polystyrene beads ...... 123 5.3.2. Images of biological samples ...... 129 5.4. Discussion ...... 132 5.4.1. Imaging theory ...... 132 5.4.2. Experimental set-up ...... 133 5.4.3. Results: TIRDF images of polystyrene beads and biological samples134

6. Conclusions 137

A. Appendix 139 A.1. Circ function ...... 139 A.2. Preparation of agarose pads ...... 139 A.3. Determination of the illumination intensity in the focal plane ...... 139 A.4. Measurement of ﬁlament length from 3D data ...... 140 A.5. Length correction of MreB ﬁlament lengths ...... 140

Bibliography 143

Abstract

High resolution light microscopy is a valuable tool of modern biology as it allows the investigation of living cells. In particular, fluorescence microscopy enables the observation of virtually any cellular component that can be labeled with a fluorescent dye. A great part of this thesis comprises the construction of a super-resolution fluorescence microscope and its application to living cells. The built microscope combines the advantages of total internal reflection fluorescence (TIRF) and structured illumination microscopy (SIM) and thus yields a twofold increased lateral resolution (≈ 100 nm) compared to the classical Rayleigh limit (≈ 200 nm) at very high contrast. A spatial light modulator is used as diffractive opitcal element, which allows a fast and flexible switching of the illumination patterns resulting in frame rates of about 1 Hz. In particular, TIRF-SIM was used to image the actin-like protein MreB in the bacteria Bacillus subtilis. MreB is part of the bacterial cytoskeleton and its dynamics are tightly linked to cell wall synthesis. TIRF-SIM imaging confirmed that MreB forms filaments which run on straight tracks. Special events like changes of tracks or reversals in direction could be observed. The transport velocity of MreB was found to depend on the filament length. The super-resolved time series obtained by TIRF-SIM enabled the deduction of a mechanistic multi motor model that accounts for the observed phenomena. In this model MreB filaments couple motors that drive the cell wall synthesis which leads to a parallelized and structured growth of new cell wall material. A second part of this thesis comprises the development of a label-free TIR microscopy technique. The sample is illuminated by an evanescent field but instead of fluorescence the light coherently scattered by the object is used for imaging. The illumination light is blocked in the detection path as in dark field (DF) microscopy, which significantly reduces the background. An imaging concept was developed that exploits multiple illumination directions. A theory for the formation of a TIRDF image is introduced and first results show that scattering samples can be imaged with great resolution and high contrast due to the special illumination scheme. This represents a new coherent imaging technique that is label-free and potentially very fast.

Zusammenfassung

Hochauflösende Lichtmikroskopie erlaubt die Untersuchung lebender Zellen und ist somit ein wertvolles Werkzeug der modernen Biologie. Insbesondere die Fluoreszenzmikrokopie erlaubt die Beobachtung praktisch jedes zellulären Bestandteils, welches mit einem Farb- stoff makiert werden kann. Ein Großteil dieser Arbeit umfaßt den Aufbau eines überauflösenden Fluoreszenz- mikroskops und dessen Verwendung zur Untersuchung lebender Zellen. Dieses Mikroskop kombiniert die Konzepte der Totalreflektions-Fluoreszenzmikroskopie und der strukturierten Beleuchtung (TIRF-SIM). Dadurch wird eine verdoppelte laterale Auflösung (≈ 100 nm) im Vergleich zur klassichen Rayleigh Auflösungsgrenze (≈ 200 nm) erreicht bei gleichzeitig hohem Kontrast. Die Verwendung eines spatialen Lichtmodulators als optisches Beugungselement erlaubt ein schnelles und flexibles Schalten der Beleuchtungs- muster. Somit können Bildraten von bis zu 1 Hz erreicht werden. TIRF-SIM wurde insbesondere angewendet um das Aktin-ähnliche Protein MreB in den Bakterien vom Typ Bacillus subtilis zu beobachten. MreB is Teil des Zytoskeletts von Bakterien und die Dynamik von MreB ist eng verbunden mit der Synthese der Zell- wand. Mittels TIRF-SIM konnte bestätigt werden, dass MreB Filamente formt, welche sich auf geraden Trajektorien bewegen. Besondere Ereignisse konnten beobachtet werden, wie z.B. Richtungswechel und -änderungen. Desweiteren wurde herausgefunden, dass die Transportgeschwindigkeit von MreB von der Filamentlänge abhängt. Die über- aufgelösten Bildfolgen, welche mit TIRF-SIM aufgenommen wurden, ermöglichten die Konzeption eines mechanischen Modells von gekoppelten Motoren, welches die Beobach- tungen qualitativ erklären kann. In diesem Modell koppeln MreB Filamente mehrere Motoren, welche die Zellwand-Synthese antreiben. Diese Kopplung führt zu einem paral- lelisierten und strukturierten Wachstum von neuem Zellwandmaterial. In einem zweiten Teil dieser Arbeit wurde eine weitere Mikroskopiemethode entwickelt, welche auf Totalreflektion basiert. Hierbei muss die Probe jedoch nicht (fluoreszenz-) markiert werden, sondern das kohärent gestreute Licht aus dem evaneszenten Beleuch- tungsfeld wird detektiert. Diese Detektion wurde kombiniert mit dem Prinzip der Dunkelfeldmikroskopie, d.h. das ungestreute Beleuchtungslicht wird detektionsseitig ge- blockt, was den Hintergrund im Bild erheblich verringert. Es wurde ein Konzept entwickelt, welches die Beleuchtung der Probe aus vielen Richtungen ausnutzt. Ebenfalls wurde eine Theorie eingeführt, welche die Bildentstehung beschreibt. Es wurden Auf- nahmen von streuenden Proben gemacht, welche die hohe Auflösung und den hohen Kontrast dieser Mikroskopietechnik beweisen. Diese neue, kohärente Abbildungstechnik bedarf keiner Markierung oder Manipulation der Probe und ermöglicht eine potentiell sehr schnelle Bildaufnahme.

Publications

The following publications contain results from this thesis:

F. Spira, N. S. Mueller, G. Beck, P. von Olshausen, J. Beig, and R. Wedlich-Söldner, Patchwork organization of the yeast plasma membrane into numerous coexisting domains, Nature Cell Biology, 14 (2012), pp. 640-648.

Further publications have been submitted:

P. von Olshausen, H. J. D. Soufo, P. L. Graumann, and A. Rohrbach, Super-resolution imaging of dynamic MreB ﬁlaments in B. subtilis - a multiple motor driven transport?

M. C. Huber, A. Schreiber, P. von Olshausen, and S. M. Schiller, Synthetic Biology Inside the Cell: Programmed Engineering of Genetically Encoded Artiﬁcial Organelles in vivo

Abbreviations

2/3D two/three-dimensional AOD acousto optical deflector AOI area of interest AOTF acousto optical tunable filter a.u. arbitrary units B. subtilis Bacillus subtilis BE beam expander BFP back focal plane CCD charge coupled device coh coherent (s)CMOS (scientific) complementary metal-oxide-semiconductor det detection DF dark field DNA deoxyribonucleic acid DO diffraction order E. coli Escherichia coli EM electron microscopy ev evanescent FTIR frustrated total internal reflection FWHM full width at half maximum (E)GFP (enhanced) green fluorescent protein i incident ill illumination inc incoherent LCOS liquid crystal on silicon max maximum min minimum NA numerical aperture OTF optical transfer function PALM photo-activated localization microscopy PBP penicillin binding protein PG peptidoglycan pol polarization PSF point spread function ROI region of interest SIM structured illumination microscopy

11 Contents

SLM spatial light modulator SNR signal-to-noise ratio STED stimulated emission depletion STORM stochastic optical reconstruction microscopy TIRDF total internal reflection dark field TIR(F) total internal reflection (fluorescence)

12 1. Introduction

Understanding the intricate mechanisms regulating living cells is among the major chal- lenges of modern biology and medicine. Light microscopy has become a valuable tool that facilitates the investigation of living cells. One of the most important light microscopy techniques is fluorescence microscopy. The possibility to specifically label almost any cellular component has proven to be enormously helpful as it allows to observe the desired component without distracting signals from other parts of the cell. The discovery of the green fluorescent protein (GFP), honored with the Nobel prize in 2008, together with the advancements in microbiology allow a simple modification of the DNA such that most proteins can be made fluorescent, which gave fluorescence microscopy another boost. Among the vast amount of research carried out on living cells with the help of light microscopy there is one field that is of particular interest to biophysicists: the cytoskeleton, which is a highly dynamic filament system present in most cells. The cytoskeletal filaments appear on length scales from 10 nm to several micrometers and thus necessitate high resolution microscopy, sometimes even beyond the diffraction limit (≈ 200 nm). This thesis aims at the implementation of a fluorescence microscope that can image dynamic biological samples beyond the diffraction limit with a resolution of about 100 nm. This microscopy technique is then applied to image the bacterial cytoskeleton. Also, the development of a new variation of dark field microscopy, label-free and based on coherent scattering, is pursued.

1.1. High-resolution microscopy

A major quality feature of every microscope is its optical resolution. Optical resolution means how well two neighboring features in an image can be separated. Resolution is always tightly linked to the contrast of an image, which defines how much the structure of interest differs in intensity from the background. Both a good resolution and contrast are highly desirable when investigating cells. Electron microscopy (EM) has been shown to achieve resolution down to the molecular or even atomic scale [1]. However, it suffers from practical limitations when it comes to the study of living cells. In order to get reasonable contrast the samples must be stained, usually with heavy salts or metals like, e.g., gold. Furthermore, the samples are mounted in a vacuum chamber. Both staining and a vacuum surrounding are not even close to physiological conditions and are thus not suitable for the study of living cells. The situation is comparable with the decryption of the DNA: to understand the meaning of any genetic sequence not only its structure must be known but also its function. As light

13 1. Introduction microscopy allows to follow the dynamics of cellular components it is an indispensable tool for the deciphering of their function. The investigation of many processes in cells necessitates a high optical resolution, ultimately down to the nanometer scale of single molecules. Though single molecules can already be observed in fluorescence microscopy, the resolution is fundamentally limited by the physics of light. As first discovered by Abbe in 1873 diffraction limits λ the resolution of a normal light microscope to about 2NA [2]. Here, λ is the wavelength of the light and NA = n · sin θ is the numerical aperture of the microscope’s objective, where n is the refractive index of the immersion medium (n ≈ 1 in air) and θ is the maximum angle that can be captured by the objective lens. For high-end objectives with NA ≈ 1.3 and a typical wavelength of λ ≈ 510 nm (GFP) this results in a resolution of about 200 nm.

1.2. Super-resolution microscopy

During the last decades several techniques have been developed to circumvent this resolution limit. These techniques can be classified into two groups [3]. First, there are localization-based techniques, which base on the detection and precise localization of single fluorophores. Many raw images, each containing a subset of single molecules that can be localized with high precision, have to be acquired so that these techniques are limited in acquisition speed. However, the resolution is theoretically only limited by the signal-to-noise ratio (SNR). Photoactivated localization microscopy (PALM) and stochastic optical read-out microscopy (STORM) follow this approach and a lateral resolution < 10 nm could be shown in fixed biological samples [4, 5, 6]. The second group of techniques bases on a spatially non-uniform illumination that can additionally be combined with a nonlinear photoresponse. Among these is stimulated emission depletion (STED) microscopy, a point-scanning technique similar to confocal microscopy [7]. The difference to a confocal microscope is that in STED a second doughnut-shaped depletion beam is overlayed to the scanning focus which depletes the excited fluorophores in the periphery of the focus by the process of stimulated emission. As the depletion process is nonlinear the remaining excitation volume can be made arbitrarily small. A lateral resolution of 15 nm to 20 nm has been shown in biological samples [8]. However, no axial super-resolution is achieved and high laser intensities have to be used to deplete the excited fluorophores. Also, due to the point-scanning nature of this technique the image acquisition rate decreases dramatically with increasing sample size. In this thesis another technique of the second group is exploited, which is structured illumination microscopy (SIM). SIM is a widefield technique, where the whole sample is illuminated by a light pattern. Several raw images illuminated by modified light patterns must be acquired. A final image with increased lateral resolution is then reconstructed from these raw images in a numerical postprocessing step. The light pattern is usually a sinusoidal grating, which can by produced by the interference of two plain waves. As long as the fluorescence signal is proportional to the intensity of the exciting light

14 1.2. Super-resolution microscopy pattern, an increase in resolution of about a factor of two can be achieved [9]. Lateral and Axial resolutions of 100 nm and 360 nm, respectively, have been shown using linear SIM [10, 11]. Exploiting additionally non-linear fluorophore responses the resolution can be further increased (< 50 nm) and is then only limited by the SNR [12, 13]. However, more raw images have to be acquired which limits the overall imaging speed and increases the problem of photobleaching. This thesis aims at an implementation of linear SIM to study dynamic biological processes. For this purpose, a set-up is built using a spatial light modulator (SLM). A SLM is a diffractive optical element in form of a pixelated display, where each pixel can be controlled and shift the phase of the reflected light. Displaying different phase distributions (as, e.g., phase gratings in the case of SIM) on the SLM leads to different beam shapes without mechnically moving any parts. This allows fast, precise, and flexible switching of illumination patterns and is thus well suited for SIM.

cell

glass coverslip

objective lens

fluorescence light

Figure 1.1.: Scheme for TIRF-SIM microscopy. TIRF-SIM is a fluorescence technique, where two counter-propagating evanescent waves create a sinusoidal illumination grating that illuminates only parts of the sample (here a cell with fluorescently labeled filaments). From several raw images, illuminated with different gratings, a final image with a twofold increased lateral resolution can be reconstructed.

The combination of SIM with total internal reflection fluorescence (TIRF) microscopy, referred to as TIRF-SIM, is ideally suited to observe events near the coverslip. In TIRF microscopy the illumination light is totally internally reflected at the coverslip-sample interface and only a thin evanescent field penetrates and illuminates the sample [14]. As the penetration depth is typically on the order of λ/4 the axial sectioning is very good. Furthermore, hardly any background signal is obtained which leads to very high contrast. Figure 1.1 shows the scheme for TIRF-SIM, where two evanescent waves create a thin sinusoidal light grid. Thus only parts of the sample are excited and give fluorescent signal. Although TIRF microscopy is limited to imaging near the coverslip, its two dimensional nature also limits the number of necessary raw images. In TIRF-SIM only nine raw images with modified illumination patterns are needed to reconstruct a final super- resolved image with a resolution of about 100 nm (≈ˆ λ/4). It is thus a good compromise between acquisition speed and lateral resolution. For this reason, TIRF-SIM was applied to study the dynamics of MreB filaments in living bacteria (see sec. 1.4).

15 1. Introduction

1.3. Label-free microscopy

Although the advantages of fluorescence microscopy for biological investigations are numerous, there is still a need to observe cells with label-free techniques. These techniques do not suffer from photobleaching and there is no need to change the sample’s native state by introducing fluorescent dyes. Also, short exposure times are often sufficient due to high signal which allows greater imaging speeds. For this reason the set-up built in this thesis was extended to combine the concept of TIR with dark field (DF) microscopy, referred to as TIRDF.

Label-free microscopy techniques like Zernike phase contrast and differential interference contrast microscopy translate phase changes into modulations of the detected intensity [15]. These techniques are employed in transmission mode which limits the axial sectioning capabilities and also the signal-to-noise ratio (SNR) due to significant background light. Another label-free technique is digital holography, where the light transmitted through the sample is overlayed with an undisturbed reference beam. Sev- eral images with phase-stepped reference beams are acquired which allows the extraction of the phase of the light. From this the differences in optical path length can be calculated. Digital holography has also succesfully been combined with TIR by Ash et al. [16, 17]. However, the maximum NA they used was 0.4 which constricts the lateral resolution. A further techniqe for label-free imaging of cells is tomographic phase microscopy as done by Choi et al. [18]. They could reconstruct the 3D distribution of the refractive index in a cell with a lateral and axial resolution of 0.5 µm and 0.75 µm, respectively. However, image acquisition speed is limited and takes about 10 s for a volume of 20 µm in diamter.

In dark ﬁeld microscopy the illumination light is blocked in the detection path and only light scattered by the sample is used for imaging [19]. This eliminates the background light and yields very high contrast. In normal implementations of dark ﬁeld microscopy white light sources are used and the oblique illumination light penetrates the sample. This impedes the use of detection objectives with very high NA and thus limits the lateral resolution. Furthermore, light scattered in defocused axial planes contributes to the signal and decreases the SNR.

Figure 1.2 illustrates TIRDF as employed in this thesis. The sample is illuminated by an evanescent ﬁeld which is created by TIR of a spatially coherent light source. The illumination light is blocked on its way back to the imaging detector. Only the light coherently scattered by the sample within the evanescent ﬁeld is used for imaging. This approach yields excellent axial sectioning and high SNR as no out-of-focus parts of the sample are illuminated. Also, a detection objective with high NA can be used and imaging is potentially fast. This thesis presents how this technique can be used to yield images of high resolution and contrast with minimized coherent artifacts.

16 1.4. The bacterial cytoskeleton

scattered light

sample

glass coverslip

objective lens

block Figure 1.2.: Scheme for TIRDF microscopy. The illumination light gets blocked in the detection path and only the light scattered by objects in the evanescent ﬁeld is used for imaging.

1.4. The bacterial cytoskeleton

The cytoskeleton of eukaryotic cells consists of three ubiquitous biopolymers made up of protein subunits, namely actin filaments, microtubules and intermediate filaments [20]. These protein structures are highly dynamic and are constantly adapting to environmen- tal influences. They often serve mechanical purposes as they play a key role in cell shape, migration, adhesion, cell division, and serve as tracks for molecular motors [20]. The constant reformation of the cytoskeleton consumes a large part of the energy available to a cell which underlines its importance. In the meantime it is also known that proteins similar to those in eukaryotes form a cytoskeleton in bacteria, which is supposed to be equally important [21]. The proteins ParM and MreB, e.g., have a similar structure to monomeric actin and FtsZ resembles the eukaryotic tubulin. These similarities suggest analog functions of these proteins in procaryotes as their eukaryotic counterparts. Deciphering their function is not simply fundamental research but might help to tackle diseases and design new medicaments against bacterial infections. Applying modern optical microscopy with high temporal and spatial resolution to living bacteria enables the precise observation of cytoskeletal dynamics. Quantitative data about filament distributions, sizes, transport velocities and dynamic changes can be gained which allows for the design of sophisticated biophysical concepts and models. In the case of MreB, e.g., dynamics are tightly linked to the synthesis of the cell wall which is important for the shape and proliferation of bacterial cells like Bacillus subtilis and Escherichia Coli. To understand the mechanics of the growth and the structure of the cell wall the microscopic observation of MreB with high temporal and spatial resolution is of uttermost importance. Thus, the major aim of this thesis is the application of super-resolution microscopy to the living bacteria B. subtilis to better understand the dynamics of the cytoskeletal element MreB.

17 1. Introduction

1.5. Outline

Here, the outline of this thesis is presented.

Chapter 2: Theoretical background The theoretical background necessary to understand this thesis is introduced. This covers basic optical concepts like a Fourier-optical description of image formation and the phenomenon of total internal reﬂection. A theoretical explanation of 2D linear structured illumination microscopy is also provided. Furthermore, the code used for the numerical reconstruction of the SIM images is summarized.

Chapter 3: Experimental TIRF-SIM set-up The experimental set-up that was built during this thesis to do TIRF-SIM imaging is described in great detail. The spatial light modulator (SLM) is presented as the central part of this set-up which controls the illumination pattern. Effects of polarization are treated explicitly due to their strong influence on the illumination grating. A scheme for the compensation of axial drift is described that enables long-term measurements. The alignment of the set-up and the task-flow during image acquisition are explained. Super-resolved images of small polystyrene beads and of biological samples are shown to demonstrate the high-resolution capabilities of TIRF-SIM and to prove its applicability to biological samples. Finally, the experimental set-up as well as the achieved results are discussed which includes a comparison with competitive techniques and an outlook on future improvements and applications.

Chapter 4: Dynamics of the actin-like protein MreB in Bacillus subtilis This chapter presents results on the structure and dynamics of the protein MreB in the bacteria Bacillus subtilis that have been obtained with the TIRF-SIM set-up. First, some biological background about the function of MreB as part of the bacterial cytoskeleton is provided. Then the obtained results, mainly time-lapse TIRF-SIM data, are presented. These results are extensively discussed and a multi motor model is introduced for their explanation. Finally, an outlook on promising future experiments is provided.

Chapter 5: Total internal reflection dark field microscopy This chapter presents the combination of TIR microscopy with the dark field (DF) principle. First, an imaging theory is derived, which explains the formation of an image in TIRDF and bases upon the theoretical foundations given in chap. 2. Then the modified experimental set-up is presented. In the results section images of polystyrene beads and of biological samples acquired by TIRDF microscopy are shown. The discussion of this chapter covers the derived theory, the experimental set-up, and the achieved results as well as an outlook an future improvements and experiments.

Chapter 6: Conclusions A summary of the most important achievements of this thesis is given together with some concluding remarks on the great potential of TIR microscopy.

18 2. Theoretical background

This chapter introduces the theoretical concepts that are necessary for the understanding of this thesis. The presentation of these concepts is compact and the reader is referred to publications and textbooks for a more detailed derivation. Section 2.1 covers basic optical concepts and presents fundamental descriptions of the image formation in a microscope which form the basis for structured illumination microscopy (SIM) and total internal reflection dark field microscopy (TIRDF). In section 2.2 the concept of total internal reflection is introduced and the relevant properties of the evanescent field are explained. Section 2.3 covers the theory of SIM and how lateral resolution enhancement is achieved. The numerical reconstruction that produces the final super-resolved image from the raw images acquired in SIM is explained in the last section 2.4.

2.1. Basic optical concepts

This section introduces a deﬁnition of the Fourier transformation and gives a mathematical formulation of coherent and incoherent image formation in terms of Fourier optics. The point spread function (PSF) and the optical transfer function (OTF) are introduced as important characteristics of an imaging system. Also, the Rayleigh criterion for the lateral resolution of an image is explained.

2.1.1. Fourier transformation

The electric field E(x, y) in the front focal plane of a lens is related to the electric field in the back focal plane, Ee(kx, ky), by a two-dimensional Fourier transformation. The forward Fourier transformation used in this thesis is defined as

Ee(kx, ky) = FT {E(x, y)} ZZ = E(x, y)eı(kxx+kyy) dx dy, (2.1) and the corresponding backward (or inverse) Fourier transform is

−1 n o E(x, y) = FT Ee(kx, ky) ZZ 1 −ı(kxx+kyy) = Ee(kx, ky)e dkx dky. (2.2) (2π)2

19 2. Theoretical background

The spatial frequency coordinates kx-ky in the back focal plane are related to the real space coordinates x0-y0 in the same plane by

x0 y0 k = k · and k = k · , (2.3) x 0 f y 0 f

f k 2π where is the focal length of the lens and 0 = λ0 is the vacuum wavenumber with the vacuum wavelength λ0 [22].

2.1.2. Coherent and incoherent image formation

Almost all imaging presented in this thesis is done in TIR-mode, which is inherently two dimensional (2D). However, the description of image formation given here as according to Singer et al. is equally valid in 3D [23]. Effects of magnification are omitted for clarity. The imaging of an object f(r) is possible because electric fields of the illuminating light interact with the object. In the most simple case the object is illuminated by a −ık r single plane wave si(r) = s0(ki)·e i from the direction ki and with amplitude s0(ki), which represents a spatially coherent illumination. The coherent point spread function (PSFcoh) describes how a point source is imaged into the image plane. For a linear shift invariant system the electric field distribution in the image plane is then described by a convolution of the object with the PSFcoh Z 0 0 0 0 E(r) = f(r ) · si(r ) · PSFcoh(r − r ) dr (2.4)

= f(r) · si(r) ⊗ PSFcoh(r), (2.5) where ⊗ denotes the convolution operator. An equivalent description of eq. 2.5 in Fourier space can be given using the convolution theorem [24]

h i Ee(k) = f˜(k) ⊗ s˜i(k) · OTFcoh(k) (2.6)

= f˜(k − ki) · OTFcoh(k). (2.7)

Here, f˜(k) is the Fourier transform of the object f(r) describing the object ﬁeld spectrum in k-space. Furthermore,s ˜i(k) = δ(k − ki) is a delta function, which leads to a shift of the object spectrum f˜(k) upon convolution for oblique incidence (ki =6 0). The coherent optical transfer function (OTFcoh) is given by the Fourier transform of the coherent point spread function

OTFcoh(k) = FT {PSFcoh(r)} . (2.8)

The OTFcoh describes how the spatial frequencies of the object ﬁeld spectrum f˜(k) are transmitted through the optical system (see sec. 2.1.3). In the following sections it will be considered that typical imaging devices measure intensities and not electric ﬁelds.

20 2.1. Basic optical concepts

Spatially coherent image formation

For the formation of a spatially coherent image two things must be considered. First, the illuminating light source must be spatially coherent. In microscopy this is usually achieved by either closing the Köhler aperture or by using a laser and illuminating the sample with a single, spatially coherent plane wave. Second, every imaging device records intensities. In the most simple approximation the intensity is given by the square of the absolute value of the electric ﬁeld. Using eqs. 2.4 and 2.5 the coherent image formation can be described in real space by

I(r) = |E(r)|2 Z 2 0 0 0 0 = f(r ) · si(r ) · PSF (r − r ) dr coh 2 = |(f(r) · si(r)) ⊗ PSFcoh(r)| (2.9)

Thus, the coherent image is linear in terms of the object ﬁeld. In Fourier space the image intensity spectrum, I˜(k), can be expressed using eq. 2.6 and applying the autocorrelation theorem [24]

nh i o I˜(k) = AC f˜(k) ⊗ s˜i(k) · OTFcoh(k) , (2.10) where AC denotes the autocorrelation. The corresponding description of the real space image, calculated in Fourier space, is

n o I(r) = FT −1 I˜(k) −1 n nh i oo = FT AC f˜(k) ⊗ s˜i(k) · OTFcoh(k) n o 2 −1 ˜ = FT f(k − ki) · OTFcoh , (2.11) where again the autocorrelation theorem was applied. The object field spectrum gets shifted by the illuminating field vector and then filtered by the OTFcoh of the system. The absolute value of the filtered, backward Fourier transformed field spectrum must then be squared to yield the intensity image.

Spatially incoherent image formation

In incoherent imaging an extended light source is assumed that illuminates the object from many directions. Integrating over a large number of different illumination directions ki renders the image spatially incoherent. The formation of an incoherent image is of special importance in this work as it also describes a fluorescence image. The spatially uncorrelated emission of light by many fluorophores is equivalent to an incoherent

21 2. Theoretical background illumination from many directions. Using eq. 2.4 the ﬁnal intensity image is given by

ZZ 2 0 0 0 0 I(r) = f(r ) · si(r ) · PSF (r − r ) dr dki coh ZZ 0 0 = f(r ) · PSFcoh(r − r )· Z ? 00 ? 00 0 ? 00 0 00 f (r ) · PSFcoh(r − r ) · si(r ) · si (r ) dki dr dr , (2.12) | {z } eq. 2.13

? where denotes complex conjugation. Assuming s0(ki) = 1 for all illumination directions −ık r and using si(r) = s0(ki) · e i the underbraced integral becomes a delta function

Z 0 00 ? −ıki(r −r ) 0 00 s0(ki) · s0(ki) · e dki = δ(r − r ). (2.13)

Consequently, eq. 2.12 can be simpliﬁed to

2 2 I(r) = |f(r)| ⊗ |PSFcoh| (2.14) 2 = |f(r)| ⊗ PSFinc, (2.15) where the incoherent point spread function is given by

2 PSFinc = |PSFcoh| . (2.16)

The incoherent image is linear in terms of the intensity of the object. Fourier transforming eqs. 2.14 and 2.15 and applying the convolution theorem and the autocorrelation theorem [24] yields a description of the image intensity spectrum n o I˜(k) = AC f˜(k) · AC {OTFcoh} n o = AC f˜(k) · OTFinc, (2.17) where the incoherent OTFinc can be expressed as the autocorrelation of the OTFcoh

OTFinc = AC {OTFcoh} . (2.18)

The corresponding description of the real space image, calculated in Fourier space, is n o I(r) = FT −1 I˜(k) −1 n n o o = FT AC f˜(k) · OTFinc . (2.19)

Thus, the transmitted spatial frequency components that contribute to an incoherent n o image are calculated by multiplying the object’s intensity spectrum, AC f˜(k) , with the incoherent optical transfer function, OTFinc.

22 2.1. Basic optical concepts

2.1.3. Point spread function and optical transfer function The point spread function (PSF) and the optical transfer function (OTF), as introduced in the previous section, are important parameters characterizing any imaging system. The PSF represents the image of a point source. The OTF, the Fourier transform of the PSF, describes the transmission of spatial frequencies through the imaging system. These properties strongly influence resolution and contrast in the final image. As this thesis covers microscopy techniques in the TIR-mode, a two-dimensional description of the PSF and OTF in the x-y- and kx-ky-plane, respectively, is sufficient. Furthermore, rotational symmetry around the optical axis is assumed. Prefactors have been largely omitted, instead the functions are normalized so that their maximum value is 1. The factor that defines the size and shape of both the PSF and the OTF is the numerical aperture (NA) of the imaging system. The NA is defined as

NA = n · sin(θmax), (2.20) where n is the refractive index of the immersion medium and θmax is the maximal angle of the light that is collected by the imaging system.

Coherent PSF and OTF

The coherent optical transfer function, OTFcoh, is given by the circular aperture of the imaging system in Fourier space. In kx-ky-coordinates it is given by ! k⊥ OTFcoh(k⊥) = circ , (2.21) k0 · NA

q 2 2 where k⊥ = kx + ky and k0 · NA is the radius of the aperture [25]. The definition of the circ-function is given in the appendix (A.1). A radial line profile of eq. 2.21 is shown in red in fig. 2.1-b. From eqs. 2.21 and 2.8 if follows that the coherent PSFcoh is 2 · J1 r⊥ · k0NA PSFcoh(r⊥) = , (2.22) r⊥ · k0NA

p 2 2 where J1 denotes the ﬁrst order Bessel function and r⊥ = x + y is the radial coordinate in the x-y-plane [26]. Figure 2.1-a shows a radial line proﬁle of the coherent PSF in red.

Incoherent PSF and OTF

According to eq. 2.18 the incoherent OTFinc is given by the autocorrelation of the coherent OTFcoh, which yields [27]  v  ! u !2 2 k⊥ k⊥ u k⊥  t  OTFinc(k⊥) = arccos − 1 −  . (2.23) π 2k0NA 2k0NA 2k0NA

23 2. Theoretical background

I (a.u.) I (a.u.) a) b) 1.0 PSFcoh 1.0 OTFcoh PSFinc OTFinc

(λ/NA) r k (k0 NA) -2 -1 1 2 -2 -1 1 2

Figure 2.1.: Radial line proﬁles of the coherent and incoherent PSF (a) and OTF (b).

It is a tent-like function that drops to zero at k⊥ = 2k0NA and is shown in blue in ﬁg. 2.1-b. Combining eqs. 2.22 and 2.16 yields the incoherent PSFinc, 2 2 · J r · k NA 1 ⊥ 0 PSFinc(r⊥) = . (2.24) r⊥ · k0NA Figure 2.1-a shows a radial line proﬁle of the incoherent PSF in blue. A characteristic measure of the incoherent PSF that will be used throughout this thesis is its lateral full width at half maximum (FWHM) given by

λ0 ∆r = 0.51 · (2.25) ⊥,F W HM NA which depends on the vacuum wavelength of the light, λ0, and the NA of the imaging system.

2.1.4. Resolution The incoherent lateral resolution of an optical microscope can be deﬁned by the Rayleigh criterion. It says that two point sources are resolvable in an image when their distance is not smaller than dR given by

λ0 d = 0.61 · . (2.26) R NA This is exactly the distance at which the maximum of one point image is at the position of the ﬁrst minimum of its neighboring point image. Figure 2.2 illustrates the Rayleigh criterion graphically. The dip in intensity between the two maxima of the point images is ∆I = 0.26.

2.2. Total internal reﬂection microscopy

This section presents the process of total internal reflection and introduces the properties of its associated evanescent field. For the microscopy techniques presented in this thesis the evanescent field constitutes the illumination.

24 2.2. Total internal reﬂection microscopy

PSFinc sum ΔI

r λNA d NA Rλ

Figure 2.2.: Rayleigh criterion for the lateral resolution of an incoherent image. The image of two neighboring point sources is the sum of the PSFs of the imaging system. According to the Rayleigh criterion two neighboring point images are resolvable if their λ0 distance is at least dR = 0.61 · NA .

2.2.1. Total internal reflection Whenever a light wave encounters the interface of two media with different refractive indices it undergoes refraction according to Snell’s law [28]. Let ni and nt be the refractive index of the incident and transmitting medium, respectively. If a plane wave hits the interface under an angle greater than the critical angle θc it will undergo total internal reflection (TIR). It occurs when the exit angle in the transmitting medium, θt, becomes 90◦. Using Snell’s law the critical angle is then described by nt θc = arcsin (2.27) ni Due to the boundary conditions set by Maxwell’s equations a thin evanescent field will form in the transmitting medium right at the interface [28]. The situation is illustrated in fig. 2.3, where a plane wave with wave vector ki undergoes TIR and the parallel wave fronts of the evanescent field are drawn in the transmitting medium. The following explanations are restricted to the x-z-plane as shown in fig. 2.3 but are equally applicable to three dimensions. The components of the wave vector of the evanescent field depend on the incident wave vector ki and the indices of refraction of the two media. From Maxwell’s equations it can be deduced that the tangential component of the electric field at an interface is conserved [29]. Thus, the tangential component of the evanescent field vector, ktx, is given by

ktx = kix

= k0 · ni · sin(θi), (2.28) where θi is the angle of incidence as shown in ﬁg. 2.3. Equation 2.28 deﬁnes the wavelength of the evanescent wave, λev, traveling along the interface by

λ0 λev = . (2.29) ni · sin(θi)

25 2. Theoretical background

z z

λev nkt ktz d I(z) tx pd ni x

I0/e I0

kix

θc kiz kr ki θi

Figure 2.3.: Scheme for total internal reflection (TIR) at a plane interface. A plane wave incident under the angle θi > θc (critical angle for TIR) with wave vector ki is totally internally reflected at a plane interface with refractive indices ni > nt. All intensity is reflected (kr) but an evanescent field penetrates into the transmitting medium. To the left the axial decay of the intensity is shown. See main text for details

The axial component of the wave vector of the evanescent ﬁeld, ktz, can be deduced from 2 2 2 q 2 2 the condition kt = ktx + ktz which results in ktz = ± kt − ktx and thus

q 2 2 2 ktz = −ık0 ni · sin (θi) − nt . (2.30)

Here, kt = nt · k0 is the wave vector in the transmitting medium. Equation 2.30 reveals that ktz is imaginary for θi > θc. Consequently, the evanescent electric ﬁeld is described by −ktz·z −ıktx·x E(x, z ≥ 0) = E0 · e · e . (2.31) This ﬁeld travels along the interface and decays exponentially in axial direction. From equation 2.31 it follows that the intensity does also decay exponentially in axial direction which can be expressed by

z − d I(z ≥ 0) = I0 · e pd (2.32) with the penetration depth

λ0 dpd = . (2.33) q 2 2 2 4π ni · sin (θi) − nt

At a distance z = dpd from the interface the intensity has dropped to I0/e. The axial decay of the evanescent intensity is illustrated in the left part of ﬁg. 2.3 .

Polarization dependent ﬁeld components of the evanescent wave

In order to also consider effects of polarization all three dimensions must be taken into account. According to fig. 2.3 a P-polarized incident wave has electric field components in the x-z-plane, whereas S-polarization corresponds to an electric field in the y-direction

26 2.2. Total internal reﬂection microscopy

(the third dimension that is not shown in fig. 2.3). Assuming an incident wave in the x-z- plane with electric field amplitudes Ei0P and Ei0S for P- and S-polarization, respectively, the electric field components of the evanescent field are, according to Axelrod et al. [30], given by

" 2 2 1/2 # 2 cos(θi)(sin (θi) − n ) E ti · E · e−ı(δP +π/2) x = 4 2 2 2 1/2 i0P (2.34) (nti cos (θi) + sin (θi) − nti) " # 2 cos(θi) E · E · e−ıδS y = 2 1/2 i0S (2.35) (1 − nti) " # 2 cos(θi) sin(θi) E · E · e−ıδP , z = 4 2 2 2 1/2 i0P (2.36) (nti cos (θi) + sin (θi) − nti) where

" 2 2 1/2 # −1 (sin (θi) − nti) δP ≡ tan 2 (2.37) nti cos(θi) " 2 2 1/2 # −1 (sin (θi) − nti) δS ≡ tan (2.38) cos(θi)

n nt E 6 and ti = ni . Remarkably, the evanescent field has a component x = 0 for the case of P-polarization. In this case, the evanescent wave is not a transversal wave but has a field component along its direction of propagation (eq. 2.34). The P-polarized field “cartwheels” along the surface. For the case of S-polarization the orientation of the incident electric field is maintained in the evanescent field. This polarization-dependent behavior of the evanescent field has two important consequences. First, the intensity at the interface, I0, depends on the polarization and is, according to Axelrod et al. [30], given by

2 2 2 2 4 cos (θi) · (2 sin (θi) − nti) I0P = |Ei0P | · 4 2 2 2 (2.39) nti cos (θi) + sin (θi) − nti 2 2 4 cos (θi) I0S = |Ei0S| · 2 (2.40) 1 − nti for P- and S-polarization, respectively. According to eqs. 2.39 and 2.40 there is a field enhancement for θi > θc. For θi being only slightly larger than the critical angle the evanescent intensity can become several times greater than the incident intensity. For θi approaching 90◦ the intensity drops towards zero for both polarizations. In this thesis ◦ S-polarization and an angle of incidence θi ≈ 68 were used which, according to eq. 2.40, 2 yields I0S = 2.4 · |Ei0S| . The second important consequence of the polarization-dependence of the evanescent field is that two counter-propagating evanescent waves can only interfere with full modulation contrast if they are S-polarized. This is illustrated in fig. 2.4, where one dimensional line profiles of the intensity at the interface (z = 0) of the resulting standing

27 2. Theoretical background

a) b) IS(x) IP(x)

IP0 IS0

x (nm) x (nm) -400 -200 0 400200 -400 -200 0 400200 Figure 2.4.: One dimensional line profiles of the polarization-dependent contrast of a standing evanescent wave. The interference pattern is assumed to be formed by two counter-propagating waves along the x-axis. (a) Intensity profile for the case of S- polarization. The resulting modulation contrast is Cmod = 1. (b) Intensity profile for the case of P-polarization, where the modulation contrast is reduced to Cmod = 0.89 (with the chosen parameters as given in the text). Also, in the case of P-Polarization the intensity is slightly higher than in the S-polarized case, IP 0 > IS0. waves are plotted for S- and P-polarization. The intensity of the evanescent standing wave is calculated according to eq. 2.43 but here the vectorial character of the electric field was considered. Subfigure (a) shows the case of S-polarization, where the modula- C Imax−Imin C tion contrast, calculated as mod = Imax , is mod = 1. P-polarization only yields Cmod = 0.89, as shown in subfigure (b). Also, the maximum intensity is higher in the case of P-polarization according to eqs. 2.39 and 2.40. Here, the parameters were chosen ◦ to be θi = 68 , nti = 1.33/1.52 and λ0 = 488 nm. The polarization-dependent contrast must be considered when doing TIRF-SIM as will be shown in the next chapter 3.

Frustrated total internal reﬂection

A special situation relevant to TIR microscopy comes up when an object with refractive index nt2 gets into the evanescent ﬁeld at a distance ≤ dpd. Assuming the most simple case, this object consists of a ﬂat surface that is parallel to the interface, where TIR occurs. In order to describe the behavior of the evanescent light at the new interface nt-nt2 the axial component of the wave vector in the object medium, kt2z, must be evaluated. As the tangential component of the wave vector is conserved the boundary 2 2 2 condition is kt2 = kt2z + kix, equivalent as for eq. 2.30. The axial component of the wave vector is then given by

q 2 2 kt2z = (k0nt2) − (k0ni sin(θi)) . (2.41)

From eq. 2.41 it results that kt2z becomes imaginary if nt2 < ni sin(θi), which means that the field in the object with nt2z is also evanescent. If, on the other hand, nt2 > ni sin(θi) then the field in the object becomes propagating. This latter effect is called frustrated total internal reflection.

28 2.3. Theory of structured illumination microscopy

Conclusions for TIR microscopy

Summarizing the eﬀects of TIR at a given interface with ni and nt the following conclusions are important for TIR microscopy as presented in this thesis:

• A lower angle of incidence θi leads to a higher penetration depth of the evanescent field, a stronger field enhancement and frustrated TIR is more likely to occur. Accordingly, a higher angle of incidence leads to a smaller penetration depth, weaker field enhancement and FTIR becomes less likely.

• FTIR is generally more likely to occur the greater the index of refraction nt2 of the object intruding into the evanescent ﬁeld.

• For proper interference of two counter-propagating evanescent waves these waves must be S-polarized.

2.3. Theory of structured illumination microscopy

This section covers the theoretical concepts behind structured illumination microscopy (SIM). First, an illustrative description of SIM in real space is given by introducing the moiré effect (sec. 2.3.1). Second, the creation of a sinusoidal illumination pattern by the interference of two plane waves is briefly explained in sec. 2.3.2. Then the formation of a two-dimensional fluorescence image with a sinusoidal illumination is described in sec. 2.3.3. In sec. 2.3.4 it is explained how this leads to an increase in lateral resolution. As SIM was done in TIRF-mode in this thesis, all descriptions are constrained to two dimensions (x-y-plane). However, the concept of SIM is also applicable in 3D which then leads to an increase in resolution also in axial direction [31]. Furthermore, only the case of linear SIM is explained, which assumes that the fluorescence intensity is proportional to the exciting light intensity and the density of fluorophores. For the case of nonlinear SIM it is referred to the work by Heintzmann [32].

2.3.1. The moiré effect A descriptive illustration of why SIM can enhance the lateral resolution is given by the moiré effect in real space which is illustrated in fig. 2.5. Subfigure (a) shows an object that contains high spatial frequencies. Let’s assume that these frequencies can not be resolved by the imaging system. When this object is illuminated by a periodic pattern (b) this results in an overlay image which contains lower spatial frequencies, as shown in (c). These lower frequencies are the result of frequency mixing and encode the higher frequency components which have been downsampled into the transmission passband of the imaging system. Thus, the observed image contains information about high frequency components which are not accessible under normal illumination. Knowing precisely the regular illumination pattern, the high frequency components of the object can in principle be extracted. These higher frequencies correspond to a higher spatial resolution.

29 2. Theoretical background

a) b) c)

Figure 2.5.: Structured illumination in real space: the moiré eﬀect. If an object containing high frequencies (a) is illuminated by a periodic pattern (b) the resulting image (c) contains low spatial frequencies encoding the higher ones. A microscope image contains only the lower spatial frequencies due to the limited support of the optical transfer function. Knowing the illumination pattern, the object’s high spatial frequency components can in principle be extracted from the image.

2.3.2. Illumination patterns in SIM The illumination patterns in SIM are usually created by the interference of two plane waves (or three in 3D-SIM [31]). Interference of two plane waves leads to a sinusoidal pattern. In TIRF-SIM two counter-propagating evanescent waves are used to create the illumination pattern. According to eq. 2.31 the two evanescent waves are described by

−ıkevr⊥+ϕ01 Eev1(r⊥, z = 0) = E01(r⊥) · e (2.42) ıkevr⊥+ϕ02 Eev2(r⊥, z = 0) = E02(r⊥) · e , ! x where k has been replaced by ±k which lies in the plane of r = and ϕ are tx ev ⊥ y 01/2 constant phase oﬀsets. S-polarization must be assured so that these evanescent waves can interfere with maximum contrast (see sec. 2.2.1). The intensity of the interference pattern, Iev, is then given by 2 Iev(r⊥) = |Eev1(r⊥) + Eev2(r⊥)| 2 2 = |E01(r⊥)| + |E02(r⊥)| + 2E01(r⊥)E02(r⊥) · cos(2kevr⊥ + ϕ0), (2.43) where ϕ0 = ϕ01 + ϕ02 is the global phase of this cosine grating. Alternatively, Iev(r⊥) can be written as

Iev(r⊥) = I0(r⊥) (1 + Cmod(r⊥) · cos(2kevr⊥ + ϕ0)) , (2.44)

2 2 2E01(r⊥)E02(r⊥) where I0(r⊥) = |E01(r⊥)| + |E02(r⊥)| and Cmod(r⊥) = is the modula- I0(r⊥) tion contrast of the interference pattern.

2.3.3. Image formation in SIM For the description of the image formation eq. 2.44 is rewritten to introduce a more n convenient expression for the intensity of the illumination grating Gd (r⊥), n Gd (r⊥) = 1 + Cmod · cos(kg,d · r⊥ + n · ∆ϕ + ϕ0). (2.45)

30 2.3. Theory of structured illumination microscopy

Here, n · ∆ϕ with n = −1, 0, 1 represent the phase steps of the illumination pattern and the index d refers to the direction of the grating. The grating vector kg,d = 2kev determines the period and orientation of the illumination pattern. The illumination grating has been normalized by the intensity I0(r⊥) and it is furthermore assumed that Cmod does not depend on r⊥. The Fourier transform of eq. 2.45 is given by

n ı(n·∆ϕ+ϕ0) Ged (k⊥) = 2π · δ(k⊥)+πCmod · δ(k⊥ + kg,d) · e +

−ı(n·∆ϕ+ϕ0) πCmod · δ(k⊥ − kg,d) · e ). (2.46)

In the case of fluorescence microscopy the object f(r⊥) represents the distribution of fluorophores. As already mentioned, it is assumed that the measured intensity is proportional to the excitation intensity and the fluorophore density. This means that f(r⊥) represents the intensity object which must be multiplied by the illumination grating. According to eq. 2.15 the image is then given by

n n Imd (r⊥) = (f(r⊥) · Gd (r⊥)) ⊗ PSFinc(r⊥) (2.47)

A more illustrative understanding of SIM is obtained in Fourier space. The intensity spectrum of the image, Img(k⊥), is then obtained by the Fourier transform of eq. 2.47

n n Imgd (k⊥) = f˜(k⊥) ⊗ Ged (k⊥) · OTFinc(k⊥), (2.48) where f˜(k⊥) is the intensity object spectrum and the convolution theorem was applied. Plugging in eq. 2.46 for the illumination grating yields

n ı(n·∆ϕ+ϕ0) Imgd (k⊥) = 2π · δ(k⊥) + πCmod · δ(k⊥ + kg,d) · e +

−ı(n·∆ϕ+ϕ0) πCmod · δ(k⊥ − kg,d) · e ⊗ f˜(k⊥) · OTFinc(k⊥) (2.49)

Performing the convolution leads to three copies of the object spectrum f˜(k⊥) at the positions of the delta-functions and eq. 2.49 simpliﬁes to

n C mod ın·∆ϕ ıϕ0 Img (k⊥) = 2π · f˜(k⊥) + · f˜(k⊥ + kg,d) · e · e d 2 C mod −ın·∆ϕ −ıϕ0 + · f˜(k⊥ − kg,d) · e · e · OTFinc(k⊥). (2.50) 2

Figure 2.6 illustrates the effects of a structured illumination in real space and in k- space with one dimensional line profiles along the grating direction d. To the left, a box-like object, a cosinusoidal illumination structure and the product of these two are shown in red from top to bottom. Upon imaging the object structure is convolved with the PSF of the imaging system which blurs the image but maintains a certain degree of modulation that comes from the illumination (not shown). To the right of fig. 2.6, the absolute values of the corresponding Fourier transforms are plotted in blue. The

31 2. Theoretical background

f(r ) f(k )

OTF object inc FT r k

-kg,d kg,d n n Gd(r ) Gd(k )

illumination FT r k

-kg,d kg,d n f(k ) n f(r ) Gd(r ) Gd(k )

illuminated object FT r k

-kg,d kg,d

Figure 2.6.: One dimensional illustration of how a structured illumination shifts high frequency information of an imaged object into the transmission passband of the OTF. To the left, a box-like object, a cosinusoidal illumination structure and the product of these two are shown in red from top to bottom. To the right, the absolute values of the corresponding Fourier transforms are plotted in blue. The incoherent OTF of the imaging system is shown in gray. The spectrum of the structurally illuminated object contains high spatial frequency components which have been shifted into the transmitting band of the OTF. incoherent OTF of the imaging system is shown in gray. According to eq. 2.48 in Fourier space the object spectrum must be convolved with the illumination spectrum, which consists of three delta functions. This leads to two copies of the object spectrum at the position of the grating vector ±kg,d, plus the central copy. From the two shifted copies high frequency spectral components are now in the transmitting passband of the OTF that are usually outside. This high frequency information corresponds to a higher spatial resolution and can be extracted as shown in secs. 2.3.4 and 2.4.

2.3.4. Resolution enhancement

As shown in ﬁg. 2.6 and by eq. 2.50 the cosinusoidal illumination leads to two extra copies of the object spectrum which have high spatial frequency components within the OTF support. In order to gain lateral resolution, these high frequency components must be extracted and shifted to their proper position in Fourier space. As there are three spectral copies that have to be separated, three images with diﬀerently modulated illuminations are required to solve the equation system. This is achieved by shifting

32 2.3. Theory of structured illumination microscopy

2π the phase of the illumination pattern. Phase shifts are chosen to be 0 and ±∆ϕ = 3 , corresponding to n = −1, 0, 1, so that the sample gets homogeneously illuminated over one grating orientation. Applying three phases for one grating direction d to get three raw images the equations according to eq. 2.50 can be written in matrix notation

Im (k ) f d ⊥ M f˜ (k ) z }| { c d ⊥  −1  z }| { z }| { Im k  Cmod −ı·∆ϕ Cmod ı·∆ϕ   ˜  gd ( ⊥) 1 2 · e 2 · e f(k⊥)  0  C C  mod mod  ·  ˜ ıϕ0,d  ·  Imgd(k⊥)  = 1 2 2   f(k⊥ + kg,d) · e   1  C ı·∆ϕ C −ı·∆ϕ −ıϕ 1 mod · e mod · e f˜(k⊥ − kg,d) · e 0,d Imgd(k⊥) 2 2

2π · OTFinc(k⊥), (2.51)

n where Imgd (k⊥) are the Fourier transforms of the acquired raw images. Using the compact vector notation eq. 2.51 breaks down to

Img d(k⊥) = Mc · f˜d(k⊥) · 2π · OTFinc(k⊥) (2.52) with the mixing matrix Mc, the image vector Img d(k⊥) and the object spectrum vector f˜d(k⊥) that also contains the global phase ϕ0,d for the corresponding direction. Inverting Mc yields the separation matrix Mc−1, which allows to separate the central copy and the two shifted copies of the object spectrum

−1 Mc · Img d(k⊥) = f˜d(k⊥) · OTFinc(k⊥) · 2π. (2.53)

The three separated spectral components, described by the right side of eq. 2.53, are in the following abbreviated by

ı·m·ϕ0,d Sem,d(k⊥) = f˜(k⊥ − m · kg,d) · e · OTFinc(k⊥), (2.54) where m = −1, 0, 1 is the order of the component. The constant factor 2π is omitted for clarity. The three spectral components Sem,d(k⊥) contain different parts of spectral information that partly overlaps. Correcting for the global phase ϕ0,d and putting the three frequency components to their proper places in k-space yields an effectively enlarged image spectrum along the direction of the grating. For an isotropic increase in resolution in the x-y-plane the above procedure is repeated three times along three symmetrically distributed grating π ◦ directions so that φ = d · 3 ˆ=d · 60 with d = −1, 0, 1, where φ is in the x-y-plane [33]. This yields an effectively enlarged image spectrum,

1 1 X X −ı·m·ϕ0,d Imgeff (k⊥) = Sem,d(k⊥) · e d=−1 m=−1 1 1 X X = f˜(k⊥ − m · kg,d) · OTFinc(k⊥) (2.55) d=−1 m=−1

33 2. Theoretical background

n f(k ) Gd(k ) a)

3 x with n = -1, 0, 1

-kg,d kg,d

b) S-1,d(k ) S0,d(k ) S1,d(k )

k k k

-kg,d kg,d -kg,d kg,d -kg,d kg,d

c) Imeff(k )

OTFeff

-2kg,d -kg,d kg,d 2kg,d

Figure 2.7.: One dimensional scheme along one grating direction d that illustrates the enhancement of lateral resolution in Fourier space. The OTF of the imaging system is shown in gray. (a) Three raw images with different phases n provide three image spectra. Each of these image spectra contains three copies of the object spectrum as shown in fig. 2.6. The spectral parts shown in light blue are not contained in the raw images. (b) Application of the separation matrix Mc−1 separates the three spectral copies. (c) Putting these copies to their true positions in Fourier space yields an effectively enlarged image spectrum Imf eff (k⊥) and consequently an image with increased lateral resolution. The effective OTFeff is shown in gray and indicates the enlarged support.

Alternatively, an eﬀective OTFeff can be deﬁned

1 1 X X Imgeff (k⊥) = f˜(k⊥) OTFinc(k⊥ + m · kg,d) d=−1 m=−1

= f˜(k⊥) · OTFeff (k⊥) (2.56)

The ﬁnal super-resolved image is then obtained by an inverse Fourier transformation of the enlarged image spectrum

−1 n o Imfinal = FT Imgeff (k⊥) (2.57)

Figure 2.7 illustrates the reconstruction process and the corresponding enhancement of resolution in a one dimensional scheme along one grating direction d in Fourier space.

34 2.4. Numerical image reconstruction in structured illumination microscopy

The OTF of the imaging system is shown in gray. Three raw images with different phases ϕ = n · ∆ϕ + ϕ0 of the illumination grating provide three image spectra as indicated in subfigure (a). Each of these image spectra contains three copies of the object spectrum as explained in fig. 2.6. Applying the separation matrix Mc−1 according to eq. 2.53 separates the three spectral copies (b). Putting these copies to their true positions in Fourier space, as illustrated in subfigure (c), yields an effectively enlarged image spectrum Img(k⊥) and consequently an image with increased lateral resolution. The effective OTFeff , as defined in eq. 2.56, is shown in gray and indicates the enlarged support. In TIRF-SIM the grating vector kg lies right outside of the OTF support. Thus, one half of the shifted copies of the spectrum is also contained in the central part of the spectrum, whereas the other half is new, additional information at higher frequencies outside of the normal OTF support. Putting these copies to their true positions in Fourier space enlarges the effective OTF support by a factor of two along the applied grating orientation. Consequently, the expected increase in lateral resolution in the final real space image is also a factor of two.

2.4. Numerical image reconstruction in structured illumination microscopy

The previous section explained theoretically how SIM leads to an increase in resolution. In practice the reconstruction must be performed numerically in a postprocessing step. Some parameters like, e.g., the global phase ϕ0 and the grating vector kg,d are not known or only known with insuﬃcient precision so that they have to be determined during the postprocessing. This necessitates an elaborate reconstruction code. The reconstruction code used in this thesis was kindly provided by Rainer Heintzmann from the Institute of Photonic Technology in Jena. It is a Matlab ( c The Mathworks) code mainly written by Rainer Heintzmann, Kai Wicker and Ondrej Mandula. This section aims at giving an overview and a principle understanding of most of the steps performed during the reconstruction. The explanations given here base fundamentally on the PhD thesis by Kai Wicker and the Master thesis by Ondrej Mandula [34, 35]. A brief summary of their code is described by Hirvonen et al. [36]. A quite detailed description of the numerical image reconstruction is also given by Gustafsson et al. [31]. The explanations of the image reconstruction in this section refer to how the code was usually employed in the frame of this thesis. Additional, optional capabilities of the code that may sometimes be relevant are brieﬂy mentioned. A mathematically strict derivation of the applied numerical steps is not provided but is rather found in the above mentioned literature. With the TIRF-SIM set-up presented in this thesis (chap. 3) nine raw images were acquired to reconstruct a super-resolved image of one time point. Three orientations π π 2π 2π (φ = − 3 , 0, 3 ) with three phases each (∆ϕ = − 3 , 0, 3 ) made up the raw data, which is referred to as one set of raw images. The reconstruction code uses one such set of digitally acquired raw images as input, extracts the high frequency information and pops

35 2. Theoretical background out a final image. In order to do so some input parameters must be provided by the user: • estimate of the grating period and orientations • number and magnitude of phase steps for each grating orientation • pixel size of the raw images • experimentally measured 2D PSF; alternatively the PSF/OTF is calculated from the numerical aperture (NA) of the objective lens, the index of refraction of the immersion medium and the emission wavelength of the fluorophores This section is subdivided into three parts, similar to how the code is structured. In the first section 2.4.1 the preprocessing of the raw images is explained. Section 2.4.2 describes the separation of the various spectral components which is done independently for each grating orientation. In the last section 2.4.3 the recombination of the shifted frequency components is described. This includes a weighted average that accounts, e.g., for effects of the OTF. Also, a deconvolution is done before the final output image is generated.

2.4.1. Preprocessing of the raw images All raw images are preprocessed to correct for experimental imperfections and then Fourier transformed. Also, the OTF of the imaging system is calculated as it is needed in the following steps.

Backround subtraction Every raw image is background corrected by subtracting a dark image to get rid of the camera oﬀset. The dark image is an average of ≥ 10 images that were acquired with the illumination laser switched oﬀ and the same exposure time as the actual data.

Miscellaneous options Optionally the intensity between single raw images can be adjusted to compensate for fluctuations of the laser intensity. Every raw image is normalized by its overall intensity, norm Imn(r⊥) Imn (r⊥) = R . This correction assumes that the overall intensity should Imn(r⊥) dr⊥ be the same for all raw images even though they are illuminated by different gratings. This approximation might only hold for large, dense samples and should be used with care on sparse samples. Another option is to correct the raw images for lateral drift between single images of one grating orientation. Due to the modulated illumination the raw images contain different information. By low-pass filtering the raw images in Fourier space most of the contributions from the grating are suppressed as this information is mainly around ±kg,d. The low-pass filtered real space images are then cross-correlated to yield the lateral drift.

36 2.4. Numerical image reconstruction in structured illumination microscopy

Fourier transformation

All raw images are dimmed down at their edges using a 2D Hanning window with a ﬂat central area. Approximately the 10 outermost pixel in each direction are damped. Then the images are Fourier transformed using a fast Fourier transformation (FFT).

Calculate OTF

Ideally, an image of an experimentally measured 2D PSF is provided for the reconstruction. The PSF is centered, rotationally averaged and then Fourier transformed to yield the OTF of the system, which is needed throughout the reconstruction. If no PSF image is provided the OTF is theoretically calculated from the NA, the index of refraction of the immersion medium, and the emission wavelength. For most of the reconstruc- tions performed in this work an experimentally measured PSF was provided that was measured by imaging a small ﬂuorescent bead of 92 nm diameter.

2.4.2. Separation of spectral components

Once the raw images are preprocessed the next step is to separate the spectral components as described in sec. 2.3.4. This is done separately for each orientation d of the illumination grating.

Separation matrix n Three raw images Imgd (r⊥)(n = −1, 0, 1) along one direction d are multiplied with the separation matrix Mc−1 according to eq. 2.53 to yield the three separate spectral components. For the unmixing it is assumed that Cmod = 1. It must be mentioned that the global phase ϕ0 is not yet known but will be corrected for later. Optionally, an iterative matrix optimization can be performed. In this process the phase steps ∆ϕ and the intensities Cmod are varied for the individual images and the resulting separation is evaluated by the suppression of residual orders in the spectral components. A detailed description of the iterative matrix optimization can be found in the works by K. Wicker and O. Mandula [34, 35].

Grating period

The grating period (or grating vector kg,d) of the illumination pattern is deﬁned by the illumination beam path. For the TIRF-SIM set-up built in this thesis the grating period is dictated by the pixel pitch of the spatial light modulator, the pixel period of the hologram and the magniﬁcation of the illumination beam path (see chap. 3). These parameters are known with some accuracy. However, to shift the separated spectral components to their true positions in k-space and to avoid artifacts in the reconstruction due to destructive interference of mismatched spectral information the grating period has to be determined with very high precision.

37 2. Theoretical background

S (k ) 0,d s k S1,d(k ) CCw ( = 0) k k est -kg,d Δ -kg,d Δ kg,d=0 kg,d=0

Figure 2.8.: Finding the precise grating vector kg,d by a weighted cross-correlation of neighboring, overlapping spectral components. (a) Shifting the ﬁrst order spectral est component, Se1,d(k⊥) (red), by kg,d is a good estimate but it remains an error ∆kg,d = est kg,d − kg,d. (b) Maximizing the central value of the weighted cross-correlation (eq. 2.60) minimizes that error and thus yields a precise overlap of the spectral information.

In TIRF-SIM there is always an overlap between the central zeroth order component, Se0,d(k⊥), and the ±1. order components, Se±1,d(k⊥), meaning that they contain the same spectral information as shown in sec. 2.3.4. To precisely determine the grating vector s kg,d the central component Se0,d(k⊥) and the shifted ﬁrst-order component Se1,d(k⊥) = est est Se1,d(k⊥ − kg,d) are cross-correlated, where kg,d is the estimate of the grating vector est provided by the user. This estimate kg,d is then varied around its initial value to maximize the central value (CCw(k⊥ = 0)) of the weighted cross-correlation

s CCw(k⊥) = Se0,d Se1,d (k⊥) (2.58) ~ w R 0 0 s? 0 0 wCC (k⊥)Se0,d(k⊥)Se1,d(k⊥ + k⊥) dk⊥ = R 0 0 (2.59) wCC (k⊥) dk⊥ s ⇒ CCw(k⊥ = 0) = wCC (k⊥) · Se0,d(k⊥) · Se1,d(k⊥), (2.60) where the weights wCC (k⊥) are given by the eﬀective OTFs of the corresponding com- ? ponents and the signal-to-noise ratio (SNR). The refers to complex conjugation and ~ denotes cross-correlation. Figure 2.8 illustrates the procedure graphically. The initial guess of the grating vector, est kg,d, is usually a good approximaion to the real grating vector kg,d, as shown in (a). est Variing kg,d and thus maximizing the cenral value of the weighted cross-correlation minimizes the error between the estimated and the real grating vector, ∆kg,d = kg,d − est kg,d, as shown in (b).

Global phase

The global phase of the illumination pattern, ϕ0, as introduced in eq. 2.45, is not known and must thus be determined during the reconstruction process. The relative phase shifts n · ∆ϕ have already been compensated for in the separation matrix. Thus, the remaining phase diﬀerence between neighboring, overlapping components is the global phase ϕ0. It can be extracted for each direction d as the phase of the central pixel from

38 2.4. Numerical image reconstruction in structured illumination microscopy a weighted cross-correlation as given in eq. 2.58 and eq. 2.60, respectively,

s ϕ0,d = arg Se0,d Se1,d (k⊥ = 0) ~ w = arg (CCw(k⊥ = 0)) (2.61)

Further options

−1 In the separation matrix Mc it has been assumed that Cmod = 1. A weighted cross correlation of neighboring, overlapping spectral components can also yield information about the order strength, i.e., the modulation contrast Cmod. Another option is the correction of lateral drift of the sample between diﬀerent grating directions. This is achieved by comparing the real space zero order components, −1 n o FT Se0,d(k⊥) , using cross-correlations.

2.4.3. Recombination of shifted spectral components

This section describes how the separated spectral components Sem,d(k⊥) are put together to yield a ﬁnal, enlarged image spectrum Imgf (k⊥) that approximates the true object spectrum f˜(k⊥) as good as possible over the enlarged frequency region.

Direction Strength Objects might exhibit a different brightness for different grating orientations d = −1, 0, 1. This may be due to fluctuations of the laser intensity, polarization of the fluorophores or photobleaching. In this case different grating orientations do not contribute spectral information with the same intensity. That includes that the central zeroth order component, Se0,d(k⊥), which is obtained separately for each grating orientation, might differ in intensity for different directions. An estimation of the power spectrum of one grating orientation relative to the first is given by a comparison of the central zero order spectral components R 2 Se (k⊥) dk⊥ s 0,d . d = R 2 (2.62) Se0,−1(k⊥) dk⊥ The direction d = −1 was always the first grating orientation in the measurements performed in this thesis. The obtained direction strengths sd are utilized in the next step.

Weighted average

The spectral components Sem,d(k⊥) are not simply shifted and added in Fourier space as this would corrupt the signal-to-noise ratio in certain frequency regions. In the areas of overlap between different components the frequency information of one component is usually transmitted by a greater or smaller OTF than the same information in the other component. This corresponds to different signal-to-noise ratios which should be considered when adding the different spectral components together. Using weights wm,d(k⊥)

39 2. Theoretical background that consider the strength of the OTF for each spectral component and the noise level an enlarged spectrum Imgw(k⊥) is obtained by a weighted average P −ı·m·ϕ sd · wm,d(k⊥) · Sem,d(k⊥ + m · kg,d) · e 0,d m,d Imgw(k⊥) = P . (2.63) sd · wm,d(k⊥) m,d

Here, the correction for the global phase of each direction, ϕ0,d, is also included. A detailed derivation of the weights, including a normalization of the noise, is given by K. Wicker [34].

Wiener filter deconvolution The image quality can be further improved by applying a deconvolution in Fourier space that tries to compensate for the OTF which transmits lower spatial frequencies better than higher ones. In this reconstruction code a Wiener filter approach is chosen. Generally, the Wiener filter function W (k⊥) performs a deconvolution with respect to the signal-to-noise ratio and minimizes the error of the deconvolved spectrum compared to the real spectrum. The deconvolved image spectrum is obtained by

Imgww(k⊥) = Imgw(k⊥) · W (k⊥). (2.64) Here, a simpliﬁed version of the Wiener ﬁlter that assumes a constant object spectrum (f˜(k⊥) = const) is applied. It is given by

OTFf (k⊥) W (k⊥) = 2 2 , (2.65) OTFf (k⊥) + w where OTFf (k⊥) is the ﬁnal overall OTF that is made up of the OTFeff (eq. 2.56), the weights used in eq. 2.63 and the direction strengths according to eq. 2.62. The Wiener parameter w is inverse proportional to the overall average signal-to-noise ratio and is chosen empirically.

Apodization The simplified Wiener filter assumes a constant power spectrum though typical samples in microscopy have more information in lower frequencies. Consequently, the Wiener filter overemphasizes high frequencies and thus also their worse SNR. To compensate for this effect an apodization function A(k⊥) is used that dims down the higher frequencies, π A(k⊥) = sin · dist (fp (OTFf (k⊥))) . (2.66) 2

Here, “fp” is the footprint of the OTFf , which is 1, where the OTF has support, and 0 otherwise. The Euclidean distance transform “dist” is the closest distance of a point k⊥ to the edge of fp and is normalized so that the maximum distance is 1. This apodization function is shown in ﬁg. 2.9. It decays from the center to the outer border of the overall OTF support, which additionally avoids ring-shaped artifacts in real space that would result from a sharp edge in Fourier space.

40 2.4. Numerical image reconstruction in structured illumination microscopy

A(k )

-2kg,d -kg,d kg,d 2kg,d

Figure 2.9.: Apodization function that was used in the numerical reconstruction according to eq. 2.66.

Final image The ﬁnal, enlarged image spectrum is given by

Imgf (k⊥) = Imgw(k⊥) · W (k⊥) · A(k⊥), (2.67) where Imgf (k⊥) is an optimized estimate of the true sample information f˜(k⊥). The ﬁnal image would then be obtained by a Fourier backtransformation

−1 n o Im(r⊥) = FT Imgf (k⊥) (2.68)

However, in this reconstruction code all spectral components are separately weighted according to eq. 2.67. The weighted spectral components are zero-padded to accommodate the increased resolution and then Fourier backtransformed to real space. The shifting of the spectral components is then done in real space by a multiplication with the corresponding phase gradient. Finally, all components are added together to produce the ﬁnal image. This somewhat unusual approach reduces artifacts in the ﬁnal real space image [31].

3. Experimental TIRF-SIM set-up

A major task in this thesis has been the construction of an experimental set-up to perform total internal reflection fluorescence structured illumination microscopy (TIRF- SIM). The set-up that was built is mainly similar to the one published by Fiolka et al. [37]. Figure 3.1 illustrates the imaging concept of TIRF-SIM in comparison with normal TIRF microscopy in 2D. As an example, a four-dot object is shown, which is assumed to be fluorescent and located right at the coverslip. In TIRF (red box) the fluorescence of the object is excited by an evanescent wave which is created via TIR of a single plane wave. The fluorescent light is collected by the microscope and an image is formed. This imaging process can be described by a convolution of the object with the PSF of the system, as explained in sec. 2.1.2. The resulting image and its Fourier transform are shown to the right. The dashed circle indicates the classical diffraction limit.

object TIRF image FT{image}

PSF

ill. grating raw images Φ=-60°

PSF FT{image} Φ=0°

postprocessing

Φ=60°

-2π/30 2π/3 image orientation Φ TIRF-SIM phase Δφ

Figure 3.1.: Imaging concept of TIRF-SIM compared to normal TIRF microscopy. As- suming a fluorescent four-dot object illuminated by an evanescent field, in TIRF (red box) this object is imaged with the PSF of the system (described by a convolution). The resulting image and its Fourier transform are shown to the right. The dashed circle indicates the theoretical diffraction limit. In TIRF-SIM (blue box) the imaging is done with the same system and PSF but the object is illuminated with various sinusoidal gratings. Three orientations of the illumination grating and three phases each are applied and lead to nine raw images (framed). A numerical postprocessing in Fourier space enlarges the image spectrum and results in an image with increased resolution.

43 3. Experimental TIRF-SIM set-up

In TIRF-SIM (blue box) the imaging is done with the same system and PSF but the object is illuminated with a sinusoidal grating. Three grating orientations (φ = ◦ ◦ ◦ 2π 2π −60 , 0 , 60 ) and three phases each (∆ϕ = − 3 , 0, 3 ) are applied (throughout this thesis phase steps are usually given in radians, whereas the orientation of the illumination grating is given in degree). This results in a set of nine raw images which encode higher spatial frequency information. A numerical postprocessing step extracts this information in Fourier space and yields an enlarged image spectrum containing information beyond the classical diffraction limit. The corresponding image has an approximately twofold higher spatial resolution. This chapter gives a detailed description of the optical set-up and also provides results that were achieved. Section 3.1 gives an overview of the optical set-up and all its components. In section 3.2 the spatial light modulator (SLM) is presented as the central device that controls the illumination. This includes an introduction to the utilized phase holograms, effects of polarization and corrections that have to be applied due to imperfections of the device. Section 3.3 briefly treats the control of the polarization of the illumination light as an important factor for an excitation pattern with high contrast. The compensation of drift, especially in axial direction, is covered in section 3.4. Section 3.5 gives a compact explanation of the critical step in aligning the set-up. Sec- tion 3.6 covers the utilization of the microscope by describing the image acquisition and its associated task-flow. Results in the form of super-resolved images of fluorescent beads and living biological cells, which prove the capabilities of the microscope, are presented in section 3.7. Finally, the experimental set-up and the achieved results are discussed in section 3.8 which also includes an outlook on future improvements and applications of TIRF-SIM.

3.1. Optical set-up

Figure 3.2 shows a sketch of the optical set-up with the excitation light drawn in light blue and the ﬂuorescent detection light shown in green. It is based on an inverted microscope (Leica DM-IRBE), which holds the sample and the objective lens. Furthermore, it provides brightﬁeld illumination (not drawn) and holds the detection path. However, in structured illumination microscopy the main challenge is to illuminate the sample with a sinusoidal light grid of high contrast, whose orientation and phase must be controlled. The main part of this illumination beam path is located on an optical table and coupled into the microscope via its rear port.

Illumination beam path A 488 nm Argon-Ion laser (2214-20SL, JDSU) delivers a beam of 0.7 mm diameter (1/e2) that goes through an acousto optical tunable filter (AOTF; Pegasus Optik) that is used to control the laser power and serves as a fast shutter. The +1. diffraction order (DO) of the AOTF is guided into a 20 x beam expander (BE, SILL Optics) which widens the beam diameter to about 14 mm. A mirror reflects the beam onto a spatial light modulator (SLM, LCR-2500, Holoeye Photonics) such that the angle ◦ αSLM between the incoming and outgoing light is minimized (αSLM ≈ 5 ). The SLM is

44 3.1. Optical set-up

SLM image plane

αSLM

BE sample AOTF image plane laser – 488 nm

objective

pupil plane-1

flip pellicle image pupil plane-2 beam plane (BFP) L1a L1b motor L splitter 2 dichroic mirror

fluorescence light pupil plane-3 pol- motorized TL L1 mask ill emission filter filter λ/2-plate TLdet

image plane image plane CCD CCD 1 2 microscope

Figure 3.2.: Optical set-up for TIRF-SIM. A 488 nm Argon-ion laser is shuttered by an acousto optical tunable filter (AOTF) and widened by a 20 × beam expander (BE). The spatial light modulator (SLM) is illuminated under a small angle (αSLM ) and acts as a phase grating that diffracts the beam mainly into the ±1. diffraction order (DO). The lens L1, implemented as a lens doublet consisting of the achromat L1a and the biconvex lens L1b, focuses the beams into the pupil plane-1, where a mask blocks all unwanted DOs. A separate bar-like block, controlled by a flip motor, stops the undiffracted light (blue-framed beam) or alternatively allows epi-illumination. A polarization (pol) filter and a motorized half-wave plate assure S-polarization in the sample plane. A further 4f-system (L2 and TLill) projects the foci into the TIR region of the back focal plane (BFP). Thus, two plane waves emanate from the objective lens and undergo TIR. Their evanescent fields interfere to form a sinusoidal illumination pattern. Fluorescence light is collected by the same objective and separated from the illumination light by a dichroic mirror. An emission filter blocks any remaining excitation light. A tube lens (TLdet) is needed to get an image on the detection camera (CCD-1). The pellicle beam splitter, the lens L3 and a second camera (CCD-2) are used to detect axial drift. Distances are not drawn to scale. See main text for details.

mounted on a theta-phi-unit for precise alignment of the set-up (see sec. 3.5). Holograms displayed on the SLM act as diffractive phase gratings to modify the beam (see sec. 3.2). For TIRF-SIM, a binary phase grating hologram diffracts the light into the ±1. DO as shown in fig. 3.2. Some light always remains in the zeroth order which is indicated by the blue-framed beam. A polarization filter is used to clean up the polarization, which is not properly maintained by the SLM (sec. 3.2.2). A motorized half-wave plate is used to control the state of polarization. This is important because the evanescent waves must

45 3. Experimental TIRF-SIM set-up be S-polarized for all illumination directions to achieve maximal modulation contrast (sec. 3.3). The lens L1, implemented as a lens doublet consisting of the achromat L1a and the biconvex lens L1b yielding an eﬀective focal length of fL1 = 392 mm (sec. 3.1.1), focuses the beams into the pupil plane-1.

In the pupil plane after the lens L1 a mask blocks all spurious DOs resulting from the pixelated structure of the SLM. This mask has an additional hole at its center. This hole can be used for epi-fluorescence illumination and it is blocked by a black plastic bar which is controlled by a flip motor (fig. 3.5 and sec. 3.1.3). Behind the pupil plane-1 a 92/8-pellicle beam splitter is placed, which transmits 92 % of the incoming light intensity and reflects 8 %. The reflection of the illumination light is not shown. This pellicle also reflects 8 % of the totally internally reflected light towards the camera CCD-2, which is used for the correction of axial drift (see “drift correction path” and sec. 3.4). As the detection of axial drift is done with only one illumination beam, only this beam is drawn in the sketch. After the pellicle a further 4f-system projects the foci from the first pupil plane-1 into the TIR-ring of the back focal plane (BFP). It consists of two achromats, lens

L2 (fL2 = 120 mm) and illumination tube lens TLill (fTLill = 200 mm), the latter being located in the rear port of the microscope. Behind the illumination tube lens a dichroic mirror (z488/532/633rpc, Chroma) reﬂects the illumination light towards the objective lens (HCX PL APO, 1.46 x 100, oil immersion, Leica) with a focal length of fOL = 2 mm. The objective lens is mounted on a z-piezo (MIPOS 100 UD SG, Piezosystem Jena) that can move ±50 µm along the optical axis with a resolution of 2 nm. As the foci are placed in the TIR-ring of the BFP, this results in plane waves emanating from the objective lens under a very high angle so that they get totally internally reﬂected at the coverslip (glass)-sample (water)-interface. In TIRF-SIM two plane waves from opposite directions create two counter-propagating evanescent waves that interfere to form a standing wave, which constitutes the sinusoidal excitation pattern (sec. 3.1.2).

Detection beam path Detection is performed as in a conventional fluorescence microscope. Fluorescence light is collected by the same objective that is used for illumination. The dichroic mirror transmits the Stokes-shifted fluorescence light which is then cleaned up by an emission filter (550/88, Semrock) to suppress any remaining excitation light. The fluorescence images are recorded by a CCD camera (CCD-1, C8484-05G, Hama- matsu). The detection tube lens TLdet (fTLdet = 200 mm) can be replaced by a Bertrand lens which has half the focal length (fbl = 100 mm) and can thus be used to image the BFP on the detection camera.

Drift correction path As stated above, the detection of axial drift is done with only one illumination beam, i.e., normal TIRF conditions. The reﬂected light from the sample plane travels back and 8 % are reﬂected out of the beam path by the pellicle beam splitter. The lens L3 (fL3 = 160 mm) is placed such that the image plane is projected onto the camera CCD-2 (GC 1350, Prosilica). See sec. 3.4 for details.

46 3.1. Optical set-up

y RBFP Ri,BFP y

rpp1 Rc,BFP x M x

TIR ring

pupil plane-1 BFP

Figure 3.3.: Illustration of the relevant radii of the TIR ring in the pupil plane-1 and the BFP. In the pupil plane-1 the foci should be at rpp1 = 1.68 mm. The pupil plane-1 is then imaged with the magniﬁcation M = 1.67 into the BFP of the objective lens. The TIR ring in the BFP is deﬁned by RBFP = 2.92 mm and Rc,BF P = 2.66 mm. The foci should approximately be at Ri,BF P = 2.8 mm.

Software control The optical set-up is controlled by self-written extensions to the software MicPy (based on the Python programming language and developed in the lab) which allows a computer controlled image acquisition. The automatized control comprises the following components: the AOTF is used to shutter the laser and adjust the laser intensity. The automatic display of phase holograms on the SLM is used for beam shaping. The rotational motor of the half-wave plate is controlled to adjust the state of polarization. The ﬂip motor is used to allow epi-ﬂuorescence illumination. By controlling the z-piezo of the objective lens axial drift can be compensated. Both cameras, CCD-1 and CCD-2, are used for image acquisition and can be completely controlled by the software.

3.1.1. Technical details of the illumination beam path In this section some details of the illumination beam path will be explained in greater detail. For an evanescent excitation all illumination light must hit the coverslip-sample interface under an angle greater than the critical angle for total internal reﬂection (TIR), θc. In this thesis coverslips with a refractive index of ni = 1.52 were used and the sample was always in watery solution so that nt = 1.33. According to eq. 2.27 the critical angle θ nt ◦ NA . is then given by c = arcsin ni = 61 which corresponds to = 1 33. The maximal NA . θ NAOL . ◦ angle supported by an objective lens with OL = 1 46 is max = arcsin ni = 73 8 (eq. 2.20). Accoring to Singer et al. [38] the radius of the BFP of the objective lens is given by

RBFB = fOL · NAOL = 2.92 mm. (3.1) The radius that corresponds to the critical angle is accordingly given by

Rc,BF B = fOL · ni · sin(θc) = 2.66 mm. (3.2)

RBFP and Rc,BF P define the TIR ring in the BFP of the objective lens as illustrated in fig. 3.3. Consequently, the first constraint for the illumination beam path is that the

47 3. Experimental TIRF-SIM set-up illumination light should be focused into the center of the TIR ring at approximately Ri,BF P Ri,BF P = 2.8 mm. This corresponds to an incident angle of about θi = arcsin = fOL·ni ◦ 68 > θc. A second constraint arises from the spatial light modulator (SLM). It has a fixed pixel pitch of pSLM = 19 µm and the holograms, which are displayed as diffraction gratings, were chosen to have a period of six pixels (see sec. 3.2 for details). Together with the focal length of the lens L1 this determines the distance of the foci from the optical axis in the pupil plane-1 after the lens L1. This pupil plane is then imaged into the BFP with a magnification M of fTL M = ill = 1.67. (3.3) fL2 Consequently, the radial distance of the foci from the optical axis in the pupil plane-1 must be Ri,BF P r = = 1.68 mm (3.4) pp1 M The different radii in the pupil plane-1 and the BFP are illustrated in fig. 3.3. Ac- cording to eq. 3.16 the necessary focal length to meet the second constraint is

6 · rpp1 · pSLM fL1 = = 392 mm. (3.5) λ0

For this reason L1 was implemented as a lens doublet whose focal length can be precisely adjusted by the distance of the two lenses. It consists of an achromat L1a with focal length fL1a = 400 mm and a biconvex lens L1b with fL1b = 1330 mm. The focal length of the doublet is then given by !−1 1 1 d fL1 = + − , (3.6) fL1a fL1b fL1a + fL1b where d is the distance between the two lenses [39]. From eq. 3.6 it can be calculated that d = 373 mm yields the necessary eﬀective focal length of 392 mm.

Illuminating evanescent ﬁeld Using the focal lengths of all the lenses in the illumination beam path, the area illuminated in the sample plane, Asp, can be calculated. The active area used on the SLM is round and has a diameter of DSLM = 9.92 mm, which is explained in sec. 3.2.3. As all lenses are placed at distances that equal the sum of their focal lengths, the diameter of the illuminated area in the sample plane, Dsp, is

fL2 fOL Dsp = DSLM · · = 30.4 µm (3.7) fL1 fTLill 2 Dsp 2 which results in Asp = π 2 = 726 µm . The beam illuminating the SLM has a Gaussian intensity proﬁle with a diameter of about 14 mm (1/e2). Consequently, the illuminated area in the sample plane has also a Gaussian intensity proﬁle which drops about 63 % from the center to its border.

48 3.1. Optical set-up

Assuming correct positioning of the illumination foci in the BFP the penetration depth dpd of the evanescent ﬁeld can be calculated according to eq. 2.33 to be

λ0 dpd = = 84 nm (3.8) q 2 2 2 4π ni · sin (θi) − nt

◦ for an incident angle of θi = 68 . The wavelength of the evanescent wave is deﬁned by λ0 λev = (eq. 2.29). As the illumination grating is formed by the interference of ni·sin(θi) two counter-propagating evanescent waves, the wavelength of this standing evanescent wave, λev,SW , is given by

λ0 λev,SW = = 173 nm. (3.9) 2 · ni · sin(θi)

3.1.2. Excitation patterns

Figure 3.4 shows how the three grating orientations correspond to pairs of spots in the BFP of the objective lens. To fulﬁll TIR conditions these spots must lie in the TIR ring. Placing them at exactly opposite positions has two reasons. First, this results in the minimal period of the standing evanescent wave which means maximum increase in resolution. Second, only S-polarized evanescent waves coming from opposite directions can interfere properly and yield 100 % modulation contrast.

G-1

Φ = -60°

ΔΦ G-1

G0 G0

G1 y Φ = 0° x TIR ring

pupil plane-2 (BFP)

Φ = 60° image plane

Figure 3.4.: Excitation foci and corresponding patterns. (a) Pairwise illumination foci are located in the TIR ring of the BFP of the objective lens. (b) Excitation gratings in the image plane corresponding to the pairs G−1, G0 and G1 shown in (a). The phase ϕ has been neglected here for clarity.

49 3. Experimental TIRF-SIM set-up

The three grating orientations are at an angle of ∆φ = 60◦ to each other which yields an isotropic increase in resolution. According to eq. 2.45 the illumination grating is generally described by

n Gd (r⊥) = 1 + Cmod · cos (kg,d · r⊥ + n · ∆ϕ + ϕ0) , ! ! x 2π sin(φd) where r⊥ = and kg,d = λ · are in the x-y-image plane (see sec. 2.3.3). y ev,SW cos(φd) ◦ The lower index d = −1, 0, 1 corresponds to the grating orientation with φd = d·60 and 2π ◦ the upper index n = −1, 0, 1 to the phase. Phase steps are chosen to be ∆ϕ = 3 ˆ=120 to equally illuminate all structures of the sample for each grating orientation. Cmod is the modulation contrast of the excitation pattern and ϕ0 is a constant phase oﬀset, i.e., the global phase.

3.1.3. Epi-fluorescence Figure 3.5 shows a front view (x,y) of the mask that blocks all unwanted diffraction orders coming from the SLM (z is always the optical axis). It has six holes that are symmetrically distributed on a circle and precisely match the positions of the illumination foci used for TIRF-SIM. An additional hole at its center can be used for epi-illumination. For TIRF-SIM imaging this hole is always blocked by a black plastic bar as there is always some undiffracted zeroth order light coming from the SLM. It is very important to block this light because it is significant in intensity and would otherwise homogeneously illuminate the hole sample. Consequently, there would be increased background fluorescence and the modulation contrast of the excitation grating would decrease.

mask

y x

Figure 3.5.: Front view (x,y) of the mask in the pupil plane-1. The mask has six holes at the positions of the illumination foci and thus blocks all other, unwanted diﬀraction orders coming from the SLM. An additional central hole is blocked by a black bar for TIRF-SIM, which can be moved by a ﬂip motor to allow epi-illumination.

The black plastic bar is controlled by a ﬂip motor that allows a fast switching between TIRF-SIM (or normal TIRF) and epi-illumination. The switching time is about 100 ms. Furthermore, this black bar has a special shape so that it does not disturb any of the illumination foci used for TIRF-SIM. The mask is placed on a x-y-positioner for precise alignment so that all desired illumination foci can pass undisturbed.

50 3.2. Spatial light modulator

3.2. Spatial light modulator

The spatial light modulator (SLM) is a central component in this set-up as it shapes the illumination beam and is thus used to control the orientation and phase of the illumination grating. The model used in this set-up is the LCR-2500 by Holoeye Pho- tonics. It is a reflective liquid crystal on silicon (LCOS) display with 1024 x 768 pixels. The optically active material is a liquid crystal that is placed in front of a reflective silicon backplane. Figure 3.6 shows a schematic drawing of the device to illustrate its dimensions. The pixel-to-pixel distance is pSLM = 19 µm which yields an active area of 19.5 mm × 14.6 mm. The SLM has a fill factor of 93 % meaning that the “dead” space between the active pixels is only 7 % of the active area. The active area is illuminated by the laser beam with a diameter of approximately 14 mm (1/e2), drawn to scale in fig. 3.6. Consequently, not the whole active area of the SLM is used.

19.5 mm (1024 pixel) 19 µml) active

area SLM l)

19 µm 19

14.6 mm 14.6 (768 pixel) (768

14 mm Figure 3.6.: Dimensions of the spatial light modulator (SLM). The optically active area is a pixelated liquid crystal on silicon (LCOS) display of size 1024 x 768 pixels. The pixel pitch is 19 µm, which yields an active area of 19.5 mm × 14.6 mm. Each pixel can be addressed individually to shift the phase of the reﬂected light between 0 and 2π. The illuminating laser beam with a diameter of about 14 mm (1/e2) is drawn to scale.

The SLM is a 8-bit device that can be addressed like a monitor via a dvi-connection. Each pixel can be addressed individually and set to 28 = 256 different values, resulting in different phase shifts. The device was calibrated such that the 256 possible phase shifts are distributed linearly in the range from 0 to 2π for the used wavelength of 488 nm. A phase pattern displayed on the SLM, that shapes and deviates the beam, is called a hologram. The holograms used in this thesis are explained in detail in the next section (sec. 3.2.1). The refresh rate of the SLM determines the time needed for the switching of illumination patterns. According to the manual the LCR-2500 can be addressed with a maximal frame rate of 75 Hz. However, with the given set-up and software control the maximal frame rate that worked reliably was 14.3 Hz, which limited the overall image acquisition speed. Furthermore, the intensity of a deviated beam showed a flickering with a period of 8.5 ms. Consequently, all experiments were performed with exposure times that were

51 3. Experimental TIRF-SIM set-up integer multiples of the ﬂickering period.

3.2.1. Holograms The effect of phase holograms displayed on the SLM can be described by Fourier optics. The electric field E(x, y) in the plane of the SLM can be expressed as ıϕ(x,y) E(x, y) = E0(x, y) · e , (3.10) where E0(x, y) is the amplitude given by the illuminating beam profile and α(x, y) is the phase hologram displayed on the SLM. Here, it is assumed that the SLM is illuminated by a plane wave. E(x, y) is related to the field distribution in the pupil plane-1, Ee(kx, ky), by a two-dimensional Fourier transform done by the lens L1 (with focal length fL1), as defined in sec. 2.1.1. Figure 3.7 illustrates the situation and the corresponding coordinate 0 0 systems. The relation of the real space coordinates x -y to the spatial frequencies kx-ky x0 y0 in the pupil plane is kx = k0 · f and ky = k0 · f , as given by eq. 2.3.

y' ~ ky

L1 SLM x' ~ kx

y z x

f f L1 L1 image plane pupil plane-1

Figure 3.7.: Illustration of the coordinate systems for the calculation of phase holograms: The phase holograms are displayed on the SLM which is placed in an image plane (x,y).

The lens L1 with focal length fL1 makes a Fourier transformation from the image to the 0 0 pupil plane-1 (x ∼ kx, y ∼ ky).

Holograms for TIRF-SIM For TIRF-SIM two foci at opposite positions in the pupil plane are needed. For example, for the illumination pattern G0 these foci must be on the kx-axis at positions kx0 and −kx0 which is described by

Ee(kx, ky) = E0 · (δ(kx − kx0, ky) + δ(kx + kx0, ky)) . (3.11) The diﬀraction limited size of the foci has been neglected here for clarity. The ﬁeld distribution on the SLM must then be −1 n o E(x, y) = FT Ee(kx, ky) −1 = FT {E0 · (δ(kx − kx0, ky) + δ(kx + kx0, ky))} ZZ 1 −ı(kxx+kyy) = E0 · (δ(kx − kx0, ky) + δ(kx + kx0, ky)) · e dkx dky (2π)2 E0 = · eıkx0x + e−ıkx0x . (3.12) (2π)2

52 3.2. Spatial light modulator

phaseshift (rad) 0 x

1 2 3 4Px

Figure 3.8.: Phase holograms for TIRF-SIM. Phase proﬁle of the hologram ϕG0 (x, y) that leads to two foci in the pupil plane along the x-axis at opposite positions of the optical axis.

Equation 3.12 represents a cosine function. The ﬁrst term is a constant amplitude which anyway can not be changed by the SLM. The argument of the second term is the phase that must be displayed on the SLM as a hologram in order to create the two foci in the pupil plane. Consequently, the hologram ϕG0 (x, y) for the illumination grating G0 is described by ıkx0x −ıkx0x ϕG0 (x, y) = arg e + e . (3.13) ϕ x, y x P P 2π Figure 3.8 displays G0 ( ) along the -axis, where x is the period given by x = kx0 . It can be seen that the hologram is a binary phase grating with phase shifts of 0 and π. In order to shift the phase of the illumination grating the phase pattern must be x Px · ϕ ϕs laterally displaced. Shifting the phase pattern by ∆ = 2π s = kx0 laterally along the ϕs x-axis the shifted pattern G0 can be described by

s ϕG0 (x, y) = ϕG0 (x + ∆x, y) = arg eı(kx0(x+∆x)) + e−ı(kx0(x+∆x)) = arg eı(kx0x+ϕs) + e−ı(kx0x+ϕs) = arg eıkx0xeıϕs + e−ıkx0xe−ıϕs . (3.14)

Performing a Fourier transform to get the electric ﬁeld distribution in the pupil plane yields

E 0 ıkx0x ıϕs −ıkx0x −ıϕs Ee(kx, ky) = FT e e + e e (2π)2 ıϕs −ıϕs = E0 · δ(kx − kx0, ky)e + δ(kx + kx0, ky)e . (3.15)

Equation 3.15 describes the same two foci as eq. 3.11 except for the phase factor e±ıϕs . Both foci are shifted in phase by ϕs but in opposite directions. Consequently, the interference pattern in the sample plane that results from two plane waves corresponding to these two foci will experience a phase shift of 2ϕs. That implies that in order to shift 2π the phase of the illumination pattern by 3 the phase of the hologram must be shifted 2π Px by ϕs = 6 or ∆x = 6 . Thus, Px was set to 6 pixels, Px = 6 · pSLM , for the phase holograms that were used for TIRF-SIM. This has the major advantage that for G0 a

53 3. Experimental TIRF-SIM set-up

2π lateral shift of one pixel leads to a phase shift of 3 of the resulting evanescent standing wave that serves as the illumination pattern.

0 k 2π k k · x Using x0 = Px and x = 0 f the distance of the foci from the optical axis in the 0 pupil plane-1 after lens L1, x0, is then given by

0 fL1 · kx0 fL1 · λ0 x0 = = . (3.16) k0 Px

Equation 3.16 is important for the construction of the set-up and was used in sec. 3.1.1 0 (where x0 was replaced by the more general rpp1).

a) b) phase shift π 0 c)

P Φ 12

Figure 3.9.: Phase Holograms used for TIRF-SIM as proposed by Kner et al. [10]. (a) Hologram for the grating orientation G0. (b) Hologram for the grating orientation G1. For G−1 the hologram is the same but reﬂected. One pixel in each unit cell (green frame) is drawn in red to illustrate the periodicity. The green arrow depicts the shift vector for the unit cells. (c) Illustration of the quantities used for the calculation of the grating orientation and of the phase shifts (see text for details).

Figure 3.9 shows the holograms used for TIRF-SIM, which were adopted from Kner et al. [10]. Subﬁgure (a) shows the hologram corresponding to the grating orientation G0 with a horizontal period of Px = 6 pixels.

The holograms for the illumination directions G−1 and G1 must have the same pixel period P = 6 pixels but at grating orientations of φ = ±60◦. Furthermore, phase shifts 2π P of 6 =b 6 must be possible. In ﬁg. 3.9-b the hologram for the grating orientation G1 is shown. For G−1 the hologram is the same but reﬂected. One pixel in each unit cell (green frame) is drawn in red to illustrate the periodicity. The orientation of the grating 7 ◦ is given by the shift vector (green arrow) and is φ = arctan 4 ≈ 60.25 . This is very close to the desired 60◦. The horizontal periodicity of the pattern is 12 pixels so that a 2π shift of 2 pixels equals the desired phase shift of 6 of the hologram. As illustrated in

54 3.2. Spatial light modulator subﬁgure (c) the period P can be calculated as

P = 12 · sin(90◦ − φ) = 12 · cos(φ) 7 = 12 · cos arctan 4 1 = 12 · r 2 7 1 + 4 12 · 4 = √ ≈ 5.95 (3.17) 72 + 42

Thus, the pixel period is very close to the desired 6 pixels. According to eqs. 3.3 and 3.16 the resulting diﬀerence in the radial focus position in the BFP is about 0.02 mm and thus negligible.

Holograms for TIRF For normal TIRF illumination only a single focus is required in the pupil plane. However, this focus must have the same distance from the optical axis as the spots in TIRF-SIM so that total internal reﬂection is achieved. Assuming one focus in the pupil plane at the same position kx0, this corresponds to an electric ﬁeld distribution in the plane of the SLM (or equally in the sample plane) described by

−1 E(x, y) = FT {E0 · (δ(kx − kx0, ky))} E0 = · eıkx0x. (3.18) (2π)2

Equation 3.18 describes a plane wave that is tilted along the x-axis and the corresponding phase hologram is given by ϕ(x, y) = arg eıkx0x . (3.19)

0 In order for the spot to have the same radial distance x0 from the optical axis Px must again be set to 6 pixels (see eq. 3.16). Generalizing this approach for arbitrary illumination directions φ in two dimensions leads to

2π ϕ(x, y) = (x · sin(φ) + y · cos(φ)) mod 2π, (3.20) P where P = 6 pixels is the fringe period of the hologram which deﬁnes the distance of the focus to the optical axis in the pupil plane. The modulo 2π operation is necessary because 2π is the maximal phase shift that the SLM can apply. ϕ(x, y) is called a blazed grating and is shown in ﬁg. 3.10 for φ = 0◦. Equation 3.20 is a slightly altered form of the hologram calculation given by Liesener et al. [40].

55 3. Experimental TIRF-SIM set-up

2π phaseshift 0

blazed grating hologram

Figure 3.10.: Blazed grating phase hologram for TIRF illumination (φ = 0◦).

3.2.2. Polarization eﬀects of the SLM

The optically active material in a SLM that is responsible for the phase shift is a liquid crystal with birefringent properties. In the device used in this thesis the active material is a twisted nematic liquid crystal. In these types of SLMs the polarization is generally not maintained but depends on the incoming polarization and on the applied phase shift [41]. However, for perfect interference of the evanescent waves in TIRF-SIM a defined and pure state of polarization is essential. Therefor a polarization (pol) filter must be placed after the SLM. To avoid undesired intensity modulations after this pol-filter and to get an effect of the phase holograms as explained in sec. 3.2.1 it must be assured that the SLM makes a phase-only modulation for the used incoming and outgoing polarizations. This means that the intensity of the outgoing light (after the polarization filter) does not change with the applied phase shift. Phase-only modulation was verified with a measurement arrangement as shown in fig. 3.11-a. The light incident on the SLM is vertically S-polarized as indicated by the red sign. The light reflected by the SLM is focused by the lens L onto a photodiode, which measures the intensity. In front of the photodiode there is a polarization filter that is also vertically oriented, just as in the optical set-up. Uniform phase shifts from ϕ = 0 to ϕ = 2π in steps of about ∆ϕ = 0.04 π are displayed on the SLM and the outgoing light intensity is measured by the photodiode. Figure 3.11-b shows the result. The measured intensity I is normalized by the intensity at zero phase shift, I0. The average relative outgoing intensity (± one standard deviation) is I/I0 = 1.04 ± 0.02. The maximum deviation from the initial value I0 is less than 8 % over the whole range of phase shifts from 0 to 2π. This result proves that phase-only modulation is almost perfectly given. However, the loss of intensity due to the polarization filter was measured to be 37 %. Alternative approaches are possible for the characterization of the polarization behavior of a twisted nematic liquid crystal. These approaches can yield a full characterization of the birefringent properties of the liquid crystal by exploiting Mueller matrices or the Jones formalism [42, 43, 44]. However, the necessary experimental effort is quite high.

56 3.2. Spatial light modulator

a) b) 1.10 1.05

1.00 0

0.95

I / SLM I photodiode 0.90 0.85 0.80 L pol-filter 0.0 0.5 1.0 1.5 2.0 π phase shift (rad)

Figure 3.11.: Verification of phase-only modulation of the SLM for vertical S- polarization. (a) Experimental set-up for the measurement of the modulation behavior. The incoming light is vertically S-polarized (red), reflected by the SLM and focused by a lens (L) onto a photodiode that measures the intensity. The reflected light goes through a polarization filter that is also vertically oriented. Uniform phase shifts from ϕ = 0 to ϕ = 2π are displayed on the SLM. (b) Result of the measurement depicted in (a). It shows the intensity (I) measured by the photodiode, normalized by the intensity at zero phase shift (I0), over the applied phase shift in steps of about ∆ϕ = 0.04 π. The transmitted intensity deviates less than 8 % from I0 over the whole range of phase shifts.

3.2.3. Correction of non-ﬂatness

One problem commonly encountered with LCOS displays is that their reflective backplane is not flat but curved [45]. As a consequence, a collimated laser beam that gets simply reflected by the SLM without applying any phase shift and which gets then focused by a lens will form a distorted focus that is not diffraction-limited. The reason is that upon reflection the formerly plane wave front adapts the form of the reflective surface. However, the SLM can be used to correct for its own imperfection. By applying a phase shift that is inverse to the present curvature of the backplane the distortion can be compensated. To do this the curvature must be measured. Several ways have been reported how the static aberration of the backplane of the SLM can be measured. Hart et al. measured the aberrated focus behind a lens and performed a phase retrieval based on Zernike polynomials [46]. Arines et al. used the SLM as a Shack-Hartmann wavefront sensor for its own wavefront distortion by applying a phase hologram that represents an array of lenses [47]. Another way is the interferometric detection of the curvature of the backplane as done by Schmidt et al. [48]. However, in this thesis the approach presented by Ciˇzmárˇ et al. was followed [49], which bases on the studies by Vellekoop and Mosk [50]. Briefly, an experimental configuration as shown in fig. 3.11-a was used, where the polarization filter was removed and the photodiode was replaced by a CCD camera. In a central window of the SLM of size 18 × 18 pixels a blazed grating hologram was displayed. This leads to a focus off the optical axis on the camera chip. The undiffracted zeroth order light was blocked. Then, a second window of the same size was placed on a different location on the SLM and the same blazed grating was displayed. This causes a focus at the same position on the camera chip, but formed by light that comes from different angles. The interference of

57 3. Experimental TIRF-SIM set-up

a) b) c) 2π intensity (a.u.) phaseshift uncorrected corrected 0 focus focus

Figure 3.12.: Correction of the non-flatness of the reflective backplane of the SLM. (a) Measured correction hologram to compensate for the non-flatness of the SLM. (b) Focus after lens L1 without correction. (c) Focus after lens L1 with the correction hologram shown in (a). Scale bar is 50 µm. the two foci leads to a stripe pattern. By shifting the phase of the blazed grating in π the second window by steps of 6 this stripe pattern changes its phase accordingly. The phase of the blazed grating for which the stripe pattern has its maximum at the center of the focus yields the phase offset between the positions of the first and second window on the SLM. Repeating this procedure for the whole SLM by moving the second window across the display delivers a phase map which corrects for the curvature of the backplane of the SLM. In the following this is called the correction hologram. Figure 3.12-a shows the measured correction hologram. It can be seen that the most dominant distortions are spherical and astigmatic. A comparison of the focus after the lens L1 without and with the correction hologram is shown in subfigures (b) and (c), respectively. The corrected focus is much smaller and more symmetric. The uncorrected focus appears slightly cross-like which represents the astigmatic distortion. Some practical details must be mentioned here. Using the correction procedure by Ciˇzmárˇ et al. as described above, a central 29 × 29 array of phase offsets was measured and then interpolated. This delivered a correction hologram which covers an area of 522×522 pixels. To compensate for the non-flatness of the SLM this correction hologram was added to all other holograms displayed on the SLM. Furthermore, a round, centered diaphragm of diameter 522 pixels was additionally applied to each hologram. Thus, the remaining active and corrected area on the SLM has a diameter of DSLM = 9.92 mm.

3.3. Polarization in the illumination beam path

In structured illumination microscopy a high modulation contrast of the excitation light grid is important. For TIRF-SIM this means that the contrast of the standing evanescent wave must be high. As explained in sec. 2.2.1, only for S-polarized light maximum interference contrast can be achieved. Consequently, polarization had to be controlled to be in the S-state for all illumination directions. The laser delivers horizontally polarized light, which is turned by 90◦ by the AOTF, resulting in vertically polarized light illuminating the SLM. As the SLM does not maintain the polarization for all phase shifts (see sec. 3.2.2), a vertically oriented polarization

58 3.3. Polarization in the illumination beam path

filter is placed before the lens L1 to assure a clear state of polarization. The subsequent half-wave plate is used to adjust the polarization for different illumination directions. For the excitation grating G0 no adjustment is necessary so that the fast axis of the half-wave plate can remain vertical. For the gratings G−1 and G1 the half-wave plate must be turned by −30◦ and 30◦, respectively. This turns the polarization by ±60◦ concomitant with the change of the illumination direction and ensures S-polarization of the evanescent waves. However, there are two more components in the optical set-up, which can affect the state of polarization: the pellicle and the dichroic mirror. Their polarization behavior was explicitly investigated and is presented in the next two subsections.

3.3.1. Pellicle

The 92/8 pellicle beam splitter necessary for the detection of axial drift transmits light polarization-dependent. According to the manufacturer (Thorlabs) P-polarized light is transmitted better than S-polarized light. The polarization-dependent transmission coefficients of the electric field were measured and are given in table 3.1. Indeed, the transmission of P-polarized electric fields (TE,P = 0.99) is much better than for S- 1 polarized fields (TE,S = 0.93) .

transmission coeﬃcient TE,S 0.93 TE,P 0.99

Table 3.1.: Measured transmission coeﬃcients for the 92/8-pellicle for the transmission of S-polarized (TE,S) and P-polarized electric ﬁelds (TE,P ).

Figure 3.13-a illustrates the positions of the pairwise illumination beams (light blue) and their state of polarization (red arrows) for the three grating orientations G0, G−1 and G1 on the pellicle. The light propagates in z-direction and is reflected in -x-direction ◦ as the pellicle is placed at 45 to the optical axis (see fig. 3.2). For G0 the illumination light is purely P-polarized with respect to the plane of incidence of the pellicle, whereas for G−1 and G1 the illumination light is a mixture of S- and P-polarization. As the different states of polarization are not transmitted equally well, this results in a turned state of polarization after the pellicle. Using the transmission coefficients from table 3.1 the angular change in the state of polarization can be calculated. Figure 3.13-b illustrates the situation geometrically ◦ for one beam of the illumination grating G−1 which is oriented at φ = −60 . The polarization is indicated by red arrows, where S and P are given with respect to the plane of incidence of the pellicle. Assuming the incident field to have the amplitude E0, then the incident S- and P-polarized components, Ei,S and Ei,P , respectively, are given

1In order to split an unpolarized beam by 92/8 the reﬂectivity of the pellicle must thus also be polarization-dependent.

59 3. Experimental TIRF-SIM set-up

a) b) P y G G S 1 -1 y Φ

G 0 x Φ pellicle x

Figure 3.13.: Polarization of the various illumination directions with respect to the pellicle. (a) Front view (x,y) of the pellicle that is oriented at 45◦ to the optical axis (see ﬁg. 3.2). The pairwise excitation beams (light blue) for all three grating orientations and their respective polarizations (red) are indicated. (b) Illustration of one single excitation ◦ beam of the grating orientation G−1 (φ = −60 ) for the calculation of its S- and P- polarized ﬁeld components and the resulting change of polarization caused by the pellicle. by

Ei,S = E0 · sin(φ) (3.21)

Ei,P = E0 · cos(φ). (3.22)

Using the measured transmission coeﬃcients from table 3.1 the transmitted ﬁeld components are

Et,S = 0.93 · E0 · sin(φ) (3.23)

Et,P = 0.99 · E0 · cos(φ). (3.24)

The new angle of the polarization behind the pellicle, φ0, can be calculated as ! Et,S φ0 = arctan = −58.4◦. (3.25) Et,P

The deviation of 1.6◦ of the state of polarization is tolerable as it only slightly inﬂuences the contrast of the illumination grating [51]. Due to symmetry this change is the same for all illumination beams of the grating orientations G−1 and G1.

3.3.2. Dichroic mirror

Dichroic mirrors are spectral filters that separate excitation light from emission light in fluorescence microscopy. Their coatings are optimized for the reflection and transmission of certain wavelengths but not necessarily for maintaining the incoming state of polarization. As the state of polarization is important in TIRF-SIM, the influence of the dichroic mirror on the excitation light under reflection was investigated. Linearly polarized excitation light was incident on the dichroic mirror placed under an angle of 45◦ as in the optical set-up (see fig. 3.2). The reflected light then passed a polarization filter, the analyzer. The intensity of the transmitted light was measured

60 3.4. Drift

S P 45◦ (S/P) Ik 0.976 I0 0.975 I0 0.976 I0 I⊥ 0.024 I0 0.025 I0 0.024 I0

Table 3.2.: Measured intensities relative to the overall intensity I0 after reﬂection from the dichroic mirror for diﬀerent polarizations. The incoming light was either S-polarized, P-polarized, or an equal mixture of both, 45◦ (S/P). The intensity after the analyzer was measured for orientations parallel (Ik) and perpendicular (I⊥) to the incoming light. The dichroic mirror maintains the state of polarization to more than 97 % for all incoming states of polarization.

for the analyzer being oriented parallel (Ik) or perpendicular (I⊥) to the incoming polarization. The incoming light was either S-polarized, P-polarized, or an equal mixture of both, 45◦ (S/P), with respect to the plane of incidence of the dichroic mirror. The overall transmitted intensity, I0, was defined as I0 = Ik + I⊥. The results are summarized in table 3.2. For all incoming states of polarization the dichroic mirror only slightly influences the polarization, as more than 97 % of the reflected intensity exhibit the same state of polarization.

3.4. Drift

Drift encountered in optical microscopy can be separated in lateral and axial drift. Lateral drift in the x-y-plane leads to a global movement of the image while the focus is maintained. This type of drift can be well corrected for numerically. Time lapses of TIRF-SIM images acquired in this thesis as ,e.g., presented in chap. 4 were drift- corrected numerically using the software ImageJ with the plug-in StackReg [52]. This plug-in alignes all images of an image sequence with subpixel precision by minimizing the mean square intensity diﬀerence between two subsequent images.

a) b) CCD - 2

Δxd sample plane Δz d image plane θ z i immersion oil y Δx'd x objective lens x

Figure 3.14.: Scheme for the compensation of axial drift. (a) Changes of the axial distance of the coverslip to the objective lens (∆zd) correspond to a lateral shift of the illumination light in the image plane (∆xd), which depends on the angle of incidence (θi). 0 (b) The camera CCD-2 is located in an image plane, where the lateral shift ∆xd can be measured. The dashed circle indicates the location of the reﬂected light without drift (∆zd = 0).

The compensation of axial drift during imaging is more important so that the sample does not move out of focus. Thus, for the detection of axial drift a custom system was developed. The compensation of the axial movement could be done with the z-piezo on

61 3. Experimental TIRF-SIM set-up which the objective lens is mounted. Figure 3.14 shows the principle of the drift detection which bases on total internal reflection (TIR). Subfigure (a) shows the objective lens and the sample plane, which has axially drifted away from the image plane. One plane wave emanates from the objective lens under the angle θi as in normal TIRF illumination and undergoes TIR. When the distance of the coverslip to the objective lens changes by ∆zd, this leads to a lateral shift of the reflected excitation light by ∆xd. Imaging the reflected light on the camera CCD-2 the shift in the image plane can be measured, as illustrated in fig. 3.14-b. Determining the center-of-mass of the reflected light on the CCD2 before 0 and after the drift yields ∆xd = MCCD2 ·∆xd, where MCCD2 is the lateral magnification 0 of the image. The relation between the measurand ∆xd and the axial drift ∆zd is then given by

1 ∆zd = · ∆xd 2 · tan θi 1 0 = · ∆xd 2 · MCCD2 · tan θi 0 = kd · ∆xd, (3.26) where the drift constant k = 1 was introduced. d 2·MCCD2·tan θi This system is very sensitive to small drifts as kd is rather small. This has two reasons: ﬁrst, the magniﬁcation of the image on the camera CCD-2 is large, given by

fTLill fL3 MCCD2 = · ≈ 133. (3.27) fOL fL2

◦ The second reason is that the angle of incidence θi = 68 is very large, too. Consequently, the drift constant is 1 kd = ≈ 0.0015. (3.28) 2 · MCCD2 · tan θi 0 The small value of kd shows that a small axial drift ∆zd corresponds to a large shift ∆xd. 0 For example, an axial drift of only ∆zd = 10 nm leads to a shift of about ∆xd = 6.7 µm that is easily detectable. In practice kd was measured before every experiment. The sample was moved in focus and then a range from ∆zd = −1.5 µm to ∆zd = 1.5 µm was scanned in steps of 50 nm. At each position the center-of-mass of the reflected light was measured on the camera CCD-2. A linear fit yielded the drift constant kd. During the acquisition of time series the compensation of axial drift was usually performed at every time point before a set of TIRF-SIM images was acquired. The laser power was kept as low as possible to avoid any photodamage of the fluorophores in the sample. With the settings typically used the detection and compensation of axial drift took about 0.8 s. Likely, other components of the set-up exhibit similar amounts of axial drift. How- ever, due to the extremely high NA of the objective lens (NAOL = 1.46) the distance objective-coverslip is most sensitive to drift. The compensation of axial drift as presented here enables long-term measurements. All time series presented in chap. 4, which usually

62 3.5. Alignment of the optical set-up

SLM y y(β) β x(γ) x γ z y x TIR ring

image plane pupil plane-2 (BFP) on CCD-1

Figure 3.15.: Crucial step in the alignment of the set-up. On the SLM a phase hologram is displayed that diﬀracts the light in all six illumination foci. Tilting the SLM by the angles β and γ results in lateral shifts of all six foci in the pupil plane. For proper alignment these foci must be placed symmetrically into the TIR ring. The pupil plane-2 (BFP) can be observed on the camera CCD-1 by the usage of a Bertrand lens (see main text for details). lasted several minutes, were acquired using this drift compensation. Also, longer experiments up to one hour have been performed without loss of focus but are not presented in this thesis.

3.5. Alignment of the optical set-up

In this section the crucial step in the alignment of the optical set-up will be described in detail. As a prerequisite, the basic alignment should be carefully done. Thus, it is assumed that the SLM is illuminated under a small angle, that all lenses are centered on the optical axis and that they are placed at the right distances corresponding to their focal lengths. For the precise alignment the following preparations have to be done: 92 nm fluorescent polystyrene beads are pipetted on a #1.5 coverslip (Roth, LH24.1, defined thickness of 0.17 ± 0.005 mm), air-dried and then reimmersed in water so that the beads still stick to the surface. The sample is put in focus so that it appears sharp on the camera CCD-1. Then the laser is switched off and the emission filter is removed. The detection tube lens of the microscope is replaced by the Bertrand lens. An additional lens with a focal length of f = 60 mm is placed between the lenses L2 and TLill so that the BFP of the objective lens is fully illuminated. Then the laser is switched on with low laser power. All the excitation light that enters through the TIR ring will undergo total internal reflection at the coverslip. As the dichroic mirror transmits approximately 5 % of the reflected excitation light, the TIR ring will become visible on the camera. Now the Bertrand lens can be fine-adjusted so that the image of the TIR ring appears sharp. This image must then be saved as a background image using the software MicPy. It will serve as the reference for the precise positioning of the illumination foci. In the next step the laser power is set to its minimal value and the additional lens is removed again. If an illumination focus is placed in the TIR region of the BFP it will

63 3. Experimental TIRF-SIM set-up be imaged on the camera. Overlapping this image with the saved background image of the whole TIR ring the precise position of the focus in the TIR region can be observed and evaluated. For proper alignment it is best to display all six illumination foci which are used in TIRF-SIM at the same time. The corresponding hologram ϕa(x, y) can be calculated according to Liesener et al. [40]. Let ϕj(x, y) be the phase hologram for the focus j (j = 1, ..., 6) that can be calculated according to eq. 3.20. The hologram for all six parallel foci is then given by  

X ıϕj (x,y) ϕa(x, y) = arg  e  . (3.29) j

Figure 3.15 illustrates the actual alignment step. The SLM displays the hologram ϕa which resembles a hexagonal lattice and diﬀracts the beam in the six illumination foci. The BFP is observed on the camera CCD-1, where the six corresponding foci can be seen with respect to the TIR ring which is displayed as the background image. Now the SLM is carefully tilted by the angles β and γ which leads to a displacement of all foci in the pupil plane-2 (BFP). When all foci are symmetrically placed in the radial center of the TIR ring the set-up is properly aligned.

3.6. Image acquisition

For the acquisition of one TIRF-SIM image a set of nine raw images with modulated illumination has to be acquired. For this purpose several tasks have to be performed. 2π 2π Generally, all three phases (ϕ = − 3 , 0, 3 ) of the grating orientation G−1 were acquired ﬁrst, followed by G0 and ﬁnally G1.

0 100 200 300 time (ms) hologram -1 G-1 laser off polarization exposure raw image 1 read-out laser on hologram laser off 0 G-1 raw exposure image 2 read-out laser on task

Figure 3.16.: Task-flow of the image acquisition. The acquisition of one single raw image, indicated by the yellow boxes, consists of the following steps: displaying the hologram for the corresponding illumination, adjusting the polarization (only first phase of each grating orientation), switching on the laser, capturing the signal from the sample with the camera (exposure), switching off the laser and reading out the camera chip. Some of these steps can be parallelized.

64 3.7. Imaging results with TIRF-SIM

Figure 3.16 illustrates the task-flow for the acquisition of the first two images and the corresponding time in ms. One cycle for the acquisition of one raw image consists of the −1 following steps: first, the hologram that controls the illumination pattern (here G−1) has to be displayed on the SLM (70 ms, see sec. 3.2). At the same time the half-wave plate can be turned to adjust the state of polarization to the grating orientation (110 ms for a 30◦ turn). This is only necessary for the first image of each grating orientation because only the phase is changed for the following two images. Then the laser light is switched on by the AOTF to illuminate the sample with the corresponding grating and the camera records the fluorescence signal. After the exposure time (here 50 ms) the laser light is switched off to avoid unnecessary bleaching of the sample. The time needed by the AOTF to switch on and off the laser light is negligible. In order to save the image the camera has to be read-out. The read-out time depends on the size of the area-of-interest (AOI) on the camera chip that is used but was less than 70 ms for all AOIs used in this thesis. During the read-out of the camera the hologram for the next image acquisition can be displayed and the same task-flow is repeated.

3.6.1. Speed

In TIRF-SIM microscopy the speed of the image acquisition is an important issue because the whole technique relies on the assumption that the distribution of fluorophores remains constant during the acquisition of one set of raw images. Especially dynamic biological process can limit the applicability of this technique. It was shown by Kner et al. that any imaged object must not move more than the final lateral resolution (about 100 nm) during the acquisition of one set of raw images [10]. The system presented here has been optimized for maximum speed under the constraints that are mainly given by the hardware. From the values given in this section the time for one TIRF-SIM image can be calculated. Assuming the shortest possible exposure time of 8.5 ms yields a total time of 936.5 ms which corresponds to a frame rate of almost 1.1 Hz. For biological samples exposure times of 34 ms or longer are more realistic which yields frame rates of about 0.9 Hz or less. That also means that the max- nm imum velocity an imaged object is allowed to move at is about 100 s or less depending on the exposure time. This imaging speed is sufficiently fast for many biological pro- nm cesses like MreB dynamics in bacteria (up to 60 s , see chap. 4) or filopodial retraction nm under large loads of up to 15 pN (about 40 s [53]) . However, very fast phenomena nm nm like depolymerizing microtubules (about 200 s to 300 s [54, 10]) or running kinesin nm motors (780 s for kinesin-1 [55]) could not be imaged with this set-up.

3.7. Imaging results with TIRF-SIM

This section presents results that were obtained with the set-up presented in this chapter. First, some data is presented that proves that the modulation contrast of the excitation gratings is high. Then, reconstructed TIRF-SIM images of ﬂuorescent polystyrene beads with increased resolution are shown. Finally, TIRF-SIM images of ﬂuorescently labeled

65 3. Experimental TIRF-SIM set-up proteins in two diﬀerent types of cells, yeast cells and the bacteria Escherichia coli, are presented. These images underline the applicability of this technique to various biological samples. Data of protein dynamics in the living bacteria Bacillus subtilis, that lead to new biophysical insights, will be shown in chapter 4.

3.7.1. Modulation contrast Fluorescently labeled 92 nm beads were used as probes to measure the modulation contrast Cmod of the illumination grating. The beads were air-dried on a #1.5 coverslip and then reimmersed in water. For each of the three grating orientations a set of three 2π 2π raw images with phases ϕ = − 3 , 0, 3 was acquired. Figure 3.17 shows raw images for the grating orientation G0. The ﬂuorescence intensity of individual beads changes for diﬀerent illumination phases.

-1 0 1 G0 G0 G0 a) b) c) intensity (a.u.)

Figure 3.17.: Raw images with different phases of one illumination grating. The grating 2π 2π G0 was applied with phases ϕ of (a) − 3 , (b) 0 and (c) − 3 . All three images are displayed with the same scaling of the look-up-table. Individual beads show different fluorescent intensities for different illumination phases. Scale bar is 1 µm.

Positions of individual beads were automatically selected by a custom Python script. For each grating orientation, the intensities of the ﬂuorescent beads, I(ϕ), were extracted from the data and ﬁt by a sine-function so that

I(ϕ) = I0 · sin (ϕ + ϕ0) + y0. (3.30)

Here, I0 is the amplitude, ϕ0 a phase oﬀset and y0 an intensity oﬀset. The modulation contrast for each bead and each direction was then determined as

Imax − Imin 2I0 Cmod = = , (3.31) Imax I0 + y0 where Imax and Imin are the maximum and minimum intensity values, respectively, of the curve fit. The results are shown in fig. 3.18. Subfigure (a) shows a histogram of the modulation contrast Cmod of 158 beads, each averaged over all three grating orientations. The overall average contrast is hCmodi = 0.701. In subfigure (b) the average contrast over all beads is given for each grating orientation separately. Assuming 100 % modulation contrast the theoretically expected value for a grating period of 173.4 nm and a round bead of size 92 nm was numerically calculated to be

66 3.7. Imaging results with TIRF-SIM

40 a) 35 b) contrast C 30 mod G-1 0.687 25 G0 0.673

# 20 G1 0.743 15 average 0.701 10 peak of 0.746 5 Gaussian fit 0 0.3 0.4 0.5 0.6 0.8 0.90.7 Cmod

Figure 3.18.: Measured modulation contrast Cmod using 92 nm fluorescent beads. (a) Histogram of Cmod of 158 fluorescent beads. (b) Table showing Cmod averaged over all beads for the three different grating orientations. The average over all grating orientations and the peak position of a Gaussian fit to the histogram are given below.

th Cmod = 0.857. This is slightly higher than the measured value. However, as the analysis was automatized it is likely that also some small clusters of two or three beads were analyzed. They would yield a lower contrast and could be responsible for the few small values of Cmod in the histogram of ﬁg. 3.18-a. Fitting the histogram with a Gaussian yields a peak position of hCmodi = 0.746 which is closer to the theoretically expected th value Cmod.

3.7.2. Polystyrene beads Fluorescent polystyrene beads of size 92 nm were imaged to compare TIRF-SIM with normal TIRF. Figure 3.19 shows a TIRF (a) and a reconstructed TIRF-SIM (b) image. The TIRF-SIM image has a significantly higher resolution as finer details become clearly visible. This is manifested by the line profile shown in subfigure (c) which goes along three neighboring beads as indicated by the white arrowheads in (a) and (b). These three beads appear like a straight bar in the normal TIRF image, whereas they are clearly resolved in the TIRF-SIM image, even though they are at distances of about 200 nm. Also, in the rather large cluster of beads down on the left hand side of the images details appear in the TIRF-SIM image that can not be observed by normal TIRF microscopy. According to eq. 2.26 the theoretically expected resolution in normal TIRF is 213 nm at an emission wavelength of λem = 510 nm. Here, the NA of the objective lens given by the manufacturer, NAOL = 1.46, was used. However, in practice the effective NA is usually smaller as shown below. In consequence, the actual resolution is lower and the experimentally measued PSF larger than the theoretically expected values. Figure 3.20 depicts the Fourier transforms corresponding to the full images of fig. 3.19 (only a small area of a larger image is shown there for clarity). The dashed green circle marks the theoretical diffraction limit and thus has a radius of 2k0NAOL (sec. 2.1.3). 2·NAOL . −1 This corresponds to a spatial frequency in real space of λ0 = 5 73 µm . The

67 3. Experimental TIRF-SIM set-up

a) b) 80 c) TIRF TIRF-SIM 100 (a.u.) intensity 60 80 60 40 40

intensity (a.u.) 20 20 intensity (a.u.) 0 TIRF TIRF-SIM 0 200 800600400 r (nm)

Figure 3.19.: Increase in resolution by TIRF-SIM with ﬂuorescent 92 nm polystyrene beads. (a) TIRF image. (b) TIRF-SIM image of the same beads. Both images are autoscaled, scale bar is 1 µm. In (b) the resolution is increased. (c) Line proﬁles along the distance r between the two white arrowheads illustrating the increase in resolution by TIRF-SIM.

a) b) |FT{intensity}| (a.u.) TIRF TIRF-SIM

Figure 3.20.: Absolute values of the Fourier transforms of the images shown in fig. 3.19. (a) In the Fourier transform of the TIRF image the frequency information is restricted to an area even smaller than the theoretical diffraction limit (dashed green circle with radius 2k0NAOL). (b) In TIRF-SIM frequency information well beyond the diffraction limit is obtained. frequency information of the TIRF image, shown in subfigure (a), does not even reach −1 the diffraction limit but rather stops at keff ≈ 4.71 µm . That equals an effective NA of NAeff = 1.2 and indicates that the effective NA of the objective lens is smaller than the value given by the manufacturer, which is usually the case. In TIRF-SIM (b) it can be seen that sample information well beyond the diffraction limit is obtained. Thus, true optical super-resolution is achieved. The point spread function (PSF) of both TIRF and TIRF-SIM is well approximated by the image of a single bead as small as 92 nm. Thus, evaluating the images of individual beads and measuring their full width at half maximum (FWHM) yields values for the size of the PSF and thus also for the resolution of the technique. Fitting individual beads in fig. 3.19 by a 2D Gaussian and averaging along the two main axes yields an average FWHM of 258 nm for TIRF which is much larger than the theoretically expected 178 nm (eq. 2.25). For TIRF-SIM an average FHWM of 101 nm was determined. This corresponds to an experimentally measured 2.5-fold increase in resolution in TIRF-SIM. Compared to the theoretically expected value the increase in resolution is about 1.8-fold. However, it must be considered that the reconstruction of the final TIRF-SIM image

68 3.7. Imaging results with TIRF-SIM

1 a) 1 b)

2 2 intensity (a.u.)

TIRF TIRF-SIM

Figure 3.21.: Increase in resolution by TIRF-SIM for a mixture of fluorescent polystyrene beads of sizes 92 nm and 190 nm. (a) TIRF image. (b) TIRF-SIM image of the same beads with increased resolution. Both images are autoscaled. Separate, autoscaled versions of the yellow framed areas are shown to the left of each image to make the dimmer 92 nm beads visible. Line profiles between the white arrowheads are shown in fig. 3.22. Scale bar is 1 µm.

a) TIRF b) TIRF 160 TIRF-SIM TIRF-SIM 7 1 15 120 2 140 (a.u.) intensity 6 (a.u.) intensity 100 120 5 10 100 80 4 80 60 60 3 5 intensity (a.u.) 2 intensity (a.u.) 40 40 20 1 20 0 300200100 600500400 0 300200100 600500400 r (nm) r (nm)

Figure 3.22.: Comparison of the line profiles of a small (92 nm) and a big (190 nm) fluorescent bead imaged by TIRF and TIRF-SIM corresponding to fig. 3.21. (a, b) Line profiles with Gaussian fits of the 92 nm bead marked by 1 and the 190 nm bead marked by 2 in fig.3.21, respectively. Both bead sizes appear similar in TIRF, whereas in TIRF-SIM the 92 nm beads appear smaller. involves a deconvolution, which has not been performed for the normal TIRF image. This accounts for the higher resolution increase measured experimentally compared to the expected factor of two for TIRF-SIM (sec. 2.3.4).

Mixture of 92 nm and 190 nm beads

A mixture of fluorescent 92 nm and 190 nm polystyrene beads was imaged by TIRF-SIM. This constitutes an excellent test, whether objects of different sizes are correctly imaged without any artifacts resulting from the reconstruction. Figure 3.21-a,b shows a TIRF and TIRF-SIM image of the bead mixture, respectively. The yellow boxed area is separately autoscaled and shown to the left to make some dimmer beads visible. The difference in radius between the two types of beads is about a factor of two. Consequently, the difference in volume is about a factor of 23 = 8. Likely, the volume of the beads corresponds to the amount of fluorescent dyes they carry, which

69 3. Experimental TIRF-SIM set-up makes the larger beads about eight times brighter in intensity. Thus, the dimmer beads are very likely the smaller 92 nm beads. For both bead sizes the increase in resolution by TIRF-SIM is well observable in the images. Figure 3.22 shows horizontal line profiles of beads according to the white arrowheads in fig. 3.21. Subfigures (a), (b) show the profiles of the beads marked by 1 and 2 in the corresponding images, respectively. All line profiles were fitted by a Gaussian (solid curves) to get the FWHM. Table 3.3 shows the FWHM of the small and large bead measured by TIRF and TIRF-SIM. The sizes measured in TIRF-SIM are close to the true values for both bead sizes. In contrast, in TIRF both beads appear with a size of about 255 nm which is close to the size of the PSF of the optical system as measured with 92 nm beads and presented in the previous section. This means that TIRF-SIM images different sizes correctly and does not introduce reconstruction artifacts. Thus, fluorescent beads of various sizes are distinguishable not only by their intensity but also by their diameter.

ø TIRF TIRF-SIM 92 nm 249 nm 111 nm 190 nm 259 nm 200 nm

Table 3.3.: Full width at half maximum (FWHM) of a 92 nm and a 190 nm bead in TIRF and TIRF-SIM as measured by the Gaussian ﬁts shown in ﬁg. 3.22.

3.7.3. Biological samples This section demonstrates that TIRF-SIM is also applicable to various biological samples. Images of ﬂuorescently labeled plasma-membrane proteins in yeast cells are presented. Also, images of GFP-labeled synthetic proteins in E. coli are shown. For both cell types sample preparation was as follows: 4 µl of the cell suspension is pipetted on a #1.5 coverslip and covered with a 2 % agarose pad (see A.2). The illumination intensity was set to ≤ 50 W/cm2 for all measurements by using the AOTF (see A.3 for how the illumination intensity was determined).

Membrane protein domains in living yeast cells TIRF-SIM images of various plasma-membrane-associated proteins in yeast cells were acquired. This work was a collaboration with the group of Roland Wedlich-Söldner at the Max Planck Institute of Biochemistry in Martinsried. The obtained results contributed to the publication by F. Spira et al., Patchwork organization of the yeast plasma membrane into numerous coexisting domains, Nature Cell Biology, 14 (2012), pp. 640-648 [56]. Generally, this study addressed the distribution of plasma-membrane-associated proteins in the budding yeast Saccharomyces cerevisiae. The lateral segregation of proteins into various domains allows the coordination of important functions like the import and export of molecules and provides a platform for signaling processes [57, 58]. By a

70 3.7. Imaging results with TIRF-SIM

Pma1-GFP Sur7-GFP Sag1-Atto488

TIRF intensity (a.u.) TIRF-SIM

TIRF TIRF-SIM intensity (a.u.) 0 1 2 3 0 1 2 3 0 1 2 3 4 distance (µm) distance (µm) distance (µm)

Figure 3.23.: TIRF and TIRF-SIM images of three plasma-membrane-associated proteins in yeast cells, Pma1, Sur7 and Sag1. Each protein was labeled with a fluorescent dye that is written in green. Line profiles along the dashed white arrows, shown in the bottom row, illustrate the increase in resolution. large-scale characterization of the plasma-membrane organization it could be shown that all investigated proteins localize into non-homogeneous, characteristic patterns. Some proteins formed rather patch-like structures, whereas others arranged into network-like patterns. The lipid composition of the plasma-membrane strongly influenced the lateral segregation of the proteins into various patterns. Furthermore, the transmembrane sequences of the proteins had a strong influence on the localization pattern, too. The results indicate that biological membranes self-organize into numerous coexisting domains. In this “patchwork” membrane the overlap of different protein domains is random and depends on their size and shape. The results of Spira et al. were obtained by TIRF microscopy and subsequent two- dimensional (2D) deconvolution. TIRF-SIM images of three plasma-membrane proteins under investigation, that showed different pattern formations, were used to verify the technical approach. The super-resolved TIRF-SIM images proved that 2D deconvolution does not create or remove any artifactual features. Figure 3.23 shows TIRF and corresponding TIRF-SIM images of the three investigated proteins in living yeast cells. GFP-labeled Pma1, an ATPase for H+ ions that regulates pH-value and plasma-membrane potential, forms an almost homogeneous network. GFP- labeled Sur7 forms discrete, sparse patches. Sur7 is a core protein of the eisosomes,

71 3. Experimental TIRF-SIM set-up

G-1 G0 G1 intensity (a.u.)

Figure 3.24.: Raw images of GFP-labeled Pma1 in yeast cells for three different grating orientations (G1,G0 and G−1). The orientation of the illumination grating is recognized in the images by the elongated appearance of the round cells due to scattering of the evanescent waves. The gratings are sketched beneath the images. All images are shown with the same scaling of the look-up-table. Scale bar is 1 µm. which are large protein complexes of unknown function. Atto488-labeled Sag1, involved in the biosynthesis of the membrane, forms a rather homogeneous network, too. For all three proteins the TIRF-SIM images yield significantly increased resolution and contrast, as illustrated by the line profiles shown in the bottom row of fig.3.23. Especially for the network-forming proteins Pma1 and Sag1 TIRF-SIM reveals the subdomains of the network-like pattern. In the line profiles it can be seen that almost all structures revealed by TIRF-SIM correspond to slight peaks, bumps or shoulders in the normal TIRF image. Consequently, the revealed structures are very unlikely to be artifacts. Looking at the raw images of the Pma1-sample illustrates some important details when applying TIRF-SIM to biological samples. Figure 3.24 shows one raw image for each grating orientation. Each illumination grating is generated by the interference of two counter-propagating evanescent waves. It can be seen that the cells are elongated along the grating orientation. This is due to scattering of the evanescent waves. As the cells are highly inhomogeneous media in terms of the refractive index, each evanescent wave is scattered mainly in forward direction. As described by Rohrbach this scattering leads to additional excitation of fluorescence in the propagation direction of the evanescent waves [59]. In TIRF-SIM the additional excitation of fluorescence by scattered light is highly unwanted as it leads to fluorescence signals which do not correspond to the applied excitation pattern. However, even though the described scattering effect is clearly present the modulation of the fluorescence intensity with the various illumination gratings (orientations and phases) is still strong enough for a reconstruction, as could be seen in fig. 3.23.

Artiﬁcial proteins in E. coli

Another cell type that was imaged by TIRF-SIM is Escherichia coli which is a rod- shaped bacterium of approximately 2 µm length. These studies were a collaboration with the group of Stefan Schiller from the Freiburg Institute of Advanced Studies (FRIAS).

72 3.7. Imaging results with TIRF-SIM

a) TIRF b) TIRF-SIM intensity (a.u.) c) intensity (a.u.) 0.0 0.4 0.8 distance (µm)

Figure 3.25.: (a,b) TIRF and TIRF-SIM image, respectively, of EGFP-labeled artiﬁcial proteins in living E. coli cells. The bright spots are mostly membrane-associated vesicles formed by the amphiphilic proteins. (c) The line proﬁle between the white arrowheads shows the increase in resolution. The hollow center is only observable in TIRF-SIM and likely is an invagination. Scale bar is 1 µm.

The presented results are part of the paper by M. C. Huber, A. Schreiber et al., Synthetic Biology Inside the Cell: Programmed Engineering of Genetically Encoded Artificial Organelles in vivo which has been submitted for publication. Well organized compartments of varying complexity such as micro compartments in bacteria or organelles in highly organized organisms are essential for spatial and temporal control of signalling and metabolism. The intention of this work is to mimick this key concept of life by implementing the de novo synthesis and assembly of defined artificial compartments in vivo. This would be a crucial step towards novel functional organelles which is one of the major goals in modern synthetic biology as it could form one basis for targeted drug delivery [60, 61]. The Schiller group designed artificial DNA sequences encoding non-natural amphiphilic proteins with an additional enhanced green fluorescent protein (EGFP) tag. These sequences were transformed into the genome of E. coli cells which then expressed the proteins with the fluorescent tag. Ideally, these proteins should form vesicles inside the living E. coli cells, as they have a hydrophilic and a lipophilic part (what makes them amphiphilic). By changing the length, orientation and aminoacid sequence of the protein domains a precise adjustment of the physico-chemical characteristics of the resulting amphiphilic proteins and formed structures can be achieved. Figure 3.25-a,b show a TIRF and a TIRF-SIM image, respectively, of living E. coli mutants. Again, TIRF-SIM provides a sharper image with higher resolution. The bright spots which can be observed in both images are likely vesicles as they have a roundish appearance. However, this can not be proven by either of the images. These bright spots are almost all membrane-associated. The TIRF-SIM image reveals that these spots are smaller than they appear in the normal TIRF image. The line profile between the white arrowheads is shown in subfigure (c) and illustrates the increased resolution in TIRF- SIM. The hollow center of this feature is only observable in TIRF-SIM. This is likely an invagination towards the center of the cell, as such features could also be observed by electron microscopy (to be published).

73 3. Experimental TIRF-SIM set-up

3.8. Discussion

This chapter presented the optical set-up that was used to perform TIRF-SIM microscopy. A detailed description of all its components were provided. It was especially focused on the SLM as a central device and also on the polarization of the light as a crucial parameter for high contrast of the excitation grating. Also, a system for the compensation of axial drift was developed that enables long term measurements. Finally, results of polystyrene beads and biological samples were presented, showing a twofold increase in lateral resolution and the applicability of TIRF-SIM to living cells. This discussion is subdevided into three parts. First, sec. 3.8.1 will present alternative experimental approaches that were realized by other groups to perform TIRF-SIM and elucidate their advantages and disadvantages. Based on the ﬁrst part, section 3.8.2 will discuss the experimental set-up as presented here. This includes a debate of its limits and drawbacks and also gives an outlook on possible future improvements. In the last section 3.8.3 the performance of this TIRF-SIM implementation and the achieved results will be discussed in the context of competitive super-resolution ﬂuorescence microscopy techniques. This also includes an outlook an future applications of TIRF-SIM.

3.8.1. Alternative experimental realizations

The first experimental realization of a combination of TIRF microscopy and structured illumination microscopy (SIM) was done by Chung et al. in 2006 [62]. They split their excitation beam and coupled it into two optical fibers. The fiber tips, where the light exits, were projected to opposite positions in the TIR ring of the BFP of the objective lens. The disadvantage of this implementation is that only one grating orientation can be applied. In order to get a resolution increase along two directions, Chung et al. rotated the sample stage by 90◦. However, this is slow compared to pattern switching on a SLM as done in this thesis. Moreover, it is likely that the sample has to be refocused. Using four or even six fibers would avoid the rotation step but would demand a complex beam path. The first implementation of TIRF-SIM using an SLM was done by Beversluis et al. in 2008 [63]. Their experimental arrangement was very similar to the one presented here but with two important differences. First, they did not adjust the polarization to the various orientations of their excitation grating, which results in a declined modulation contrast for some orientations. Second, they used a neat trick to minimize the angle of illumination of the SLM. They placed a small mirror under approximately 45◦ close to the pupil plane-1 and right next to the desired foci. Illumination of the SLM was then done through the lens which corresponds to L1 here (fig. 3.2) and thus under a very small angle. An alternative approach exploiting techniques of microsystems engineering was followed by Beck et al. [64]. They used an electrically tunable polymeric sinusoidal 2D phase grating as diffractive element which they imaged into the sample. This 2D grating produced four diffraction orders and consequently an illumination pattern that modu- lates in two orthogonal directions. Also, the grating period could be electrically tuned

74 3.8. Discussion resulting in different fringe periods of the illumination grating. One beam of each pair passed an electrically tunable polymeric phase plate to control the phase of the illumination pattern. Also, small half-wave plates had to be used to turn the states of polarization of the different beams independently. The advantage of this design is that no mechanical parts have to be moved. However, the devices used are custom made and require advanced engineering skills. Furthermore, applying only two illumination directions does not result in an isotropic increase in resolution [33, 65], as achieved in this thesis. Extending this scheme to three or even four illumination directions may become a tedious task. A diffractive polymer grating would need a more complex structure and the phase retarders and half-wave plates would have to be built even smaller. Even another experimental implementation was presented by Gliko et al. [66]. They split their illumination beam into two and displaced each of these beams using a pair of orthogonally oriented acousto optical deflectors (AOD). Applying a complex beam path, each beam can be individually placed in the BFP of the objective lens. Using four AODs they could switch between different grating orientations, periods and phases within less than 100 µs without moving any mechanical parts. However, polarization was not controlled which resulted in an approximately 20 % reduced modulation contrast. A lower contrast of the excitation pattern will inevitably lead to longer exposure times when imaging biological samples with poor signal. This implementation is very fast and flexible albeit at the cost of four AODs, a rather complicated beam path and a reduced modulation contrast. All the studies mentioned above showed images of fluorescent polystyrene beads of size ≤ 100 nm to prove their increase in resolution. In their reconstructed TIRF-SIM images they measured FWHMs of 100 nm to 120 nm. The first experimental prove that an approximately two fold increase in resolution by TIRF-SIM can also be achieved in living cells was presented by Kner et al. in 2009 [10]. As presented here and also done by Fiolka et al. [37] their implementation of TIRF-SIM based on a spatial light modulator as diffractive element and was all optimized for fast imaging. They used a ferroelectric SLM that allowed to switch patterns in 0.6 ms. Furthermore, they built a polarization- rotation unit made of custom ferroelectric liquid crystal switchable retarders which had a switching time of less than 100 µs. They used an electron-multiplying CCD camera that allowed short exposure times due to its high sensitivity. Also, the read-out time of that camera is short. However, these improvements in speed come at the cost of more expensive hardware and a more complex set-up. The flexibility of the system is also reduced as the ferroelectric SLM is a binary device that can only apply phase shifts of 0 and π. Normal TIRF illumination is then only possible by physically blocking one of the two beams that are used in TIRF-SIM. However, Kner et al. showed that frame rates of up to 11 Hz are possible in living cells. In summary, the ideal TIRF-SIM set-up must allow at least three orientations of the illumination grating. Furthermore, switching between different orientations and phases should be possible within 1 ms including the adaption of the polarization. Faster switching times, although possible as shown by Gilko et al., do not manifest a significant advantage in biological applications because exposure times are usually ≥ 15 ms per

75 3. Experimental TIRF-SIM set-up raw image to collect enough fluorescence signal. As the exposure time is ultimately limiting the acquisition speed, it is important to adjust the polarization to get maximum modulation contrast for all illumination patterns. Considering these boundary conditions an implementation of TIRF-SIM using a SLM seems to be a very good solution. A ferroelectric binary SLM allows maximum speed, whereas a 8-bit LCOS display, as used in this thesis, has greater flexibility. An additional advantage of a SLM is that its pixel pitch, and thus any applied phase shifts of the illumination grating, are known with great accuracy which eases the numerical reconstruction. An implementation as presented by Gliko et al., where each illumination beam is de- flected separately by two AODs, is also very fast and flexible. The four AODs could also be replaced by two scan mirrors and one piezo-mounted mirror in one arm of the illumination beam path for phase shifting. A further advantage would be that the incor- poration of additional laser lines would be straighforward because no diffraction grating is used, where the radial positions of the illumination foci are wavelength-dependent. In any case the polarization should be adapted. One option is to use fast, switchable liquid crystals which do not contribute substantially to the time needed for pattern switching. Another option would be to built a small, static device made up of six cone- shaped half-wave plates with appropriate orientations of their fast axes. Placing this device after the pupil plane-1 (fig. 3.2) each illumination beam would always be turned to its proper state of polarization without moving or switching any device.

3.8.2. Strengths and limits of the presented optical set-up The experimental TIRF-SIM set-up presented in this chapter can yield a twofold increased lateral resolution at frame rates of up to 1.1 Hz. It has a high modulation contrast and allows a fast and easy switching between TIRF-SIM, normal TIRF mode, and even epi-fluorescence illumination. However, it suffers from some limitations and drawbacks. One of the main issues is acquisition speed. As already mentioned in sec. 3.6.1 this does not only involve higher TIRF-SIM frame rates but is also essential for the imaging of fast moving objects. The acquisition speed of the set-up is related to several optical components that could be replaced by faster ones. No changes in the principle design of the set-up would be necessary. In the meanwhile 8-bit spatial light modulators are available from Boulder Nonlinear Systems with frame rates of up to 200 Hz (about 17500 e without tax). The same company offers liquid crystal polarization rotators that are electronically addressable with switching times below 1 µs (about 10000 e without tax). This would also remove the last component that has to be moved mechanically. Concern- ing the image acquisition, the new scientific complementary metal-oxide-semiconductor (sCMOS) technology offers high sensitivity and signal-to-noise ratio with negligible read- out times and large chip sizes. This is especially relevant as TIRF-SIM is a widefield technique. Applying these changes would enable frame rates of up to 3.1 Hz at exposure times of 30 ms per raw image, or even up to 7.4 Hz if short exposure times of 10 ms are applicable.

76 3.8. Discussion

Although the modulation contrast was measured to be high, removing the pellicle beam splitter should still slightly increase it for the two grating orientations G−1 and G1. Axial drift could then also be controlled by directly measuring the position of the sample holder as done by Rego et al. [13]. The compensation of axial drift worked well for all measurements presented in this thesis. However, the detection and compensation of the drift take about 0.8 s. Instead of applying a different, low-intensity illumination and acquiring an extra image for the detection of axial drift it should also be possible to acquire an image with the camera CCD-2 during the illumination of one of the nine raw images. In this case only the compensation of the measured drift by moving the z-piezo would have to be done between two TIRF-SIM time points. The movement of the z-piezo should be accomplished in less than 50 ms which is much faster than the 0.8 s currently needed. The numerical image reconstruction, as presented in sec. 2.4, is not limiting the image acquisition as it is done in a postprocessing step. However, when working with biological samples it can be helpful to quickly get a reconstructed image as this might be used as the basis for decisions concerning the next experiments. The code used here takes about 140 s to 185 s to process a set of nine raw images of size 512 × 512 pixels, depending on the parameters chosen. However, this could be highly speeded up. It was shown by Lefman et al. that a reconstruction of the same set of raw images can be completed within 25 ms when done on graphic processing units (GPU) [67]. Even though their implementation of the reconstruction code might be more simple than the one used here that implies that video-rate reconstruction during the data acquisition is possible. For the imaging of biological samples it would be beneficial to equip the set-up with additional laser lines. This would enable multi color experiments and the colocalization of various structures in living cells. Apart from adding the lasers before the AOTF by the use of dichroic mirrors, some adaptions would have to be applied. First, the holograms for the SLM would have to be changed. This is important to ensure TIR conditions. Due to the different wavelengths the diffraction orders will be at a different distance from the optical axis (eq. 3.16). For binary phase holograms it is explained by Fiolka et al. how to find the appropriate hologram [68]. The dichroic mirror currently used in this set-up is a triple band filter, which reflects the wavelengths 488 nm, 532 nm and 633 nm. The emission filter would have to be replaced by a multiband filter to match additional emission wavelengths.

3.8.3. Comparison with competitive techniques It was shown in sec. 3.7 that the presented optical TIRF-SIM set-up yields a lateral resolution down to about 100 nm and that it can be applied to biological samples. Com- petitive ﬂuorescence super-resolution techniques comprise photo-activated localization microscopy (PALM), stochastic optical reconstruction microscopy (STORM) and stimulated emission depletion microscopy (STED) which will be discussed in the following. Also, the combination of SIM with nonlinear eﬀects to achieve theoretically unlimited resolution is considered. Localization-based techniques like PALM and STORM [4, 5] are often done in TIRF

77 3. Experimental TIRF-SIM set-up mode and in the meanwhile have been shown to achieve < 10 nm lateral resolution [6]. They rely on the precise localization of individual fluorophores that are photo-activatable. Hundreds to thousands of raw images are needed in which subsets of single fluorophores must be optically resolvable. The localization precision, limited only by the signal-to- noise ratio, determines the lateral resolution. The maximum frame rate is limited by the number of raw images that have to be acquired for one time point. Shroff et al. showed that PALM can be done as fast as 25 s per final image over 4 − 20 time points yielding a lateral resolution of about 60 nm [69]. However, this is still more than one order of magnitude slower than the TIRF-SIM set-up presented here, albeit at higher resolution. Jones et al. proved that STORM can deliver frame rates up to 2 Hz at about 25 nm lateral resolution but only six time points could be acquired due to the high light intensities of 15 kW/cm2 resulting in strong photobleaching. TIRF microscopy has inherent axial sectioning as the evanescent excitation field pen- λ etrates the sample only to about 4 , depending on the illumination angle. However, by introducing optical astigmatism in the detection path of a STORM microscope axial positions can be further discriminated, yielding a resolution in axial direction below 20 nm [6]. This principle was first demonstrated by Huang et al. [70] and then applied to living cells by Jones et al. [71]. This is superior to TIRF-SIM in terms of axial sectioning but can only be applied to PALM or STORM. Another competitive super-resolution fluorescence microscopy technique is stimulated emission depletion microscopy (STED) [7]. STED is a point-scanning technique in which the periphery of the illumination focus is actively depleted resulting in an effectively smaller PSF. It has been shown to yield 15 nm to 20 nm lateral resolution in biological samples [8]. Applying STED to living cells frame rates of up to 28 Hz have been achieved MW at a lateral resolution of 62 nm. Therefor intensities in the range of several cm2 are needed and imaging is limited to a two-dimensional field of view of about 4.5 µm2 [72]. Due to the point-scanning nature of STED frame rates would decrease significantly for larger fields of view. Also, photodamage might limit the acquisition of time series due to the high intensities used. In addition, photodamage happens in a large part of the sample as the excitation light is not restricted to an evanescent field. In summary, STED can achieve higher lateral resolution than TIRF-SIM but needs much higher light intensities inducing stronger photobleaching. The image acquisition speed is limited by the field of view and frame rates comparable to TIRF-SIM are restricted to areas smaller than 10 × 10 µm2. Having a nonlinear dependence of the fluorescence emission rate on the excitation intensity in combination with a structured illumination can yield theoretically unlimited spatial resolution [3]. Gustafsson used nonlinearities resulting from the saturation of the excited states of fluorophores and showed a resolution of less than 50 nm [12]. However, the disadvantages compared to linear SIM as presented here are twofold: first, high laser intensities are required to saturate the excited states which needs very photostable fluorophores. Second, more raw images (108 in this case) are required for one reconstructed super-resolved image, which limits the acquisition speed. Rego et al. used reversibly switchable fluorescent proteins to get nonlinearities and demonstrated a lateral resolu-

78 3.8. Discussion tion of about 40 nm [13]. This allowed much lower light intensities than in saturation but increased the image acquisition time for one time point even further due to the slow switching behavior of the fluorescent proteins. Nonlinear SIM, which works well in TIRF mode, yields higher spatial resolution at the cost of slower frame rates. A combination of TIRF-SIM and surface-plasmon resonances was presented by Chung et al. [73]. They used a TIRF-SIM set-up with gold-coated coverslips and coupled in P-polarized light. This leads to surface-plasmon resonances which show a strong field- enhancement. Consequently, they detected a higher fluorescence signal and thus had a better signal-to-noise ratio than in normal TIRF-SIM. However, the gold coating leads to a doughnut-shaped detection PSF which has to be compensated for. Furthermore, this concept has not yet been applied to living cells to prove its feasibility with biological samples. Altogether, linear TIRF-SIM, as presented in this chapter, is a super-resolution fluorescence microscopy technique that yields an increase in resolution of about a factor of two. It is applicable to living biological samples and employs moderate excitation intensities. Linear TIRF-SIM is the best compromise between increase in resolution and imaging speed. As a widefield technique it is especially beneficial when large fields of view are desired. It has been proven by the images of yeast cells and E. coli cells presented in this chapter that new biological insights can be gained due to the high resolution and contrast of TIRF-SIM. Likely, in the future TIRF-SIM will be applied to a broad range of biological samples for which the structures of interest are on a length scale of 100 nm to 200 nm. Especially, it will be beneficial for the super-resolution imaging of fast processes like, e.g., filament dynamics or transport processes due to the high imaging speed. Photo-switchable fluorophores are under heavy development and they are more and more used in biological applications. If their switching times can be reduced to the range of milliseconds nonlinear TIRF-SIM might become a competitive technique for the imaging of biological samples with a resolution below 100 nm. It applies moderate excitation intensities which minimizes photobleaching and its temporal and spatial resolution can be tuned by the number of raw images.

4. Dynamics of the actin-like protein MreB in Bacillus subtilis

In this chapter the studies on the dynamics of the actin-like protein MreB in the bacteria Bacillus subtilis are presented. MreB is part of the bacterial cytoskeleton and its function is tightly linked to cell wall synthesis. For rod-shaped bacteria like B. subtilis the constant fabrication of cell wall material is essential for growth and the maintenance of their shape. Many antibiotics like, e.g., penicillin take effect on the cell wall synthesis of bacteria. Understanding the fundamental processes involved will help the design of new medicaments. Imaging one of the key-players, MreB, with the high resolution and contrast of TIRF-SIM reveals so far unknown details of the localization and dynamics of this protein. This work was a collaboration with the group of Prof. Graumann from the biology department of the University of Freiburg1. Many of the results presented in this chapter contributed to the paper P. von Olshausen, et al., Super-resolution imaging of dynamic MreB filaments in B. subtilis reveals a length dependent transport velocity that has been submitted for publication. In the first section of this chapter the biological background is explained (sec. 4.1). The cytoskeletal protein MreB and its connection to cell wall synthesis are introduced. In sec. 4.2 the results of TIRF-SIM imaging of fluorescent GFP-MreB are presented. A discussion of these results is given in sec. 4.3. This includes an analysis, why TIRF-SIM is the ideal super-resolution technique for MreB, and also proposes a model based on molecular motors to explain the observed data. Finally, an outlook on promising future experiments is given in sec. 4.4.

4.1. Biological background

B. subtilis is a rod-shaped bacteria with an average length of 2 µm to 4 µm and an average diameter of Dcell ≈ 1 µm. It is found in the soil and the human gut and belongs to the group of gram-positive bacteria, which have an exterior cell wall that is made up of several layers of peptidoglycan (sec. 4.1.2). During exponential growth phase it arranges into long chains as can be seen in the brightﬁeld image in ﬁg. 4.1. B. subtilis is used as a model system for the study of the bacterial cell wall, in whose synthesis the intracellular protein MreB plays an important role (sec. 4.1.1).

1Now at LOEWE-center for synthetic microbiology, University of Marburg.

81 4. Dynamics of the actin-like protein MreB in Bacillus subtilis

Figure 4.1.: Brightﬁeld image of B. subtilis during exponential growth. Longitudinal chains consisting of many cells form, typical for the exponential growth phase. Scale bar is 1 µm.

4.1.1. MreB

MreB is a cytoskeletal protein present in several rod-shaped bacteria. This protein occurs in three isoforms (different forms of the same protein produced from related genes), namely MreB, Mbl and MreBH, which show a high degree of colocalization [74]. Con- trarily to Escherichia coli, the functionality of MreB in B. subtilis is essential for the cells in order to maintain their rod-like shape and to proliferate [75]. Its primary structure, the amino acid sequence, equals that of actin to only 15 % but its secondary structure resembles that of actin to a large extent [76]. For this reason MreB is regarded as an actin homologue (same protein in a different organism, implying that the two organisms share a common ancestor) and is expected to fulfill similar cytoskeletal functions in prokaryotes as actin does in eukaryotic cells.

Indeed, MreB has been reported to form filaments in vitro and in vivo [75, 76, 77]. Also, it has been claimed that MreB forms long range helices underneath the cell membrane that are supposed to stabilize the bacteria mechanically and direct cell wall growth [78, 79]. Furthermore, its observed dynamics have been explained by treadmilling, which results from equal polymerization and depolymerization rates at opposite ends of the filament [80]. Lately, this view has been challenged by several groups [81, 82, 83]. They studied fluorescently labeled MreB in B. subtilis and E. coli with optical diffraction limited microscopy and reported the motion of patches rather than filaments. This contradicts the claim of helical structures with possible long range interactions and limits the possible filament length to about the value of the optical resolution, i.e., roughly 200 nm. Filamentous functions like coupling, cross-linking or mechanical stabilization are then restricted to the close proximity of MreB. Another conclusion they drew is that the observed dynamics are not due to treadmilling but rather powered and directed by cell wall growth. They hypothesize that processively working enzymes, which belong to the cell wall synthesis machinery, are the driving motor for MreB motion. Applying the TIRF-SIM technique to B. subtilis cells expressing GFP-labeled MreB allows a considerable contribution to some of these ongoing discussions, as presented in this chapter.

82 4.1. Biological background

Figure 4.2.: Schematic cross section of a B. subtilis cell showing the cell wall and its connection to MreB. The cell wall consists of many layers of peptidoglycan (PG) strands surrounding the cell, of which only two are shown here for clarity. The structural subunit of a PG strand consists of two sugars (light and dark brown) and a short polypeptide (orange). These are synthesized in the cytoplasm as precursors, transported across the membrane and attached to the existing PG strands by penicillin-binding proteins (PBPs). PBPs are connected to MreB by transmembrane proteins among which are MreC, MreD, RodA and RodZ.

4.1.2. Cell wall

B. subtilis is a gram-positive bacteria and as such has a cell wall made up of many layers of peptidoglycan with a thickness of about 33 nm in the case of B. subtilis [84]. Pepti- doglycans are long polymer chains of repetitive disaccharide subunits. These chains are referred to as strands and are cross-linked by short peptides. The currently predominant picture is that parallel peptidoglycan (PG) strands surround the cells perpendicularly to their long axis, stabilizing the cell and assuring the rod-like shape. According to Hay- hurst et al. [85] the average length of the strands is 1.3 µm and their maximum length is about 5 µm, though other length distributions have also been reported [86]. The connection of the cell wall to MreB is thought of to consist of a number of proteins. These include penicillin binding proteins (PBPs), that attach and cross link new PG subunits, and transmembrane proteins such as MreC, MreD, RodA and RodZ [87]. Altogether, these proteins form a big complex often referred to as the cell wall synthesis machinery. A simpliﬁed, schematic image of the current conception is shown in ﬁg. 4.2. Due to the thick cell wall the cells must produce a lot of new cell wall material during exponential growth in order to divide. Extending the cell wall is accomplished by adding subunits, so called precursors, to the existing PG strands. A precursor consists of two non-identical sugar rings (a disaccharide) and a short polypeptide of 3-5 amino acids. It has a length of about 1 nm [88] and carries energy in a phosphate group [89]. Pre- cursors are transported from the cytosol across the membrane where they get attached and cross-linked to peptidoglycan strands by PBPs (this step requires the energy). The length of the peptide cross-bridge and thus the lateral distance of two neighboring PG strands is 4.1 nm [90]. Although the proper functioning of MreB is essential for the synthesis of the cell wall, the precise function of MreB in this process has so far remained elusive. Based on the results presented in sec. 4.2 a suggestion for the role of MreB in

83 4. Dynamics of the actin-like protein MreB in Bacillus subtilis cell wall synthesis will be made.

4.2. Results

In this section images of mainly MreB, but also Mbl, in B. subtilis and their analysis are presented. Deconvolved epi-fluorescence stacks show the 3D distribution and allow the measurement of the whole filament length, albeit with limited accuracy. Mainly TIRF-SIM is used as the ideal technique to investigate the localization and dynamics of MreB in living B. subtilis with high resolution and contrast. Also, MreB in protoplasts that lack a cell wall is imaged. The interpretation of these results in the context of what is currently known about the function of MreB and its connection to cell wall synthesis is subject to the discussion in sec. 4.3. If not otherwise stated, all MreB samples presented in this section were genetically modified such that they expressed MreB with an additional green fluorescent protein (GFP) at its N-terminus from the original locus under the xylose inducible promoter (pxyl-gfp-mreB). All Mbl samples expressed GFP-Mbl from the original locus under its original promoter (pmbl-gfp-mbl). All cells were prepared and provided by Hervé JoëlDefeu Soufo from the lab for microbiology of Prof. Graumann. For all the data shown, sample preparation was as follows: 4 µl of a suspension of living B. subtilis cells in exponential growth phase are pipetted on a 1.5# coverslip and covered with a 2 % agarose pad (A.2). All images were acquired within 90 min after mounting of the sample.

4.2.1. 3D distribution of MreB In order to get an overview of the 3D distribution of MreB in B. subtilis epi-fluorescence image stacks were acquired. The axial z-spacing was chosen to be 150 nm. The stacks were then deconvolved using an experimentally measured PSF and the commercial software Autodeblur c . A volume-rendered pseudo 3D-view of typical cells is shown in fig. 4.3. In this representation the cells have a cylindrical, tube-like appearance with all the MreB filaments localized on a cylindrical surface and perpendicular to the cells’ long axis. The amount of MreB in the cytosol seems negligible. An average number of NF = 10.6 filaments per cell were measured from this data.

4.2.2. Filamentous Structure of MreB As already mentioned in sec. 4.1.1, it is an ongoing discussion whether MreB forms long, extended filaments or rather short structures that appear patch-like in diffraction limited microscopy. Using TIRF-SIM this question can be addressed with clarifying high resolution. Figure 4.4 shows the comparison of a TIRF (a) and a TIRF-SIM image (b) of MreB in live B. subtilis (same cells as in fig.4.1). Even the TIRF image partially reveals an extended, filament-like appearance of MreB. However, in the TIRF-SIM image it is clearly visible that MreB forms straight filaments, some of which expand over the whole

84 4.2. Results

Figure 4.3.: Volume-rendered pseudo 3D-view of a deconvolved 3D epi-ﬂuorescence stack of B. subtilis expressing GFP-MreB. All MreB is membrane-associated which leads to a cylindrical appearance of the cells. Here, longitudinal chains of cells are arranged along three axes that lie in one plane. Scale bar is 1 µm but must be regarded as a rough estimate due to the perspective view on the 3D data.

width of the cells observable in TIRF mode (≈ 740 nm for a cell with a diameter of 1 µm). Furthermore, filaments can be separated that appear like a blurred single patch in normal TIRF. This is illustrated by the line profiles shown in (c), that are drawn along the tilted white lines in (a, b). From the line profiles in fig. 4.4-c the lateral resolution of TIRF-SIM in living B. subtilis cells can be estimated, as illustrated in subfigure (d). Fitting the two peaks by Gaussian functions yields a mean FWHM of 123 nm which is well beyond the classical diffraction limit. The filaments are at a distance of 185 nm and can thus be clearly resolved. To evaluate a possible overexpression a second actin homologue, Mbl, was investigated. This is available as a GFP-fusion expressed under its original promoter, so that the expression level is likely to equal the native one. In fig. 4.5 a TIRF-SIM image of GFP- Mbl expressing B. subtilis cells is shown. Albeit recorded at a weaker signal level, the filamentous appearance resembles that of MreB to a high degree. Furthermore, length distributions of MreB and Mbl were measured from deconvolved 3D epi-fluorescence stacks. The lengths were measured as the full width at half maximum (FWHM) of the filaments’ intensity distribution (see A.4 for a detailed description of the length measurement). The resulting histograms are shown in fig. 4.6. The maximum length measured is Lmax = 1.46 µm and Lmax = 1.17 µm for MreB and Mbl, respectively. This is about half a circumference (C = πDcell ≈ 3 µm) for a cell with a diameter of Dcell = 1 µm. Considering also the mean length and its standard deviation, which is hLi = 0.58 µm ± 0.32 µm (N = 52) for MreB and hLi = 0.44 µm ± 0.32 µm (N = 39) for Mbl, the results for both proteins show slight differences.

85 4. Dynamics of the actin-like protein MreB in Bacillus subtilis

Figure 4.4.: MreB forms filaments in live B. subtilis. (a, b) TIRF and TIRF-SIM image, respectively, of GFP-MreB of the same cells as shown in fig. 4.1. (c) Line profiles along the white line in (a, b), illustrating the increased resolution in TIRF-SIM. What appears like a blurred dot in (a) can be clearly identified as two separate filaments in (b). (d) Fitting Gaussian functions to the peaks of the TIRF-SIM profile yields a mean FWHM of 123 nm and a peak-to-peak distance of 185 nm. Scale bar is 1 µm.

Figure 4.5.: Mbl forms ﬁlaments in live B. subtilis. GFP-Mbl expressed under its original promoter is likely to represent the native expression level. It resembles MreB, thus providing a control for overexpression. Scale bar is 1 µm.

4.2.3. Dynamics of MreB

TIRF-SIM time lapses were acquired to observe the dynamics of MreB. This provides information about the time-dependent distribution and the velocities of MreB ﬁlaments. Furthermore, these time series allow conclusions about the underlying transport mechanism. First, some details regarding the image acquisition have to be mentioned. In or-

86 4.2. Results

Figure 4.6.: Length distributions of MreB and Mbl filaments, measured as the FWHM from deconvolved 3D epi-fluorescence stacks. der to get images with reasonable signal-to-noise ratio and without reconstruction artifacts some constraints had to be followed. The maximum measured velocity of MreB nm is vmax = 51.4 s (sec. 4.2.5). Assuring that the maximum displacement during the acquisition of one set of nine raw images is not more than the optical resolution means that the acquisition of one time point has to be accomplished within about 2 s. This sets upper limits for the exposure time of the single frames and the size of the region of interest, which determines the read-out time of the camera. On the other hand, the illumination intensity must not be too high because this seemed to increase photobleaching, as already reported by White et al. [91]. Depending on the signal strength of the sample, typical values that worked well were: 34 ms − 59.5 ms exposure time, regions of interest between 12 µm × 12 µm and 30 µm × 30 µm and illumination intensities of 27 W/cm2 − 49 W/cm2 in the focal plane (see A.3 for the determination of the illumination intensity). Furthermore, to minimize photobleaching the illumination intensity was usually increased incrementally over time during the acquisition of a time series. The time step between two images was usually chosen to be 5 s, though some series were acquired at 2.2 s intervals. Depending on the signal strength of the sample, 20 - 50 time points could be acquired, which results in a total observation time of 100 s − 250 s and 44 s − 110 s for the given time steps, respectively. This is a good compromise in such a way that on the one hand, fast filaments crossing the cell are imaged at 3 - 4 time points, and on the other hand, a good impression of the overall dynamics in the cells is obtained. Figure 4.7 shows 6 time points of a typical time series at 10 s intervals for better visibility of the dynamics. It can be seen that MreB is a highly dynamic component of the bacterial cytoskeleton. Many filaments are moving and movement occurs always along straight tracks that are parallel to the filaments’ orientation, as indicated by the white arrows. A question that immediately arises is, whether the observed dynamics are a passive polymerization process, namely treadmilling, or if some sort of molecular motor is push- ing or pulling the filaments. Treadmilling is a well-known transport mechanism for actin. It requires that the polymerization rate (ron) at one end of the filament is about as high + − + − as the depolymerization rate (roff ) at the opposite end, ron ≈ roff or roff ≈ ron (+

87 4. Dynamics of the actin-like protein MreB in Bacillus subtilis

Figure 4.7.: MreB is a highly dynamic component of the bacterial cytoskeleton. 6 time points at 10 s intervals of a typical time series show MreB filaments moving on straight tracks. The white arrows indicate the directions of movement. Scale bar is 1 µm. and - referring to the plus and minus end of the actin filament). As the on-rates depend on the concentration of free monomers in the cytosol, so does the whole treadmilling process. In the case of molecular motors causing the transport of MreB, these motors are likely to be connected to the cell membrane as all MreB filaments are membrane-associated. For eukaryotes it is well known that processive motors can move cargos along actin filaments, and also that non-processive motors can displace actin filaments.

MreB is transported by molecular motors

The image sequences in fig. 4.8 represent typical events of single MreB filaments, which are presented the following way: A part of a cell or a long chain of cells is shown, the outline indicated by dashed white lines, where a region of interest (ROI) is marked by a green box. To the right, images of different time points of the ROI are shown with the exact time given at the bottom. In these images the maximum value of the look-up- table is often individually adjusted in order to highlight the structure of interest over the whole series. Usually, an additional sketch illustrates motors that transport the MreB on straight tracks as suggested in sec. 4.2.3, 4.2.4 and 4.3.4. In these sketches blue arrows indicate directional trajectories, MreB filaments are shown in red and green and orange circles are plus and minus motors, respectively. In fig. 4.8-a a filament revealing an inhomogeneous intensity structure along its main axis is shown. This can be due to a malfunctioning of fluorophores or, in case of a MreB bundle, to a change in monomer density. Upon propagation of the filament this intensity structure moves along with the filament’s propagation. This can also be well observed in the kymograph to the right which in this case replaces the sketch. In the case of treadmilling the monomers of the filament are stationary and consequently, the intensity structure should be stationary, too. In fig. 4.8-b it is shown how a single filament reverses in direction, which can frequently be observed. Again, this is difficult to explain by treadmilling, because it would require a change of the (de-) polymerization rates at both ends, respecting the constraint that the absolute values of the (de-) polymerization rates remain unchanged as no change

88 4.2. Results

Figure 4.8.: MreB is transported by molecular motors. (a) The inhomogeneous intensity structure of the filament in the ROI moves along with the filament. The time is given in seconds on the buttom of each subimage. To the right a kymograph of the vertical line profile of the filament is shown. (b) A filament reverses its direction of movement concomitant with an angular change of orientation. Both events can not be explained by treadmilling. Scale bar is 1 µm. in total filament length can be observed. Furthermore, the reversal of direction occurs concomitant with a change of orientation. Assuming treadmilling that would require another unknown factor influencing the orientation. Altogether, these results make a transport by treadmilling highly unlikely. Conse- quently, some sort of molecular motor must be responsible for the dynamics of MreB.

4.2.4. Tracks of MreB motion If MreB is transported by molecular motors then the filaments’ trajectories should reflect the tracks on which these motors run. As can be seen in figs. 4.7 and 4.8, these tracks are straight and always parallel to the filaments, but have slight variations in the angular orientation. A statistical analysis of the orientation of the trajectories reveals that the mean angle to the bacteria’s long axis is hθi = 89.9◦ with a standard deviation of ∆θ = ±9.7◦. The maximal deviations from the mean value span a range from 63.8◦ to 111.5◦. Figure 4.9-a shows the corresponding histogram. The angular divergence is further manifested by fig. 4.9-b, where two neighboring filaments move at an angle of about 35◦ to each other. Another remarkable observation is that the tracks never cross each other. Figure 4.10- a,b shows the maximum time-projections of a series of 30 images over 150 s. The areas marked by yellow circles highlight neighboring filaments that seem to hinder each other, but never cross. Figure 4.10-c shows the example of a short moving filament that is stopped by an opposing static one. In fig. 4.11 more characteristic events of single MreB filaments are shown. In (a) a filament first slightly changes its orientation and then reverts its direction of movement. In (b) a filament changes significantly its orientational direction of propagation. The filament shown in (c) follows a trajectory like in (a), but with breaks in between where

89 4. Dynamics of the actin-like protein MreB in Bacillus subtilis

Figure 4.9.: Angular distribution of MreB filaments and their corresponding tracks. (a) Histogram of angular orientations of MreB filaments, respectively their tracks. (b) Two neighboring filaments move on different tracks at an angle of about 35◦ to each other. Scale bar is 1 µm.

Figure 4.10.: MreB trajectories hinder each other. (a, b) Maximum time-projections showing that filaments and their corresponding trajectories never cross (yellow circles). (c) Single filament event of a short MreB filament that gets stopped by an opposing static filament. Scale bar is 1 µm. it doesn’t move. All these filaments move on tracks that are composed of straight sections and even though the filaments are only slighty longer than the optical resolution it can be seen that they always move parallel to their long axis.

4.2.5. Transport velocities of MreB

The velocities of MreB filaments are investigated by analyzing the kymographs of single filaments from TIRF-SIM time series. A typical kymograph is shown in fig. 4.12-b. The diagonal edges resulting from the movement of the filaments were fitted by eye ds with straight lines. From the angle of the fit the velocity was calculated, using v = dt = tan(α). The velocity histogram resulting from the analysis of N = 105 filaments is shown

90 4.2. Results

Figure 4.11.: Characteristic dynamics of single MreB filaments. (a) This filament first changes its orientational direction of propagation and then reverts completely. (b) A short filament changing significantly its direction of propagation. (c) This filament follows a trajectory similar like in (a), but with breaks in between where it stalls. Scale bar is 1 µm.

Figure 4.12.: Velocities of MreB filaments. (a) Single image of a TIRF-SIM time series. The kymograph along the green dashed line, s, is shown in (b). From the angle α the velocity of the filament can be calculated. (c) Histogram of velocity distribution of MreB filaments.

nm nm in 4.12-c. The measured velocities range from vmin = 0 s to vmax = 51.4 s with an nm nm average of hvi = 18.7 s and the majority of the filaments being slower than 30 s . Figure 4.13 shows a histogram of the same filament velocities with respect to their direction of motion. Positive and negative velocities correspond to filaments being transported to the one or the other side of the cell, respectively. Clearly, there is no correlation between transport velocity and direction of motion.

91 4. Dynamics of the actin-like protein MreB in Bacillus subtilis

Figure 4.13.: Histogram of direction-dependent velocities of MreB ﬁlaments. Transport velocities are equally distributed for both directions of motion in the cell.

Transport velocity depends on ﬁlament length

The dependency of the transport velocity on the filament length was also investigated. Therefor, kymographs of single filaments, extracted from TIRF-SIM time lapses, were analyzed as explained before. Additionally, the lengths of the filaments were extracted as the FWHM of a line profile along each filament with pixel accuracy.

Figure 4.14.: Transport velocity depends on the ﬁlament length. (a) Velocity and corresponding length of 105 ﬁlaments (red: full length measurable, dark blue: only a minimal length could be determined). (b) Mean values for bins of 80 nm and 100 nm of the data points, where the full length could be measured. The error bars depict one standard deviation and the size of the markers corresponds to the number of data points. The big blue circle is a mean value of a length-corrected version of the data points whose length could not be measured (see text for details).

In fig. 4.14-a all measured velocities (N = 105) are plotted over their length. Red diamonds refer to filaments whose full length could be well measured in TIRF-SIM (N = 57), whereas filaments for which only a minimal length could be determined are shown in dark blue (N = 48). This is due to the fact that filaments that are too long or static (or both) can not be completely observed in TIRF mode. In fig. 4.14-b the “full length” data is plotted as mean values for bins of 80 nm and 100 nm. The size of the

92 4.2. Results

Figure 4.15.: MreB forms stationary, membrane-associated filaments in round protoplasts lacking a cell wall. (a) Epi-fluorescence image of the axial middle plane of protoplasts. The cells are round and all MreB is membrane-associated. (b, c) TIRF images of protoplasts. (d, e) TIRF-SIM images of the same protoplasts revealing mainly parallel MreB filaments. The yellow box represents an area of 1 µm2. In the magnified view to the right filaments are indicated by blue lines. (f) TIRF image sequence showing stationary filaments over a period of 40 s. Scale bar is 1 µm. diamonds corresponds to the number of data points in the bin. The “minimal length” data was length-corrected based on the length distribution determined from the 3D data and then a mean velocity and a mean length were determined. The length correction is explained in detail in the appendix (A.5). All error bars depict plus/minus one standard deviation. From fig. 4.14-b it can be seen that the transport velocity of the MreB filaments decreases with increasing filament length. At a length of about 350 nm a peak velocity nm of about 30 s is reached. Very short filaments seem to be even faster though there are very few data points.

4.2.6. Stationary ﬁlaments in protoplasts

The structure and the dynamics of MreB in cells lacking a cell wall were investigated. B. subtilis cells were kept in an osmotically stabilizing medium and treated with lysozyme which digests the cell wall. These cells become round protoplasts lacking the rigid cell wall that ensures their rod-like shape. Epi-fluorescence images of the cells’ center confirm that the cells are round and that the MreB is still membrane-associated (fig. 4.15-a). The observed mean diameter of these cells is hDproti ≈ 3.9 µm. Albeit suggested by normal TIRF images, TIRF-SIM images clearly confirm that even in the absence of a cell wall MreB forms long, mainly parallel filaments that don’t cross each other (fig. 4.15-b,c,d,e). A time series of normal TIRF images, shown in fig. 4.15-f, reveals that the filaments are constant in length and stationary.

93 4. Dynamics of the actin-like protein MreB in Bacillus subtilis

According to the data presented here, protoplasts without cell wall are less prone to devision and extend their volume to much bigger sizes. Compared to a normal rod- shaped cell, typically having a diameter of 1 µm and a length of 3 µm, a spherical pro- toplast of diameter hDproti ≈ 3.9 µm has an approximately 14 times greater volume and 5 times greater surface area. From the 3D data presented in sec. 4.2.1 the number of # filaments per normal rod-shaped cell could be determined to be NF,rod = 10.6 cell . Us- ing the mean filament length of hLi ≈ 0.6 µm, this yields a filament surface density of 2 ρrod ≈ 0.55 µm/µm . Measuring the filament surface density in protoplasts, as depicted 2 in the magnified cut-out in fig. 4.15-d,e, yields ρprot ≈ 4.5 µm/µm , which is about 8 times higher.

4.3. Discussion

The structure and the dynamics of MreB filaments in B. subtilis could be well observed by TIRF-SIM. The main purpose of this discussion is to try to give an explanation for the observed dynamics by the means of a multi motor model. However, first the issue of overexpression will be discussed (sec. 4.3.1). Then, it will be elucidated why TIRF-SIM is the ideal super-resolution technique to image MreB (sec. 4.3.2). Following this, the observed structure and dynamics are compared with results from recent publications, in particular the studies by Dominguez-Escobar et al. and Garner et al. (sec. 4.3.3) [81, 82]. In the next section a hypothetical, qualitative motor model describing MreB dynamics will be introduced. It is assumed that multiple, independent motors, that can act in different directions, are coupled by MreB filaments and undergo a tug-of-war (secs. 4.3.4 and 4.3.5). This gives a possible explanation for many of the results presented in the previous section, including the filament length dependent velocity (sec. 4.3.6). Furthermore, the already hypothesized connection between MreB dynamics and cell wall synthesis will be discussed (sec. 4.3.7). The coupling of motors as well as the assumed relation to cell wall synthesis with all its consequences must be regarded as a model, although founded on data and reasonable assumptions. It’s a contribution to the understanding of the highly intricate cell wall growth mechanisms in prokaryotes, following the demand of Vollmer and Seligman that ”more data and more models are required to decipher the complex cell wall architecture in bacteria” [92].

4.3.1. Overexpression

This section discusses a possible overexpression of GFP-MreB because protein expression was always controled by an inducible promoter. Comparisons with Mbl will mainly serve for this purpose, as this was expressed under control of its native promoter and can thus be expected to have the native expression level. The fluorescence images in sec. 4.2.2 show that the structural appearance of the Mbl samples resemble the MreB samples to a very high degree (figs. 4.4 and 4.5). However, the length distributions for MreB and Mbl derived from 3D epi-stacks are slightly different,

94 4.3. Discussion with Mbl having less long filaments (fig. 4.6). This contradicts the measured amounts of molecules per cell, that are 12000 − 14000 for Mbl and only 8000 for MreB [75]. Furthermore, the fluorescence signal of GFP-MreB was always significantly higher than for GFP-Mbl, which might also indicate an overexpression of MreB. On the other hand, fluorescence can be strongly influenced by the environment, leading, e.g., to strong quenching in the case of GFP-Mbl. This implies that the measured signal is not necessarily proportional to the amount of fluorophores. Altogether, there is no clear evidence for or against an overexpression of GFP-MreB under the P-xylose promoter. A more meaningful investigation would have to apply quantitative immunoblotting to get comparable values for the number of molecules per cell as done by Jones et al. [75].

4.3.2. TIRF-SIM as the ideal super-resolution microscopy technique to study MreB in B. subtilis In order to get super-resolved time series of MreB filaments in B. subtilis several criteria have to be fulfilled. First of all, the acquisition must be fast enough to image the nm movement of filaments with velocities of up to vmax = 51.4 s without artifacts. This is especially important in SIM, which relies on the assumption that the imaged structure does not change during the acquisition of one set of raw images that are subsequently reconstructed to yield one super-resolved image. The occurrence of typical but non- intuitive artifacts resulting from a too slow image acquisition has been discussed by Kner et al. [10]. The practical constraints for the measurements presented here resulting from this criterion are explained at the beginning of sec. 4.2.3. Assuming an optical resolution of ∆r ≈ 120 nm (sec. 4.2.2), the maximum time T for the acquisition of one time point is given by ∆r T = ≈ 2.3 s (4.1) vmax A second problem generally encountered in fluorescence microscopy is photobleaching. However, this holds especially true for super-resolution techniques as more photons have to be collected to circumvent the classical resolution limit and gain optical resolution. Consequently, the illumination energy deposited in the sample should be kept as low as possible in order to be able to acquire a sufficient number of time points, which allows to properly follow the dynamics of MreB. The third criterion refers to spatial resolution and contrast which must be high enough to clearly identify the filamentous structure of single MreB filaments. As shown in sec. 4.2.2 this is the case for the TIRF-SIM set-up used in this thesis. Here, the advantages of doing SIM in TIRF mode are threefold and exactly match the described demands. First, only the image plane adjacent to the coverslip gets illuminated, thus avoiding the exposure and bleaching of fluorophores in the rest of the sample. Second, in TIRF-SIM only nine raw images are required to get a super-resolved image of one time point (versus 15 in 3D-SIM for one plane). This limits the increase in illumination energy to a factor of 4.5 compared to normal TIRF, which in turn increases the number of time points that can be acquired before significant photobleaching occurs.

95 4. Dynamics of the actin-like protein MreB in Bacillus subtilis

The limited number of necessary raw images allows the acquisition of time series with frame rates of up to 0.9 Hz. Even faster frame rates up to 11 Hz would be possible using more sophisticated hardware [10]. Third, TIRF inherently delivers images of higher contrast as hardly any out-of-focus structures are illuminated. These advantages are exploitable for the investigation of MreB in B. subtilis because first, MreB is membrane-associated and thus accessible by TIRF, and second, B. subtilis are rod-shaped bacteria with cylindrical symmetry. As shown by the deconvolved 3D stacks in sec. 4.2.1, a 3D high-resolution image of the whole cell is helpful to get an overall impression of the distribution of MreB. Time series of 3D stacks would allow an even more precise and complete tracking of the filament dynamics. However, due to the cylindrical symmetry it is sufficient for most purposes to image one outer plane, as done by TIRF-SIM. Thus, the advantages of imaging in TIRF mode, as explained above, largely outweigh the disadvantages of 2D image information compared to 3D for the measurements presented here. This argumentation holds still true for 3D-SIM, which would be one alternative super- resolution technique. It has been shown to yield 120 nm lateral and 360 nm axial resolution at frame rates of 0.2 Hz [11]. Acquiring only 7 axial planes with 15 raw images each of the rather small B. subtilis cells, the frame rate could be slightly increased to about 0.3 Hz. However, 105 raw images per time point have to be acquired, instead of nine in TIRF-SIM. This reduces the overall number of time points by more than a factor of ten which compromises the imaging of filament dynamics. As already introduced in sec. 3.8.3, another competitive technique is stimulated emission depletion (STED) microscopy. It has been shown to yield 62 nm spatial resolution at frame rates up to 28 Hz on a field of view comparable to the size of one B. subtilis cell [72]. However, photodamage would likely be a big problem as intensities in the MW range of several cm2 have to be used. Furthermore, there is no axial limitation of the illumination as in TIRF, which leads to a higher background signal and photobleaching in the whole sample volume. The axial detection PSF is not decreased either, so that the sectioning is worse than in TIRF microscopy. Localization-based techniques like photo-activated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM) have been shown to achieve < 10 nm lateral resolution [6]. These techniques are usually also operated in TIRF mode, but limiting the illumination to tolerable intensities, they are by far too slow to image MreB dynamics (see also sec. 3.8.3).

4.3.3. Structure and dynamics of MreB - a comparison with recent publications

The 3D distributions of MreB in B. subtilis, as measured by deconvolved epi-fluorescence stacks (sec. 4.2.1), show membrane-associated filaments that are oriented perpendicular to the cells’ long axis. These findings agree with previous reports and also with the results from Salje et al., who showed that one part of the MreB protein from E. coli has a membrane binding site [75, 93].

96 4.3. Discussion

In sec. 4.2.2 it is shown that MreB forms filaments of lengths up to 1.46 µm. Espe- cially images acquired by TIRF-SIM confirmed that MreB assembles into filamentous structures. This stands in contrast to recent studies which observed only MreB patches by TIRF microscopy, meaning that no filaments longer than 200 nm (classical optical resolution limit) were present [81, 82]. The measured dynamics of MreB filaments, as presented in sec. 4.2.3, coincide gen- nm erally with previously reported values. The average velocity of hvi = 18.7 s as well nm as the maximum velocity of vmax = 51.4 s agree quite well with the measurements of Dominguez-Escobar et al. and Garner et al. [81, 82]. One remaining difference is that neither of these two reports observed any static filaments. Length-dependent velocities were not presented by any other group, likely because they applied diffraction limited microscopy and observed only patch-like appearing filaments. However, the angular distributions of the MreB filaments, as presented in sec. 4.2.4, also coincide well with their results. The same two authors also claimed that the dynamics of MreB are driven by the cell wall synthesis machinery and not by treadmilling, as previously reported [80]. The results of the time series of MreB (sec. 4.2.3) confirmed that MreB is not driven by treadmilling, but rather transported by molecular motors. Also, the lack of dynamcis in cell wall-less protoplasts, as presented in sec. 4.2.6, suggests a transport by motors, assuming that the absence of the cell wall does not influence a potential treadmilling process.

4.3.4. MreB ﬁlaments are transported by coupled molecular motors that likely belong to the cell wall synthesis machinery A great deal of arguments and observations, collected in this thesis as well as from the literature, support the hypothesis that the transporting motors are part of the cell wall synthesis machinery:

• As many other rod-shaped bacteria B. subtilis maintains its cell shape due to their rigid cell wall and MreB is known to be an essential component for them to build up their shape and proliferate properly [87].

• As shown by the 3D epi-ﬂuorescence stack in sec. 4.2.1, MreB ﬁlaments are membrane-associated, which means that any putative motor must be localized near the membrane. It is known that new cell wall material is added from the inside of the cell in the form of precursors, building new layers of peptidoglycan strands between the membrane and the existing cell wall (see sec. 4.1.2).

• Cells lacking a cell wall not only lose their rod-shape and become round. They also exhibit no MreB dynamics, indicating that a functional cell wall is essential for MreB to be transported (sec. 4.2.6).

• So far, no molecular motor like myosin, kinesin or dynein in eukaryotic cells has been found in prokaryotes. The cell wall synthesis machinery encompasses enzymes

97 4. Dynamics of the actin-like protein MreB in Bacillus subtilis

Figure 4.16.: Proposed scheme of the coupling of molecular motors that putatively par- ticipate in cell wall synthesis by MreB filaments. (a) Top view of a schematic B. subtilis cell with homogeneously distributed motors. The framed MreB filament (red) is transported by two p-motors (green) along a straight track (blue). m-motors (orange) are needed to transport the filament in opposite direction. These motors might run along a slightly tilted track. (b) Cross-sectional view: motors participating in PG strand synthesis are outside the cell membrane and are coupled to MreB via transmembrane protein complexes. The connection of MreB to the motors has on- and off-rates, schematically shown between the motors and the linking proteins. (c) Many proteins are involved in the complex that is connected to MreB and that synthesizes the cell wall: MreC, MreD, RodA, RodZ, and penicillin binding proteins (PBPs) are among these.

belonging to the group of penicillin binding proteins (PBPs) that attach the precursors to the existing PG strands (sec. 4.1.2). At least one of these enzymes, the peptidoglycan glycosyltransferase, although from E. coli, has been reported to work processively in vitro and might thus act as the driving motor [82, 94]. Fur- thermore, it is known that the PBPs are connected to MreB via transmembrane proteins.

Although not proven, this vast amount of indications justifies the hypothesis that the MreB transporting motors are part of the cell wall synthesis machinery. It is reasonable to assume that the motors are homogeneously distributed across the cell surface. Consequently, MreB filaments of different length will get into contact with a variable, length-dependent number of motors, which effectively leads to a mechanical coupling of these motors. This coupling may be the main function of MreB filaments. Its consequences will be discussed in sec. 4.3.7. Filament transport has been shown to occur perpendicularly to the bacteria’s long axis, though equally often in both directions. That means that there is an equal amount of motors acting in each direction. This might be due to two types of motors, each running into one direction of a polar track, as it is known for myosin Va and VI on actin [95]. It could as well be only one type of motor acting on non-polar or polar, but equally distributed tracks. However, these details are not known to date and can be neglected for the further discussion, so that it will simply be referred to (p)lus- and (m)inus-motors in order to distinguish the opposite directions of movement. It is assumed that these motors are not constantly bound to the MreB filaments but have on- and off-binding rates as known for motors in eukaryotic cells. As no differences for motors acting in either p- or m-direction could be observed, it is furthermore assumed that the binding rates are independent of the motor type, so that kon,p ≈ kon,m and

98 4.3. Discussion

koff,p ≈ koff,m. Figure 4.16 illustrates the proposed scheme of a MreB-coupled cell wall synthesis. In subfigure (a) homogeneously distributed p- and m-motors (green and orange, respectively) transport MreB filaments (red) along straight tracks (blue). In (b) a cross- sectional view shows how one MreB filament couples two PG strand-synthesizing machineries, each including one p-motor. The connection of the filament to the motors is supposed to have an on- and off-rate (kon and koff , respectively). Subfigure (c) provides a detailed view of the connection of MreB to the PG synthesis complexes across the cell membrane including some of the known proteins (see sec. 4.1.2). The motor is assumed to belong to the group of penicillin binding proteins (PBPs) but is illustrated separately due to its relevance for the observed dynamics.

4.3.5. Reversal and orientational change of the ﬁlament transport direction

Whenever two types of motors, which act in opposite direction, bind to the same MreB filament a tug-of-war situation comes up, as described theoretically by Müller et al. [96]. First of all, this is governed by statistics, meaning that an unbinding of one motor type results in the “winning” of the other motor type. In this model it is assumed that a rebinding of the motors to the filament is possible, which should also be the case with MreB as explained in sec. 4.3.7. Furthermore, it could play an important role that the unbinding rate is usually force-dependent, koff (F ), meaning that the force-exertion of one motor type favors the unbinding of the opposing motor type. A frequently observed event is the reversal of transport direction. Changes in the orientation of propagation, sometimes occurring concomitant with a reversal of direction, can also be observed (see fig. 4.11 in sec. 4.2.3). These events can be explained qualitatively by the tug-of-war model. The basic idea is that a MreB filament which is transported in one direction is taken over by other motors that run on different tracks. The new tracks may also have a different orientation. Assuming a short filament being transported by one p-motor. If this filament encounters a m-motor that binds to it, a tug-of-war will start. If the m-motor wins, the transport direction will be reversed. The same holds true if, instead of a m-motor, another p-motor is encountered that runs on a track with different orientation. If the new p-motor wins, an orientational change of transport direction occurs. This explanation is represented in the schematic sketches of figs. 4.8-b, 4.9 and 4.11.

4.3.6. Coupled molecular motors might explain ﬁlament length dependent transport velocity

The coupling of molecular motors can provide a qualitative understanding of the measured length-velocity-dependency. The slight increase in velocity for filament lengths of up to L = 350 nm can be explained by the cooperative work of several motors because the probability that at least one motor binds and transports the filament is increased. The mean filament velocity reaches a maximum and then decreases for longer MreB filaments. Concomitant with the increase in filament length, the number of motors bound

99 4. Dynamics of the actin-like protein MreB in Bacillus subtilis

Figure 4.17.: Coupling of PG strand synthesizing motor complexes by MreB filaments and corresponding direction of transport. (a) The coupling of, e.g., three p-motors (green) by one MreB filament (red) leads to the synchronous synthesis of three parallel PG strands (reddish brown). The resulting angle β between the orientation of the filament and its direction of propagation is negligible for a reasonable number of motors per filament (see text for details). to it will augment. The slowdown for these long filaments is likely due to co-acting motors, obstructing each other’s synthesis, as well as to counter-acting motors that hinder the first type of motors during filament transport. Generally speaking, this can be un- derstood as an internal friction which is proportional to the number of motors attached. However, the few short but fast observed filaments can not be explained by this model. These considerations include that the coupling of cell wall synthesis complexes by MreB leads to a faster synthesis of a few PG strands, whereas many PG strands are synthesized more slowly due to the mutual hindrance of the motors. Seen the other way around, the coupling of cell wall synthesis motors determines the transport velocity of MreB filaments.

4.3.7. MreB ﬁlaments organize the synthesis of the cell wall

In sec. 4.3.4 it is introduced that the cell wall synthesis machinery likely is the driving motor for MreB motion. The putative motors are connected to MreB via transmembrane proteins that are part of the cell wall synthesis machinery (fig. 4.16-c). This connection facilitates the mechanical coupling of several PG synthesis machineries and thus of several PG strands at different points of the cell periphery by MreB (fig. 4.16-a,b). The maximal coupling length is given by the length of the MreB filament. The coupling strength is determined by the mechanical properties of the filaments and the linking transmembrane proteins, specifically their Young’s modulus and bending rigidity. As shown in sec. 4.3.6, this coupling leads to a faster synthesis of cell wall material for a few PG strands, whereas for many PG strands the participating motors usually hamper or even block each other.

Estimation of the motor density

If, for example, a L = 300 nm long filament coupled 3 p-motors, i.e., 3 cell wall synthesis machineries that work into the same direction, that would mean that 3 parallel PG strands were simultaneously synthesized, as illustrated in fig. 4.17. The PG strands must be in close proximity to each other since otherwise the angle β between the filament orientation and the trajectory would become significant. As this is not visible in the data,

100 4.3. Discussion it is assumed that the neighboring PG strands are parallel and cross-linked and thus have a lateral distance of dPG = 4.1 nm [90]. For the mentioned example, which corresponds −1 3·dPG ◦ to a motor density of ρM = 10 µm , the angle would be β = arcsin( L ) = 2.3 . It is reasonable that this small angle can not be observed in the data. In view of this negligibly small tilt angle and the fact that MreB has membrane aﬃnity it is a reasonable assumption that a temporarily unbound motor can quickly rebind to the MreB ﬁlament even if it was transported by other motors in the meantime.

An estimation of the motor density ρM can be made considering the amount of cell wall material that is necessary for the cells to proliferate. Approximating a rod-shaped cell of diameter Dcell = 1 µm and length Lcell = 3 µm by a cylinder yields a surface 2 of Acell = 11 µm . On average, the peptidoglycan cell wall is about 33 nm thick [84]. Assuming one layer to be effectively as thick as the lateral distance between two cross- linked PG strands, dPG = 4.1 nm, this means that it consists of about n = 8 layers. The surface covered by cell wall material that is newly synthesized during one doubling time Tdouble = 90 min is NPG · dPG · hvi · Tdouble, where NPG is the number of PG strands, nm dPG their lateral distance and hvi = 18.7 s the mean filament velocity, i.e., the mean synthesis velocity. NPG can be expressed by the motor density, NPG = NF · hLi · ρM , where NF ≈ 11 is the mean number of filaments per cell and hLi = 0.58 µm the mean filament length of MreB. Assuming each layer of the cell wall to consist of PG strands only, the area of n = 8 layers of the cylindrical surface of B. subtilis can be identified with the area covered by new cell wall material, n·Acell = NF ·hLi·ρM ·dPG ·hvi·Tdouble. The motor density is then given by

n · Acell −1 ρM = = 33.3 µm . (4.2) NF · hLi · dPG · hvi · Tdouble

This is certainly an upper limit for the motor density as the cell wall does not consist −1 of peptidoglycan only. However, the earlier assumed motor density of ρM = 10 µm is −1 well within the scope of this estimation. Regarding ρM = 33.3 µm as the maximum motor density, the maximum tilt angle β between the MreB filament and its direction ◦ of transport would be βmax ≈ 7.8 . What is the consequence for very short MreB filaments? The shortest observed filaments are about 130 nm in length which is approximately the optical resolution of TIRF-SIM in B. subtilis cells, but they might be even shorter. According to the estimated motor density ρM these filaments would not always be in contact with a transporting motor. However, short filaments did not appear to be static in any case, which can only be explained by the following consideration: a short filament that is once bound to a motor will not lose contact. If the motor unbinds, the filament will not be transported, but due to the membrane affinity of MreB a rebinding will always be possible. This effect might be measurable with an even faster imaging technique depending on the magnitude of the on- and off-binding rates.

101 4. Dynamics of the actin-like protein MreB in Bacillus subtilis

Overall structure of the cell wall

If cell wall synthesis is the driving motor for MreB motion, the traces of MreB transport reflect the synthesis of new PG strands. The distribution and orientation of these traces thus represent the spatial arrangement of these new PG strands. As these traces never cross each other, one layer of the cell wall should consist of mainly parallel PG strands. Figure 4.18 illustrates the distribution of newly synthesized PG strands based on TIRF-SIM data. In (a) an image of GFP-MreB in a B. subtilis cell is shown. Blue arrows indicate the direction of motion of the dynamic filaments as observed in the corresponding time series. Longer arrows correspond to faster filaments. Filaments with no arrow appeared static. In (b) the same MreB filament distribution is shown in red and one possible constellation of motors (green and orange) and PG strands (reddish brown) is illustrated. The motor density could be higher which would result in more parallel PG strands. In subfigure (c) only the distribution of newly synthesized PG strands according to (a) and (b) is shown.

Figure 4.18.: Possible distribution of PG strands. (a) TIRF-SIM image of GFP-MreB in a B. subtilis cell. The blue arrows indicate the direction of motion as extracted from the following time points. A longer arrow corresponds to a higher velocity and no arrow to static filaments. (b) Schematic illustration of the same image according to the motor model presented here, with MreB filaments in red, PG strands in reddish brown and p- and m-motors in green and orange, respectively. The distribution of motors and PG strands represent one possible configuration. The motor density could be higher resulting in more parallel PG strands but was chosen low for clarity. (c) Distribution of newly synthesized PG strands according to subfigures (a) and (b). Scale bar is 1 µm.

It was shown in sec. 4.2.4 that the transport traces of MreB have an angular divergence of about ±10◦. According to the presented conception, the different angles would correspond to areas of parallel PG strands with slightly different orientation. However, it could also be that the more tilted traces (θ =6 90◦) correspond to locations, where the cells are about to devide. At these pole regions the cell wall must be shaped to a sort of cap. According to sec. 4.3.5, a reversal of transport direction of a MreB filament always corresponds to a takeover by at least one motor that runs in opposite direction. First, this prerequisites the synthesis and cross-linking of anti-parallel PG strands. Second, these reversals of direction could be induced by blockade situations, e.g., if the synthesis gets stopped by an opposing MreB filament that hinders a further synthesis (fig. 4.10-c). How- ever, the blockade might as well result from the PG strands, or even other components

102 4.4. Outlook that hinder a further synthesis. The latter explanation might account for spontaneous reversals that could frequently be observed (ﬁgs. 4.8-b and 4.11-a,c), complementing the explanation by a tug-of-war as described in sec. 4.3.5. However, it remains unclear why random transport reversals could be beneﬁcial for the shape and stability of the cell.

4.4. Outlook

MreB is an essential protein for the rod-shaped bacteria of type B. subtilis. It has been shown that MreB forms filaments and that these filaments are transported by motors which belong to the cell wall synthesis machinery. It has been suggested in this thesis that the main function of MreB is the coupling of several cell wall synthesis complexes, which leads to a concerted synthesis of parallel PG strands. However, a thorough understanding of why this coupling is essential for B. subtilis remains elusive and should be tackled by future experiments and calculations. Future experiments should include multicolor imaging for the time-resolved colocalization of dynamic proteins. A TIRF-SIM set-up equipped with multiple laser lines would be the method of choice due to its high temporal and spatial resolution. First of all, this would allow for a direct proof that MreB and proteins of the cell wall synthesis complex colocalize. So far, this has only been shown indirectly. Second, it might be possible to indentify and understand the reasons for events like reversals and changes of direction of MreB filaments. One protein that should be of special interest in any further study is the glycosyltransferase, which has been suggested to be the motor for MreB movement. Single molecule experiments might extract important parameters like on- and off-binding rates, stall force, detachment force, forward and backward velocity, as it has been done for eukaryotic motor proteins. These parameters crucially influence the transport behaviour. Knowing them would enable precise mathematical modeling, e.g., applying the tug-of- war model by Müller et al. [96]. Furthermore, numerical simulations would be possible that might contribute to the understanding of the observed behaviour. In particular, such simulations would deliver a model of the distribution of PG strands in the cell wall, which could be compared to measurements performed with atomic force microscopy or electron microscopy.

103

5. Total internal reﬂection dark ﬁeld microscopy

Total internal reflection fluorescence (TIRF) microscopy is a well-established fluorescence imaging technique that offers the big advantage of evanescent excitation which is limited to a thin layer (< λ0/4 ≈ 120 nm) at the coverslip-sample interface. Thus, hardly any background fluorescence is excited. However, labeling with a fluorescent dye is usually necessary which is a change of the native state of the sample and not always straightforward to accomplish. Additionally, fluorophores are subject to photobleaching, which causes a loss of signal and often leads to free radicals that are harmful to living cells [97]. However, if the structure of interest differs from its surrounding in its index of refraction this leads to scattering of the excitation light which can be exploited for imaging purposes. Imaging the scattered laser light avoids the need of labeling and in turn also circumvents the problems related to photobleaching. However, the scattered light is spatially coherent which leads to interference effects. The implementation of scattered light imaging presented in this chapter is a combination of TIR and dark field (DF) microscopy, in the following abbreviated by TIRDF microscopy. Fig. 5.1 illustrates the arrangement in TIRDF microscopy. The illumination is formed by an evanescent wave created by TIR as explained in sec. 2.2.1. A plane wave with wave vector ki is incident on the coverslip-sample interface from the optically thicker medium, here the immersion oil and the glass coverslip with refractive index ni = 1.52, and gets totally internally reflected. Thus, an evanescent wave is created that penetrates into a thin section of the optically thinner medium, here water with nt = 1.33. Axially, the intensity decays exponentially which resuls in a penetration depth of about ddp ≈ λ0/4 ≈ 120 nm. The evanescent wave travels along the interface (kev according to eq. 2.28). The object f(r) is embedded in the optically thinner medium but is located right at the interface so that it gets illuminated by the evanescent field. The reflected light is subsequently blocked in the detection path and only the light scattered by the sample is used for imaging. The great advantage of dark field microscopy is its high contrast due to the blocking of the illumination light. Equivalently, the light scattered into the transmitting medium could be used for imaging. The magnified view of the sample to the left in fig. 5.1 illustrates the occuring wave fronts, which are marked by their corresponding electric fields. The incident field (Ei) is reflected at the interface (Er) and creates an evanescent field (Eev). The illuminating evanescent field is scattered by the sample into the transmitting (Est) and incident medium (Esr). The part of the scattered light that is reflected towards the objective lens, Esr, is used for imaging. This same approach has already been followed by several other groups. However, it

105 5. Total internal reﬂection dark ﬁeld microscopy

Est

Eev fr E E i Er sr kev nt ni ni

Figure 5.1.: Concept of TIRDF microscopy. The sample f(r) is in watery solution (with refractive index nt), located right at the interface to the glass coverslip (ni > nt) and illuminated by an evanescent wave (kev). The illumination light (light blue) is scattered by the sample, as shown here in daker blue for better visibility although the scattered light has the same wavelength as the illumination light. The magnified view to the left shows the wavefronts of the various electric fields (E) that occur. The light scattered into the incident medium (Esr) is collected by the objective lens and exploited for imaging. The reflected illumination light (Er) is blocked in the detection path to ensure dark field conditions. See main text for details. is always used to image single particles in order to perform a fast and precise tracking. Mainly gold particles are used due to their strong scattering. This allows for the detection of very small particles down to 20 nm in diameter [98] and a very fast and precise tracking with a temporal resolution of 9.1 µs and a spatial precision of about 1 nm for 40 nm gold particles [99]. Also, small polystyrene beads down to a diameter of 60 nm have been imaged [98]. Using small gold beads this tracking technique has been used, e.g., to follow the rotational motion of the F1-ATPase, a motor protein that pumps ions across a membrane [99]. Also, epidermal growth factor receptors in the membrane of HeLa cells have been tracked [100]. For the tracking of single particles it is sufficient to illuminate the sample with one evanescent wave from one direction. As long as the particles are not too close to each other their coherent field PSFs do not interfere. In this thesis the goal was to establish a two-dimensional imaging technique. This involves that nearby features of an object should get resolved. For the illumination of the object by one plane wave the signals of neighboring features would interfere coherently. Therefor, imaging was performed as an average from several illumination directions. This approach yields a potentially fast and label-free imaging technique with high resolution and contrast without significant artifacts resulting from the coherent illumination. This chapter describes how the scattered light from the evanescent field is used for

106 5.1. Imaging Theory imaging. First, a mathematical formalism to describe the imaging process is given in sec. 5.1. The experimental set-up used to acquire TIRDF images is described in sec. 5.2. Images of polystyrene beads and living bacteria that demonstrate the imaging capabilities of this microscopy technique are presented with a detailed analysis in sec. 5.3. Finally, the results and the potential of TIRDF microscopy are discussed in sec. 5.4.

5.1. Imaging Theory

This section covers some mathematical concepts that describe the imaging process. Co- herent scattering is brieﬂy treated as the fundamental process that allows dark ﬁeld imaging. Starting with the Born-approximation it will be deduced that the coherent imaging process, which forms the basis for TIRDF microscopy, can be described in 2D. This will lead to the expressions for spatially coherent image formation and the 2D coherent optical transfer function that were introduced in chap. 2. Furthermore, a formalism based on the Abbé theory is introduced that describes the formation of an TIRDF image in real space and in k-space using Fourier optics.

5.1.1. Coherent scattering of an evanescent wave The fundamental process that makes dark ﬁeld microscopy possible is light scattering. Light waves are scattered whenever they encounter heterogeneities in the optical density of matter. A suitable description of the coherent scattering process that happens when an evanescent wave interacts with matter is the Born-approximation [101]. The scalar, three- dimensional distribution of the scattered electric ﬁeld Es(k) is then described by

Es(k) ∝ (f(r) · Eev(r)) ⊗ G(r), (5.1) where G(r) is the free-space Green’s function and Eev(r) is the incident electric field in the case of TIRDF as illustrated in fig. 5.1. Fourier transforming eq. 5.1 yields Ees(k) ∝ fe(k) ⊗ Eeev(k) · Ge(k), (5.2) where Ge(k) represents the Ewald-sphere which is approximately the Fourier transform G r Ge k k n 2π of ( ). ( ) is the surface of a sphere with radius = λ0 that defines all possible wave vectors. Here, λ0 is the vacuum wavelength and n the index of refraction. fe(k) is the object spectrum, i.e., the Fourier transform of the object f(r). Eeev(k) is the Fourier transform of the incident field, which is an evanescent wave in the case of TIR. In real −ktzz ık r space it is given by Eev(r⊥, z > 0) = Eev0 · e · e ev ⊥ (eq. 2.31), where r⊥ is in the x-y-plane and kev is in the kx-ky-plane. ktz describes the exponential decay in axial direction and Eev0 is the amplitude of the evanescent field. For the relation of ktz and kev to the incident wave vector ki see sec. 2.2.1. For a glass-water interface, an illumination wavelength of λ0 = 488 nm (in vacuum), ◦ and an angle of incidence of θi = 68 the penetration depth is dp = 84 nm (eq. 2.33).

107 5. Total internal reﬂection dark ﬁeld microscopy

In contrast to that, the axial extent of the detection PSF in terms of the full width at 1.77·λ0 ◦ half maximum is ∆zPSF = 2 = 742 nm for θmax = 61 (equals NA = 1.33) n·sin (θmax) and thus rather large [102]. Consequently, the part of the sample that is illuminated by the incident ﬁeld is much thinner in axial direction than the PSF so that it is legitimate to treat the imaging process in two dimensions only (x,y). This also means that the object is assumed to be inﬁnitely thin in z-direction. Neglecting the z-dependency of the incident wave, the Fourier transform of Eev is then given by

Eeev(k⊥) ∝ δ(k⊥ − kev). (5.3)

Considering the convolution in eq. 5.2 this implies that the illumination by an evanescent wave leads to a shift of the object spectrum in the kx-ky-plane.

Figure 5.2.: Ewald construction for an inﬁnitely thin object at a glass-water interface. The absolute value of the object spectrum is independent of kz. (a) For straight illumination the object spectrum is centered. (b) Oblique illumination leads to a lateral shift of the object spectrum. The Ewald sphere Ge(k) (white) has a larger radius in glass (ni) than in water (nt) due to the diﬀerence in refractive index. The evanescent parts of the Ewald sphere in water are drawn in red as they are in the kx-ıkz-plane. The product fe(k) · Ge(k) is independent of kz. As Ge(k) is rotationally symmetric around the kz-axis, this holds true for the whole kx-ky-plane.

Treating the imaging in 2D results in further simplifications for the multiplication with the Ewald sphere Ge(k) in eq. 5.2. If the object is approximated as infinitely thin, then the object spectrum fe(k) does not depend on kz. As an example, fig. 5.2 shows an object spectrum in the kx-kz-plane of a bead of arbitrary but finite size, which has no extension in z. In subfigure (a) the case of straight illumination is illustrated, where the object spectrum is centered on the kz-axis. Subfigure (b) shows the case of oblique illumination which leads to a lateral shift of the object spectrum. In the case of TIR the imaging plane is the interface of the optically thicker medium with refractive index ni, from which the illumination occurs, and the optically thinner medium, usually water, with nt < ni. Consequently, the Ewald sphere Ge(k), shown in white, has different radii for positive and negative kz. The evanescent parts of the Ewald sphere in water, representing near field components, are drawn in red as they are in the kx-ıkz-plane.

108 5.1. Imaging Theory

However, for reasons of simplicity they will be omitted in the following discussion. For negative kz, which represent the optically thicker medium with n = ni, the Ewald sphere k n k 2π k has a larger radius 0 i. Here, 0 = λ0 is the vacuum wavenumber. Positive z represent the optically thinner medium with n = nt in which the Ewald sphere has an accordingly smaller radius of k0nt. Due to the rotational symmetry of the Ewald sphere around the kz-axis the situation is the same in the ky-kz-plane. As can be seen in ﬁg. 5.2, the remaining kx- and ky-components after the multiplication of the object spectrum f˜(k) with Ge(k) are the same for all kz. This means that the Ewald sphere can be projected onto the kx-ky-plane. The sample is embedded in the transmitting medium and the corresponding Ewald sphere is thus described by ! k⊥ Ge(k⊥) = circ , (5.4) k0nt

q 2 2 where k⊥ = kx + ky. Plugging this expression into eq. 5.2 all coherently scattered light ﬁelds in the far ﬁeld are then given by ! h i k⊥ Ees(k⊥) ∝ fe(k⊥) ⊗ δ(k⊥ − kev) · circ k0nt ! k⊥ ∝ fe(k⊥ − kev) · circ (5.5) k0nt

The meaning of equation 5.5 is schematically illustrated for the spectrum of a single bead in the kx-ky-plane in fig. 5.3. The object spectrum is shifted by kev and then multiplied with the projection of the Ewald sphere Ge(k⊥). The remaining part of the object spectrum is shown in (b). This part contains the spatial frequencies which exist after the scattering process and which can potentially be detected and used for imaging. For the sake of simplicity, near fields are not considered here although they might contribute to the image. As the scattering happens right at the interface, near field components as shown in fig. 5.2 might be transformed into propagating waves and enlarge the far field object spectrum after the scattering process. This could quantitatively change the situation, but is not essential for a principal understanding.

5.1.2. 2D Coherent optical transfer function As introduced in sec. 2.1.2 imaging by an optical system can be described in k-space by an optical transfer function (OTF) that ﬁlters the object spectrum. Equivalently, in real space the formation of an image is described by the convolution of the object with the point spread function (PSF), the Fourier transform of the OTF. Based on the explanations of the previous section it will be shown that the 2D coherent optical transfer function (OTFcoh), as introduced in sec. 2.1.3, is a good approximation for the case of TIR imaging. The three dimensional coherent OTF of an optical system is deﬁned by a cap on the Ewald sphere with lateral radius |k⊥| = k0NA, where NA = NAmax if the full detection

109 5. Total internal reﬂection dark ﬁeld microscopy

Figure 5.3.: Limited object spectrum after the scattering process in the kx-ky-plane. (a) Absolute value of the full object spectrum of a single bead of ﬁnite size. Illumination with an evanescent wave in -x-direction leads to a shift of the spectrum by the incident kev-vector. The border of the Ewald sphere with radius k0nt is indicated by a white circle. (b) Shifted object spectrum after multiplication with the Ewald sphere, which represents the existing frequency components in the far ﬁeld.

NA of the objective lens is used [103]. To get dark field conditions in the detection path the NA is effectively reduced to NAdet = nt to exclude all reflected illumination light. As explained in the previous section the Ewald sphere can be projected onto the kx- ky-plane in TIR imaging. Consequently, the detection OTF can be projected, too. The coherent optical transfer function of the detection system in the kx-ky-plane is then given by ! k⊥ OTFcoh(k⊥) = circ . (5.6) k0 · NAdet From the coherent OTF the coherent field PSF can be derived as shown in sec. 2.1.3. The NA of the objective lens limits the accessible illumination angles that result in an evanescent illumination. This is illustrated in fig. 5.4, which shows the different radii on the kx-axis. Due to rotational symmetry around the kz-axis the situation is the same on the ky-axis. The radius of the Ewald sphere Ge(k) (white) depends on the refractive index of the medium and is k0nt in water (positive kz) and k0ni in glass (negative kz). The full NA of the objective lens (NAmax, green) defines the maximal illumination and detection angle. The TIR-region between k0nt and k0NAmax defines the illumination angles that result in total internal reflection and thus in an evanescent illumination. To exclude the illumination light in the detection path and thus get dark field conditions the detection NA is reduced to coincide with the lower limit of total internal reflection, NAdet = nt.

5.1.3. Image formation

The formation of an image by TIRDF microscopy as implemented in this thesis will be described both in k-space and in real space in 2D. Each of the two descriptions helps to understand the information content in the ﬁnal image.

110 5.1. Imaging Theory

Figure 5.4.: Illustration of the various radii in k-space in the kx-kz-plane. The radius of the Ewald sphere Ge(k) (white) depends on the refractive index of the medium and is k0nt in water (positive kz) and k0ni in glass (negative kz). The full NA of the objective lens (NAmax) defines the maximal illumination and detection angle. The TIR-region between k0nt and k0NAmax defines the accessible illumination angles that result in total internal reflection and thus in an evanescent illumination. An exemplary illumination under an angle θi with wave vector ki is shown in dark blue. The lateral part of the corresponding evanescent wave vector is shown in yellow. To exclude the illumination light in the detection path and thus get dark field conditions the detection NA is reduced to coincide with the lower limit of total internal reflection, NAdet = nt. Due to rotational symmetry around the kz-axis the situation is the same in the ky-kz-plane.

General image formation in Fourier space Equation 5.5 describes the scattered far-field distribution of the electric field for an illumination with Eeev,m(k⊥) ≡ Eem(k⊥) = Ee0m(km) · δ(k⊥ − km), where ! − cos(φm) km = k0 · ni · (5.7) sin(φm) is the lateral component of the evanescent wave vector (formerly denoted by kev) and φm denotes the illumination direction. Upon imaging with the microscope the electric field distribution Ees(k⊥) (eq. 5.5) gets filtered with the OTFcoh. However, as the sample is embedded in the transmitting medium (water) the radii of the Ewald sphere and the effective detection NA coincide (fig. 5.5). Consequently, the object spectrum in the pupil plane of the imaging system is described by the electric field components in k-space

Ees(k⊥) ∝ Ee0m(km) · fe(k⊥ − km) · OTFcoh(k⊥) (5.8) which is equivalent to eq. 2.7 except for the prefactors. Figure 5.5 summarizes the imaging process in k-space. The objective lens Fourier transforms the object which is illuminated by an evanescent field (kev respectively km). The shifted object field spectrum gets filtered by the detection OTFcoh(k⊥) with radius k0NAdet (green circle),

111 5. Total internal reﬂection dark ﬁeld microscopy

Figure 5.5.: TIRDF imaging in k-space (pupil plane). The sample is obliquely illuminated by an evanescent wave. The objective lens Fourier transforms the electric field distribution from the sample plane. As explained in the text, only a shifted (by kev) and limited object spectrum with radius k0nt = k0NAdet is detectable, whereas the reflected illumination light (Eer) is blocked. The detected part of the object spectrum is Fourier back transformed by a second lens and the resulting intensity image is recorded by a camera. leaving out the unscattered illumination light (see also fig. 5.4). Blocking the illumination light fulfills dark field conditions and thus yields a very high contrast as no unscattered light is collected. For one illumination direction km the intensity image obtained in the image plane is then, according to eq. 2.11, given by

n o 2 −1 Im(r⊥) = FT fe(k⊥ − km)OTFcoh(k⊥) . (5.9)

Here, all constant prefactors are omitted including the illumination amplitude Ee0m(km) which is assumed to be constant for all illumination directions. 0 For the further analysis it is helpful to move to a coordinate system k⊥ = k⊥ − km, so that n o 2 −1 0 0 Im(r⊥) = FT fe(k⊥)OTFcoh(k⊥ + km) . (5.10) Writing the Fourier transformation and the absolute square explicitly, the intensity distribution of an image with one coherent evanescent illumination wave is ZZ 0 ? 0 Im(r⊥) = OTFcoh(k⊥1 + km) · OTFcoh(k⊥2 + km)· 0 0 0 ? 0 −ı(k⊥1−k⊥2)r⊥ 0 0 fe(k⊥1) · fe (k⊥2) · e dk⊥1dk⊥2. (5.11)

The ? denotes complex conjugation. Evanescent illumination can be applied from diﬀerent angular directions (see eq. 5.7). Applying multiple illumination directions φm subsequently means that the light sources

112 5.1. Imaging Theory are mutually uncorrelated. Adding the single intensity images from several illuminations is an incoherent summation of coherent raw images. Generally, this is described by Z Ifinal(r⊥) = Im(r⊥)dkm ZZZ 0 ? 0 = OTFcoh(k⊥1 + km) · OTFcoh(k⊥2 + km)· 0 0 0 ? 0 −ı(k⊥1−k⊥2)r⊥ 0 0 fe(k⊥1) · fe (k⊥2) · e dk⊥1dk⊥2dkm. (5.12)

Equation 5.12 represents a general description of a ﬁnal TIRDF image. Bundling up the terms from eq. 5.12 that depend on the illumination and on the optical system yields a transmission function TF for the ﬁnal image Z 0 0 0 ? 0 TF (k⊥1, k⊥2) = OTFcoh(k⊥1 + km) · OTFcoh(k⊥2 + km)dkm. (5.13)

According to this general transmission function the final image intensity depends bi- linearly on the transmitted object spectrum. That means that the imaging process is neither linear in amplitude nor in intensity of the object spectrum fe(k). Thus, no an- alytical expression for the optical transfer function, which describes the transmission of the spatial frequencies and thus defines contrast and resolution, can be given for the final TIRDF image. However, fig. 5.6 illustrates the different parts of the object’s field spectrum that are transmitted in the single raw images for different illumination directions. For rotationally symmetric illumination directions the OTFs (shown in green) corotate around the center of the object spectrum. These different parts of the object spectrum are then incoherently added to yield the final TIRDF image. The incoherent summation is done by autocorrelating the various object field spectra to get the intensity spectra, which are then added to form the final image spectrum (see sec. 2.1.2).

Image formation in real space

According to sec. 2.1.2 an equivalent description to eq. 5.9 for the formation of a coherent image in real space is given by

2 Im(r⊥) = |f(r⊥) · Em(r⊥) ⊗ PSFcoh(r⊥)| . (5.14)

Equation 5.14 describes the formation of an image with illumination Em(r⊥) = E0m(r⊥)· −ık r e m ⊥ . Again, applying multiple illumination directions φm subsequently and adding the single raw images incoherently the ﬁnal TIRDF image is described by Z 2 Ifinal(r⊥) = |f(r⊥) · Em(r⊥) ⊗ PSFcoh(r⊥)| dφm (5.15)

However, in all the measurements performed in this thesis the final image is calculated as the average of a finite number N of coherent raw images with different illuminations

113 5. Total internal reﬂection dark ﬁeld microscopy

Figure 5.6.: Optical transfer for raw images with different illumination directions φm. (a) Absolute value of the field spectrum of a single bead of finite size. The green circles outline the coherent OTFs of individual raw images for different illumination directions φm. For rotationally symmetric illumination directions the OTFs are symmetrically distributed around the center of the object spectrum. Only five OTFs corresponding to five different illumination directions are shown for clarity. (b) Schematic line profile of the coherent ◦ OTF along ky at kx = −km for an illumination along the kx-axis (φ0 = 0 ). that are symmetrically distributed along the TIR region. The final image intensity is then described by N 1 X I (r ) = I (r ), (5.16) final ⊥ N m ⊥ m=1

360◦ where the illumination directions are given by φm = N · m Plugging the expression for a single coherent image (eq. 5.14) into eq. 5.16 the ﬁnal intensity can be rewritten as

N 1 X I (r ) = |f(r )E (r , φ ) ⊗ PSF (r )|2 . (5.17) final ⊥ N ⊥ m ⊥ m coh ⊥ m=1

The object f(r⊥) can be expressed as the sum of diﬀerent scatterers indexed by j, P f(r⊥) = fj(r⊥) which yields j

  N 2 1 X X Ifinal(r⊥) =  fj(r⊥) · Em(r⊥, φm) ⊗ PSFcoh(r⊥) N m=1 j N 2 distributivity 1 X X → = ((fj(r⊥) · Em(r⊥, φm)) ⊗ PSF (r⊥)) , (5.18) N coh m=1 j | {z } Fm,j (r⊥,φm) where Fm,j(r⊥, φm) is the amplitude image of the j-th scatterer under illumination with Em(r⊥, φm). Generally, Fm,j can be expressed as Fm,j(r⊥, φm) = Fm,j(r⊥, φm) ·

114 5.1. Imaging Theory e−ıϕ(r⊥,φm). Expansion of the multi ﬁeld interference of eq. 5.18 then yields

N 1 X X I (r ) = |F (r , φ )|2 + final ⊥ N m,j ⊥ m m=1 j ! X 2 |Fm,j(r⊥, φm)| · |Fm,k(r⊥, φm)| · cos (ϕm,j(r⊥, φm) − ϕm,k(r⊥, φm)) j6=k N 1 X X = |F (r , φ )|2 + N m,j ⊥ m m=1 j N 2 X X |F (r , φ )| · |F (r , φ )| · N m,j ⊥ m m,k ⊥ m m=1 j6=k

cos (ϕm,j(r⊥, φm) − ϕm,k(r⊥, φm)) , (5.19) where a second index k is introduced for the j scatterers that make up the object. The second double sum represents all the interference terms between diﬀerent scatterers j and k that result from the coherent illumination. Remarkably, only two beam interferences occur. Assuming only point scatterers, further approximations can be made. In this case, every scatterer j is a source of spherical wavefronts after the scattering process. That means that for diﬀerent scatterers j, k their phases depend on the direction of incidence but their amplitudes do not. Thus, rewriting eq. 5.19 yields

X 2 Ifinal(r⊥) = |Fj(r⊥)| + j N 2 X X |F (r )| |F (r )| cos (ϕ (r , φ ) − ϕ (r , φ )) . (5.20) N j ⊥ k ⊥ m,j ⊥ m m,k ⊥ m j6=k m=1

The ﬁrst term represents the incoherent image of the point scatterers fj(r⊥). The second term sums the phase diﬀerences between pairwise scatterers over all illumination directions weighted with a cosine. This sum is generally not zero but depends crucially on the distance of the scatterers j and k and on the location r⊥.

5.1.4. Two-point resolution in coherent imaging In spatially coherent imaging the two-point resolution depends on the phase relation of the two waves emitted from, e.g., a double slit or two point scatterers. This is of particular relevance as according to eq. 5.20 an image of many point scatterers contains only pairwise interference terms. Figure 5.7 compares the coherent amplitude and intensity images of two point scat- 0.61·λ terers at a distance d = NA with diﬀerent phase relations ∆ϕ, as done by Singer et al. [104]. The distance d is exactly the Rayleigh resolution limit for incoherent imaging as introduced in sec. 2.1.4. In coherent imaging the complex amplitudes are added before

115 5. Total internal reﬂection dark ﬁeld microscopy

Figure 5.7.: Two-point resolution in coherent imaging according to Singer et al. [104]. (a) 0.61·λ Two point scatterers at a distance d = NA under straight (left) and oblique illumination under the angle φ (right). (b, c) Amplitude and intensity images, respectively, for phase differences of ∆ϕ = 0 (left) and ∆ϕ = π (right) for the point scatterers. The coherent intensity image under oblique illumination yields maximum contrast but also an increased peak-to-peak distance dmes = 1.26 · d. the intensity is formed by the square of the sum (see sec. 2.1.2). Straight illumination (fig. 5.7-left) means no phase difference (∆ϕ = 0) and leads to identical amplitude images. The resulting intensity image, as observed on a camera, can’t resolve the two points. Only a single peak in the middle is formed. On the contrary, an oblique illumination that leads to a phase shift of ∆ϕ = π leads to amplitude images of inverse sign (fig. 5.7-right). The resulting intensity image resolves the two points at maximum 0.77·λ contrast, albeit at an approximately 26 % increased distance dmes = NA = 1.26 · d. To fulfill the condition of opposite phases the following equation must be satisfied λ d · sin(φ) = (5.21) 2 where λ is the wavelength and φ the angle of the illumination direction as depicted in fig. 5.7. The minimal distance between two point scatterers, dmin, for which this π condition can be satisfied is under an evanescent illumination with φ = 2 and thus given by 1 λ0 dmin = · (5.22) 2 ni sin(θi) where λ0 is the vacuum wavelength, ni the index of refraction of the incident medium and θi the angle of incidence. The minimal distance dmin is approximately the Rayleigh 0.61·λ0 resolution limit, dmin ≈ NA . This means that two point scatterers which can barely

116 5.2. Experimental set-up be resolved in an incoherent image can be resolved at maximum contrast in a coherent image under adequate oblique illumination. However, their apparent distance in the image is increased.

5.2. Experimental set-up

The set-up used for TIRDF microscopy is a slight modification of the one used for TIRF- SIM that is described in detail in chapter 3. A schematic sketch of the modified set-up is given in fig. 5.8. The illumination path is basically the same as in TIRF-SIM. Merely the mask in the pupil plane is replaced by a simple zero order block that only blocks the central zero order coming from the SLM. This way almost all illumination directions are accessible (see fig. 5.10-a). In the detection path some important changes have to be made. First of all, as now coherently scattered light is imaged which has the same wavelength as the illumination

Figure 5.8.: Sketch of the TIRDF microscope set-up. It’s very similar to the TIRF-SIM set-up presented in detail in chapter 3. The mask is replaced by a more simple zero order block that only blocks the central zero order coming from the SLM (indicated by a blue frame). The pellicle beam splitter reflects 8 % of the light collected by the objective towards the CCD-camera. A diaphragm in the pupil plane (“dark field”) of the detection path blocks the non-diffracted illumination light that is totally internally reflected. The transmitted scattered light (shown in darker blue for better visibility although it has the same wavelength as the incident light) forms an image on the CCD-camera.

117 5. Total internal reflection dark field microscopy light, the dichroic mirror can not be used to separate illumination from detection light as in fluorescence microscopy. Instead, this separation is done by assuring dark field conditions, which means that the illumination light is blocked in the detection path so that only the scattered light can reach the detector. Therefor a beam splitter, in this case a 92/8-pellicle with 92 % transmission and 8 % reflection, is placed in the beam path such that 8 % of all the light collected by the objective lens is reflected out of the detection beam path (that so far equals the reverse illumination beam path). A conjugate pupil plane (“dark field”) is then accessible in the detection path without interfering with the illumination light path. Also, a detection camera is placed after the beam splitter (in terms of the backscattered light). Here, the pellicle and the CCD-camera that are used for the detection of axial drifts in TIRF-SIM can be used (sec. 3.4). In order to fulfill dark field conditions a round diaphragm is placed in the pupil plane (“dark field”) of the detection path, which is conjugate to the BFP of the objective lens. In fig. 5.9 the front view of the diaphragm illustrates its effect with the TIR-region highlighted by the black, dashed circles. As the diaphragm is placed in a pupil plane it determines the effective NA of the detection path, NAdet. Its opening diameter should ideally be chosen such that NAdet = NATIR, where NATIR = 1.33 is the lower limit for total internal reflection when the sample is in watery solution. This setting assures that all illumination light, which is totally internally reflected, is blocked. That comprises the whole TIR-region given by NATIR and NAmax, the objective’s maximal NA. The blocking of the illumination light is illustrated by the blue dots representing illumination foci at six typical positions in fig. 5.9.

Figure 5.9.: Front view (x,y) of the diaphragm in the detection path that ensures dark field imaging conditions. It is placed in a pupil plane and its opening diameter is chosen such that the effective detection NA equals the critical NA for total internal reflection (NAdet = NATIR). This ensures that all illumination light that is reflected under TIR- conditions is blocked (annular region between the black dashed lines). The blue dots are exemplary illumination foci.

The theoretically exact diameter of the diaphragm, DDF,NATIR , is given by the diameter of the non-TIR region of the BFP of the objective lens, DBF P,NATIR , times the magniﬁcation from the BFP to the conjugate pupil plane where the diaphragm is placed, f2 120 mm DDF,NA = DBF P,NA · = 5.32 mm · = 3.19 mm. In practice, the diam- TIR TIR fT Lill 200 mm eter is adjusted manually so that no illumination light hits the detection camera. The ﬁnal diameter matches the theoretical value to ±0.2 mm. The diaphragm is placed onto

118 5.2. Experimental set-up a x-y-positioner so that it can be manually centered onto the optical axis. The fluorescence detection path (not shown in fig. 5.8) is not influenced by the mod- ifications and can be used to acquire reference images to compare with. Especially the option to do TIRF-SIM with a resolution of about 100 nm provides an excellent comparison for fluorescent samples as will be shown in the results section (sec. 5.3).

5.2.1. Imaging modalities For the acquisition of one TIRDF image the following approach is chosen: One set of raw images with different illumination directions of the evanescent wave is acquired. Here, it must be mentioned that concerning the illumination, “direction” refers to the angular direction of the incident evanescent wave in the x-y sample plane (denoted by φ), whereas the “angle of incidence” relates to the angle of total internal reflection of the incoming illumination (denoted by θ). The illumination directions are symmetrically distributed from 0◦ − 360◦ as illustrated in fig. 5.10. For each illumination direction one coherent raw image is acquired. The final TIRDF image is the average of one such set of raw images, as described in sec. 5.1. For each raw image a blazed grating hologram with a period of six pixels is displayed on the SLM so that a focus is created in the radial center of the TIR-region of the ◦ BFP, corresponding to an azimuthal angle of incidence of about θi = 68 (see chap. 3). According to eqs. 2.29 and 2.33 this results in an evanescent wave with wavelength λev = λ0 = 346 nm coming from one direction and a penetration depth of d = 84 nm. ni sin(θi) pd Here, ni = 1.52 is the refractive index of the glass coverslip and λ0 = 488 nm the vacuum wavelength of the laser. By changing the orientation φ of the blazed grating hologram the focus in the BFP is subsequently rotated around the optical axis, always remaining in the ring of TIR-illumination. This is shown for the pupil plane after lens L1 (which is conjugate to the BFP) in fig. 5.10-a. It is also visible that blocking the undiffracted light from the SLM inhibits certain illumination directions (here: 320◦ − 340◦). Fig. 5.10-b shows the corresponding directions of evanescent wave illumination of the sample in the image plane. The polarization is controlled using a motorized half-wave plate and is indicated by red arrows. The change in illumination direction ∆φ is chosen to be either 60◦ or 5◦, resulting in 6 or 72 raw images, respectively. The pixel period of the hologram is always kept constant so that the azimuthal angle of incidence and consequently the penetration depth into the sample and the effective evanescent wavelength are also constant. The polarization is adjusted to the S-state with regard to the total internal reflection at the coverslip for all illumination directions. This means that the polarization is corotated with the illumination direction as explained by fig. 5.10-a. The final TIRDF image is then calculated as the pixel-wise average of all raw images, according to eq. 5.16. By this the interference effects of coherent imaging, which can be observed in the single raw images, can be suppressed to a great extent. This includes interferences of the signal with the background. Additionally, the background gets flattened by the averaging as it strongly depends on the illumination direction. This will be analyzed in detail in sec. 5.2.3.

119 5. Total internal reﬂection dark ﬁeld microscopy

Figure 5.10.: Illustration of the imaging modalities. (a) X-y-view of the pupil plane in the direction of propagation of the illumination light after the lens L1. The focus is sequentially moved along the annular ring that represents the TIR-region. The central undiﬀracted zeroth order light coming from the SLM is blocked by a black bar which inhibits a narrow range of illumination directions (here: 320◦ − 340◦). The state of polarization is exemplarily shown with red arrows for two foci. (b) Top view of the coverlip. Corresponding to the position of the focus as shown in (a), the real part of the k-vector of the evanescent illumination (kev) rotates in the sample plane.

5.2.2. Corrections for an imperfect system With a perfect system the final TIRDF image would be obtained as described in the previous section. However, in practice the optical set-up suffers from imperfections which have to be corrected for. First, the polarization-dependent reflectivity of the pellicle leads to nonuniform intensity levels within one set of raw images. Second, the zero order beam block inhibits certain illumination directions. The corrections for these effects undertaken in the postprocessing are described in the following paragraphs.

Intensity corrections The acquired raw images do not all exhibit the same amount of overall intensity. This is due to the polarization-dependent reflectivity of the pellicle. As shown in sec. 3.3.1 the pellicle reflects S-polarized light much better than P-polarized light. As can be seen in fig. 5.10-a, ensuring S-polarization for total internal reflection at the coverslip means that the state of polarization rotates along with the position of the illumination focus in the pupil plane and thus the illumination direction. Referring to the pellicle, over a full continuous turn of 360◦ all intermediate mixed states of polarization between S and P occur four times. The states of pure S- or P-polarization occur twice each. Assuming that the state of polarization is basically maintained during the scattering process in the sample this means that the amount of light reflected by the pellicle towards the imaging camera depends on the direction of illumination. In order to weight every raw image equally in the averaging process one has to compensate for this effect and adjust the intensities accordingly. The most intuitive approach would be to normalize every raw image by its overall image intensity. This can not be

120 5.2. Experimental set-up done as reflections from interfaces contribute differently to images acquired with different illumination directions, which is due to an imperfect alignment of the optical system. Instead, the raw images were normalized by their peak intensity value. This is only valid as long as multiple scattering can be neglected so that the peak intensity can be assumed to be independent of the illumination direction. Although this assumption is not completely fulfilled (see sec. 5.3.1), this approach was chosen as the best possible compromise. Furthermore, the brightest pixel in all raw images must be a signal from the sample and not from the background. The resulting average image is then given by a modification of eq. 5.16:

N 1 X I (r ) = I (r , φ ) (5.23) final ⊥ N m,norm ⊥ m m=1

I Im where m,norm = Max(Im) . One drawback that cannot be overcome by this postprocessing is the worse signal-to-noise ratio of the dimmer raw images.

Corrections for illumination directions

As illustrated in ﬁg. 5.10-a, certain illumination directions are not accessible due to the zero order block. For steps of ∆φ = 60◦ of the illumination directions there are no constraints. For steps of ∆φ = 5◦ the directions 320◦ − 340◦ are not accessible. The corresponding images are neglected for the calculation of the ﬁnal TIRDF image. As no directional bias can be observed the lack of these directions seems to be negligible.

5.2.3. Eﬀects of image averaging on the background

Illumination with a highly coherent light source leads to a typical speckle pattern background [105]. This is caused by reflections from rough surfaces and interfaces, e.g., lenses, producing phase-random stray light that leads to speckles. The background occurring in the images that were acquired with the set-up presented here can be subdivided in two populations. First, there are rather bright reflexes with a speckled appearance for which the origin, i.e., the interface they result from, can be clearly identified. Second, there is a general speckle background that is difficult to assign to a specific optical component. In fig. 5.11 different contributions to the background and the effects of different illuminations and averaging are illustrated. Subfigures (a) and (b) are autoscaled raw images of 190 nm polystyrene beads with illumination directions of 160◦ and 300◦, respectively. In (a) a strong reflex from the lens L2 is present, whereas in (b) the overall intensity is slightly higher, as can be seen from the line scans shown in (d). In the averaged final image shown in (c) no more speckles are visible, neither from reflexes nor from the background. This becomes even clearer in the line profiles. In this case the final image is an average of 72 raw images. The strongest reflex stems from the illumination tube lens TLill. It has a very distinct and roundish appearance and is located only at the outskirts of the camera chip. With

121 5. Total internal reﬂection dark ﬁeld microscopy

Figure 5.11.: Speckle background reduction through averaging. (a,b) Coherent raw images of 190 nm polystyrene beads with illumination directions of 160◦ and 300◦, respectively. (c) Final TIRDF image (72 raw images). (d) Line profiles along the white line drawn in (a-c). The raw images (red: 160◦, blue: 300◦) have different signal intensities for the bead, stronger background fluctuations and in (a) also a dominant reflex is present. In the final TIRDF image (green) the background is flattened and the influence of the reflex has almost completely vanished. All images are autoscaled, scale bar is 1 µm. the change of the illumination direction this reflex moves in a more or less circular fashion in the camera image plane. Due to imperfections in the alignment of the optical path it disappears completely for certain directions. However, by confining the effective imaging area to a central part this reflex did not influence the measurements presented here at all.

Another distinct reflex is caused by the lens L2. This reflex appears more to the center of the imaging area. It is also roundish but with a very inhomogeneous, speckled appearance. In terms of intensity, this reflex is usually dimmer than the brightest signal from the sample (this holds true for the measurements done with beads in this thesis). It also moves in a more or less circular fashion, though not centered in the image due to imperfections in the optical path. It gets flattened by the averaging process and hardly influences the final image (fig. 5.11-c). Fig. 5.11-d yields intensity values of the final TIRDF image of hIbgi = 0.119 for the average background level, Ireflex = 0.148 for the maximal value in the area of the reflex and Ibead = 0.282 for the maximal value of the single bead at the position of the line scan, all in arbitrary units. In terms of contrast Max−hIbgi in the final TIRDF image, calculated as K = Max , the single bead in this example

122 5.3. Results

is 2.9 times higher than the reflex, with Kbead = 0.58 and Kreflex = 0.2, respectively. Consequently, this reflex does not affect the image quality significantly, as can also be seen in the averaged final image in fig. 5.11-c. Furthermore, a general speckle background is visible in all raw images. Most likely, reflections from the coverslip, the objective lens and the pellicle contribute to that. This background is much lower in intensity and as it also alters with the change of illumination direction it gets very well flattened by the averaging process. This can well be seen in fig. 5.11-c,d.

5.3. Results

An appropriate sample to investigate the performance of a microscope is polystyrene beads. They form a well-defined test structure in terms of size and refractive index. Here, small, fluorescently labeled beads with a diameter of 190 nm were used. This size is just slightly below the optical resolution for TIRF-imaging which is about 213 nm in theory (eq. 2.26). However, using the TIRF-SIM technique every single bead can be very well resolved. Thus, an accurate reference is available that permits the evaluation of the performance of the TIRDF-microscope. The difference in refractive index of the beads (nPS = 1.6 at λ = 488 nm) [106] to that of the surrounding water (nH20 = 1.33) leads to scattering, a prerequisite for the acquisition of a dark field image. Eventually, microscopes are supposed to deliver images of more challenging, inhomogeneous samples such as living cells. Some components of cells have different refractive indices, but most are quite similar to that of water [107]. Consequently, the question arises whether a biological sample (or more precisely: which component of a cell) yields enough contrast to be distinguishable from the background. Theoretically, a small difference in refractive index should be sufficient as the background in dark field microscopy is very low and small signals can be detected. However, in practice, a sufficient signal strength is desirable to have a reasonable signal-to-noise ratio. Here, the bacteria B. subtilis was imaged as a biological test sample. The results are presented in the second part of this section.

5.3.1. Images of polystyrene beads

Fluorescent 190 nm beads were air-dried on a # 1.5 coverslip and then reimmersed in water. A set of 72 raw images with angular changes of the illumination direction of ∆φ = 5◦ were acquired and processed as described in 5.2.1. Additionally, the flattened background was subtracted as a constant offset, which was determined in a region with no image content. In fig. 5.12-a the final TIRDF image is shown. As a comparison, fig. 5.12-b and -c show the corresponding TIRF and TIRF-SIM image, respectively. It becomes very clear that the distribution of beads is correctly imaged. Single beads as well as bead clusters are well reproduced in position and shape. The background is much lower in signal than the beads and due to the averaging of many (72) images with different illumination

123 5. Total internal reﬂection dark ﬁeld microscopy

Figure 5.12.: Comparison of TIRDF with ﬂuorescence techniques. (a) TIRDF image of 190 nm polystyrene beads (average of 72 raw images). (b) TIRF image of the same sample. (c) TIRF-SIM image that serves as a high-resolution control. The distribution of beads is well reproduced in the TIRDF image. Some adjacent beads can even be better separated than in the TIRF image. On the other hand, many clusters appear “blown up”. A detailed analysis of the imaging eﬀects is given in the main text. All images are autoscaled, scale bar is 1 µm. directions also very homogeneous. Most clusters of several beads appear “blown up” in size which will be discussed in sec. 5.4.3. The following sections will describe the particularities and characteristics of the TIRDF image in greater detail.

Single raw images

Fig. 5.13 illustrates the effects of different illuminations by exemplarily showing coherent raw images for the illumination directions 5◦ (b), 20◦ (c) and 110◦ (d). The final TIRDF image is shown as a reference (a). All raw images show the interference effects typical for coherent images. At the same time they hardly resemble the final TIRDF image. For similar illumination directions of 5◦ and 20◦ the raw images are quite similar. However, changing the illumination direction significantly, e.g., to 110◦, results in a completely different interference pattern. In fig. 5.13-e two regions of interest (ROI) are magnified. In ROI 1 two adjacent beads are shown. The beads are resolved with high contrast for an illumination parallel to their connecting axis (20◦), or almost parallel (5◦). An illumination perpendicular to the connecting axis of the two beads leads to a very different image. Only one single peak in the middle between the beads is observed. The same holds true for the symmetric cluster of four beads shown in ROI 2. Beads are separated along the direction of illumination but not perpendicular to it. For the illumination direction of 20◦ the beads to the left appear much dimmer than the ones to the right. Likely, this is due to destructive interference as a result of multiple scattering induced by neighboring beads. Below the ROIs the distances between the beads as measured from the corresponding TIRF-SIM image are given. The apparent bead distances in the raw images are given in the corresponding subimages. All distances are measured as peak-to-peak distances from one-dimensional line scans using local Gaussian fits. The dependency of the two-point

124 5.3. Results

Figure 5.13.: Influence of the illumination direction on the appearance of beads in the coherent raw images. (a) Final TIRDF image as a reference. (b, c, d) Single raw images for illumination directions 5◦, 20◦ and 110◦, respectively. (e) Comparison of the different illumination directions for two magnified ROIs. The separation of neighboring beads depends on the direction of illumination. Below the ROIs the distances between the beads as measured from the corresponding TIRF-SIM image are given. The apparent bead distances in the raw images are given in the corresponding subimages. All images and subimages are autoscaled. Scale bar is 1 µm resolution in ROI 1 on the illumination direction coincides qualitatively with the theory explained in sec. 5.1.4. The single raw images shown in fig. 5.13 exhibit the typical interference effects of coherent imaging. Examining the magnified ROIs and applying the concept of coherent two-point resolution (sec. 5.1.4) gives a qualitative understanding of the improved separation of neighboring beads. The two beads in ROI 1 have a distance of 156 nm, which λ0 is almost half the illuminating wavelength (λev = = 346 nm with ni = 1.52 and ni sin(θi) ◦ θi = 68 ). Consequently, an illumination along their connecting axis results in a phase difference of ∆ϕ ≈ π. According to sec. 5.1.4 this means that the beads will appear separated in the image, albeit at increased peak-to-peak distance, as can be seen in the subimages (b) and (c) of ROI 1 of fig. 5.13-e. An illumination perpendicular to their connecting axis results in an in-phase scattering. The image will only exhibit a single peak and the two point scatterers are not separated, as confirmed in subimage (d) of the ROI 1 of fig. 5.13-e. For the cluster of four beads shown in ROI 2 of fig. 5.13 the same principal holds true. The horizontal distances between neighboring beads are 173 nm and 174 nm which

125 5. Total internal reﬂection dark ﬁeld microscopy

Figure 5.14.: Overview of the positions of the line profiles and the single beads that are analyzed. Scale bar is 1 µm is again half the illuminating wavelength. In the subimages with roughly horizontal ◦ illumination (b, c) two distinct peaks can be observed at increased distance. For φi = 20 the left peak appears strongly reduced in intensity, which might be due to destructive interference resulting from multiple scattering from neighboring beads. For the vertical direction (subimage (d)) the distances are slightly bigger (≈ 205 nm) so that the phase difference is not exactly pi, ∆α =6 π. However, the separation along the vertical direction still appears with good contrast. For all raw images in which the neighboring beads appear clearly separated their apparent distance is largely increased but covers a very narrow range of 313 nm - 332 nm. As the illumination directions are symmetrically distributed from 0◦ to 360◦, neighboring beads appear separated in some raw images but exhibit only a single peak in others. Considering the final TIRDF image the averaging seems to maintain some of the sepa- rating contrast and consequently some of the increased peak-to-peak distance. This is quantified by several line profiles as explained in the following paragraphs.

Separation of beads

Many beads that cannot individually be observed in the TIRF image are resolved in the TIRDF image. This is quantified by several line profiles that are shown in fig. 5.15 and 5.16. Figure 5.14 shows the positions of the corresponding line profiles and also highlights the single beads that will be analyzed in the following section. Figure 5.15-a shows the line profile of three linearly adjacent beads which appear as a single straight bar in the TIRF image. In the TIRDF image the beads are resolved in terms of individually observable peaks, which is validated by the TIRF-SIM image. K Imax−Imin K . Calculating the contrast of the profile as = Imax yields TIRDF = 0 245 and KTIRF −SIM = 0.286 for the TIRDF and the TIRF-SIM image, respectively. For the TIRF image the contrast cannot be calculated. In the case of TIRDF the contrast is almost as high as for TIRF-SIM, albeit at lower overall intensity. The distances1 between the single beads, d1 = 187 nm and d2 = 180 nm for the case of TIRF-SIM, appear

1Distances are measured by local Gaussian ﬁtting of the individual peaks and measuring the peak-to- peak distances.

126 5.3. Results

Figure 5.15.: Line profiles of three (a) and two (b) adjacent beads corresponding to the lines 1 and 2 in fig. 5.14, respectively. Line profiles of TIRDF, TIRF and TIRF-SIM are compared. (a) These three beads are well separated in the TIRDF image but not in the TIRF image. (b) These two beads are not resolved by TIRDF but the line profile shows a significantly more extended plateau than in TIRF. The peak-to-peak distances of the beads (d, d1, d2) and the contrast, calculated from the intensity levels (Imin,Imax), are given in the main text.

increased with d1 = 250 nm and d2 = 225 nm in the case of TIRDF. This corresponds to an increase of 34 % and 25 % for d1 and d2, respectively. Figure 5.15-b shows the line profiles of two adjacent beads. The beads are not resolved by TIRDF but the line profile shows a significantly more extended plateau compared to TIRF. However, in this case the distance of the beads, d = 161 nm, is slightly smaller compared to line profile 1.

Figure 5.16.: Line profiles of bead clusters corresponding to the lines 3 and 4 of fig. 5.14, respectively. Line profiles of TIRDF, TIRF and TIRF-SIM are compared. (a) Diagonal line profile of a cluster of four symmetrically arranged beads. (b) Line profile of a cluster of seven beads in random arrangement. The resolution in the TIRDF image is comparable to TIRF-SIM but the distances are not accurate.

Figure 5.16 shows line proﬁles of clusters of several beads. In (a) the diagonal line proﬁle of a symmetric cluster of four beads is depicted. Compared to the TIRF image, in which the individual beads cannot be resolved, the resolution in the TIRDF image

127 5. Total internal reflection dark field microscopy is about as good as in the case of TIRF-SIM. In terms of local contrast, the TIRDF image yields KTIRDF = 0.573, even slightly more than with TIRF-SIM, KTIRF −SIM = 0.562. However, regarding the peak-to-peak distance measured in the TIRF-SIM image, dTIRF −SIM = 263 nm, as the reference, the distance in the TIRDF image, dTIRDF = 323 nm, is increased by approximately 23 %. In fig. 5.16-b the line profile of a cluster of seven beads is shown. Again, the structure cannot be resolved in the TIRF image, whereas in TIRDF the individual beads exhibit distinct peaks comparable to TIRF-SIM, albeit at a lower average contrast. The measured contrast values are KTIRDF = 0.42 and KTIRF −SIM = 0.645. Measuring the distance from the first to the last peak as depicted in the graph yields dTIRF −SIM = 642 nm for the TIRF-SIM image and dTIRDF = 724 nm for the TIRDF image which marks a 13 % increase in the latter case.

Single beads - PSF

The point spread function (PSF) is an important parameter to characterize the imaging properties of a microscope, including resolution and aberrations. It can experimentally be measured by imaging a bead that is smaller than the FHWM of the theoretical PSF. The 190 nm beads used here barely fulfill this criterion for TIRF imaging. Nevertheless, the image of a single bead of that size provides a good measure of the shape of the PSF that can be compared between different imaging techniques. Although the beads are bigger than the expected PSF for TIRF-SIM, they are sufficiently small to measure the decreased size of the PSF.

imaging mode FWHM (nm) TIRDF 249 ± 28 TIRF 248 ± 3 TIRF-SIM 148 ± 6

Table 5.1.: Measured mean FWHM and standard deviation of ﬁve single beads of diameter 190 nm for diﬀerent imaging modes.

Figure 5.17.: Exemplary line profiles of a single 190 nm bead for TIRDF, TIRF and TIRF-SIM. The line profiles were taken along the dashed orange line in fig. 5.14.

128 5.3. Results

Figure 5.18.: Astigmatism in TIRDF imaging. (a) Magnified image of the single bead marked by an asterisk in fig. 5.14. Scale bar is 0.5 µm. (b) Line profiles corresponding to the directions marked in the left image. In the gray encircled areas the line profiles of the horizontal and vertical direction exhibit shoulders typical for astigmatism.

The FWHM of the five single beads marked by orange circles in fig. 5.14 was measured by fitting a 2D Gaussian and averaging the widths along the two main axes. The mean values and standard deviations measured for the three different imaging techniques are given in table 5.1. The measured FWHM for TIRDF imaging (249 nm) is about the same as for normal TIRF (248 nm). This is in good agreement with theoretical expectations as will be shown in the discussion (sec. 5.4.3). However, the standard deviation is about ten times bigger in TIRDF. In TIRF-SIM the FWHM is significantly decreased (148 nm) and is even smaller than the actual bead size. This might be due to the deconvolution that is done during the image reconstruction. In fig. 5.17 exemplary one-dimensional line profiles of one single bead are shown, which all have a symmetric, Gaussian-like shape. An aberration that is present in the TIRDF images shown here is astigmatism. Fig- ure 5.18 shows a magnified image of a single bead (a) and corresponding line profiles along different directions (b). In the image the cross-like appearance typical for astigmatism, here along the horizontal and vertical axis, can be clearly seen. This leads to “shoulders“ in the line profiles of the corresponding directions (0◦ and 90◦) which are not present for the diagonal directions (45◦ and 135◦). This can be seen in subfigure (b) in the areas marked by dashed circles. The effects of astigmatism become even clearer when the image is slightly defocused in positive or negative direction (not shown). It is not clear which optical component is responsible for this aberration.

5.3.2. Images of biological samples

To test the TIRDF microscope with a biological sample Bacillus subtilis cells were imaged (see sec. 4.1 for biological background information). The cells were prepared and mounted as described in sec. 4.2. Imaging was performed from six illumination directions (∆φ = 60◦), the normalization of the intensities of the raw images could not be done due to a bright, dominating reﬂex in some of the raw images. Accordingly, the ﬁnal

129 5. Total internal reflection dark field microscopy image was calculated as the unweighted average of all raw images as given by eq. 5.16. In fig. 5.19 the resulting TIRDF image (a) is shown and compared to a brightfield (b) and a fluorescence TIRF-SIM (c) image in which GFP-MreB is imaged (see chap. 4). In (d-f) raw images for the illumination directions 0◦, 60◦ and 180◦ are shown, respectively. In the final TIRDF image some cells are overshadowed by background, which was very high in some of the raw images due to a strong reflex in these experiments (fig. 5.19-f). However, the chain of cells to the left can be well distinguished and give an idea of the principal performance. The outline of the cells appears very distinct in the TIRDF image. This is probably due to the cell wall, which is made up of mainly peptidoglycans

Figure 5.19.: TIRDF imaging of the bacteria B. subtilis compared with brightfield and TIRF-SIM. (a) Final TIRDF image. The outline of the long chain of cells, shown as a dashed line in all other images, is well visible. The other cells are overshadowed by high background. (b) Brightfield image. The cells appear larger than in the TIRDF image. (c) TIRF-SIM image. Although the fluorescently labeled protein MreB is imaged the cells appear roughly as wide as in the TIRDF image. (d-f) TIRDF raw images with incident directions of 0◦, 60◦ and 180◦, respectively. The direction of the incident evanescent wave is indicated by the black arrows in the white boxes. Scale bars are 1 µm.

130 5.3. Results

and has a high refractive index of nCW = 1.45−1.46 [108]. This leads to strong scattering and consequently a high signal, as illustrated in ﬁg. 5.20. As the observed signal is very strong reﬂections at the edge of the bacterium might be the main contribution to all the scattered light.

Figure 5.20.: Scattering of the incident excitation light (kev) at the cell wall of B. subtilis cells leads to a detectable signal in TIRDF. Supposedly, the main signal stems from reflections of the evanescent wave at the cell wall. The measured lateral diameters of the cell by different microscopy techniques are illustrated by a bacterial cross-section. The measured diameters and the penetration depth are drawn to scale relative to each other. The axial intensity profile and the penetration depth of the evanescent field are drawn in the graph to the right.

Furthermore, it can be seen from the raw images (d-f) that the part of the structure that becomes visible depends on the direction of the evanescent wave illumination. Ap- parently, contrast yielding scattering only happens when the evanescent wave travels from the optically thinner medium, in this case water, into the optically denser medium, here the cell wall. The other way around no signal is obtained. This effect will be further discussed in sec. 5.4.3. Also, in some raw images (d, f) interference stripes parallel to the outline of the cells can be observed. Another interesting feature of the TIRDF image is that the observed width of the cells is narrower than in the brightfield image. The dashed lines indicate the shape measured in the final TIRDF image (fig. 5.19-a). Supposedly, in a brightfield image the full diameter of a cell is obtained, measured here to be dbf = 0.97 µm. In TIRDF, where the illuminating light field is evanescent and does not penetrate the whole sample, a smaller effective diameter of dTIRDF = 0.58 µm is observed. In TIRF-SIM, although the fluorescence of the labeled protein MreB is imaged, the diameter appears similarly small, dTIRF −SIM = 0.5 µm. The situation is illustrated in fig. 5.20. The arrows indicating the measured diameters are drawn to scale relative to each other. The value obtained from the TIRDF image corresponds well with the diameter at the height of the penetration depths of the evanescent field which is given by

q 2 2 dev = 2 R − (R − dpd) = 0.54 µm (5.24)

131 5. Total internal reﬂection dark ﬁeld microscopy

dbf with R = 2 and the evanescent penetration depth dpd = 84 nm.

5.4. Discussion

In this chapter a novel microscopy technique termed total internal reflection dark field (TIRDF) microscopy was introduced. It bases on evanescent illumination via total internal reflection and uses the dark field principle to form an image by exploiting the scattered light. Here, the various sections of this chapter are discussed, including an outlook on experimental improvements and future experiments.

5.4.1. Imaging theory

The theoretical formulation of the coherent scattering process given in sec. 5.1.1 uses the Born approximation and the Ewald construction. It provides the basis for the understanding of the imaging process in k-space. It is shown that the imaging process can be treated in 2D (x-y or kx-ky) including the Ewald sphere and the coherent optical transfer function (OTF). Furthermore, this description explains the shift of the object spectrum relative to the OTF. Section 5.1.3 gives a general derivation of the image formation in k-space. It yields an illustrative view of which spatial frequencies of the object field spectrum are transmitted for the single raw images under various illumination directions. However, due to the incoherent averaging of the raw images, the resulting transmission function of the optical system is neither linear in amplitude nor in intensity of the electric field. Thus, no OTF and PSF can be analytically defined, as can be done for coherent or incoherent imaging. In sec. 5.1.3 a second approach is followed that describes the image formation in real space. Assuming that the sample consists of identical point scatterers a formula for the image formation is derived (eq. 5.20). Its last term sums over pairwise phase differences for all illumination directions. The resolution of two points in a coherent image depends on the phase relation of the two emitters. It is the basis for the last term of eq. 5.20 and provides the basis for the understanding of some of the typical effects observed in the final TIRDF image, as the improved resolution and the increased distances of neighboring beads. However, a detailed analysis of this term for various distances between the point scatterers and different illumination directions will be necessary to further clarify its influence on the final image. The theoretical formalism introduced here treats the evanescent illumination and the subsequent formation of the dark field image in two dimensions only. Considering the axial direction, too, and accounting for the exponential decay of the evanescent illumination might open the doors for additional information in z-direction. This could for example be extracted by exploiting the effects of variable penetration depths, as for example done by Stock et al. in fluorescence mode [109]. Furthermore, the provided theory should serve as a good basis for computational simulations of the imaging process. Such simulations would allow the investigation of certain imaging effects in dependency of the illumination and the sample.

132 5.4. Discussion

Further properties that are not considered in the theoretical description given here are the polarization of the illuminating light source and also the effects of different degrees of coherence. Also, multiple scattering has been neglected by applying the Born approximation in sec. 5.1.1, although present in the raw images (sec. 5.3.1). Including these effects into a more sophisticated theory might facilitate the optimization of the experimental set-up and the image acquisition. As explained by Rohrbach [59], evanescent waves are scattered mainly in forward direction by inhomogeneous objects and the intensity of the scattered light accumulates along the direction of propagation. Multiple scattering is likely contributing to this ac- cumulation. Performing simulations using the beam propagation method (BPM) effects of multiple scattering could be estimated and investigated [110]. Even evanescent fields can be described by BPMs [111]. This might be of special importance as the proximal glass-water-interface might turn them into propagating fields.

5.4.2. Experimental set-up In sec. 5.2 the experimental set-up is described. Due to the SLM it is very flexible concerning the illumination, but rather slow concerning the image acquisition speed. It’s main drawback for dark field imaging is the bad signal-to-noise (SNR) ratio due to high background and the waste of 92 % of the signal at the pellicle beam splitter. Thus, a major improvement would be the augmentation of the SNR. The main sources of background are reflections from the lenses. Although the lenses are anti-reflection coated for the used wavelength of 488 nm they still reflect a small fraction of the light. As the illumination intensity is significantly higher than the scattered light from the sample (i.e. the signal) the small amount of reflected light is enough to decrease the SNR dramatically. One option to increase the SNR would be a different design of the set-up, as employed by Ueno et al. [99]. They used a perforated mirror with a central hole in place of the dichroic mirror in their fluorescence filter cube. This should reduce the background as only unwanted reflections from the objective lens and the coverslip can reach the detection camera. Also, hardly any signal is discarded and no polarization-dependent pellicle has to be used. A disadvantage of this design is that the perforated mirror, that actually serves as the diaphragm that separates the illumination light from the scattered light, can not be placed in a pupil plane. First of all, it is tilted by 45◦ and second, the pupil plane is usually located inside the objective lens and thus not accessible. Consequently, the NA is not clearly defined and the maximal detection NA of 1.33 can not be reached. Furthermore, this design does not allow to perform fluorescence imaging at the same time in a straightforward manner. Another set-up design which promises a better SNR would be similar to the one suggested by Braslavsky et al. [98]. In this design the dichroic mirror would be replaced by a 50/50 beam splitter. In the detection path an additional 4f-system must then be placed after the detection tube lens to make the pupil plane accessible so that the reflected illumination light can be blocked before it reaches the camera. This design would allow the usage of the maximum detection NA, NAdet = 1.33, and thus yield

133 5. Total internal reflection dark field microscopy maximum resolution. However, 50 % of the signal would be discarded. The dependency of the intensity on the polarization caused by the pellicle in the set-up used in this thesis could be corrected for experimentally with a linear polarization filter after the pellicle. A better compensation of this effect than done in this thesis could also be done in a postprocessing step: The dependency of the signal intensity on the illumination direction could be measured by the light reflected from a plane coverslip without sample. The measured dependency could then be used as the basis for the correction. Speed and signal strength were not important in the measurements presented here. However, instead of the SLM a fast scan-mirror or an acousto optical deflector (AOD) could be used for steering the illumination beam. This would increase the acquisition speed significantly at the cost of little flexibility. It would be easily possible to scan at least one full ring in the BFP (or sample 100 points on it) during an image acquisition as short as one millisecond. The incoherent averaging of different illumination directions would then be implicitly done during one image acquisition. Fast image acquisition could be accomplished using a high-speed complementary metal-oxide-semiconductor (CMOS) camera. Frame rates of up to 1 kHz would then be possible which could be very interesting for the imaging of fast biological processes including diffusive processes. It has been shown by Chang et al. that 3D structured illumination microscopy can be combined with scattered light imaging [112]. They applied a spatially partially incoherent light grid and detected the backward scattered light from 100 nm gold nanoparticles, which is very similar to dark field imaging. Their reconstructed images showed a lateral and axial resolution of 117 nm and 428 nm, respectively. If this concept could be expanded to a spatially coherent light grid as used in TIRF-SIM this would allow true optical super-resolution in TIRDF imaging. However, for an application to biological samples much lower signals than obtained from the gold particles would have to be sufficient.

5.4.3. Results: TIRDF images of polystyrene beads and biological samples

The results of imaged polystyrene beads of size 190 nm are discussed. The approximation of these beads as point scatterers yields an understanding of the eﬀects observed in TIRDF images. The discussion of the images of the bacteria B. subtilis provides a ﬁrst glimpse of what biological structures could possibly be imaged.

Polystyrene beads

In sec. 5.3.1 TIRDF images of 190 nm polystyrene beads are presented. The single raw images show strong interference effects that depend on the direction of illumination, as it is typical for spatially coherent imaging. However, in the final TIRDF image most of these effects have disappeared through the averaging of many illumination directions. The distribution of beads and the shape of even large bead clusters are correctly imaged. Furthermore, the resolution of adjacent beads is improved although the images of single beads are comparable to the ones obtained with TIRF. However, the distances

134 5.4. Discussion of neighboring beads appear increased in the final image which is due to the oblique illumination and the high degree of coherence of the illumination light source. The images of single beads are consistent with theoretical expectations. Approximat- ing a single 190 nm bead as a point source, its appearance in the final TIRDF image reflects the intensity PSF of the optical system. As for a single bead there is no other partner to interfere with, its image should equal the incoherent intensity PSF in every raw image, independent of the illumination direction. Consequently, in the final TIRDF image an average of all the equal PSFs from all the raw images is obtained for single beads. As soon as beads are close to each other so that their amplitude images can interfere, only the amplitude PSF of the system is relevant and the intensity PSF can not be applied. However, analyzing the single bead images is helpful in testing the performance of the microscope and in identifying aberrations. The theoretical intensity PSFs of TIRDF and TIRF differ only due the longer, stokes- shifted emission wavelength of the fluorescence compared to the laser wavelength and the reduced detection NA in TIRDF. According to eq. 2.25 the theoretically expected values 488 nm for the FWHM are FWHMTIRDF = 0.51 · 1.33 = 187 nm and FWHMTIRF = 0.51 · 515 nm 1.46 = 180 nm. These values are the same to within less than 5 %, which explains well that the measured values for TIRF and TIRDF are almost equal. The experimentally increased FWHM of about 250 nm is due to the finite size of 190 nm of the measured beads which are not perfect point sources. Furthermore, the effective NA is usually smaller than the value given by the manufacturer (see sec. 3.7.2). The increased standard deviation of ±28 nm in the case of TIRDF compared to ±3 nm in TIRF might be due to random interferences with the background. Another reason could be the astigmatism that may influence the 2D Gaussian fit for the determination of the FWHM. The astigmatism identified in the images of single beads is not very strong but likely responsible for the prominent edging around the bead structures in the TIRDF image of fig. 5.12. Also, the mean FWHM of single beads should be slightly smaller without astigmatism and, consequently, the separation of beads should be even better, too. Nev- ertheless, for the principal characterization of TIRDF imaging its influence is negligible. The higher resolution and the increased distance of beads result from the oblique illumination and the coherence of the raw images. These effects should be investigated for beads of different sizes. Furthermore, the number of illumination directions and their distribution on the angular spectrum should be investigated on their influence on the final image.

Biological samples The rod-shaped bacteria B. subtilis were imaged by TIRDF microscopy (sec. 5.3.2). The outline of the cells could well be imaged. Likely this is the result of scattering by the cell wall which has a signiﬁcantly higher refractive index (nCW ≈ 1.45) than water (nH2O = 1.33). However, the raw images reveal that only an evanescent illumination from the outside of the cells yields a detectable signal. The areas where the evanescent wave vector should point from the inside of the cell to the outside do not show any scattering. Here, the inﬂuence of the higher index of refraction of the cell wall on the

135 5. Total internal reflection dark field microscopy process of total internal reflection must be considered. The glass coverslip from which the illuminating light is incident has a refractive index n . θ nCW ≈ ◦ of i = 1 52. That means that the critical angle for TIR is c = arcsin ni 74 (eq. 2.27) which is also the theoretically highest angle of incident with an objective lens with NAmax = 1.46 (eq. 2.20). In all the measurements presented here the angle ◦ of incidence was chosen to be θi = 68 , which means that no total internal reflection occurred at the coverslip-cell wall interface. Rather, TIR might happen at the interface of the cell wall and the cytosol, although this is hard to tell due to the inhomogeneities of living cells. However, there is no evanescent light inside the cell wall with a k-vector whose real part points to the outside of the cell. For this reason no scattered light signal can be observed. Only because the illumination is rotated the outline of the cells can be well observed in fig. 5.19-a. The breaking through of light, as observed in the raw images of the B. subtilis sample, could be avoided to the greatest possible extent by using an objective lens with a higher NA. Special objectives, requiring the use of special oils and coverslips, are available with NAs of up to 1.65. Utilizing a set-up with drastically reduced background with a number of different biological samples should give an idea of the structures in biological samples that can potentially be imaged. Theoretically, even features well below the resolution limit with only a slight difference in refractive index should provide a detectable signal. On the other hand, if too many small cellular structures yield a signal they might be neither distinguishable nor resolvable. In vitro motility assays would define a good biological sample of limited complexity compared to living cells. In such experiments molecular motors are attached to the surface of a coverslip and the corresponding filaments (actin or microtubules) are transported over the surface. Usually, the filaments are stabilized and labeled with a dye so that they can be observed by fluorescence microscopy. Using TIRDF microscopy no fluorescent labeling would be necessary. As microtubules are much thicker than actin filaments they are more likely to be observable by TIRDF microscopy. This would allow a bleaching-free and possibly faster observation of the transport dynamics of microtubules.

136 6. Conclusions

This thesis presents a self-made optical set-up that combines the advantages of structured illumination and total internal reflection fluorescence microscopy, referred to as TIRF-SIM. This variant of a fluorescence microscope yields twofold increased lateral resolution with minimized background at frame rates that allow the observation of dynamic processes in biological samples. It is implemented using a spatial light modulator (SLM) that allows a fast and flexible switching of illumination patterns. Applying TIRF-SIM to various living cells with fluorescently labeled proteins lead to new insights into the localization and dynamics of the investigated proteins due to the super-resolution capabilities of the built microscope. Also, a modification of the set-up was developed that combines the dark field principle with an evanescent illumination, referred to as TIRDF microscopy. The coherently scattered light by the sample is collected and an image is produced by an average over multiple illumination directions. First results are shown that demonstrate that the effective optical resolution of an unlabeled, scattering sample can be higher than in normal TIRF microscopy, albeit at the cost of some coherence artifacts in the final image. Chapter 3 gives a detailed description of the experimental TIRF-SIM set-up and shows results proving the increased lateral resolution of about 100 nm. Biological samples were investigated that demonstrate the applicability of TIRF-SIM to living cells. Images of artificial, GFP-labeled proteins in E. coli revealed substructures of the formed vesicles that could only be observed due to the high resolution of TIRF-SIM. Also, images of fluorescently labeled membrane proteins in yeast cells were acquired, which showed the protein patterns with clarifying high resolution and contrast. Chapter 4 presents the extensive studies on the dynamics of the cytoskeletal protein MreB in the bacteria Bacillus subtilis. Due to the high resolution and acquisition speed of TIRF-SIM the filamentous structure of MreB could be clearly resolved and their dynamics imaged on a second timescale. Tracks, transport velocities and events like stops and reversals in directions of MreB filaments could be observed. Also, a length- dependent transport velocity of MreB filaments could be measured. The cell wall of B. subtilis is made up of long peptidoglycan strands that are synthesized by large enzyme complexes which are the driving motors for MreB dynamics. Based on this view, a multi motor model is described that can qualitatively explain the observed events. On- and off-binding of the motors can lead to changes of transport tracks, reversals and stops. In this model MreB serves as a mechanical coupler that parallelizes the synthesis of PG strands both in direction and velocity. The presented model strengthens the view that many biological process can be described by physical principles like, e.g., mechanic coupling and statistical on- and off-binding.

137 6. Conclusions

Concluding from chapters 3 and 4 it can be stated that TIRF-SIM is a highly competitive super-resolution microscopy technique that can verifiably lead to new insights in living cells. TIRF-SIM has an increased lateral resolution of about 100 nm at frame rates of about 1 Hz. In the meantime imaging speeds up to 11 Hz have been shown [10]. Fur- thermore, TIRF-SIM benefits from the inherent advantages of TIRF microscopy which are axial sectioning, very low background, and minimized photobleaching, as only the imaged plane is illuminated. Other super-resolution techniques like STED, PALM, STORM and nonlinear SIM achieve higher lateral resolutions but are usually also slower. For STED this is especially true for large fields of view. Also, many of the mentioned techniques have to apply high illumination intensities. In this context TIRF-SIM is the ideal compromise between a moderate increase in resolution and fast frame rates at moderate excitation intensities. It might thus become a standard super-resolution technique for the observation of coverslip near events and for samples whose features of interest are on a length scale of 100 nm to 200 nm. The results of biological samples presented in this thesis strongly support this vision. Chapter 5 presents a new microscopy technique developed during this thesis. In TIRDF microscopy the evanescent illumination via TIR is combined with the principle of dark field (DF) detection. No labeling of the sample is necessary. Rather, the light coherently scattered by inhomogeneities in refractive index in the sample is detected. The experimental realization is explained and a theoretical concept for the image formation is introduced. The highly oblique illumination leads to the transmission of high spatial frequencies with extremely high contrast. Averaging over many, symmetrically distributed illumination directions yields a final image with minimized interference effects and an increased resolution. The images obtained from 190 nm polystyrene beads and Bacillus subtilis cells show promising results. For polystyrene beads the effective resolution is higher than in comparable TIRF images, though the final images are not completely free of coherence artifacts. The images of B. subtilis cells reveale the outline of the cells due to the strong scattering of the cell wall. A broad application to biological specimen is yet to be tested. Therefor, an experimental implementation with optimized signal-to-noise ratio should make even weakly scattering features visible due to the dark field principle. As a potentially fast, sensitive, and label-free imaging technique that yields high lateral resolution TIRDF might face a promising future.

138 A. Appendix

A.1. Circ function

The circ-function is deﬁned as ( |r⊥| 1 if |r⊥| < a circ = (A.1) a 0 else

p 2 2 where |r⊥| = x + y and a is a constant, positive scalar.

A.2. Preparation of agarose pads

Thin ﬁlms of agarose on round glass coverslips (agarose pads) are created as follows:

1. Melt at least 5 ml of a 2 % solution of agarose in phosphate buﬀered saline (PBS).

2. Place 80 µl of the hot solution on a big glass coverslip.

3. Place a round glass coverslip of 12 mm diameter on the droplet. The agarose solution will spread to a homogeneously thick layer under the round coverslip.

4. After the agarose has cooled down and solidiﬁed, carefully shift the agarose pad from the big glass coverslip. Store it in a humid atmosphere, (e.g., a petri dish with a soaking tissue), and use it within 24 h.

A.3. Determination of the illumination intensity in the focal plane

Removing the objective lens, the power of a TIR illumination focus in the BFP, PBFP , can be measured using a powermeter. The illuminated area in the sample plane, Asp, 2 was calculated in sec. 3.1.1 to be Asp = 726 µm . Neglecting the Gaussian profile of the illuminating beam the intensity would thus be given by I = PBFP . Aill However, two more corrections have to be applied. First, some energy gets lost in the objective lens. This factor was determined to be kloss = 0.431 by measuring the power of a central beam before and after the objective. Second, as total internal reflection occurs at the interface of the coverslip and the sample, the evanescent wave experiences a field enhancement (see sec. 2.2.1). For the case of S-polarized light the enhancement 2 4·cos (θi) nt factor is 2 , where θi is the angle of incidence and nti = n is the relative index 1−nti i

139 A. Appendix of refraction of the transmitting and the incidence material. The ﬁnal intensity is then given by 2 PBFP 4 · cos (θi) Iill = · kloss · 2 (A.2) Aill 1 − nti ◦ which is valid for the z = 0 plane right at the interface. Typical values are θi = 68 , ni = 1.52, nt = 1.33 and PBFP = 0.33 mW (maximum transmission of laser light by the AOTF and the laser operating in idle-mode). This results in an illumination intensity 2 of Iill = 46.9 W/cm . Here, two things must be considered. First, the Gaussian intensity proﬁle of the illumination beam has been neglected which drops by 63 % from the center to its border. Thus, Iill represents an average value over the sample plane. Second, in TIRF-SIM the interference of two waves leads to peak intensities that are greater than Iill.

A.4. Measurement of ﬁlament length from 3D data

The length of MreB and Mbl filaments was measured from deconvolved 3D epi-fluorescence stacks. At each filament position a xz-cross-section was sliced out. This slice was thresholded at half the maximum intensity value present to yield a binary image, typically resembling a ring segment. It was then convolved with a binary ring representing a full-turn filament. The maximum of the convolution represents the position of maximal overlap between the full ring and the thresholded slice. A multiplication of these two images at this position yields a defined ring segment, representing the filament length.

A.5. Length correction of MreB ﬁlament lengths

MreB filaments that could not be completely observed in the TIRF-SIM time series were length-corrected. From the length-corrected data a mean value of the velocity and length of this group of filaments was determined, as shown in fig. 4.14.

Figure A.1.: Length correction procedure for ﬁlaments whose full length could not be measured. (a) Number density functions of the ﬁlament length distributions. (b) Graph- ical illustration of the length correction. See text for details.

140 A.5. Length correction of MreB ﬁlament lengths

Filament lengths were measured with pixel accuracy, which equals an effective bin- ning of 32 nm. All data points from one bin of minimal length L are homogeneously distributed to values bigger than L according to the length distribution obtained from the 3D data. More precisely, the 3D length distribution is expressed as a number density function ξ(L) by using a kernel density estimation with a Gaussian kernel of width σ = 125 nm. ξ(L) is shown in orange in fig. A.1-a. Assuming Z data points Li with i = 1, ..., Z in the bin corresponding to the length L0, the curve ξ(L) was devided into Z sections from L0 to ∞, each section area representing the same probability. In mathematical terms the borders of the Z sections, Lj and Lj+1 with j = i − 1 = 0, ..., Z − 1, are defined by the following criteria

Z Lj+1 R ∞ ξ(L) dL ξ(L) dL = L0 (A.3) Lj Z

0 Then each data point is shifted to the expectation Li of one of the Z sections, which is deﬁned by R Lj+1 j ξ(L) · L dL L0 L L i( i) = R Lj+1 (A.4) Lj ξ(L) dL

The whole procedure is graphically illustrated for 3 data points at L0 = 400 nm in fig. A.1-b. The result of the shifting process is shown in fig. A.1-a, where all length distributions are shown as number density functions as explained above. Here, red represents the distribution of filament lengths that could be measured, whereas dark blue shows the distribution of minimal filament lengths. In light blue the distribution of all filament lengths after the length correction process is shown, which includes the data points from the red curve. It approaches the true filament length distribution (orange). All length-corrected data points were then summarized into one mean value as the correlation of the real length and the velocity of the individual data points is not known. nm nm 0 This mean value is hvi = 10.9 s ± 10.9 s at hL i = 790 nm ± 240 nm and it is plotted in fig. 4.14-b.

141

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152 Acknowledgements

• Most importantly, I thank Prof. Alexander Rohrbach for the excellent guidance through this thesis. Alexander’s expertise in optics, his constant ﬂow of new ideas, and his positive attitude have been largely motivating. He always got me out of the “valleys”. I’m also grateful for the nice time spent on international conferences.

• I thank Jun.-Prof. Maximilian Ulbrich for acting as a second reviewer of this thesis.

• In particular, I thank my parents who have supported me throughout my whole life. They always encouraged me to follow my own ideas and plans which would not have been possible without them.

• I’m very grateful for the great atmosphere in our oﬃce! I thank Markus Grießhammer for leading the hard pitches, acting as my scattering teacher, and, as a good friend, for helping out whenever necessary. I thank Felix Kohler for being the mathematician, for answering all the diﬃcult questions, and for many advices during every day work. I thank Benjamin Landenberger for countless advice in python programming, for bringing structure not only into my code but also into my work, and for polit- ically elaborate breaks from science. I also thank Jochen Stephan for his preparatory work on structured illumination microscopy and many patient explanations at the beginning of my thesis.

• I thank Lars Friedrich for uncountable advice in all sorts of issues, for setting up and introducing me to MicPy, making my camera work properly, making me solder the right circuits, and for juggling distractions.

• I thank Cristian Gohn-Kreuz for extended imaging discussions which allowed me to understand what I do.

• I thank Florian Fahrbach for sharing a set-up for a long time without destructive interference. Even more, I’m grateful for all the discussions on microscopy, sectioning, structured illumination, and many other issues.

• I thank Benjamin Tränkle for his Igor-expertise and for sharing the exciting teaching of the practical electronics course.

• I thank Philipp Simon for his help with programming C-python-mixed-code in order to “talk” to hardware.

153 Bibliography

• I thank Anne Rottler for cheerful chats, delicate cookies, and for the fast and eﬃcient execution of any administrative task.

• I thank Birgit Erhard for tips and tricks in the lab and for cell preparations.

• Generally, I want to thank the whole BNP group for the great atmosphere in the lab. The climat of mutual help makes research so much more enjoyable.

• I thank Hervé Jo¨elDefeu Soufo and Prof. Peter Graumann for a very fruitful and enjoyable collaboration on the dynamics of MreB in Bacillus subtilis.

• I thank Felix Spira for putting much eﬀort in getting nice images of yeast cells. It was a highly enjoyable collaboration.

• I thank Andreas Schreiber aka “Klaus” for sending me the funniest e-mails on earth and for an interesting, eﬃcient, and amusing investigation on compartment formation in E. coli.

• I thank Reto Fiolka and Prof. Andreas Stemmer for my lab visite at ETH Zürich and for all the explanations on TIRF-SIM.

• I thank Kai Wicker and Prof. Rainer Heintzmann for the very powerful reconstruction code with which they kindly provided us. Also, I’m very grateful for the invitation to their lab in Jena, where they provided me with endless advice on their reconstruction code and also a nice evening program.

154