Measuring Protein Diffusion in Living Cells by Raster Image Correlation Spectroscopy (RICS)

A Thesis Submitted for the Award of Master of Science

Raz Shimoni

CENTREOF MICRO-PHOTONICS The Faculty of Engineering and Industrial Sciences (FEIS) Swinburne University of Technology, Melbourne, Australia

PETER MACCALLUM CANCER CENTRE St Andrews Place, East Melbourne, Australia

Supervised By: Prof. Sarah Russell, Dr. Ze’ev Bomzon, Prof. Min Gu

January 2010 Dedicated to my partner Olga iii

”Anyone who has never made a mistake has never tried anything new.”

-Albert Einstein (1879-1955) iv

Abstract

T ime-lapse ﬂuorescence imaging has revolutionized studies of biology in the last 15 years. In addition to the now routine tracking of bulk ﬂuorescence, for instance of a protein moving into the nucleus in response to an extracellular signal, technologies are now emerging that enable much more sophisticated analysis of the motion and interactions of proteins within living cells. The potential of these approaches to elucidate biological processes is clear, but they have not yet been developed and validated for broad use by biologists.

This thesis describes the adaptation of a recently introduced method, Raster Image Correlation Spectroscopy (RICS). RICS is a novel approach to assess the dynamic properties of fluorescent macromolecules in solutions and within living cells by confocal laser scanning microscopy. Based on RICS theory, we developed novel software with which to analyse confocal images and to measure diffusion coefficients of the fluorophores. This new software has several advantages compared with published RICS software, and its ability to give accurate diffusion coefficient values was characterized under a range of settings.

Once a RICS routine was established, it was applied to measure the diffusion coefﬁcient of PAK-interacting exchange factor (βPIX) within living ﬁbroblast cells as a paradigm for RICS analysis. The interaction between βPIX and the adaptor protein, Scribble, plays a critical role in cell polarity and actin polymerization. These preliminary measurements indicate the potential of RICS in elucidating the dynamics of proteins within living cells, and demonstrate how the use of RICS will open new opportunities in the cell biology research. Acknowledgments

The last two years have been an amazing experience for me. I have been introduced to novel technologies in the BioPhotonics field, interacted with leading biologists and physicists, met new friends from different nationalities and travelled extensively around beautiful Australia. It was a great honour for me to be a part of the Centre of Micro-Photonics (CMP) at Swinburne University of Technology and I am grateful for this opportunity. I would like to thank my research supervisors- Professor Sarah Russell, the group leader of Immune Signalling at the Peter MacCallum Cancer Centre and the head of the Cell Biology group in the CMP and Dr. Zeev Bomzon for this opportunity and for their kind support along the way. Of course, without financial support all this could not be possible. For the generous financial support that allowed me to conduct my research I would like to thank Professor Min Gu- the Director of the CMP and the Faculty of Engineering and Industrial Sciences (FEIS) at Swinburne University of Technology.

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I would like to acknowledge the contribution of my supervisor Dr. Zeev Bomzon to the RICSIM. Dr. Bomzon built the initial stage of the RICSIM GUI, including the image-processing ﬁlters procedures.

I would like to thank Mandy Ludford-Menting the senior research assistant from Sarah Russell‘s lab at Peter MacCallum Cancer Centre for teaching me to generate and to validate the cell lines that were used for this thesis, and

I thank Kim Pham, a PhD student from the CMP for providing the EYFP- βPIX∆CT construct and the EYFP-βPIX cells.

I would also like to thank Dr. Andrew Clayton and Dr. Noga Kozer from Ludwig Institute for Cancer Research for supplying BaF3 cell lines including supportive materials, GFP samples, and for our fruitful discussions.

I thank the Nanostructured Interfaces and Materials Group at the department of Chemical and Biomolecular Engineering, the University of Melbourne, for contributing the PVPON.

For the microscopy training and for taking care that the microscope equipment is in the best condition - I would like to thank Sarah Ellis, the core manager of the microscopy unit at the Peter MacCallum Cancer Centre.

For his professional help with the ﬂow cytometry and our interesting conversa- tions, I would like to thank Ralph Rossi from the Peter MacCallum Cancer Centre.

I would like to extend my thanks to all the CMP members and my colleagues from Russell’s group for providing a supportive intellectually environment with a friendly atmosphere.

Finally, I would like to thank my family and close friends in Israel and Australia who supported and encouraged me throughout this research. vii

Declaration

I declare that:

I This thesis contains no material of any other degree or diploma, except where due reference is made in the text of the thesis.

I To the best of my knowledge, this thesis contains no material previously published or written by another person except where due reference is made in the text of the thesis.

I Contributions of respective workers are mentioned in this thesis.

Raz Shimoni Abbreviations

1-D One-dimensional 2-D Two-dimensional 3-D Three-dimensional A/D Analog-to-Digital ACF Autocorrelation Function AF488 Alexa R Fluor dye 488 nm AOBS Acoustic Optical Beam Splitter AOTF Acoustic Optical Tuneable Filters APD Avalanche Photodiode Detector ATP Adenosine Triphosphate βPIX Beta PAK- Interacting Exchange Factor βPIX∆CT βPIX mutant that lack (-TNL) BSA Bovine Serum Albumin c Speed of light (≈3×108 m·s−1) C Concentration CHO Chinese Hamster Ovary CLSM Confocal Laser Scanning Microscopy

viii ix

D Diffusion coefficient (µm2/s) DLS Dynamic Light Scattering DMEM Dulbecco’s Modified Essential Medium DMSO Dimethyl Sulphoxide Dstop βPIX∆CT ECL Enhanced Chemiluminescence EDTA Ethylenediamietetraacetate EGF Epidermal Growth Factor EGFP Enhance-Green-Fluorescence Protein EGFR EGF-Receptor EYFP Enhance-Yellow-Fluorescence Protein f Fourier Transform f −1 Inverse Fourier Transform FACS Fluorescence Activated Cell Sorting FCS Fluorescence Correlation Spectroscopy FFS Fluorescence Fluctuation Spectroscopy FFT Fast Fourier Transform fl femtoliter (10−15 liter) FRAP Fluorescence Recovery After Photobleaching FRET Fluorescence Resonance Energy Transfer G(0,0) amplitude of 2-D ACF before normalization g(0,0) amplitude of 2-D normalized ACF g(ξ,0) horizontal vector of the normalized ACF g(0,ψ) vertical vector of the normalized ACF GDP Guanosine diphosphate GEF Guanine nucleotide Exchange Factors GFP Green Fluorescence Protein GTP Guanosine triphosphate GUI Graphical User Interface x

h Planck constant (≈6.62×10−34 J·s) HRP Horse Radish Peroxidase I(X,Y) Intensity of pixel at coordinates (X,Y) in 2-D matrix I(t) Intensity value at time in a vector ICM Image Correlation Microscopy ICS Image Correlation Spectroscopy ICCS Image Cross Correlation Spectroscopy IF ImmunoFluorescence ii index image from series jj index counter

−23 −1 KB Boltzmann constant (≈1.38×10 J·K ) kDa Kilo Dalton µg micro-gram (10−6 gram) µl micro-liter (10−6 liter) µM microMolar µs micro-second (10−6 second) M Molarity MEF Mouse Embryonic Fibroblasts mg milli-gram (10−3 gram) ml milli-liter (10−3 liter) mM milli-Molar (10−3 Molar) mQ H2O milliQ water ms milli-second (10−3 second) MSD Mean Square Displacement N Number of particles n length of discrete intervals refractive index NA Numerical Aperture

23 −1 Na Avogadro constant (≈6.02×10 mol ) nM nano-Molar (10−9 Molar) xi

ns nano-second (10−9 second) PAK p21-activated serine threonine kinase PAO Phenylarsine oxide PBS Phosphate Buffer Saline PCH Photon Counting Histogram pH Power of Hydrogen PMT Photomultiplier Tube PSD Power Spectrum Density PSF Point Spread Function PVPON Poly(N-vinyl pyrrolidone) Q Quantum yield r radius rcf relative centrifugal force RICS Raster Image Correlation Spectroscopy ROI Region of Interest RPMI Roswell Park Memorial Institute medium RT Room Temperature s seconds S/N, SNR Signal to Noise ratio SPT Single-Particle Tracking STICS Spatial-Temporal Image Correlation Spectroscopy T absolute Temperature (K) t time, index image from series Tiff Tagged Image File V Volt, Volume

Veff effective volume WT Wild Type X height of an image in pixels X(t) trajectories of individual particle Y width of an image in pixels xii

Symbols

δ fluctuation ε excitation efficiency γ correction shape factor η signal-to-noise ratio constant ι instrumental counting efficiency λ wavelength µ micro (10−9) ν viscosity π mathematical constant (π≈3.14159) θ angular aperture ρ density of material τ lag time (characteristic delay time)

τD diffusion time

τ l line time

τ p pixel time ξ spatial displacement along X-axis ψ spatial displacement along Y-axis

ωxy XY-waist of the PSF (µm)

ωz Z-waist of the PSF (µm) Contents

Abstract iv

Acknowledgmentsv

List of Abbreviations viii

Contents xvii

List of Figures xx

1 Introduction- The Biological Context1 1.1 βPIX and Scribble in Cell Polarity ...... 2 1.2 βPIX-Scribble Interaction in RAC1/Cdc42 Mediated Actin Polymerization ...... 4 1.3 The Research Questions and an Outline of the Chosen Methodology7

2 Theoretical Background 10 2.1 Introduction ...... 10 2.1.1 The diffusion coefﬁcient in cell biology ...... 13 Fick’s 1st law for diffusion ...... 13 Brownian motion and Einstein-Smoluchowski equation . . 15 The Stokes-Einstein relation ...... 18 2.1.2 The principles of ﬂuorescence ...... 20

xiii CONTENTS xiv

2.1.3 Fluorescence proteins technology and traditional respective fluorescence based techniques ...... 21 Time-lapse fluorescence microscopy ...... 23 Computational image analysis of fluorescence microscopy images ...... 23 Single-particle tracking ...... 24 Fluorescence Recovery After Photobleaching (FRAP) . . 24 Forster Resonance Energy Transfer (FRET) ...... 26 Summary ...... 27 2.2 Principles of Fluorescence Correlation Spectroscopy (FCS) ...... 28 2.2.1 The theory behind FCS ...... 28 2.2.2 The ACF ...... 32 2.2.3 FCS fitting model for Brownian motion ...... 34 2.2.4 FCS in cell biology ...... 42 2.3 Principles of Image Correlation Spectroscopy (ICS) ...... 43 2.3.1 ICS is based on raster CLSM ...... 43 2.3.2 The 2-D ACF ...... 45 2.3.3 ICS fitting model ...... 46 2.3.4 Advances in Image Correlation Spectroscopy ...... 47 2.4 Principles of Raster Image Correlation Spectroscopy (RICS) ...... 48 2.4.1 Time and space domains in RICS ...... 52 2.4.2 RICS fitting model for Brownian motion ...... 52 2.4.3 Advances in RICS ...... 53 2.4.4 Cross correlation approach in FFS ...... 55 2.5 Summary ...... 56 CONTENTS xv

3 Materials and Methods 57 3.1 Conditions for Cell Maintenance ...... 57 3.2 Plasmid DNA ...... 58 3.3 Antibiotic Titration ...... 58 3.4 Cell Transfection ...... 59 3.5 Preparation of Cell Lines ...... 59 3.6 Western Blotting ...... 60 3.7 Antibodies ...... 62 3.8 Preparation of Microscope Samples ...... 62 3.9 Microscope Setup ...... 65 3.10 Data Processing and Manipulation ...... 68

4 Computational Implementation of RICS by the RICSIM software 70 4.1 Introduction ...... 70 4.2 General RICS Procedure ...... 73 4.3 The RICSIM Process Scheme ...... 82 4.3.1 Control modes in RICSIM ...... 83 4.3.2 Threshold algorithm (6) ...... 87 4.3.3 Photobleaching correction algorithm (7) ...... 87 4.3.4 Normalization (8) ...... 89 4.3.5 Input User Selection (9) ...... 90 4.3.6 Fitting (10) ...... 91 4.4 Summary ...... 92

5 Experimental Studies and Validation of RICS 93 5.1 Introduction ...... 93 5.2 Validation of RICS with Microspheres ...... 94 5.2.1 Estimation of the PSF waist by microspheres scanning . . 94 CONTENTS xvi

5.2.2 Effect of viscosity on the ACF of diffusing microspheres . 97 5.2.3 Effect of viscosity on the ACF of diffusing microspheres . 98 5.2.4 Effect of scanning speed on the ACF of diffusing microspheres ...... 104 5.3 ACF Studies by Using PVPON Solutions ...... 106 5.3.1 Effect of laser power ...... 107 5.3.2 Effect of scan speed ...... 112 5.3.3 Effect of pinhole ...... 115 5.3.4 Effect of viscosity ...... 119 5.4 ACF of Diffusing GFP in Isotropic Solutions ...... 122 5.4.1 Effect of the scanning direction in RICS ...... 124 5.5 The Effect of Immobile Fraction Removal on RICS measurements 126 5.6 Discussion ...... 134

6 RICS Measurements in 3T3 Cells 139 6.1 Introduction ...... 139 6.2 Validation of Cell Lines ...... 141 6.3 Calibration of RICS to 3T3 Cells ...... 144 6.3.1 RICS measurements in Fixed Cells ...... 144 6.3.2 Workflow of RICS experiments ...... 145 6.3.3 Adjustment of the scanning speed ...... 146 6.3.4 Determination of the optimal pixel size ...... 147 6.3.5 Determination of the pinhole diameter and laser power . . 147 6.3.6 The effect of the ROI Size on the ACF ...... 149 6.3.7 Effect of removing data points before fitting the ACF . . . 151 6.3.8 Adjustment of the MA subtraction ...... 152 6.3.9 Adjustment of the cut-off frequency of high pass filter . . . 153 6.3.10 Summary ...... 157 CONTENTS xvii

6.4 Measurements Under Optimal Conditions ...... 157 6.4.1 Spatial Diffusivity of βPIX in living cells ...... 157 6.4.2 Measurements of diffusion coefﬁcients for a large population ...... 165 6.5 Summary ...... 170

7 Conclusions and Future Work 172 7.1 Conclusions and Outlook ...... 173 7.2 Recommendations for Future Work ...... 175

Bibliography 202

Appendices: 202

A Theoretical Studies of the ACF 203 A.1 Simulation of diffusion ...... 203 A.2 The effect of the number of particles on the statistical distribution . 205 A.3 Effect of number of particles on the ACF ...... 207 A.4 ACF of FCS Change as function of diffusion ...... 210 A.5 ACF of RICS Change as function of diffusion ...... 212

B List of lab recipes 214

C Classes in RICSIM 217

D RICSIM GUI 218

E Photobleaching curve for a ROI 220

F Spatial correlation at the cell edges 221 List of Figures

1.1 The cycle of actin polarization during cell motility ...... 5 1.2 Proposed model for the βPIX-Scribble interaction in RAC1/Cdc42 mediated actin polymerization ...... 6

2.1 Diffusing particle enters the observation volume ...... 12 2.2 Diffusion of particles resulting from a concentration gradient . . . 14 2.3 Illustration of random one-dimensional motion of a particle . . . . 16 2.4 Brownian motion of diffusing particles ...... 17 2.5 Liquid molecules pass part of their momentum to diffusing particles through collusion impact ...... 18 2.6 Jablonski diagram ...... 20 2.7 Graph of FRAP experiment ...... 25 2.8 Scheme for a standard FCS experimental set up ...... 30 2.9 Convolution of point source in raster LSCM ...... 44 2.10 RICS is a combination between ICS and FCS ...... 48 2.11 The principle behind RICS ...... 51

3.1 βPIX and βPIX∆CT plasmids ...... 58 3.2 Molecular structure of PVPON ...... 63 3.3 Scheme of Leica TCS SP5 components ...... 67

4.1 An example of the RICS analysis for EYFP expressed in living 3T3 cell ...... 74

xviii LIST OF FIGURES xix

4.2 RICSIM ﬁtting ﬂowchart ...... 79 4.3 Fitting the experimental ACF to theoretical RICS equation . . . . 81 4.4 RICSIM process scheme...... 83 4.5 Effect of averaging on the ACF ...... 85 4.6 Interpolated detailed Diffusion maps for EYFP cell ...... 86

5.1 ACF map of freely diffusing ﬂuorescence microspheres ...... 95 5.2 Average grid of ACF map obtained from diffusing microspheres . 96 5.3 Diffusing microspheres in glycerol/water solutions ...... 99 5.4 ACF of diffusing microspheres in glycerol/water solutions . . . . 100 5.5 Horizontal and vertical ACF curves of diffusing microspheres in glycerol ...... 101 5.6 Horizontal and vertical ACF curves of diffusing microspheres imaged using various scanning speeds ...... 105 5.7 Effect of laser power on the ACF measured with PVPON . . . . . 108 5.8 Photobleaching of PVPON-Alexa at different laser power . . . . . 109 5.9 Photobleaching of PVPON-Alexa at different scanning speeds . . 110 5.10 Photobleaching of PVPON-Alexa at different viscosities . . . . . 112 5.11 Effect of scanning speed on the ACF measured with PVPON . . . 113 5.12 Effect of scanning speed on the ACF measured with adjustable gain 114 5.13 Effect of pinhole diameter on the ACF measured with PVPON . . 117 5.14 Effect of pinhole diameter on the ACF measured with adjustable gain ...... 118 5.15 Effect of glycerol concentration on the accumulating intensity distribution histogram ...... 119 5.16 Effect of viscosity on the ACF measured with PVPON ...... 121 5.17 Horizontal ACF of diffusing GFP in PBS and glycerol ...... 122 5.18 Unsuccessful ﬁtting of ACF describing PVPON ...... 123 LIST OF FIGURES xx

5.19 The effect of scanning direction on the ACF in RICS ...... 125 5.20 Starved BaF3 cells expressing EGFP-EGFR ...... 128 5.21 Measuring Diffusion of EGFP-EGFR in BaF3 cells with RICS . . 131 5.22 Graphical illustration of the effect of the function of the cut-off frequency of high pass ﬁlter on the ACF ...... 133

6.1 EYFP-βPIX and EYFP-βPIX∆CT FACS profile ...... 142 6.2 EYFP-βPIX and EYFP-βPIX∆CT are expressed in the transfected 3T3 cell lines ...... 143 6.3 ACF of fixed fibroblast cells expressing EYFP-βPIX∆CT and EYFP145 6.4 The effect of pinhole and laser on the diffusion values ...... 148 6.5 Effect of ROI size...... 150 6.6 ACF under different numbers of ignored pixels ...... 152 6.7 Effect of Moving average subtraction on the diffusion values . . . 154 6.8 Effect of high pass filter on the ACF ...... 155 6.9 Effect of high pass filter on the calculated diffusion coefficients . . 156 6.10 Interpolated detailed Diffusion maps for EYFP cell ...... 159 6.11 Interpolated detailed Diffusion maps for EYFP-βPIX cell . . . . . 160 6.12 Interpolated detailed Diffusion maps for EYFP-βPIX∆CT cell . . 161 6.13 Histograms of diffusion maps ...... 163 6.14 Horizontal and vertical ACF vectors for large population of cells . 166 6.15 Diffusion coefficients of cell populations ...... 169 Chapter 1

Introduction- The Biological Context

Living cells can be characterized by different shape properties, which are commonly connected with the biological activity and function of the cells. While many different cell shapes can be deﬁned, this thesis emphasizes one particular phenomenon in cell shape that is known as cell polarity. Cell polarity describes the asymmetrical cell geometry and asymmetrical distribution of cellular components such as proteins, carbohydrates, cytoskeleton structures and lipids [1–4]. The importance of cell polarity derives from its connection to biological functions and from a potential connection to tumor development [5, 6].

Recent experiments have revealed a family of scaffolding proteins that contain PDZ domains, and regulate cell polarity. The PDZ domains are protein-protein recognition domains that target the associated proteins to speciﬁc cell membranes and play an important role by assembling proteins into localized signalling complexes [7, 8]. The PDZ-containing proteins can interact with actin, Rho GTPases proteins and Rho Guanine nucleotide Exchange Factors (GEF) proteins [9, 10]. 1 1.1. βPIX and Scribble in Cell Polarity 2

Rho GTPases proteins are members of the Ras super-family, which serve as a biomolecular switch by cycling between active (bound to Guanosine-triphosphate (GTP)) and inactive (bound to Guanosine diphosphate (GDP)) states [9, 11, 12]. This cycle is regulated by GEFs, which stimulate the release of GDP and allow binding of GTP [13, 14]. More than twenty different mammalian Rho GTPases have been identiﬁed, among them RAC1 and Cdc42 [10, 15]. It is now becoming apparent that the activity of many Rho GTPases is controlled by interactions with the PDZ-containing polarity proteins [16].

1.1 βPIX and Scribble in Cell Polarity

Scribble is a polarity protein

Scribble is a cytosolic scaffolding protein and a member of the PDZ-containing family, which contains multiple PDZ domains and has an important role in the regulation of cell polarity [8, 17, 18]. Deﬁciency in Scribble impairs many aspects of cell polarity and cell movement [19], and has an important role during tumourigenesis [16]. The mechanisms by which Scribble regulates cell migration are unclear, but one downstream effector that has the potential to link Scribble with Rho GTPase function is the Rho GEF, beta PAK-interacting exchange factor (βPIX) [6].

βPIX is a GEF

βPIX (also called cool-1) is a cytosolic protein that upon stimulation is recruited by Scribble to the plasma membrane and the leading edge, where it plays an important role in cell polarity [6, 20]. Once βPIX is localized by Scribble, it can interact with GIT1 [21, 22]. It is thought that GIT1 has no afﬁnity for Scribble, but 1.1. βPIX and Scribble in Cell Polarity 3

by directly binding to βPIX, a complex of βPIX-Scribble-GIT1 is formed [20, 23]. Consequently, βPIX can serve as a GEF for the small GTPases Cdc42 and RAC1 [24]. RAC1 and Cdc42 are cytoplasmic proteins that can be recruited to the plasma membrane under certain conditions, and are linked to the regulation of cell morphology and division cycle [13, 25]. In particular RAC1 and Cdc42 control the actin cytoskeleton in protrusions, as demonstrated with 3T3 ﬁbroblast cells [14, 26]. It is important to note that there is evidence that βPIX does not activate RAC1 directly, but rather may be involved in controlling RAC1 localization at the leading edge where it is needed [6, 27].

βPIX and Scribble interaction

The last 15 amino acid residues at the carboxyl terminus in βPIX contain the PDZ binding motif, a -Threonine-Asparagine-Leucine sequence (-TNL) that interacts strongly with the PDZ domain of Scribble to form a complex [20]. Using GST pull-down and two-hybrid assays, it was proven that the (-TNL) motif is sufﬁcient for the interaction with the PDZ domain of Scribble but not with the PDZ domains of other polarity proteins such as Erbin, Dlg, AF6, PICK1, PAR3, and PAR6 [20]. Removal of the (-TNL) motif in βPIX peptide abrogated the interaction with Scribble and affected βPIX localization[20].

The βPIX-Scribble complex was found in cellular lysates by using tandem mass spectroscopy [28], and biochemical assays [20]. It was shown that Scribble controls βPIX recruitment to the leading edge in migrating astrocytes, and perturbation of Scribble localization or βPIX-Scribble interaction inhibits the polarization of βPIX as shown by immunoﬂuorescence localization experiments [29]. Furthermore, there was a difference in localization between βPIX and a βPIX mutant that cannot interact with Scribble in neuronal cells [20]. 1.2. βPIX-Scribble Interaction in RAC1/Cdc42 Mediated Actin Polymerization 4

βPIX enables RAC1/Cdc42 mediated actin polymerization

Activation of Cdc42 by βPIX leads to the auto-phosphorylation of PAK (p21- activated serine threonine kinase), which dissociates from the βPIX-Scribble complex [6, 30–32]. Since PAK competes with RAC1 to bind to βPIX [6, 33], once PAK is released, βPIX can recruit and activate RAC1, as demonstrated in membrane rufﬂes of ﬁbroblasts [34]. Finally, activation of RAC1 enables RAC1- Cdc42 mediated actin polymerization at the plasma membrane, protrusions, and focal adhesions [28].

Actin polymerization is important in many cell polarization processes. One example of the role of actin in polarity is in migration of ﬁbroblastic and epithelial cells, which is enabled by crawling motility. This motility is facilitated by extending ﬁlopodia or protrusions that start from the front of the cell and extrude in the direction of migration [35], and by periodic lamellipodial contractions that are substrate-dependent [35]. This dynamics requires actin polymerization, and consequently may required activation of RAC1/Cdc42- βPIX dependent signalling pathway βPIX [23].

1.2 βPIX-Scribble Interaction in RAC1/Cdc42 Mediated Actin Polymerization

The major structural component of the filopodia is filamentous actin (F-actin), which is made of polymerized actin monomer subunits (G-actin). The actin monomers diffuse to the leading edge to be assembled in an actin network, and to extend the filopodia. As the cell progresses forward, the actin filaments move to the rear of the cell to be disassembled [36]. Simultaneously, the filopodia 1.2. βPIX-Scribble Interaction in RAC1/Cdc42 Mediated Actin Polymerization 5

elongation continues, and the required actin monomers diffuse back to the front of the cell to be assembled again [37], as shown by Figure 1.1.

Figure 1.1: The cycle of actin polarization during cell motility. While a fibroblast cell moves to the left, an asymmetrical cell shape between the two opposite edges of the cell is formed. The red net resembles the branched network of polymerized actin filaments at the leading edge and the red dots resemble the actin monomers. The black arrows illustrate the flow direction of the actin subunits to the leading edge from the rear of the cell. The white arrows illustrate the flow direction of filamentous actin back to the rear of the cell where they disassemble to monomers. The extension of the filopodia protrusion requires actin polymerization at the leading edges. [37, 38].

The importance of βPIX in the asymmetric organization during migration was demonstrated by reducing the expression of βPIX in ﬁbroblasts. As a result, there was a decrease in actin-based protrusions and migration [27, 39]. Figure 1.2 shows the proposed model for the role of βPIX-Scribble interaction in mediating RAC1/Cdc42 GIT1/βPIX/PAK dependent signalling pathway during cell migration. 1.2. βPIX-Scribble Interaction in RAC1/Cdc42 Mediated Actin Polymerization 6

Figure 1.2: Proposed model for the βPIX-Scribble interaction in RAC1/Cdc42 mediated actin polymerization. 1.Scribble recruits βPIX to the leading edges by forming a tight complex, and localizes βPIX where it is required in the asymmetric organization of the actin network. 2. Once βPIX is directed to the leading edges, it binds to GIT1 and a complex of βPIX-Scribble-GIT1 is formed. 3. βPIX activates the small GTPase Cdc42 and regulates a Cdc42 dependent polarization pathway. 4. Activation of Cdc42 by βPIX leads to the auto phosphorylation of PAK which dissociates from βPIX. 5. RAC1 replaces PAK. 6. This process activates RAC1 and enables RAC1-mediated actin polymerization at the plasma membrane and focal adhesion. 1.3. The Research Questions and an Outline of the Chosen Methodology 7

1.3 The Research Questions and an Outline of the Chosen Methodology

The data presented in the previous sections shows the important role of the βPIX- Scribble complex in polarity processes. Thus, many questions remain open, as:

• Where is the complex between βPIX and Scribble initiated?

• What is the mechanism by which Scribble recruits βPIX? Is it due to random motion that drives the βPIX-Scribble to where its biological activity is needed, or is there an active transport mechanism involved? What is the time scale of this process?

• Does Scribble remain in the complex once βPIX is localized in the protrusions and leading edges?

• Does Scribble remain in the complex while βPIX activates Cdc42?

The questions mentioned above are all related in one way or another to protein motion within living cells. While various biochemical and biomolecular techniques such as immunolocalization, pull-down assays, and immunoprecipitation have been extensively used to demonstrate protein-protein interactions, they are limited to cell extracts and fixed cells [40]. Hence, it is difficult to use these techniques to study the time-dependent processes. Time-lapse imaging with fluorescent proteins including optical and image process computing are reliable techniques that offer new opportunities to study such biological questions by monitoring the dynamic properties of proteins inside living cells [41]. 1.3. The Research Questions and an Outline of the Chosen Methodology 8

One of the most basic properties of mobile proteins within living cells is the diffusion coefficient, which is a physical value that describes the rate of protein random motion. Hence, measuring the diffusion coefficient of βPIX in living cells might be an important key to answer these questions. Here we show non-invasive measurements of the diffusion coefficient of βPIX by applying a novel technique known as Raster Image Correlation Spectroscopy (RICS). The analysis of βPIX serves as a paradigm for the use of RICS to study any protein-based biological process.

The primary aim of this thesis was to establish a RICS routine to measure diffusion coefficients of proteins in living 3T3 fibroblast cells. Once this aim was achieved, this routine was applied to monitor the interaction between βPIX and Scribble indirectly by measuring the diffusion coefficients of βPIX Wild Type (WT) in fibroblast cells, and comparing it to the diffusion coefficient of a βPIX mutant that is unable to bind to Scribble. Given that the molecular weight of the WT and the mutant is almost identical, the assumption of this thesis is that the diffusion coefficient of βPIX can be related to the molecular interaction between βPIX and Scribble. For instance, the molecular weight of βPIX-Scribble complex is larger than the molecular weight of βPIX alone. Since there is a connection between the molecular weight and the diffusion coefficient of a diffusing molecule, an interaction with Scribble might reduce the measured diffusion coefficient of βPIX. It is important to note that the investigation of the interaction between βPIX and Scribble could be done with complementary strategies such as mutating Scribble and measuring the diffusing coefficient of WT βPIX. Such measurements are out of the scope of this thesis but may be done in future work. 1.3. The Research Questions and an Outline of the Chosen Methodology 9

To explore possible differences in diffusion between WT and mutant βPIX the following steps were performed:

1. The theoretical background behind the autocorrelation analysis approach, as well as literature review in this ﬁeld were performed. (Chapter 2)

2. An automated RICS software was created especially for this thesis to deal with the challenge of diffusion coefﬁcient measurements. (Chapter 4)

3. The experimental setup was characterized and validated with diffusing ﬂuorophores in isotropic solutions and EGFP-EGFR in living BaF3 cells. These validations discovered effects in RICS that have not been reported in any published RICS literature, but were discussed in similar techniques based upon ﬂuorescence correlation spectroscopy. In addition, it raises the requirement to optimize the acquisition parameters.(Chapter 5)

4. The effect of photobleaching was supported by using fixed transfected fibroblast 3T3 cells expressing Enhanced Yellow Fluorescence Protein (EYFP) as control. Living 3T3 cells expressing EYFP were used to indentify the optimal framework for accurate RICS measurements, which was used to compare between the diffusion coefficient of WT βPIX and the mutant βPIX. (Chapter 6) Chapter 2

Theoretical Background

2.1 Introduction

Biological functions in living cells require localization and intracellular redistribution of proteins between subcellular regions [42]. For instance, redistribution of different proteins in speciﬁc regions of the cell is necessary for the assembly and disassembly of biomolecular complexes [43–45]. These processes can play important roles in various cellular functions such as cellular motility, cellular signalling [46], and cell polarity as explained in Chapter 1.

various mechanisms control the molecular movement of proteins within the cell, and can involve either active or passive transport [47–49]. While passive transport occurs spontaneously, active transport is usually characterized by fast and speciﬁc directional mobility that requires energy exchange [47, 50]. One common type of passive transport is diffusion, whereby molecules move spontaneously down their concentration gradient due their random motion [47].

10 2.1. Introduction 11

An example of a process that involves both passive and active transport is the transport of G-actin during actin polymerization. This transport can be facilitated by translational diffusion, or can be carried out by active transport to regions that already contain an excess of G-actin [51, 52]. Active transport in cells usually involves motor proteins, which commonly mediate active transport processes by hydrolysis of Adenosine Triphosphate (ATP) or GTP and by converting the released energy from this reaction to mechanical movement [42, 53].

Since protein-protein interactions and interactions of proteins with various cellular components can alter the diffusion coefficient of proteins in living cells [54–56], measuring the rates of diffusion can provide indications of biological activity, and can provide an important method for understanding many phenomena in cell biology [57]. Recently, major developments in a broad collection of microfluorimetric techniques known as Fluorescence Fluctuation Spectroscopy (FFS) have significantly enhanced our capabilities to measure diffusion. These techniques enable study of the molecular motion of fluorophores by illuminating a defined volume with a laser beam, and by characterizing the frequency of the fluctuations in the emission intensity collected from this volume. The measured fluctuations are indicative of how the fluorophores are being transported, and can be analysed quantitatively to give the dynamic motion of the fluorophores.

Figure 2.1 illustrates the principle behind FFS methods. A laser is focused into a solution to define a small optical detection volume with a size usually on the scale of a femtoliter. Since the solution contains diffusing fluorophores, fluorophores will eventually enter to this volume. When a fluorophore enters the observation volume, it will begin to fluoresce. When it exits the volume, it will stop fluorescing. Thus, the fluorescent signal will fluctuate in a random manner that reflects the entrance and exit of particles to and from the volume. The probability for a particle to enter or exit the volume will depend on its average rate 2.1. Introduction 12

of movement, which is related to its diffusion coefficient. Thus, the statistics of the fluctuations in fluorescence (which reflect the probability of particles to enter and exit the volume) will depend on the diffusion coefficient of the fluorophores. FFS techniques utilize statistical methods and mathematical models to derive the diffusion characteristics of the fluorophores from the measured fluctuations in fluorescence.

Figure 2.1: Diffusing particle enters the observation volume. Diffusing fluorescent molecules moving in and out of the focal volume causes a temporal change in the concentration, and as a result, there are fluctuations in the collected fluorescence intensity. Quantitative analysis of the frequency of these fluctuations can give information about how fast the fluorophores are moving into the focal volume. If the sample is homogenous, the dynamics of the fluorophores inside the focal volume gives statistical information for the all sample.

In 2005 a new FFS technique was introduced by E. Gratton and M. Digman (University of California, Irvine, CA), who demonstrated how a standard confocal microscope can be used to accurately measure the diffusion coefficient of fluorophores [58]. This development was based on two previous FFS techniques- Flu- orescence Correlation Spectroscopy (FCS) and Image Correlation Spectroscopy (ICS), and was used to measure diffusion coefficient of proteins in solutions and within living cells [58–67]. 2.1. Introduction 13

In this thesis, we utilized Raster Image Correlation Spectroscopy (RICS) in order to characterize βPIX-Scribble interactions in ﬁbroblasts.

In order to provide an insight into RICS, this chapter provides a comprehensive explanation of its principles. Section 2.1.1 begins with a theoretical overview of the diffusion coefficient and its importance in cell biology field. Sections 2.1.3 and 2.1.3 explain the principles of fluorescence phenomena and show a number of fluorescence-based techniques in the emerging interdisciplinary field of Photonics in the cell biology research. Since RICS is based on concepts that originated in FCS and ICS, these techniques are explained in sections 2.2 and 2.3. Finally, section 2.4 explains RICS and shows its applications.

2.1.1 The diffusion coefﬁcient in cell biology

Fick’s 1st law for diffusion

A concentration gradient of a solute exists if the particles of that solute are not equally distributed over space. If the particles are free to move spontaneously (for example, in the case of particles in liquid), there will be a thermodynamic force that will act to make the particle distribution uniform. The phenomenon by which mass is passively transported through thermodynamic forces from a region of high concentration to a region of low concentration is known as diffusion.

Mathematical quantification of the diffusion process is possible by using Fick’s 1st law (2.1), which describes the flux of particles across a defined area over time, as a function of the diffusion coefficient and the concentration gradient of the particles: 2.1. Introduction 14

F~ = −D∇~ C(~r, t) D − diﬀusion coeﬃcient (2.1) ∇~ C(~r, t) − concentration gradient

Figure 2.2 illustrates diffusion of small solid particles in a liquid down their concentration gradient.

NA NB

NA>NB

NA NB

NA=NB

Figure 2.2: Diffusion of particles resulting from a concentration gradient.

At the beginning of the process, the number of particles in the left tank (NA) is larger than the number of particles in the right tank (NB). Both of the tanks have the same size, and therefore the number of particles in each tank is equivalent to the concentration of particles in the tank. When the barrier between the tanks is removed, the particles are free to move between the two tanks. This results in a net flux of particles from tank A to tank B. This flux will decrease to zero when the concentration of particles in tank B is equal to the concentration of particles in tank A. The hashed line is an imaginary border between the two sides of the tanks, which is removed to enable diffusion. Fick’s 1st law can be used to calculate the flux of particles from tank A to tank B at any given time after the boundary is removed. 2.1. Introduction 15

Although Fick’s ﬁrst law describes diffusive processes, it does not provide insight into the physical mechanisms that cause diffusion. We will discuss these mechanisms in the following few sections.

Brownian motion and Einstein-Smoluchowski equation

If you suspend dust in a cup of water, you will notice that the dust specks tend to move around in a random manner. The phenomenon by which small particles suspended in liquid move around in a random manner is known as Brownian motion. It was ﬁrst reported in the middle of the 19th century by the botanist Robert Brown who made careful observations with small particles resuspended in solutions with a light microscope [68]. A computer simulation that demonstrates Brownian motion is shown in Appendix A.1.

Since at any given time the direction of particles undergoing Brownian motion is random, the path followed by the particles will be erratic [69]. If the path is divided into small intervals, the total displacement of the particle at time t, ∆X(t), is the sum of the motion over all small intervals up to time t [69]. Because at any time point there is an even chance for the particle to move in any direction, it is possible to prove mathematically that the mean displacement over any time increment will be equal to zero. This becomes evident if you consider a one- dimensional (1-D) case in which the particle is limited to moving along a line. Since at any time there is an equal probability to find the particle on the right as there is to find it on the left (or up and down), then the mean displacement is equal to zero. However, it is possible to show that the probability of finding the particle at its point of origin decreases with time. In fact, it is possible to show that the expected value (mean) of the distance travelled by a particle will increase with time. Thus the Mean Squared Displacement (MSD), which is the mean of the square of the displacement of an ensemble of diffusing particles, will increase 2.1. Introduction 16

over time. Figure 2.3 illustrate random 1-D motion of a particle, and the concept of the MSD. It provides an intuitive explanation about why the MSD increases with time. up up up up up up up up up up up up up up up down up up down up down up up down down down up down down up down down up up up down down down up up down down down down up up down down down up down up Location down down up up down up Time up up up up up up up up down down up up up up down down up down up down down down up up down down up down down down down up up down down down down down down down down down down

Figure 2.3: Illustration of random one-dimensional motion of a particle. The particle is limited to move randomly along a line up and down. Since at any time there is an equal probability that the particle will move up, as there is that the particle will move down, and then the mean displacement is equal to zero. However, the probability of ﬁnding the particle at zero decreases with time.

The Mean Square Displacement (MSD) of the particles (the square of the displacement is always positive) is used to describe the average distance of a randomly moving particle from the starting point at time t. The MSD of a particle undergoing Brownian motion (free diffusion) will increase linearly with time and the rate at which the MSD increases depends on the diffusion coefﬁcient. This is 2.1. Introduction 17

expressed in the Einstein-Smoluchowski equation:

for 1D : hX2(t)i = 2 · D · t for 2D : hX2(t)i = 4 · D · t for 3D : hX2(t)i = 6 · D · t (2.2) hX2(t)i − mean of the squared displacement D − translational diﬀusion coeﬃcient

This equation shows that the larger the diffusion coefﬁcient, the larger the MSD of the particles at any given time. This random motion is the source of the diffusion, as can be seen in Figure 2.4.

NA NB

NA>NB

Figure 2.4: Brownian motion of diffusing particles. When small particles are immersed into a liquid, they do not remain stationary. If you were to observe the individual particles, you would notice that they move about in a random manner. This movement is responsible for the diffusion deﬁned in Fick’s 1st law.

However, two questions remain open:

(a) What causes the random movement of each individual particle? 2.1. Introduction 18

(b) What are the factors that affect the diffusion coefﬁcient?

These two questions are addressed in the next sub-section.

The Stokes-Einstein relation

By the beginning of the 20th century, the kinetic theory of gases and liquids was already established and it was well known that the atoms (or molecules) in a gas or liquid move about in a random fashion similar to the Brownian motion described above. If small particles are placed into the liquid then the molecules of the liquid will collide with them, and a transfer of momentum from the liquid to the particles will occur. Since the collisions between the atoms and the particles are random, the movement of the particles are random as well (Figure 2.5).

Figure 2.5: Liquid molecules pass part of their momentum to diffusing particles through collision impact.

As the temperature of the liquid increases, the kinetic energy of the liquid atoms (or molecules) increases. Consequently, the liquid molecules will collide with the particles more frequently and the exchange of momentum will increase. The increased rate of momentum exchange between liquid and particles, leads to an increase in the MSD of the particles over a given time. Since the diffusion 2.1. Introduction 19

coefficient is proportional to the MSD, we can conclude that a rise in temperature causes an increase in the diffusion coefficient. Similarly, we might conclude that larger liquid viscosity and larger particle sizes will increase the drag experienced by the particles moving about in the liquid. Thus, larger viscosities and particle sizes will tend to reduce the MSD, and therefore reduce the diffusion coefficient of the particles in the liquid.

In 1905 Einstein formulated the relationships mentioned above into a mathematical formula, known as the Stokes-Einstein relationship [70]. This relationship expresses the diffusion coefﬁcient of a spherical particle in liquid in terms of the temperature and viscosity of the liquid and the hydrodynamic radius of the particle:

K T D = B 6πνRH

KB − Botzmann‘s constant T − absolute temperature (2.3) ν − viscosity

RH − hydrodynamic radius

The upper term in the Stokes-Einstein relation is the temperature-dependent driving force of the liquid molecules on the particles. This force is derived from the relation between the thermal energy and the motion of the liquid molecules as a function of temperature. The lower term expresses the drag force experienced by the diffusing particle. We thus conclude that random forces originating from the thermodynamic kinetics of the solute in which the diffusion occurs cause diffusion. We also conclude that the diffusion coefﬁcient is determined by the temperature of the solute, the viscosity of the solute and the hydrodynamic radius of the diffusing particle. 2.1. Introduction 20

In addition to diffusion, the next physical effect that is involved in RICS is fluorescence. Sections 2.1.2 and 2.1.3 explain the principles of fluorescence, explain how fluorescence proteins can be used to monitor proteins in living cells, and show how advanced technologies from non-biological fields can be used to monitor protein dynamics in living cells.

2.1.2 The principles of ﬂuorescence

The principles of fluorescence can be explained by the Jablonski diagram (2.6). In brief, when a photon strikes a fluorophore, there is a statistical probability that the h·c molecule will absorb the photon energy ( λ , where λ is wavelength, h is Planck’s constant, and c is the speed of light). As a result, the electronic ground state of the molecule will be excited to a high-energy state. Since the high-energy state is unstable, it subsequently returns spontaneously to the ground state, followed by fluorescence emission of the energy that was absorbed by the molecule.

Intersystem Absorption Fluorescence crossing T* (~fs) (~ns) (~µs-ms)

Irreversible photobleaching

Figure 2.6: Jablonski diagram for the energy states. The time scales of each physical process mentioned in the brackets. S, S∗, and T∗ resemble the ground state, excited state, and triplet state (explained in 2.4.3), respectively. Figure was adopted from [71]. 2.1. Introduction 21

Since energy is lost due to vibrations and heat transfer during the fluorescence process, the wavelengths of the emission are longer than the excitation wavelengths [72]. This shift in fluorescence spectra is termed the Stokes-shift. The Stokes-shift of a specific molecule is like the fingerprint of the molecule, and it is associated with the molecular structure of the molecule and its conformation. In addition, the Stokes-shift allows spectral separation between the emitted fluorescence from the specimen and the excitation light source in fluorescence microscopy. Illumination of the specimen with specific wavelengths that can be absorbed by the specimen, and analysis of the emitted light from the specimen is one of the most basic principles behind any fluorescent-based technique.

Exciting fluorophores with high illumination intensity increases the probability that the fluorescent molecules irreversibly lose their characteristic fluorescence. With a laser as an excitation source, this phenomenon so-called photobleaching, can occur in as little time as a few microseconds [73]. A more detailed description about the photobleaching effect can be read somewhere else [74, 75]. A major breakthrough in the field of molecular biology field was achieved at the beginnings of the 90s, when fluorescent protein technology emerged. This technology enabled fluorescence labelling of specific proteins within live cells, thereby enabling scientists to monitor their protein of interest in a specific and efficient manner [76]. A brief introduction about the fluorescence protein technology and its contribution to cell biology research is presented in section 2.1.3.

2.1.3 Fluorescence proteins technology and traditional respective ﬂuorescence based techniques

The first naturally fluorescent protein to be identified and purified was derived from the jellyfish Aequorea victoria by O. Shimomura 50 years ago [77]. This 2.1. Introduction 22

protein has a special molecular structure, which is characterized by a barrel shape core that serves as a fluorophore. Since its fluorescence emission is in the lower green portion of the visible spectrum (∼500 nm), it was later termed as Green Fluorescent Protein (GFP). The GFP was firstly cloned and sequenced by Prasher and co-workers [78] and expressed in E. coli and C. elegans by M. Chalfie [79]. Because GFP is genetically encoded, the encoding DNA can be fused with that of any other protein of interest. Once transfected into a cell, this DNA will then be transcribed and translated into a fusion protein where the fluorescence of the GFP effectively reports the expression, localization and movement of the protein of interest [80]. In 1995 R. Tsien succeeded for the first time to genetically engineer a new variant of GFP [81, 82]. Since then, many GFP variants have been created with improved properties, such as photo-stability, pH-stability and temperature- stability and various spectral properties (For instance- EGFP (Enhanced GFP), EYFP that was used in this study, and many more.) [83].

In recent years there has been a huge acceleration in the use of fluorescent protein technology to provide unprecedented insight into specific processes involving proteins. Genetic modifications of GFP are commonly used as standard tools in cell, developmental and molecular biology as reporters of protein expression. Combined with novel microscopy and other photonic techniques, fluorescent proteins technologies allow mapping of the stoichiometry and interactions of proteins non-invasively within living cells [77, 84, 85]. 2.1. Introduction 23

The power of this technology was acknowledged in 2008 when the Nobel Prize in chemistry was awarded to Shimomura, Tsien, and Chalﬁe for the discovery of GFP, and the development of related technologies. A concise overview of a number of ﬂuorescence-based techniques relevant to this thesis is given in the following subsections:

Time-lapse ﬂuorescence microscopy

Time-lapse microscopy is based on the capacity to record sequences of microscope images of a cell or a group of cells at constant time intervals and to analyse those images to give information about dynamic cellular processes. At the crudest level, combining the power of fluorescence microscopy and time-lapse microscopy allows, for instance, tracking of bulk flow of a protein into the nucleus to mediate transcriptional regulation upon activation of a signalling pathway. More sophisticated analysis can allow single-molecule fluorescence tracking of, for instance, the motion of motor proteins within living cells [86]. Moreover, biomolecular processes within the cell can be correlated with the trajectory analysis of individual cells to give data about the activity of specific proteins during cell migration [87, 88].

Computational image analysis of ﬂuorescence microscopy images

Data analysis and image processing can be applied to describe biophysical effects and biological processes quantitatively by using mathematical algorithms [89]. Computational methods automatically quantify objects, distances, concentrations, and velocities of cells and sub-cellular structures [90]. An example of how image processing algorithms can play a role in cell biology is the generation of quantitative spatial-temporal maps of F-actin localization and velocity during migration of Keratocytes (ﬁsh epithelial cells) [91]. 2.1. Introduction 24

Single-particle tracking

Using mathematical algorithms to analyse the trajectories of single particles such as small fluorophores, organelles, viruses or colloidal microspheres is known by the term Single-Particle Tracking (SPT) [92]. Once the trajectory of the particle is recorded over time, its MSD can be calculated to measure the diffusion coefficient and velocity [[89, 93]. Although SPT is an extremely useful method, its limitations should be considered. Firstly, individual particles have to be distinguishable. Evidently, applying SPT to βPIX conjugated to fluorescence protein requires ultrasensitive optical equipment. Next, there is a requirement that the trajectories of the particles can be recorded over enough time points. Finally, merging and splitting trajectories can make it difficult to quantify the physical motion of the practices [92].

Fluorescence Recovery After Photobleaching (FRAP)

While photobleaching is usually an undesired effect in fluorescence microscopy measurements, as it decreases the signal intensity and lowers the Signal to Noise ratio (S/N) [94], it can also be exploited as an extremely useful tool for measuring the mobility of fluorophores from time-lapse fluorescence microscopy by a technique known as FRAP. The principle of FRAP is that a defined volume within the sample is photobleached by exciting the fluorophores with high illumination intensity. The photobleaching results in a fast decline in the total fluorescence intensity that is collected from the bleached volume. Once the volume has been significantly photobleached, the laser power is reduced, so that no further bleaching occurs. Subsequently, there is a measurable recovery in the fluorescence intensity of the volume due to the diffusion of unbleached fluorophores from other areas in the sample. The rate of recovery strongly depends on the rate of fluorophore diffusion, Hence by fitting the experimental 2.1. Introduction 25

recovery curve to a physical model that describes the mobility properties of the fluorophores, quantitative information about the diffusion coefficient and the fraction of immobile fluorophores in the sample can be obtained [95, 96]. Recently, several FRAP methods that consider recovery of fluorophores during photobleaching were developed [97–99]. A schematic diagram explaining the concept of FRAP is shown in Figure 2.7.

Bleached area

100% Pre-

Percent fluorescence photobleach Partial Recovery

Recovery Y X

Photobleach

0% Time

Figure 2.7: Graph of FRAP experiment. Graph describes recovery of fluorescence intensity collected from a defined area during a FRAP experiment. X is the fluorescence intensity before it was bleached. After the area was photobleached, the intensity is drastically reduced. If there is no significant recovery of un-bleached molecule during the photobleaching process, the area is photobleached very fast and a sharp curve will form. Once most of the fluorophores in the defined area are irreversibly photobleached, the defined area is stopped being expose to excitation light. Therefore, there is a recovery in the fluorescence intensity as unbleached fluorophores diffuse into the area, taking the place of photobleached fluorophores. The value of Y is the intensity where the recovery is stabilized. The ratio between Y and X gives the percentage of recovery, which is proportional to the percentage of immobile components. The time it takes for the intensity to reach Y gives the diffusion coefficient 2.1. Introduction 26

Although FRAP is a very useful technique and has been used extensively in cell biological studies, its resolution is limited, as the measured diffusion coefficient describes the average value of diffusion for all molecules within the photobleached region, which is usually several square microns in size. Another problem arises from the difficulty to predict the exact model that describes the dynamic property of the fluorophores due to the complex behaviour of proteins within living cells [100, 101]. As will be explained in section 2.2 this is also a problem in several FFS techniques that also requires fitting models. In addition, FRAP cannot measure interactions between two different species directly [102, 103].

Forster Resonance Energy Transfer (FRET)

FRET is based on energy transfer between an excited molecule (the donor) to a coupled acceptor fluorophore (the quencher), which absorbs the energy released from the donor while its energetic level returns to ground state. This mechanism requires an overlap between the emission spectrum of the donor and the absorption spectrum of the acceptor, and a distance that is typically not greater than 10 nm between the two-coupled fluorophores. When the acceptor quenches the donor there is a reduction in the donor emission (if the donor is also a fluorophore) and an increase in the acceptor emission. Since the energy transfer depends on the proximity between the two fluorophores, visualization of the donor-acceptor fluorescence with appropriate filters can give information about their complex formation [104, 105]. However, FRET also suffers from several limitations. For example, FRET is sensitive to concentration. If the ratio between the concentrations of the acceptor/donor is not approximately equal, high background fluorescence will hamper the sensitivity of the FRET measurements and will make it difficult to detect shifts in fluorescence spectra that indicate an interactions 2.1. Introduction 27

between the proteins [85].

Summary

In summary, the methods mentioned above are extraordinarily powerful in studying the properties of proteins in cells. They are now standard tools in many areas of cell biology. However, given the heterogeneity of mammalian cells, and the fact that any given protein within a cell can demonstrate multiple different properties depending upon, for instance, interactions with other proteins, posttranslational modiﬁcations, and intracellular localization, other complimentary approaches that can measure diffusion with a higher spatial or temporal resolution are also called for. FFS techniques are ideal for this purpose. 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 28

2.2 Principles of Fluorescence Correlation Spectroscopy (FCS)

2.2.1 The theory behind FCS

When a beam of light passes through a colloidal suspension, the incident light is scattered by spontaneously moving particles. As a result, there are stochastic fluctuations in the intensity of the scattered light. The connection between the intensity fluctuations and the concentration of the moving particles was established by Smoluchowski and Einstein [106] as the “fluctuation theory of light scattering”. This connection can be formulated through the Autocorrelation Function (ACF), which is a mathematical function that is used in signal processing and stochastic systems as a statistical tool for measuring the self-similarity of fluctuating signals.

The ACF is an extremely useful tool in the field of physics and is the cornerstone for many fluctuation based techniques. One of the first fluctuation based techniques to be introduced was Dynamic Light Scattering (DLS), which could be used to accurately measure diffusion coefficient values of macromolecular solutions using an optical system. The development of DLS through the pioneering work of Pecora, Cummins and Dubin [69, 107, 108] was enabled due to improvements in optical instrumentation that occurred in the early 1960s, in particular the invention of the laser, electronic correlators, and sensitive detectors. By using coherent and monochromatic light, such as the light emitted from a laser, DLS has the capability to measure the fluctuations in the intensity of the scattered light that is collected from a defined observation volume. Since the fluctuations are influenced by both the optical system and the dynamic properties of the particles, by calculating the ACF of the intensity fluctuations, and by fitting the derived ACF to a physical model, information about the physical values of the molecular 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 29

movement (i.e. - diffusion coefﬁcient) can be obtained [105].

FCS was developed in the early 1970s as the fluorescence analogue to DLS. It was developed by Magde, Elson and Web who showed the first FCS measurements of thermodynamic kinetic rates [109], diffusion coefficients of diffusing fluorescent particles [110, 111] and velocity of fluid solutions [112]. Although FCS and DLS are based on a similar concept, instead of using fluctuations in the scattered light, FCS utilizes fluctuations in the collected fluorescence intensity. The fact that FCS utilizes fluorescence means that it can be used to monitor specific fluorophores in heterogeneous populations of molecules. Furthermore, the use of fluorescence allows filtering of noise by using an emission bandpass filter. In addition, the use of a laser for FCS enables the focusing of a high intensity beam to a near diffraction-limited spot [113] thereby improving the sensitivity of the method.

Figure 2.8 illustrate a typical FCS setup. A laser beam is focused into the sample, which contain diffusing fluorophores. The movement of the fluorophores in and out of the focal volume cause fluctuations in the fluorescent intensity. These fluctuations are subsequently picked up on a detector. Only the fluorescence from the objective focal volume is confocal with the pinhole and therefore passes through the pinhole aperture, while most of the out-of-focus light is blocked by the pinhole and therefore cannot be received by the detector. Each photon from the emission that passes through the pinhole strikes the photocathode of the detector and has a statistical probability to produce a single photoelectron. The electronic signal is amplified about a million times by charge multiplication, and the current is then converted into an analogue electrical signal. The Analogue-to-Digital (A/D converter) processing algorithm converts the analogue signal into discrete digital increments, which are correlated by hardware processors or software correlators to yield the autocorrelation function (ACF). 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 30

3 2

1 11

6 12

7 10

APD 8 9

Figure 2.8: Scheme for a standard FCS experimental set up. Excitation light arrives from the Laser source (1), collimated by lenses (2), and reflected on the dichroic mirror (3). The laser beam is focused into the sample (4) by the objective (5), and the diffusing fluorophores in the sample are excited. The emitted fluorescence is collected by the objective and is transmitted onto the dichroic mirror through the emission bandpass filter (6). The emission is focused by a lense (7) through the pinhole (8), and continues to the detector (10) via an optic fiber (9). The detector (10) translates the fluctuations in the emission intensity into an electronic signal. Finally, computer software (or electronic hardware) calculates the ACF from the electronic signal. A physical model is fitted to the ACF, and information about the dynamic properties of the fluorophores is derived. . 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 31

The ACF is then fitted to a mathematical model to yield the diffusion coefficient of the fluorophore. It is important to note that FCS involves the analysis of a continuous voltage stream that corresponds to variations in light intensity collected. Thus, it FCS cannot be strictly classified as single-molecule methods because the signal is averaged over thousands of molecules. Nevertheless, FCS is based upon the contribution of small number of molecules in a defined volume [114].

A couple of brute force methods are commonly used to calculate the ACF, and are based on the idea that shifting the intensity vector, and multiplying it with the un-shifted vector, gives the ACF, as described in (2.4).

∼ 1 Pn G(τ) = n ii=1 I(ii) · I(ii + n) n − length of discrete intervals (2.4) I(ii) − value of vector at the iith interval I(ii + n) − value of vector at the (ii + n)th interval

Another way is to use the Fast Fourier Transform (FFT) of the intensity power spectrum, as can be seen in Equation (2.9):

G(τ) = f −1([f(I(t))] · [f(I(t))]) f − Fourier transform (2.5) f −1 − inverse Fourier transform f(I(t)) − complex conjugate of the transform

FCS measurements can be performed by using either a designated setup for FCS, or with a modern commercial system that offers a Confocal Laser Scanning Microscope (CLSM) combined with FCS. 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 32

2.2.2 The ACF

In order to obtain quantitative information on the frequency of the fluctuations in the collected intensity signal, which is directly connected to the diffusion coefficient of the fluorophores, the experimental ACF has to be fitted to a theoretical model by computational curve fitting. The fitting model has to consider the following:

J The properties of the experimental system.

J The type of motion that the detected particles are expected to exhibit.

J Biophysical characteristics of the ﬂuorophore and photophysical effects that can inﬂuence the ACF.

The difficulty in developing such models is derived from the large number of parameters and complex interactions between them. What follows is a brief overview of how the ACF is calculated and how it can be fitted to a mathematical model to yield diffusion coefficients of fluorophores in solution.

Equation (2.6) expresses the one-dimensional second-order ACF as an integration of the function multiplied by itself in lag time, τ.

G(τ) = lim 1 R T I(t)I(t + τ)dt T →∞ T 0 (2.6) τ lag time

As τ increases, I(t+τ) is shifted more before being multiplied by the function I(t), and the deviation of I(t+τ ) from I(t) increases. In this manner, the decay of the ACF characterizes the similarity between the function at different lag times, or in other words, how strong the correlation of elements within the function is. The 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 33

rate and shape of the decay of the ACF, G(τ) provide statistical information about the duration and form of the random signal, I(t+τ). For instance, the G(τ) of a rapidly ﬂuctuating random process will decrease faster than the G(τ) of a slowly ﬂuctuating random process [69].

In Equation (2.6) the integral limits are between 0 and ∞, and the G(τ) is a symmetric function with the axis of symmetry at τ=0. Since the function is symmetric, it is sometimes more convenient to use integral limits between 0 and ∞. Although the pattern of the signal fluctuation is random, if the function is integrated over a sufficiently long time (much longer that the period of the fluctuations) the average of two different times will give the same value. Hence:

hI(t)i = lim 1 R T I(t)dt T →∞ T 0 (2.7) hI(t)i − mean vector

Another common notation of the ACF:

G(τ) = hI(t) · I(t + τ)i = lim 1 R T I(t)I(t + τ)dt (2.8) T →∞ T 0 where the brackets <> symbolizes the time average over the ﬂuorescence signal.

The amplitude of the ACF at the lag zero (G(0)) is the average of the function multiplied with itself and is equal to the average intensity of the signal. Normalizing the ACF with the average intensity, as shown in Equation (2.9), yields a function. g(/tau) for which g(0)=1. This normalization makes it possible to compare the frequencies of ﬂuctuating signals with different average intensities.

2 g(τ) = G(τ) − 1 = hI(t)·I(t+τ)i−hI(t)i (2.9) hI(t)i2 hI(t)i2 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 34

The ﬂuctuations in the signal are equal to the signal at a speciﬁc time from which the average of the signal is subtracted. Therefore:

δI(t) = I(t) − hI(t)i (2.10) δI(t + τ) = I(t + τ) − hI(t + τ)i where δ stands for ﬂuctuations in the signal. Using the last equation gives one more useful notation for the normalized ACF:

g(τ) = hδI(t)·δI(t+τ)i (2.11) hI(t)i2

2.2.3 FCS ﬁtting model for Brownian motion

As an example of how FCS is used to derive quantitative information about diffusive processes, we now show how an FCS model for single-component three- dimensional Brownian motion is developed. This model assumes:

1. Free diffusion of ﬂuorophores as a result of Brownian motion, without the presence of ﬂow dynamics.

2. That the observation volume has an ellipsoidal 3-D Gaussian intensity proﬁle.

3. That the fluctuations in the fluorescence intensity are only due to temporal changes in the number of particles and their locations within the focal volume as a result of the fluorophore diffusion.

The ﬁrst assumption is usually valid for an isotropic macromolecular solution, and when motion due to active transport or unidirectional ﬂow can be discounted. 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 35

However, in many cases this assumption is not entirely realistic, as dynamics that are more complex can be found in living cells. For instance anomalous diffusion, hop diffusion and conﬁned diffusion all commonly occur in cells [115]. As a result, there is not necessarily a linear relationship between the MSD of intracellular macromolecules and their diffusion coefﬁcient as predicated by Equation (2.2) for free diffusion [93]. Therefore, integrating models that can account for other diffusion behaviour into the FCS model can correct inaccuracies [116].

The geometry of the observation volume is defined by a combination of the illumination and collection point spread functions (PSF) of the optical system. The PSF is determined by the confocal pinhole and the illumination profile of the laser beam [117]. For most of the confocal microscopes and FCS systems, the assumption that the observation volume has an ellipsoidal 3-D Gaussian shape is correct [118]. The PSF usually has the shape of an airy disk modified with a Gaussian profile as the result of the Fraunhofer diffraction of the focused laser illumination passing through a circular aperture. It is common practice to characterize the beam by its waist, which is defined as the distance between the maximum intensity of the beam and the point at which the beam drops to e−2 of its maximum intensity [119].

The third assumption comes to simplify the mathematical model. It forms the basis for most FCS measurements. More complicated FCS models do exist. For example, models that consider the contribution of photophysical effects into intensity ﬂuctuations have been derived [118]. However, the derivation of these models is based on the same formulas used to derive the model based on the assumptions mentioned above. Furthermore, these assumptions are the basis for the standard RICS model, which is developed using a similar mathematical procedure. Therefore, an outline of how the basic FCS equations are derived is 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 36

presented. A more detailed description of this model can be found in [118, 120]). Abstract computer simulations demonstrating the concepts of the autocorrelation analysis in FCS for these assumptions are shown in Appendix A.

When the assumptions mentioned above are used, then the intensity of light that is incident on the detector is given by Equation (2.12):

n R n for d :I(t) = α Rn W (~r) · C(~r, t)d r n − number of dimensions W (~r) − exciting radiation C(~r, t) − concentration (2.12) α = ιεQ ι − instrumental counting eﬃciency ε − excitation eﬃciency Q − quantum yield of the molecules

The meaning of Equation (2.12) is that the collected intensity at time t is the sum of the collected intensities emitted from all the fluorescent particles in the excitation volume. The collected intensity of each individual particle depends on the excitation radiation, fluorophore concentration and the detection efficiency (instrumental counting efficiency, pinhole, gain, and detector sensitivity), excitation efficiency, and the quantum yield of the molecule (the ratio between the particle fluorescence intensity and the excitation intensity). The excitation intensity of the particles is weighted with the laser profile at the location of the particle at time t. When the particles are moving in and out of the excitation volume, and within the excitation volume, the collected intensity fluctuates as a result of the differences in the excitation intensity. Note that I(t) can also represent the current registered by the PMT. In this case, the PMT gain voltage will be accounted for in 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 37

the instrumental counting efﬁciency, ι [113].

The next step is to express the ACF by substituting Equation (2.12) into (2.7). The new expression is:

RR W (r)W (r0) hδ(η · C(r, t))δ(η · C(r0, t + τ))i dV dV 0 g(τ) = (2.13) R W (r) hδ(η · C(r, t))i2 where δ denotes ensemble fluctuations, τ ensemble the lagged intensity signal, hδ(η · C(r, t))δ(η · C(r0, t + τ))i ensemble the fluctuations in intensity reflected by the spatial-temporal change in the concentration, and η ensemble the S/N ratio constant.

Since this specific model assumes that the fluctuations are only due to the change in concentration, fluctuations in η are neglected. Hence

δ (η · C (r, t)) = C · δη + η · δC = η · δC (2.14)

Another general assumption is that the overall collected intensity is propor- 1 tional to the number of the particles in the focal volume. Therefore, hCi is used instead of α and η. Therefore Equation (2.15) takes on the simpliﬁed form of:

RR W (r)W (r0) hδ(C(r, t))δ(C(r0, t + τ))i dV dV 0 g(τ) = (2.15) hCi R W (r)2

The ﬂuctuations are caused only by the spatial and temporal propagation of concentration distribution δ(C(r, t))δ(C(r0, t + τ)), which is described by Fick’s 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 38

2nd law:

∂C(~r, t) = D · ∇2C(~r, t) (2.16) ∂t

Solving Equation (2.16) for a simple case of Brownian motion gives:

h −x2 i for 1d : C(r, t) = N e 4·D·t 1/ (4·π·D·τ) 2 h −r2 i N 4·D·t for 2 − D : C(r, t) = 4·π·D·t e h −r2 i N 4·D·t for 3 − D : C(r, t) = 3 e /2 8·(π·D·t) (2.17) t − time N − number of particles D − diﬀusion coeﬃcient x − position where C(r,t) expresses the probability that a particle originally located at r=0 and t=0 can be found in location r at time t. This probability has a Gaussian shape [121, 122].

The Equation (2.17) can replace the concentration ﬂuctuation term in Equation (2.15), as demonstrated for 2-D diffusion in Equation (2.18):

2 −(~r−~rτ ) hδC(~r, t) · δC(~r, t) i = C e 4·D·τ t t+τ 4·π·D·τ (2.18)

And the new expression is:

" 2 # −(~r−~rτ ) RR 0 4·D·τ 0 1 W (r)W (r )e dV dV (2.19) g(τ) = 2 4·π·D·τ·hCi (R W (r)dV ) 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 39

The effective detection function describes the optical combination between the PSF and the pinhole. Its exact shape is largely determined by the numerical aperture (NA) of the objective lenses:

NA = n · sin(θ) θ − angular aperture (2.20) n − refractive index of the medium where n denotes the refractive index of the medium, and θ denotes the half angle of the cone from which the objective is able to collect light. The waist of the effective detection function are described in Equation (2.21):

0.44·λ ωxy(confocal) ' NAobjective

ωz(approximated) ' 3 · ωxy (2.21) λ − excitation wavelength where the 0.44 value in Equation (2.21) is ﬂexible and dependent on the characterization of the optical setup.

Equation (2.22) shows the excitation radiation for a Gaussian focal spot in the cases of 2-D and 3-D diffusion. For 2-D diffusion, there is no contribution to the intensity ﬂuctuations from the Z direction. Since the particles diffuse in the XY-plane, the weighted excitation intensity is also planar. This is in contrast to 3-D diffusion where the particles can diffuse in and out of the XYZ-plane and detection is 3-D. In such a case, the waist of the focal volume in the Z-plane, ωz, has to be considered. The ratio between ωz and ωxy depends on the experimental 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 40

system and the objective [123].

X2+Y 2 −2 2 ωxy for 2 − D : W (~r) = W0 · e X2+Y 2 Z2 −2 2 + 2 ωxy ωz for 3 − D : W (~r) = W0 · e (2.22) W (0) − maximum excitation X,Y,Z − cartezian coordinates

For an ellipsoidal 3-D Gaussian proﬁle, the last equation can be expressed with the next simple formula ([118]):

RR 0 0 1 W (r)W (r )dV dV = 2 Veff (R W (r)dV ) 3 2 V = π 2 · ω · ω eff−for Gaussian V olume xy z (2.23) ωxy − radial waist

ωz − axial waist

And the ACF will take the shape:

2 ZZ −(~r−~r0) g(τ) = 1 · 1 e 4·D·τ dV dV 0 (2.24) Veff ·hCi 4·π·D·τ

The limits of integration take the deﬁnition of the observed volume into account (W(r)=0 outside the observed volume [113]. Therefore, the integral in Equation (2.19) can be solved analytically to yield:

! 1 1 g(τ) = · τ Veff ·hCi 1+ τ | {z } D 1 (2.25) hNpi

τD − diﬀusion time 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 41

Equation (2.25) gives two useful parameters. The ﬁrst parameter is the mean number of particles in the focal volume, 1 , which is the amplitude of the hNpi normalized ACF. The normalized ACF is expressed by:

g(τ) = hδI(t)·δI(t+τ)i hI(t)i2 hδI(t) · δI(t)i − variance of intensity hI(t)i − mean of intensity (2.26) and for τ = 0 : g(0) = hδI(t)·δI(t)i hI(t)i2

Assuming that the number of particles observed in the focal volume has a Poisson distribution, and therefore the variance of the collected intensity is equal to the mean of the intensity, and assuming that the overall collected intensity is proportional to the number of particles, I∝∝, when τ = 0 the ACF amplitude is proportional to the average concentration of the particles:

Assuming Poisson probability, var(I) = mean(I): g(0) ∝ 1 hI(t)i (2.27) Assuming I ∝ hNpi ∝ hCi : g(0) ∝ 1 , g(0) ∝ 1 hNpi hCi

The second parameter is the diffusion time, τ D, which is the time molecules spend on the average in the observation volume [117]. The diffusion time is proportional to the half-maximal of the maximum ACF value. For the simple case of 2-D diffusion, the diffusion time is deﬁned as: 2.2. Principles of Fluorescence Correlation Spectroscopy (FCS) 42

ω2 for 2 − D : τD = 4·D (2.28)

Hence, measurement of fluctuations in fluorescence within a focal volume and calculation of the ACF can be used to measure the diffusion time. Thereby knowing the ωxy and the characteristic diffusion time providing useful knowledge about the dynamic properties of the fluorophore, and can give the diffusion coefficient of a specific fluorophore.

2.2.4 FCS in cell biology

The first FCS setups lacked the ability to measure diffusion in living cells. The difficulty in adopting FCS for cell biology begins when trying to measure the intensity fluctuation in single spots with a volume of only few femtolitres. Selecting the location of this observation spot has enormous importance as the cell dynamics and structure are very heterogeneous. More problems can arise in the presence of autofluorescence, photobleaching and blinking. Finally, the interpolation of the ACF to derive the exact value of the diffusion requires sensitive FCS setup and knowledge about the size and shape of the PSF. Some of these difficulties have been overcame in the last 10 years, and these days FCS has the potential to become a major biophysical technique for studying molecular interactions in living biological specimens [114, 124–127]. Moreover, by modelling FCS fitting models that consider more complex dynamic properties, FCS can be used to measure molecular distribution, direct flow, give information about binding kinetics, and about multiple component interactions of expressed labelled proteins in living cells [120, 128–132]. . 2.3. Principles of Image Correlation Spectroscopy (ICS) 43

2.3 Principles of Image Correlation Spectroscopy (ICS)

2.3.1 ICS is based on raster CLSM

When a single point source with a size that is smaller than the PSF is visualized by raster CLSM, the point source is excited by the laser beam, and the emitted ﬂuores- cence is detected and translated to electronic signal. In confocal microscopy, the resolution limit is determined by the waists of the observation volume (or simply the PSF), ωxy and ωz, as deﬁned by the Rayleigh criterion (Equation (2.21)). This means that the smallest object in the reconstructed confocal image is actually the convolution of the point source with the PSF, and that information below the resolution criteria cannot be resolved between adjacent pixels. Thus, information below the resolution criteria will be correlated between close pixels.

The concept that there is hidden correlated information between the pixels was introduced by Petersen and Wiseman in 1993, who introduced a technique known as Image Correlation Spectroscopy (ICS) (known also as Image Correlation Microscopy (ICM)). By using computer analysis of the 2-D ACF of images acquired by raster CLSM, ICS was shown to give statistical information about the number of particles in the sample [133].

Figure 2.9 shows a schematic illustration of convolution by raster LSCM. 2.3. Principles of Image Correlation Spectroscopy (ICS) 44

Raster scan

Reconstructed image

Smoothed Image

Figure 2.9: Convolution of point source in raster LSCM. The laser beam horizontally scans the sample that contains a fixed point source (the red diamond shape). The point source is excited, and the emitted fluorescence is detected and translated to an electronic signal. Since the mirrors that control the raster scan are coordinated with the collected intensity at any specific time, computer software divides the intensity into discernments, and gives each pixel a value. Pixel by pixel the confocal image is reconstructed, and the point source is spread over a number of pixels (the pixelated shape in the middle of the figure) as a consequence of the convolution. Over sampling (i.e. - capturing a series of images over time and averaging the series) will give a smoother image with a perfect airy-disk shape as predicted by Rayleigh criterion. The figure was adopted from [74]. 2.3. Principles of Image Correlation Spectroscopy (ICS) 45

2.3.2 The 2-D ACF

The 2-D ACF is the extension of the 1-D ACF presented in FCS (section 2.2). While in FCS the 1-D ACF describes the temporal laser signal, in ICS the 2-D ACF describes images, which can also be regarded as a 2-D matrix:

G(ξ, ψ) = hδI(X,Y ) · δI(X + ξ, Y + ψ)i I(X,Y ) − detected intensity at each pixel from matrix (image/ROI) δI(X,Y ) − ﬂuctuations around the mean intensity of the image (2.29)

Similar to FCS, the 2-D ACF can be calculated in two manners: brute force and through the 2-D Fast Fourier Transform. When brute force is used to calculate the 2-D ACF is represented by:

for speciﬁc t : 1 PX PY I(X,Y )I(X+ξ,Y +ψ) X·Y k=1 l=1 g(ξ, ψ)t = h 1 i2 − 1 (2.30) PX PY I(X,Y ) X·Y k=1 l=1 t − frame number

This matrix is shifted relative to the original image and the shifted and original images are multiplied and the result summed. Where X-axis is the horizontal axis (parallel with the scanning direction), and Y-axis is the vertical axis. This process is repeated for all possible magnitudes of shift (the maximum magnitude of shift is limited to the largest dimension of the image) in all possible directions. The complete expression of the ACF after its normalization with the spatial mean intensity is:

G(ξ, ψ) g(ξ, ψ) = − 1 (2.31) < I(X,Y ) >2 2.3. Principles of Image Correlation Spectroscopy (ICS) 46

A more convenient way to calculate the 2-D ACF is to use the 2D-FFT. This method also has the advantage that it enables application of frequency ﬁlters which are essential for RICS (Equation (2.32)):

h i G(ξ, ψ) = f −1 [f (I(X,Y ))] · (f (I(X,Y ))) (2.32)

Generally, it is better to minimize the noise originating from the contribution of random correlations to obtain an accurate estimate of the ACF. This can be achieved by averaging the normalized ACF over a number of images [134]. In contrast to the spatial correlation due to the effect of the convolution by PSF, random shot noise is not correlated between adjacent pixels, and appears at zero time lag [135]. Therefore, by ﬁtting the ACF to a theoretical shape which is dictated by the PSF, random noise can be discounted.

2.3.3 ICS ﬁtting model

The two-dimensional ACF in ICS gives the dominant spatial correlation in the image which is the result of the convolution of the point sources with the shape of the focal volume, which is commonly assumed to have a Gaussian shape. Therefore, the normalized ACF has to be ﬁtted to a Gaussian shape:

(ξ2+ψ2) − ω2 g(ξ, ψ) = g(0, 0)e xy + g∞ (2.33) where g∞ express the offset constant for the possibility of long range spatial correlation. The peak of the ACF after the ﬁtting gives the number of particles without counting the noise in the image (Equation (2.34)). 2.3. Principles of Image Correlation Spectroscopy (ICS) 47

g(0, 0) = lim lim g(ξ, ψ) = 1 (2.34) ξ→0 ψ→0 Veff ·hCi | {z } 1 hNpi

The ACF amplitude, the g(0,0), is equivalent to the g(0) in FCS ((2.25)), and is proportional to the inverse of the average number of the particles in the image.

2.3.4 Advances in Image Correlation Spectroscopy

ICS provides information about the number of particles within an image. How- ever, it does not provide information about the dynamic properties of the ﬂuo- rophores in the sample. However, in the last 10 years there has been extensive development of ICS-based techniques to exploit the spatial-temporal correlation in images from commercial CLSM to retrieve quantitative information about the ﬂuorophores dynamics. These concepts were mainly contributed by Wiseman and coworkers (McGill University, Montreal, Quebec, Canada), who developed a series of ICS-based techniques.

An example of an ICS-based technique is Spatial-Temporal Image Correlation Spectroscopy (STICS), which gives spatial-temporal maps of macromolecules dynamics by calculating the temporal correlation of the spatial correlation of aggregations of fluorescence proteins within living cells. If the motion of the molecules is non-isotropic (i.e. - directed flow), STICS can extract the directional information over time points. It has been used to generate velocity maps of α- actinin in living CHO (Chinese Hamster Ovary) cells, were arrows gives the speed and direction of the α-actinin flow [136]. 2.4. Principles of Raster Image Correlation Spectroscopy (RICS) 48

2.4 Principles of Raster Image Correlation Spectroscopy (RICS)

Firstly, RICS was introduced by E. Gratton and M. Digman who noticed that there is an additional component to the ACF of ICS, in which the apparent diffusion coefficient of the fluorophores increases while the laser beam raster scans the sample. Briefly, this additional component was formulated and the RICS technique was than introduced with the aptitude to combine the capability of FCS to measure fast diffusion with the capability of ICS to obtain quantitative information about molecules from confocal images. Unlike STICS, RICS does not measure the direction of the flow, but rather measures the average diffusion coefficient due to Brownian motion of the fluorophores. Figure 2.10 illustrates the advantage of RICS through integration of FCS and ICS. While FCS is based on the 1-D ACF from single point locations, RICS is based on the ACF analysis from CLSM images in 2-D.

FCS ICS

Advantage Limitation Advantage Limitation Measure temporal correlation Data from single point Data is in 2D from CLSM Only spatial correlation of dynamic movement

RICS STICS Measure 2D spatio-temporal correlation of dynamic spatio-temporal 2-D ACF between the frames movement between pixels from CLSM images

Figure 2.10: RICS is a combination between ICS and FCS.

RICS has the capability to provide temporal and spatial information about the diffusion coefﬁcients and concentration of ﬂuorophores in solutions. Like FCS, 2.4. Principles of Raster Image Correlation Spectroscopy (RICS) 49

it is a non-contact measurement technique, and therefore is a non-invasive tool for studying dynamic processes within living cells. Evidently, RICS does inherit some of its limitations from FCS. Measurements in cell edges, the movement of the cells, and the dependency of the measurements on the size and shape of the observation volume all have a strong effect on the ACF (and the calculated diffusion coefficients). However, RICS also has some advantages over FCS. For instance, RICS has a better capability to filter out the immobile fraction. Moreover, it allows mapping the diffusion coefficient within living cells by generating spatial-temporal plots.

While STICS can also give spatial-temporal plots, there is a major difference between these two approaches. While STICS is based on temporal correlation between the ACF of a defined region over consecutive confocal images and therefore is limited to measuring relatively slow dynamics, RICS is based on the correlation of fluctuation between successive pixels and is used for faster diffusion coefficients.

The principle of RICS is that the ACF of the image collected by CLSM contains correlated information about diffusing fluorescence molecules in time and space domains. The key to understanding RICS is to note that CLSMs create images by raster-scanning the sample and collecting the intensity emitted from each point in a sequential manner. Hence, different points on the image are actually acquired at different times. Thus, if the CLSM picks up a molecule at a certain point I(X,Y) then there is a finite probability that the laser will pick up the same molecule at a later point delta I(X+ξ ,Y+ψ). The probability to detect the molecule depends on the PSF, scanning speed of the CLSM and the diffusion coefficient of the particle. Thus, analysing the statistics of the fluctuations in a CLSM image could provide information about the diffusion of the particles being imaged. RICS is a method for deriving this information by analysing the ACF of 2.4. Principles of Raster Image Correlation Spectroscopy (RICS) 50

the confocal image. If the fluorophores are not moving, the ACF will correlate only the spatial correlation due to convolution with the point source. Under constant scanning speed, as the diffusion coefficient of the fluorophores increases, the probability to detect the same particle at a different point will change. The ACF reflects the probability of imaging the same diffusing particles at two or more different points in the image. This probability depends on the diffusion coefficient of the particle. Hence, fitting the ACF to a RICS equation can give the diffusion coefficient.

Figure 2.11 shows a schematic illustration of the principle behind RICS. 2.4. Principles of Raster Image Correlation Spectroscopy (RICS) 51

Particle diffusing during raster scan

Less probability to detect the particle in parallel lines

Reconstructed image

Smoothed ACF

The probability to detect the particle is correlated in the ACF

Figure 2.11: The principle behind RICS. Similar to ICS, the laser beam raster scans the sample, which contains fluorescence particles. However, in RICS the assumption is that the fluorophore randomly diffuses and therefore its probability to be detected is correlated between adjacent pixels. This correlation is translated by using the ACF, and can be fitted to the theoretical RICS model to give the physical value of the diffusion coefficient. 2.4. Principles of Raster Image Correlation Spectroscopy (RICS) 52

2.4.1 Time and space domains in RICS

The Time domain in RICS is controlled by the scanning speed of the microscope. Since the ACF in RICS is two dimensional, the lag time accounts for the difference in time between the horizontal line and the vertical line (Equation (2.35)) [66].

τ(ξ, ψ) = τpξ + τlψ ξ − spatial displacements along X direction (2.35) ψ − spatial displacements along Y direction

Rather than using the lag time, τ, which is used in the 1-D ACF, τ l and τ p are multiplied in ξ and ψ, respectively. The pixel dwell time, τ p, indicates the time in which the signal to the detector is integrated to be displayed as a single point in the resulting image [74, 137]. The line time, τ p, is the time that it takes the laser beam to complete a scan of the full line.

2.4.2 RICS ﬁtting model for Brownian motion

The 2-D experimental ACF has to be fitted to the RICS model in order to yield the diffusion coefficient and concentration. The standard RICS model makes the same assumptions as the standard FCS model discussed in section 2.2. The RICS model has two components. The first RICS component assumes that the location of fluorophores changes in space and time, therefore the collected intensity fluctuates over time while the image is being reconstructed.

When the laser beam scans the sample with a suitable speed, each pixel gets a value that is different from the values of the pixels before and after it, but there is still correlated information between adjacent pixels, as explained in ICS for a case where the particles are fixed. As the diffusion coefficient of the fluorophores 2.4. Principles of Raster Image Correlation Spectroscopy (RICS) 53

is faster, there is less correlation between adjacent pixels and the frequency of ﬂuctuation will increase, as in FCS (Equation ((2.25) ). Equation (2.36) expresses the RICS Equation for a single photon laser and 3-D diffusion.

−1 −1/ 1 4D(τpξ+τlψ) 4D(τpξ+τlψ) 2 GD(ψ, ψ) = · 1 + 2 1 + 2 Veff ·hCi ωxy ωz (2.36) | {z } 1 hNpi

The second component is the correlation due to the raster scans and due to the spatial differences in concentrations, in a similar way to ICS but considering that diffusion can cause a broadening of the PSF (Equation (2.37)):

  1 [( 2ξδr )2 + ( 2ψδr )2] S(ξ, ψ) = exp − 2 wxy wxy (2.37)  4D(τpξ+τlψ)  (1 + 2 ) wxy

The overall RICS expression that was used in this thesis is:

G(ξ, ψ) = GD(ξ, ψ) · S(ξ, ψ) (2.38)

A graphical 2-D image that illustrates this function is presented in Appendix A.5.

2.4.3 Advances in RICS

Returning back to the Jablonski diagram, the ﬂuorophores can also go through a process that is known as intersystem crossing, which means a nonradiative transition between different electronic spins. This process leads to a triplet 2.4. Principles of Raster Image Correlation Spectroscopy (RICS) 54

electronic energy level, and results from saturation in the total number of high- energy states, which leads to energetic instability. The duration of this transition is in µs-ms, and it causes the ﬂuorophore to blink. [118, 138].

Several improvements and extensions have been made to the RICS technique in the last two years. For instance, a third component known as the ”time dependent” component was introduced by Digman et al. in 2009 [66] to consider the contribution of additional ﬂuctuations in ﬂuorescence while the molecules enter and leave their triplet states. Equation (2.39) expresses the time dependent component:

−(τpξ+τlψ)/τ GT (ξ, ψ) = 1 + Ae A − fraction of blinking molecules (2.39) τ − characteristic time

The temporal change in the intensity of the fluorophore can occur either due to conformational changes of the molecule that alter its fluorescence, or due to blinking, which naturally occurs in some fluorophores. For example, quantum dots exhibit significant blinking when they fluoresce [139]. The ”time dependent” component was not applied in this thesis. However, it does emphasize the idea that the standard RICS model is not always sufficient, that there is still a place for improvements and considerations of biophysical effects, and that modelling of correction factors is a standard procedure. As will be shown next in this thesis, a similar idea of applying RICS in conjunction with photobleaching phenomena to detected fluorophores diffusion can be applied by using more sophisticated modelling.

Another improvement was introduced in 2008 by Digman et al. who demonstrated that by dividing an image into a grid of overlapping regions and applying 2.4. Principles of Raster Image Correlation Spectroscopy (RICS) 55

RICS to each region, they could create spatial-temporal maps of diffusion of EGFP-paxillin in Chinese Hamster Ovary cells [60]. These results were veriﬁed by using complementary techniques such as: scanning FCS, temporal ICS and Photon Counting Histogram analysis (PCH)[60].

2.4.4 Cross correlation approach in FFS

One particular development in FFS is the highly desirable approach of Fluores- cence Cross Correlation Spectroscopy (FCCS) technique to measure functional associations of two different fluorophores by correlating their two ACFs, and its biological applications to measure protein-protein interactions within living cells [125, 140–143]. Image Cross Correlation Spectroscopy (ICCS) is the analogous to FCCS based on the 2-D ACF similar to ICS. ICCS was used to generate spatial maps of the dynamic interaction between actin and its bundled protein, α-actinin, to the leading edge of a migrating cell [144]. In more recent times cross correlation between vinculin, focal adhesion kinase (FAK), and paxillin tagged with fluorescence proteins within living Mouse Embryonic Fibroblasts (MEF) cells was demonstrated by employing Cross Correlation RICS (cc-RICS) to study protein complexes [66, 67]. Although very novel, cc-RICS is likely to prove extremely powerful in dissecting the relationships between protein interactions and biological processes. As compared with the often-misleading observations of co-localization of two proteins, finding that diffusion properties are identical in a given region of the cells is likely to be very strong evidence that they physically interact. 2.5. Summary 56

2.5 Summary

The importance of fluorescent imaging to study biological questions by using fluorescence proteins was emphasized. In addition, the advantages of several FFS were discussed. Yet, more advances in this field are required before it will become a standard routine in cell biology, and will reach to its maximum potential. RICS was introduced as a novel technique, and its principles were explained. This theoretical background helps to understand the concept of this thesis. Chapter 3

Materials and Methods

3.1 Conditions for Cell Maintenance

3T3 cells (fibroblast cells from mouse embryo tissue) were maintained in ◦ humidified, 10% CO2 at 37 C in standard Dulbecco’s Modified Essential Medium (DMEM) supplemented with 10% v/v Fetal Bovine Serum (FBS) and a final concentration of 3 mM GlutaMAX (Glutamine, Gibco BRL, Invitrogen Corp. Life Technologies, CA, USA). Cells were harvested with trypsin and passaged to maintain exponential growth. BaF3 cells (naive pro B cells) were maintained

◦ in humidiﬁed, 5% CO2 at 37 C in RPMI medium (GIBCO,11875-093) supplemented with 10% Fetal Bovine Serum (FBS), 10% v/v WEHI 3BD conditioned medium (contains IL-3, supplied by Andrew Clayton from Ludwig Institute for Cancer Research) and 1.5 mg/ml geneticin (G418, Gibco). The cells were frozen in FBS containing 10% Dimethyl sulphoxide (DMSO, Sigma), stored in liquid nitrogen, and were thawed and cultured for a week prior to any experiment.

57 3.2. Plasmid DNA 58

3.2 Plasmid DNA

The DNA was extracted from E.coli and was puriﬁed with a Qiagen plasmid maxi kit (Qiagen GmbH, Hilden, Germany) by Kim Pham from Peter MacCallum Cancer Centre, Melbourne, Australia. pEYFP-βPIX and pEYFP-βPIX∆CT (also known as pEYFP-βPIX-DSTOP) plasmids were constructed by Kim Pham and the pEYFP plasmid was purchased from Clontech (Clontech Laboratories, USA).

Figure 3.1: βPIX and βPIX∆CT plasmids. The βPIX plasmid has three Src homology domains (SH3) that interact with sequences rich in proline residues of PAK, GIT and PLC. The DH is Dbl homology domain that interacts with Cdc42 and RAC. PH is Plec homology domain. T1 domain inhibits GEF activity. PR is proline-rich region. GBD is GIT binding domain. CC domain contain leucine zipper that mediates βPIX dimerization. The last domain is the PDZ domain- binding motif that interacts with the PDZ domain of Scribble is located at the carboxyl terminus. While the wt-βPIX has the (-TNL) site, βPIX∆CT stops at (-D) and lacks the (-TNL) site of binding to Scribble. The domain map was adapted from [23]

3.3 Antibiotic Titration

The pEYFP, pEYFP-βPIX and pEYFP-βPIX∆CT plasmids contain the gene for neomycin resistance for positive selection with G418. In order to determine the optimal concentration of G418 for selection of transfected cells, cells were plated at 1×105 cells/well in a Cellstar R 6-well plate (Greiner bio-one, Frickenhausen, 3.4. Cell Transfection 59

Germany) and cultured for at least 24 hours to achieve 80% conﬂuency. G418 was added at different concentrations and was refreshed every two days. The cultures were checked daily under transmission light microscope and the survival rates of the cells was assessed by subjective judgment of the cells appearance. The optimal concentration of G418 that achieved rapid killing of the cells was 1000 µg/ml. This optimal concentration of G418 was determined to be sufﬁcient to use for selection of transfected cells.

3.4 Cell Transfection

3T3 cells were plated at 1×105 cells/well in a Cellstar R 6-well plate and were cultured for at least 24 hours to achieve 80% conﬂuency under same condition as the culture at the section 3.1.

Transfections were achieved by using metafectene (Biontex Laboratories GmbH Munich, Germany) at a 1:3 ratio of DNA to metafectene, respectively. Metafectene was incubated with DMEM (not supplemented) for 5 minutes at Room Temperature (RT) and 500 ng of DNA was added to the metafectene mix, followed by another 15 minute of incubation in RT. The diluted mixture was added drop wise to the plated cells. After one hour, G418 was added for positive selection and was refreshed every two days.

3.5 Preparation of Cell Lines

The transfected cell lines were cultured with G418 until they reached 100% conﬂuence then sorted by Fluorescent Activated Cell Sorting (FACS) for YFP ﬂuorescence expression level on DiVa (Becton Dickinson, NJ, USA) for two rounds of sorting. The bulk population of βPIX∆CT was single cell cloned in 96 3.6. Western Blotting 60

ﬂat-well cell culture plates. When the cultures reached 80% conﬂuence, random clones were selected and expanded. Expression levels of the clones were checked by DiVa FACS and analysed using Flow Cytometry Software (FCS express v3.0 software, Becton Dickinson). At the end of the process, FACS and Western blot were used to characterize the three cell lines.

3.6 Western Blotting

Sample preparation

Whole cell extracts were prepared from 106 to 107 cells/ml of media. The cells were incubated in NETN lysis buffer (see appendix B) that contained (1 tablet/10 ml) Complete Mini protease inhibitor cocktail (Roche Diagnostics Australia, NSW, Australia) for 15 minute on ice. The lysates were cleared by centrifugation at 15.7×103 relative centrifugal force (rcf) for 15 minutes at 4◦C and the supernatants were aliquoted into clean Eppendorf tubes. The supernatants were used immediately or stored at -80◦C.

Determination of protein concentration

A colorimetric assay was used to determine protein concentration in the super- natant using the Bio-Rad DC Protein Assay Reagent kit, according to manufacturer’s instructions (BIO-RAD laboratories, Hercules, Canada). The absorbance was read by spectrophotometer at 650 nm and the protein concentrations were calculated with SoftMax Pro v5.2 software (Molecular Devices Corp., Downington, PA). 3.6. Western Blotting 61

Gel electrophoresis and transfer

Lysates were diluted with lysis buffer to generate equivalent concentrations of 30 mg protein per loading well in the SDS gel. Reducing 5×loading buffer (see appendix B) was added to the dilution (in 5:1 ration v/v). This mixture was incubated for 5 minutes at 95◦C and then was loaded to 9% SDS PAGE (see appendix B). The proteins were resolved for 1 hour in 100 Volts at RT with SeeBlue R Plus2 (Invitrogen) as a pre-stained standard.

Transfer

The proteins were transferred for one hour in 100V at 4◦C in wet Bio-rad elec- trophoretic transfer cell containing transfer buffer (see appendix B) to Immobulon- P (PVDF) membrane (Millipore Corp., MA, USA) wetted with methanol.

Detection

Membranes were blocked in blocking solution (5% w/v Skim milk powder (Diploma, Mount Waverly, Australia) in PBS that contained 0.05% v/v Tween- 20 (Polysorbate 20, Sigma-Aldrich, MO, USA)) for one hour rotating at RT. Membranes were probed with the appropriate primary antibodies (see Table 3.1) in blocking solution for one hour at RT or overnight at 4◦C. The membranes were washed in 0.05% v/v Tween-20 in PBS three times over 15 minutes and incubated with cognate Horse Radish Peroxidase (HRP) linked secondary antibody (see Table 3.2) in blocking solution for 30 minutes at RT. The membranes were washed in 0.05% v/v Tween-20 in PBS three times over 15 minutes.

The proteins were detected by using Enhanced Chemiluminscence (ECL) western blotting detection kit (GE Healthcare, Buckinghamshire, UK) according 3.7. Antibodies 62

to manufacturer’s instructions and visualized by autoradiography using X-ray ﬁlm (Fujiﬁlm Europe GmbH, Heesenstrasse, Germany).

3.7 Antibodies

Both primary and secondary antibodies for Western Blot (WB) were diluted in western blocking solution (PBS contained 5% w/v Skim milk powder and 0.05% v/v Tween-20). The antibodies dilutions are presented in Table 3.1.

Table 3.1: Primary antibodies

Antigen Source Supplier WB βPIX Rabbit Chemicon Int., 1:200 polyclonal Billerica, MA GFP Rabbit Supplier 1:3000 polyclonal α-tubulin Mouse Supplier 1:1500 monoclonal

Table 3.2: Secondary antibodies

Reactivity Fluorochrome Supplier WB sheep anti mouse HRP GE Health care 1:10000 Donkey anti rabbit HRP GE Health care 1:10000

3.8 Preparation of Microscope Samples

Preparation of ﬂuorescent samples

A template of wells was punched in a double-sided sticky tape that was attached onto 25 mm×75 mm×1 mm glass microscope slides (Esco, Biolab Scientiﬁc). 3.8. Preparation of Microscope Samples 63

Each well was used to contain 6.5 µl ﬂuorescent solution sample for microscope imaging. The slide was sealed with 24 mm×50 mm glass covered slips (Esco). Three kinds of samples were prepared:

1. GFP (molecular weight of ≈27 kDa, Invitrogen) diluted in PBS-glycerol solution, ﬁnal concentration 44 nM at pH=7.4 . The collected emission wavelengths for the GFP sample were chosen automatically by λ-scan emission spectra with increments of 10 nm.

2. Poly(N-vinyl pyrrolidone) (PVPON, molecular weight of 21 kDa, contributed by Melbourne University, VIC, AU). PVPON was covalent bonded to Alexa R Fluor dye 488 nm, (molecular weight of ≈0.64 kDa, Molecular

Probes, Invitrogen), and diluted in dH2O, ﬁnal concentration 5 µM. The collected emission wavelengths for the Fluor dye 488 nm were chosen according to the manufacturer’s instructions.

Figure 3.2: Molecular structure of PVPON.

Polymer chain of PVPON covalent bonded to Alexa R Fluor dye 488 nm (AF488) to one of its attachment sites.

3. Green-yellow ﬂuorescent polystyrene sub-resolution 0.1 µm diameter microspheres (Duke Scientiﬁc Corp., Palo Alto, California, USA) were diluted

in dH2O or glycerol-dH2O solution to a ﬁnal concentration containing 7.8×10−3% solid (1:128 dilution between the stock (containing 1% solid)

and dH2O/glycerol-dH2O solution, respectively. Excitation maxima λ=468 3.8. Preparation of Microscope Samples 64

nm, emission maxima λ=508 nm. The density of microspheres is 1.05 g/cm3.

In order to control the solutions viscosity, the solutions were made in different concentrations of glycerol (LabServ Biolab). The viscosity of water/glycerol mixture was interpolated from the Dorsey sheet [145]. Samples were assumed to be at 37◦C. Prior to imaging, the samples were stored at 4◦C in the dark to prevent photobleaching.

Preparation of biological samples

3T3 cells were plated at 5×103 cells/well on 35 mm optic glass bottom dishes (Matek, MA) and were cultured for 24 or 48 hours as in 3.1.

BaF3-EGFR-EGFP is a cell line that over expresses EGFR (epidermal growth factor receptors) fused by its carboxyl terminus to EGFP. This line was supplied by Andew Clayton from Ludwig Institute for Cancer Research. The cells were grown at a concentration of 1×106 cells/ml, and were serum-starved for 5 hours prior to the experiment. Cells were collected by centrifugation, and resuspended at 1.25×106 cells/well. To immobilize the cells, 5×104 cells/ml were transferred onto 35 mm optic glass bottom dishes (Matek) containing soft agarose mix (0.8% w/v agarose (Promega, Corp., Madison Wl, USA) and 1% w/v BSA in PBS. This concentration of agarose was found to restrict cellular movement without compromising cell viability. The ratio between the medium and agarose mix was 1:5 respectively. The agarose mix was pre-warmed in a microwave to 45◦C and then cooled to 37◦C before the cells were pipetted to the bottom of the dishes to penetrate the agarose layer. The cells which were located between the glass and the agarose were randomly chosen for RICS measurements. The BaF3 were imaged under similar conditions as the 3T3 with three exceptions: Firstly, since 3.9. Microscope Setup 65

movement of large receptor aggregations (larger then the PSF) were observed, the focus was manually adjusted to be at the cell membrane ring (the cross section was exactly at the centre of the cell). Secondly, the zoom factor was increased as the BaF3 are smaller then 3T3, allowing to increase the resolution into approximately 30 nm pixel widths. Finally, both the excitation line and emission spectrum were chosen differently, as the BaF3 expressed EGFP and not EYFP as in the 3T3 lines.

3.9 Microscope Setup

Data for RICS experiments was acquired with a Leica TCS SP5 multispectral commercial CLSM (Leica Microsystems CMS GmbH, Germany) in direct mode, controlled by LAS AF v2.0 software interface. It is multispectral in the sense that it contains optical components that enables the user many degrees of freedom in determining the spectra of the excitation illumination and detected emission. The unique components incorporated in the system enable fast switching between different excitation sources and flexible determination of the spectra detected on each of the five PMTs in the system. Thus, the SP5 can provide detailed information on the spectrum of fluorescent emission thereby enabling FRET, and possibly cc-RICS measurements in the future.

Three special optical components allow the Leica SP5 its special feature of multispectral confocal imaging: an Optical Tuneable Filter (AOTF), an Acoustic Optical Beam Splitter (AOBS), and the Spectrophotometer detection apparatus (SP) [146, 147]. These components are coupled and work synchronously together, as shown in Figure 3.3.

Both the AOTF and the AOBS are based on the same approach of generating an acoustic-optical ﬁeld within piezoelectric crystal (i.e.-quartz) while the poly- chromatic light is passing through the crystal. When the crystal is excited by 3.9. Microscope Setup 66

a modulated ultrasonic wave field, local changes in its refractive index result in the formation of an effective diffraction grating that deflects the passing light in a wavelength-dependent manner. A wavelength is deflected, dependent on the period of the grating, which is determined by the frequency and intensity of the ultrasonic excitation. Thus, by controlling the ultrasonic frequency and intensity within the crystal, and selecting the light deflected at a certain angle from the crystal, it is possible to select the wavelength of choice. [74].

The AOTF is an adjustable quartz crystal that is acoustic-optically modulated to select the speciﬁc wavelengths of the excitation. One important advantage of the AOTF is that it can be switched very rapidly, thereby enabling the selection of multiple active excitation laser lines for acquisition of a single frame. Secondly, the AOTF can be used to adjust the percentage of the laser intensity passing through. It is important to note, that the AOTF control does not affect the laser power from its source [74, 146].

The AOBS is a novel beam splitter that was introduced in 2002 by Leica to replace the dichroic mirror and to improve the separation between the illumination and the detection paths [146]. It works by exciting the piezoelectric crystal with a signal that is the sum of several speciﬁc frequencies, thereby enabling diffraction of several wavelengths simultaneously. Thus, the AOBS allows simultaneous detection in multi ﬂuorescence channels [146].

The last optical apparatus that allows of multispectral detection is the spectrophotometer detection module. This module comprises a prism that disperses the emission into a moveable mirror that directs the light into tuneable slits placed in front of the PMTs. These slits are mechanically adjustable to any position in the spectrum. By adjusting the width of the slits, it is possible to determine the spectral band to be collected by the PMTs [148]. 3.9. Microscope Setup 67

Figure 3.3: Scheme of Leica TCS SP5 components relevant to this thesis work. Excitation light arrives from the Laser sources (1-3) and its intensity is controlled by an Acoustic Optical Tuneable Filter (AOTF), which is controlled by the LAS AF v2.0 software(4-6). The laser beam is reﬂected by an Acoustic Optical Beam Splitter (AOBS) (8) and scan the sample through the scanner and calibration target units (10-11). The beam is focused into the sample by the objective and the emitted ﬂuorescence light is collected by the same objective. The collected light passes through a pinhole (16), which eliminates all light emitted from outside the focal volume. After passing the detection pinhole, the light emitted from the focal plane is passed through a spectrophotometer prism (19). The light continues from there to the PMTs, which are mounted with slits that can be widened or narrowed to determine the portion of the spectrum collected by each (PMT) (20-24). Figure was printed from [123] with permission. 3.10. Data Processing and Manipulation 68

The microscope is enclosed in an environmental chamber that keeps a constant

◦ temperature of 37 C, humid, and constant concentration of CO2/O2 gas mixture around the microscope stage. The image acquisition was 16 bit and the maximum upper limit of gray levels was set to 65,535. The ampliﬁer offsets were set to zero in all RICS measurements. The frequency of scanning was measured in lines per second (Hz). The power output of the laser was focused, and measured upon the objective for each laser settings with a power meter (Nova,Ophir Optronics Ltd.,Israel). The focus was found by using the “automatic optimal focus”option in the Leica LAS AF software. For all RICS measurements a glycerol immersion objective was used (Leica HCX PL APO 63× / 1.3 NA GLYC). As will be shown in section 5.2, the Leica acquisition software kept the scan speed and line time constant during the image acquisition. These properties are required for proper RICS measurements [149]. However, another sensitivity problem was discovered in the Leica system. This issue will be discussed in more details next in this thesis.

3.10 Data Processing and Manipulation

Tagged image file format (.Tiff files) were exported by LAS AF v2.0 software, and were merged by time sequence order to multi-images files by using the ImageJ v1.41a macro language. ImageJ is free software for quantitative image analysis that is JAVA based and is useful for many quantitative image processing calculations [150].

Confocal images were processed using the RICSIM program, which stands for RICS analysis and simulation. RICSIM is a custom RICS program written in a Matlab environment (MatlabR2008a version 7.6, The MathWorks, Inc). The ACF was calculated based on the Wiener-Khnichin theorem to reduce the amount of computation time, as described for ICS by Petersen et al. 1993 [133]. RICSIM 3.10. Data Processing and Manipulation 69

implements the RICS technique with a Graphical User Interface (GUI) based on Matlab-GUIDE especially for this thesis. A screen capture of the RICSIM GUI can be seen in appendix D. An explanation about how RICSIM works is presented in the next chapter. The Matlab toolboxes that were used in RICSIM are the Image Processing Toolbox for the background and cells filters, the Optimization Toolbox for fitting procedures and the Spline Toolbox for polynomial fitting to generate smoothed diffusion maps. Calculations were performed on a personal laptop equipped with a 2 GHz Intel CoreTM 2 Duo processor and 3GB of RAM. Calculation time for generating a smoothed diffusion map of cells and for calculating the average diffusion coefficient for a group of 10 cells is between 5 and 10 minutes, depending on the available computer resources. Chapter 4

Computational Implementation of RICS by the RICSIM software

4.1 Introduction

Previous RICS measurements were achieved by using commercial CLSMs, such as the- FV300 and FV1000 systems (Olympus Inc, Japan), and the LSM 510 META (Carl Zeiss Inc, Germany), all in analogue mode employed with standard PMTs [58, 65]. These studies showed that RICS is not a straightforward technique, and several aspects regarding its sensitivity have to be considered before it can be applied to more precise measurements. For instance, the accuracy of the autocorrelation analysis was shown to be dependent on the system setup. Calculating the ACF under several different experimental conditions and ﬁtting the corresponding ACF to RICS equation yielded dramatically different apparent diffusion times [61, 135]. In addition, the PMTs of both the FV300 and the LSM 510 META systems have an inherent residual that is correlated in the ACF, and 70 4.1. Introduction 71

might affect the apparent diffusion time. This effect was mainly in the central horizontal (X direction) and vertical (Y direction) ACF pixels, and was noticed to increase with the scanning speed [61, 65, 135].

Recently, it was also reported by Gielen et al. (2009) that it might be better to utilize Avalanche photodiode detectors (APD) rather than PMTs for RICS measurements [65]. PMTs have a high dynamic range and noise-free signal ampliﬁcation and are generally the standard detectors in many research laboratories, while APDs are usually used in FCS applications due to their superior sensitivity over the PMTs [151]. However, the installation of APDs on commercial confocal systems is not practical in many labs, and therefore other approaches are required to gain more accuracy in RICS measurements using the PMTs in a direct analogue mode.

Hence, in the absence of published data about RICS measurements with the Leica SP5 (to our knowledge), it was a requirement to characterize the ACF obtained by the Leica SP5, and to establish a RICS routine that will allow precise measurements of diffusion coefficients within living cells. Such a characterization was even more necessary because of the sensitivity limit when performing RICS with the Leica SP5 was stated by E. Gratton, the inventor of RICS [152]. While the first problem that was mentioned in the RICS literature describes ”over- correlation”, potentially due to the sensitivity of the PMT detector, our Leica SP5 system had the opposite trend, and did not gave enough correlated pixels. As explained in Chapter 2 RICS relies on the relative intensity fluctuations generated by each single molecule. Consequently, such an effect will probably abate its sensitivity for RICS measurements. One possible explanation for the insufficient number of correlated pixels in the ACF is that while the Leica SP5 raster scans the sample in direct analogue mode by using standard PMT, fluctuations in intensity of the collected emission are partly averaged due to the detector time response, 4.1. Introduction 72

software manipulation, or possibly non-linear response of the detector [152]. Although the exact source of this problem has not been veriﬁed, we developed an approach to overcome this problem, as will be shown next in this thesis.

Measuring and characterizing intracellular diffusion in living cells presents additional challenges from both the biology and methodology aspects. For instance, the values of the diffusion coefﬁcients for different membrane proteins in different cells are highly variable [55], and therefore a large number of repeats is required to increase the accuracy of these measurements. Moreover, spatial correlations due to cell components can control the spatial-temporal correlation and therefore can interfere with accurate measurements [61].

To handle these challenges, we had to gain a better understanding of the precision limitations of our SP5 system when used for RICS measurements. Therefore, we aimed to develop generic procedures that would enable us to derive quantitative data from RICS-like analysis of images acquired with the SP5. At the same time, we wanted to identify factors related to imaging and image processing that might introduce artifacts into RICS measurements in general, and develop imaging and image processing techniques that would help to negate these effects. Since our ultimate aim was to perform RICS measurements in living cells, the methodologies we used were developed to enable efﬁcient examination of artifacts that could arise when testing cellular samples.

The methodologies we developed involved statistical analysis of RICS-like measurements performed on large image sets of cells and well-characterized ﬂuorescent solutions. RICSIM is a software package we developed to perform the autocorrelation analysis in automated manner. It implements the RICS theory and has the ability to efﬁciently handle large data sets, thereby enabling rapid analysis of the large image sets we used in this study. The aim of this chapter is to describe 4.2. General RICS Procedure 73

the general RICS procedures we used and the computational implementation of RICS by RICSIM.

Section 4.2 of this chapter will describe the general routine for RICS analysis that we adapted to measure diffusion within living cells. This routine will be used to measure diffusion coefficients EGF-EGFR in BaF3 Cells in section 5.5, and to measure diffusion coefficients of EYFP, EYFP-βPIX and EYFP-βPIX∆CT within a 3T3 cells in Chapter 6. We will also provide a detailed description of the (RICSIM) package and its algorithms that were designed to solve problems that are specific for living cells in section 4.3.

4.2 General RICS Procedure

The ﬁrst step in the RICS analysis was to load a sequential series of 2-D images of the sample. As an example, a representative frame from an image series of a 3T3 cell expressing EYFP is presented in Figure 4.1a. The acquisition of the images had to be under an optimal RICS measurement framework, which usually required a high NA objective. Further discussions about optimal setup are in Chapter 6. Figure 4.1 demonstrates the RICS routine we used on living 3T3 cells expressing EYFP.

Tiff images are exported into RICSIM for analysis. Tiffs are high-quality graphics files that can contain multiple images (referred also as stack files). Tiff files contain the raw data in a lossless compression format, which is important as RICS relies on small fluctuations that would be smoothed out if a lossy compression algorithm were applied to the images. Next, a Region Of Interest (ROI) within the images is chosen for analysis. Figure 4.1a shows an image of the EYFP fluorescence intensity expressed in a 3T3 cell with a blue square defining the ROI to be analysed. A magnified image of the ROI is shown in Figure 4.1b. 4.2. General RICS Procedure 74

(a) EYFP cell (b) Selected ROI

Figure 4.1: An example of the RICS analysis for EYFP expressed in living 3T3 cell. (a) representative frame out of a series of a 3T3 cell expressing EYFP; (b) the ROI that was selected by the user is reﬂected by the blue bordered square at (a); (c) image after applying immobile subtraction; and, (d) ACF for the selected ROI. Images were collected using: Laser power (Multi-ion Argon, visible): 50%. AOTF (λexcitation=514 nm): 40% [90 mW]. Emission band collected:523-537 nm. Gain: 1000 V. Pinhole diameter: 130 µm. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 60 nm × 60 nm [zoom factor of 8]. Images size: 512 × 512 pixels [30.8 µm × 30.8 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. MA subtraction: 10/15. Total time: 73.4 s. Resolution: 16 bits. 4.2. General RICS Procedure 75

The ROI has to be 2n × 2n pixels in size, where 2n is limited by the number of pixels in the image. The reason for this requirement will be explained later in this section.

When working with living cells, the ACF contains the intensity correlation that arises from the fluctuations of the moving molecules together with the immobile structures component. It is a requirement to filter out the spatial correlation due to the immobile structures prior to the RICS analysis; otherwise, the obtained diffusion coefficient will be lower than the real value [58, 59].

The next step of RICS analysis is to apply an immobile subtraction algorithm to ﬁlter out cellular components such as cell organelles (i.e. - mitochondria, endosmose, Golgi) and cell structures (i.e.- cell edges, protrusions, protein aggregations, large multimolecule complexes, internal networks), which have spatial structures that could dominate the ACF if not removed properly. This can be achieved by using the next two complementary ﬁltering stages:

The first filtering stage is called Moving Average (MA) subtraction. Each processed frame for the entire stack file is calculated by subtracting its value with the updated cumulative Moving Average subtraction of (ii-1)/2 frames, where ii is the index image before and after the current frame (the MA value). The MA value has to be adjusted accordingly to the cells movement: if the cell movement is fast it is less likely that cell will stay at the same position between successive frames. Therefore, there is no point to subtract many images before and after the index image, and smaller MA value should be applied. The internal loop (jj) is used to calculate the updated cumulative MA subtraction. The average pixel of the updated cumulative MA subtraction is added to the subtracted frame to prevent decreasing of intensity in the obtained image [61]. Although the amplitude of the ACF is normalized after the MA subtraction ends, it was found that adding 4.2. General RICS Procedure 76

the average pixel of the updated Moving Average subtraction is essential for appropriate subtraction. Mathematically, it is expressed by:

N− MA value I +I I +I P 2 Pii+MA value h (jj−1)i jj h (jj−1)i jj I = MA value jj=ii+ MA value I(ii) − JJ + JJ ii= 2 2 I− subtracted stack ii, jj− Image index N− Nuber of images MA value− user input

I(ii)− image ii before subtraction

hI(jj−1)i+Ijj JJ − updated moving average hI(jj−1)i+Ijj JJ − average pixel for moving average (4.1)

Figure 4.1c shows a representative image out of the new subtracted series. It can be seen that the cell looks uniform with fewer visible cell components. While the spatial correlation due to the cell components was mostly eliminated, the fluctuations due to the diffusion are mostly kept. However, some components are still visible in the image, and could influence the ACF, which is the basis for deriving diffusion coefficients using RICS. Therefore, additional filtering to eliminate the unwanted correlation due to cellular features is required.

To this end, we note that RICS is based on analysis of fluctuations in intensity that occurs on the scale of several pixels, whereas the cellular features appear on much larger scales. Hence, RICS analysis is based on the analysis of high-spatial frequencies within images, whereas the background features appear in lower spatial frequencies. Hence, it should be possible to filter out the background by applying a high-pass filter to the images. This filter will suppress all low frequency 4.2. General RICS Procedure 77

components in the image, thereby suppressing all cellular components. If designed properly it should leave all the information required for RICS unscathed. The first step in applying such a filter is to determine its cut-off frequency, which is the frequency below which the filter suppresses all spatial frequencies.

One method for determining this frequency is to observe the Power Spectrum Density (PSD) of the image. The PSD shows the distribution of spatial frequencies within an image. It is calculated by multiplying the Fourier Transform of an image with its complex conjugate, to give frequency domain images. The power spectrum is widely used in image analysis. It is one of the most powerful tools used in RICSIM. It can be used to determine a cut-off frequency, below which all spatial frequencies present in the image are set to zero, thereby eliminating residual cellular structures that could affect RICS measurements. In the RICSIM software, as the cut-off frequency increases, more points from the central power spectrum (low frequencies) are ignored. This comprises the second filtering stage, in which we apply a high pass filter to the acquired images (also named as high spatial frequency mask)[153]. An example of an image of cell after high pass filtering will be shown in section 6.3.9.

When no high pass ﬁlter is applied to images, the ACF will be dominated by the shape of the cell. For example, the ACF of BaF3 cells will be round, while the ACF of 3T3 cell will be less deﬁned. From experience after adjusting the cut-off frequency to around 1000 pixels (the 1000 central pixels from the power spectrum were set to 0) for a 512 ×512 pixels image, the dominant shape of the cell and the characteristic spatial correlation of the receptor aggregations are removed from the ACF (section 5.5). For cytoplasm proteins in 3T3, it was found that by setting the cut-off frequency value to approximately between 400 to 500 pixels we eliminate most of spatial correlation due to cell components (section 6.3.9). On the other hand, increasing the cut-off frequency value gives 4.2. General RICS Procedure 78

higher diffusion coefﬁcients than expected. Hence, adjustment with a well-known standard is required. Experience showed that applying this ﬁlter is a requirement for accurate measurements, as will be shown in section 5.5.

The next step in the RICS analysis is to calculate the ACF according to the Wiener-Khinchin theory (Eqation 2.32). Once the low frequency has been filtered from the power spectrum, the real part of the Inverse FFT2 of the filtered power spectrum gives the ACF. To shift the zero-frequency component to the centre of the spectrum, the Matlab function FFTSHIFT is used. This ensures consistency between different ACFs, which will allow a quantitative fitting procedure and easier comparison. As noted above, there is a requirement for the region of interest to be 2n × 2n pixels size, where is n=5,6,7 This requirement is derived from the quadratic operation of FFTSHIFT that centres the ACF on the symmetry axes of the image. Figure 4.1d shows the corresponding ACF of the selected ROI. Figure 4.2 illustrate RICSIM fitting flowchart. 4.2. General RICS Procedure 79

RICSIM flowchart

User selection Input Images to correlate Microscopy Images (*.Tiff) Immobile filters: · MA subtraction · High pass filter Grids size ROI size Microscopic parameters · Pixel size · Line time User selection · Pixel time Parameters: · Estimated Diffusion · · PSF waist Normalization mode · Pixels to ignore · Pixels to fit Fitting mode · Original RICS · Original RICS+ blinking (+ find A and tau) Calculate 2D ACF Type of fitting inside_power=fft2(RREAD).*conj(fft2(RREAD)); · 2-D surface ACF=fftshift(real(ifft2(inside_power))); · Horizontal ACF (X axis) · Vertical ACF (Y axis)

Fitting Least-squares fitting with Matlab lsqcurvefit function

Diffusion Residual, R-squared

Figure 4.2: RICSIM fitting flowchart. Tiff images of diffusing fluorophores visualized by confocal images are exported. By knowing the properties of the confocal system that was used while the image acquisition, and by fitting the experimental ACF into theoretical RICS model, information about the diffusion of the fluorophores can be derived. 4.2. General RICS Procedure 80

The last step in RICS analysis is to fit the ACF to the assumed RICS model that gives the physical values of the diffusion coefficient. However, in some cases fitting the experimental ACF to the theoretical model is not a straightforward procedure, and the assumptions of the dynamic properties of the fluorophores and the geometry of the detection region that were shown in section 2.2.3 for FCS can lead to inaccuracies [154]. Figure 4.2 shows the fitting flowchart of RICSIM. The result of the fitting gives the average diffusion of the fluorophores in the ROI.

Similar to Globals for Images, RICS gives the user the ability to define the type of fitting to be used- entire surface, vertical/horizontal ACF. Currently, three fitting modes exists in RICS- the original RICS equation; the original RICS equation with a blinking component; and the original RICS equation with a blinking component while the variables of the blinking components are not fixed during the fitting operation. The power value is regarded as the number of pixels masked from the power spectrum when the high pass filter is applied. Figure 4.3 shows fitting of the obtained ACF from Figure 4.1c with the standard RICS model (Equation 2.38).

Fitting the experimental ACF gives the diffusion coefficient and the residual between the experimental and the theoretical model. As can be seen there is a significant residual in the central horizontal axis, indicating a deviation between the experimental ACF and the used model. Nevertheless, the calculated diffusion value was close to the theoretical diffusion of freely diffusing fluorescent protein in living cells (around 20 µm2/s [155]). This deviation and more accurate measurements are shown in Chapter 6.4.

The accuracy of the fit relies heavily on the assumptions used and on how well they reflect the dynamic properties of the fluorophores and the geometry of the detection region [154]. In addition, the contribution of biophysical effects and the experimental setup have to be considered [118]. While many FCS models 4.2. General RICS Procedure 81

Figure 4.3: Fitting the experimental ACF to theoretical RICS equation. The upper surface is a 2-D plot of the experimental ACF that was calculated at 4.1. The red mesh is the residual between the experimental and theoretical ACF according to the RICS equation at each pixel. have been extensively investigated over the last 30 years, and several experimental factors that can affect the ACF were characterized, RICS is very limited in known models. This raises two major questions: How well does the ACF describe the dynamic properties of the ﬂuorophore? Moreover, how can we increase the accuracy of measurement? The former question was partly answered by Brown et al. in 2008, who demonstrated the rule that system adjustment is critical to increase the statistical accuracy of the ACF [61]. The second question is asking how to decode the ACF correctly to get quantitative measurements of diffusion coefﬁcient.

A systematic study of the questions mentioned above requires software for performing RICS that allows interactive adaptation of all parameters related to the analysis steps mentioned in section 4.2. We found that Globals for Images, which is the software used in most of the published RICS measurements was difﬁcult to adapt for this purpose. Therefore, we decided to write our own RICS code 4.3. The RICSIM Process Scheme 82

in Matlab, and base the algorithms on the RICS theory. This software has some procedures that overlap with procedures available in Globals for Images, as well as new additions that allow handling of large datasets. Another essential property of RICSIM is its ability to support the RICS analysis with interactive tools that allow the user to track each step during the analysis process. In addition Globals for Images is already compiled and therefore the code is not accessible, whereas RICSIM is in-house software with open code and can be adjusted by demand, and can contribute to the understanding of less familiar users.

4.3 The RICSIM Process Scheme

RICSIM consists of three main elements. The first element calculates the ACF, and is composed of five different control modes that determine the degree of automation. The second element is the fitting procedure, and the third element contains different tools that allow interactive screening of the data. A schematic representation of the RICSIM process scheme is shown in Figure 4.4. 4.3. The RICSIM Process Scheme 83

RICSIM- process flowchart Load tif files of microscope Load 2D ACF (10) Fitting images in fig format Fitting parameters (8) (9) Filters options: 2D ACF Select and open Wiener High pass filter Roi Fitting Fit of ROI file Tophat (1) normalization Thresh-background Manual control (8)

2D ACF Select manual Manually thresh High pass filter Map Fitting diffusion map manual

- thresh method To binary (2) normalization thresh ACF

ACF curser (8) 2D ACF Select ACF for High pass filter Map Fitting diffusion map ROI method (3) ACF vs. Intensity normalization map/group ACF for ROI ACF for

(8) List Fitting

Select ACF for 2D ACF high resolution High pass filter Map Fitting diffusion map (4) map method normalization Roi Fitting Fit of ROI ACF for group ACF for (8) Smooth diffusion 2D ACF map Select ACF for High-res Map map High pass filter (5) - group method Fitting normalization res ACF for high ACF for

Thresh-background Moving Average Diffusion (6) (option) Imobbile filter Histogram Export data Bleaching correction as fig/emf/jpg (7) (option)

Figure 4.4: RICSIM process scheme (1-5) Different control modes that allow various automation levels. (6) threshold algorithm to subtract the background of the cell (7)Photobleaching correction algorithm for the image series (8) Calculation of the ACF and normalization (9) Input user selection that is required for the ﬁt (10) Fitting the ACF into theoretical RICS model.

The next sections provides an overview of various features of RICSIM:

4.3.1 Control modes in RICSIM

1. Manual Control : The most basic operation while performing RICS analysis is to specify the ROI by using the cursor dragging box that deﬁne the ROI location over the image. For example, the main method of Globals 4.3. The RICSIM Process Scheme 84

for Images works by using this principle.

2. ACF manual threshold : This mode works similar to the manual control mode with one exception. In this mode, the ROI is cross-divided into small square region (grids) to give ACF and diffusion maps. For living cells, the ROI can be weighted with a thresholded image of the cell. This gives the ability to ignore the background of the cell (the surrounding media). Such diffusion maps were recently described by [60, 65]. Figure 4.6 shows an example of a diffusion map of EYFP expressed in 3T3 cells.

3. ACF for ROI : Works similar to the ACF manual threshold mode, but the background ﬁlters are adjusted automatically.

4. ACF for group : In order to achieve higher accuracy in the analysis, there is a need to enlarge the statistics by using stacks of frames that are taken over time, or by using relatively large ROIs [156]. The original approach that is shown in this thesis is that the ACF can be averaged not only over space and time, but also over a whole cell population. In the ”ACF for group” mode, a group of ﬁles is loaded from a whole cell population, and the ACF for each individual cell is calculated. This fast RICS calculation allows processing of much data in a short time, allowing better statistics for large populations of cells in an elegant way. The output can be ACF, ACF map or the selected ROI. The user controls the type of the output that will be collected into the collection box. Figure 4 demonstrates the new approach of RICSIM to achieve more accurate ACF by averaging the ACF for a population of 3T3 cells. A group of 10 cells expressing EYFP was visualized under suitable setup for RICS, and the ACF for a ROI of both 64 × 64 and 512 × 512 pixels were calculated for each cell. The ACFs of the entire group were averaged and were compared to a representative ACF of one cell from the group. 4.3. The RICSIM Process Scheme 85

Figure 4.5: Effect of averaging on the ACF. A. ACF of one cell, ROI size: 64 × 64. B. Averaged ACF of 10 cells, ROI size: 64 × 64. C. ACF of one cell, ROI size: 512 × 512. D. Averaged ACF of 10 cells, ROI size: 512 × 512. The small difference between C. and D. indicates a small variation between the ACF of one cell and the average ACF for the all group. The larger variation between A. and B. suggest that a ROI of 64 × 64 pixels does not give the average diffusion coefﬁcient of the all cell population. Fitting of the ACFs will be shown in Chapter 6. Images were collected using the parameters : Laser power (Multi-ion Argon, visible): 20%. AOTF (λexcitation=514 nm): 60% [60 mW]. Emission collected: 531-591 nm. Detector gain was set to: 1200 V. Pinhole diameter: 160 µm. Objective: 63× 1.3 NA. Pixel resolution in the x and y, δr= 68 nm×68 nm [zoom factor of 8]. Images size: 512 × 512 pixels [35.2 µm ×35.2 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. Total time: 73.4 s. Resolution: 16 bits

5. High-resolution diffusion maps : In order to improve the resolution of the diffusion map, sequential grids are shifted and overlapped to generate an averaged ACF map. The resolved diffusion map is than interpolated by using the function SPLINE in Matlab. 4.3. The RICSIM Process Scheme 86

Figure 4.6: Interpolated detailed Diffusion maps for EYFP cell. Images were collected using the parameters : Laser power (Multi-ion Argon, visible): 50%. AOTF (λexcitation= 514nm): 40% [90mW]. Emission band collected:523-537 nm. Gain: 1000 V. Pinhole diameter: 130 µm. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 60 nm × 60 nm [zoom factor of 8]. Images size: 512 × 512 pixels [30.8 µm × 30.8 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. MA subtraction: 10/15. Total time: 73.4 s. Resolution: 16 bits. a. Fluorescence image. The color bar maps the intensity in pseudocolor scale from 0 to 65535. b. Color bar maps the diffusion values in pseudocolors from 0 to 40. Grids size: 32 × 32 pixels with an overlap of 8 pixels. 4.3. The RICSIM Process Scheme 87

The important computational components in the RICSIM process scheme are discussed next.

4.3.2 Threshold algorithm (6)

The morphological threshold algorithm was written especially for living cells and uses a combination of Matlab built-in functions to threshold the space between the cell and the background. In the first stage the images are converted to binary images, based on Otsu‘s method [157] to automatically choose the threshold value that gives minimum interclass variance of the black and white pixels. Pixels identified as background are set to zero, while the pixels indentified as the cell are set to one in the reconstructed binary image. Next, the binary image is dilated with squared structure elements with a size of four pixels and then eroded with larger square structure elements with a size of five pixels. This step is repeated consecutively three times, and each time the size of the structure elements is enlarged by one pixel. Finally, the structure is eroded with a structural element of 8 square pixels. This feature is used in particular for generating diffusion maps, where an overlap of 8 square pixels between the grids is required. At the end of this process, small objects are removed from the image, and small gaps are morphologically closed. The image is then converted back to 8-bit or 16- bit greyscale image, depending on the original type of the input images. It is important to mention that since RICSIM is an open code program, the structure elements can be easily adjusted by size and shape for performing RICS analysis with different cell shapes.

4.3.3 Photobleaching correction algorithm (7)

One artifact that we noticed is that photobleaching affects RICS measurements. In fact, we found that under certain conditions, inducing high excitation intensities 4.3. The RICSIM Process Scheme 88

during RICS measurements might enhance the accuracy of the technique. This is the topic of discussion in section 5.3.1, where PVPON (Poly(N-vinyl pyrrolidone), 3.8), was used to study how the intensity of the excitation laser affects the ACF. Consequently, we incorporated a photobleaching correction algorithm into RICSIM. This algorithm can correct for the decreasing fluorescence intensity between successive images because of the fluorophore photobleaching over time [158]. More specifically, when photobleaching occurs the first images in a series are brighter than the later images, leading to biases towards the earlier images when the immobile subtraction algorithm described in section 4.1 is applied. This is more of a problem in cells than large bulk of solution because of the limited pool of fluorophores [135].

The photobleaching correction algorithm is designed to compensate for this effect. The first step in the algorithm is to determine the bleaching kinetics. For this purpose, the intensities of pixels within the ROI or cell are measured over time for each image of the series. Background intensity is subtracted and values of pixels outside the ROI/cell are set to zero, therefore the total frame intensity comes only from the ROI/cell. The total frame intensity is divided by the size of the ROI/cell in the same frame and a graph of the normalized ROI/cell intensity over time is plotted. Fitting the intensity graph to a mono or bi-exponential decay gives the photobleaching coefficients without the filtered noise. Normally, the mono- exponential approach considers a homogeneous fluorophore population, while the bi-exponential models consider two different populations [159]. However, it was decided to use the bi-exponential model as it gave smaller residuals. The intensity for each frame is then corrected by using the inverse of the average between the photobleaching coefficients. (Curve fitting of photobleaching measured from the ROI in Figure 4.1 is shown in Appendix E). Finally, it is also suggested that the use of the photobleaching correction algorithm means that there is not actually 4.3. The RICSIM Process Scheme 89

upper concentration limit of ﬂuorophores for our RICS measurements. This aspect should be investigated in future work.

4.3.4 Normalization (8)

G(0,0) is proportional to the inverse number of fluorescent molecules in the focal volume (1/N). Since the effective focal volume is constant during ICS/RICS experiments, the number of particles (N) is proportional to the concentration of particles in the sample [133]. In RICSIM the ACF for RICS is calculated as in ICS, as introduced by D. Kolin [134], but instead of normalizing the ACF with the average temporal intensity, the ACF was normalized to have a maximum value of 1. Because of normalization, the concentration cannot be measured and the only output is the diffusion coefficient. This is for five main reasons:

1. Experiments with different dilutions of ﬂuorescence microspheres showed that although there was a trend of increasing detection of number of particles as the concentration of particles increased, this trend was not linear (data is not shown). This data indicated that there is a certain systematic error in generating concentration measurements with the current system.

2. A constant g(0,0) gives a more stable curve/surface ﬁtting procedure as there is one parameter less in the least square ﬁtting.

3. In absence of a RICS equation that considers many other types of dynamics, plotting different ACFs in the same graph and comparing the horizontal (g(ξ,0)) and vertical (g(0,ψ)) vectors gives an indication of the relationship between the diffusion coefficient even without the fitting process. For example, if one horizontal ACF vector declines faster than the other does, it suggests that the fluorophore represented by the faster decaying curve is diffusing faster than the fluorophore represented by the curve with the 4.3. The RICSIM Process Scheme 90

slower decay. Since it is easier to compare two ACF decays if they both start from the same point, normalization is useful.

4. The autocorrelation amplitude can be affected by the presence of photobleaching, as reported in FCS [160].

5. Finally, the g(0,0) is affected by the immobile subtraction. Although it is possible to compensate the Moving Average subtraction ﬁlter by adding the average intensity of the updated Moving Average subtraction in Equation (4.1), there is no standard method to compensate for the use of the high pass ﬁlter in RICS, which manipulates the amplitude of the ACF [65].

4.3.5 Input User Selection (9)

Before ﬁtting the ACF to the RICS equation there is a need to enter the physical variables and analysis parameters as follows:

Pixel size: δr, the plain size of the pixels in the image in µm.

Pixels to fit: Define the number of pixels to be used when forming horizontal or vertical line fitting.

Diffusion: The estimated diffusion coefﬁcient for ﬁtting in µm2/sec.

Pixel time: τ p the exposure time of individual pixel to the laser beam in µs.

Line time: τ l, the time that takes the laser to scan one line in ms.

ROI size: The number of pixels along the sides of the ROI.

Grid size: In order to create a diffusion map in the ROI, the ROI is cross- divided into grids with the same size. The Grid size parameter refers to the number of pixels along sides of the grids. The grids have to be 2nx2n size. 4.3. The RICSIM Process Scheme 91

Grids jump: The distance between adjacent grids in pixels. Increasing the overlapping will increase both the resolution and calculation time.

g∞: The convergence value of the ACF for long times in ICS and RICS in the fitting model(the interception of the minimum value in the experimental ACF image with the fit). Fit size: The size of the ACF surface to be fitted.

Spap: To create smoothed topographic maps of the diffusion coefﬁcients the parameters of the cubic polynomials matrix (the diffusion map before it was smoothed) has to be interpolated. The SPLINE function is used to obtain the piecewise polynomial form of the cubic spline interpolation, taking the spap parameter as an input to determine the degree of interpolation [161].

4.3.6 Fitting (10)

The Matlab function LSQCURVEFIT is used to determine how various factors contribute quantitatively to the RICS curve by comparing the experimental ACF to the theoretical ACF as presented in Section 2.4. LSQCURVEFIT is a nonlinear curve-fitting solver in the least-squares sense that also returns the residual curve/surface for each pixel in the fit, in addition to the R squared value that defines if the fit is optimal or unsatisfactory. The mathematical operation of LSQCURVEFIT is described as [161]:

1 Pm 2 2 i=1 F (x, xdatai) − ydatai) x : initial guess (4.2) ydatai: experimental ACF

xdatai : RICS ACF 4.4. Summary 92

4.4 Summary

RICSIM is new RICS software that contains original routines as described in this chapter. It imparts some of the Matlab advantages and provides the user with efficient data manipulation and visualization tools. RICSIM uses built-in filters to ignore the background and the cell edges, and has a convenient and stable Graphical User Interface that is user-friendly. Writing RICSIM as open- code provides accessibility of modifications to its mathematical and programming operations. Those modifications could include the incorporation of other fitting equations, different cell segmentation, and averaging algorithms.

A major part of RICS involves fitting the ACF to a mathematical model. It is important to note that although fitting the experimental ACF to the RICS equation is essential for quantitative information, it is definitely not essential for gaining half- quantitative information. For instance, comparison of the experimental ACF of an unknown sample to an ACF of a well-characterized standard can provide information about the diffusion within the unknown sample as long as imaging of both samples was performed under the same conditions. For this propose, RICSIM has some unique features that were built in order to gain better control over the analysis process. This is achieved by giving the user the ability to screen and compare interactively the ACF without the fitting procedure. In addition, RICSIM improve the experimental statistics by automatically calculating the diffusion coefficient of a large population. It also provides statistical analysis of these results and can generate ACF plots for multiple positions and organize ACF vectors as functions of the ROIs intensities. At the same time, RICSIM can give the user full manual control over each step in the analysis of the ACF obtained from confocal images. For example, it provides the user with the ability to adjust the high pass filter and the Moving Average subtraction algorithm separately. Chapter 5

Experimental Studies and Validation of RICS

5.1 Introduction

The computational implementation and the use of RICSIM as a new program to handle the complexity involved in RICS analysis within living cells is discussed in Chapter 4. In order to ensure that the performance of RICSIM is satisfactory, and to demonstrate that performing RICS measurements with the Leica SP5 by using a PMT is possible, RICSIM had to be validated experimentally before any measurements within living cells. We now show the experimental studies and the validation of RICSIM accordingly with the RICS theory.

93 5.2. Validation of RICS with Microspheres 94

Characterization studies using fluorescence microspheres diffusing in solutions are shown in section 5.2 of this thesis. To evaluate a number of effects that influence the ACF and have to be considered in RICS measurements section 5.3 shows ACFs under changeable settings of visualized freely diffusing polymer. The capability of RICSIM to measure qualitative diffusion of fluorescent proteins from the autocorrelation function is shown in section 5.4. These measurements, in addition to the measurements in section 5.5 will show measurements within living cells by fitting the derived ACF into a RICS model, and in particular the effect of the high pass filter on the apparent diffusion coefficients.

5.2 Validation of RICS with Microspheres

5.2.1 Estimation of the PSF waist by microspheres scanning

The XY-axial waist of the PSF, ωxy, is one of the parameters that influences the shape of the autocorrelation function. More specific, ωxy is of the same magnitude of the length of g(ξ,0), and therefore it is an important parameter in the RICS fitting equation (as can be seen in Equation (2.21). To measure (ωxy) during RICS experiments and to validate that the laser beam scans the image in a uniform fashion, a series of 25 images of diffusing sub-resolution 100 nm diameter green-yellow fluorescence microspheres suspended in a viscous solution (aqueous solution containing 75% glycerol w/w) was acquired at a fast scanning speed of 1400 Hz (1400 lines per second). The series was cross-divided into grids of 64×64 pixels per grid, and the ACFs were calculated for each grid yielding a new series of ”ACF maps”, showing the ACFs calculated in each grid. A final ACF map describing the average ACF for each crossed-grid was created by averaging over the entire series of ACF maps. Figure 5.1 shows a map of the averaged ACF for each grid. 5.2. Validation of RICS with Microspheres 95

(a) 0% Glycerol

(b) 75% Glycerol

Figure 5.1: ACF map of freely diffusing ﬂuorescence microspheres. To evaluate the uniformity of the beam scanning across the images, a map of freely diffusing ﬂuorescent microspheres was generated by using the next parameters: Laser power (Multi-ion Argon, visible): 20%. AOTF (λexcitation=488 nm): 15% [7 mW]. Emission collected:500-550 nm. Detector gain was set to: 1193 V. Pinhole diameter: 103 µm. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 50 nm×50 nm [zoom factor of 39]. Images size: 128 × 128 pixels [6.3 µm×6.3 µm]. Pixel dwell time, τ p=5.6 µs and Line time, τ l=0.71 ms [scanning speed: 1400 Hz]. Moving Average subtraction: 0/200. Total time: 20 s. Resolution: 8 bits. 5.2. Validation of RICS with Microspheres 96

It can be seen from Figure 5.1 that the ACF map is relatively homogenous, confirming that the Leica SP5 acquisition software kept the scan speed and line time constant during the image acquisition. Assuming that the PSF in our system has a Gaussian shape, the average grid from Figure 5.1 was calculated, and the horizontal ACF vector was curve-fitted to a Gaussian profile. The beam waist was estimated as the distance from the peak of the Gaussian to the points where the intensity had dropped to e−2 of the maximum intensity at g(0,0).

Figure 5.2: Average grid of ACF map obtained from diffusing microspheres. 2-D pseudocolor image of the average grid (left) and a graph that shows the ﬁrst ﬁve horizontal ACF curves (right).

Figure 5.2 shows the average ACF of the ACF map obtained from the diffusing microspheres. The beam waist was measured to be approximately 5.2 pixels, which is equivalent to 0.26 µm. This value matched the manufacturer‘s information about the speciﬁc objective that was used for green excitation [162]. Since the emission of the ﬂuorescence microspheres was in the green-yellow spectrum (500-550 nm), and because the evaluation of the PSF is actually from the emission rather the excitation, it was decided to use this beam waist for all RICS measurements. It is important to note however, that small variations in the laser beam radius are common, and that ideally, the exact value of the beam radius would be determined at the beginning of each experiment. 5.2. Validation of RICS with Microspheres 97

5.2.2 Effect of viscosity on the ACF of diffusing microspheres

Performing measurements on well-characterized samples is a standard procedure for validating RICS systems [58, 65]. To validate our RICS approach and more particularly to estimate the accuracy of our system, control measurements of diffusing sub-resolution microspheres in solutions with known viscosities were performed. These solutions were prepared by mixing glycerol into water at different concentrations and adding ﬂuorescent microspheres with a diameter of 100 nm as explained in section 3.8.

Since the diffusion coefﬁcient of microspheres in a solution can be calculated using the Stokes-Einstein relationship, performing these experiments enabled us to estimate the accuracy of RICS measurements with our setup. By repeating the measurements on several image sequences and examining the spread of the measurements, it was possible to estimate the repeatability of the system and the error in measurement.

Figure 5.2 shows the average grid of the ACF map obtained from the diffusing microspheres. The beam waist found from this ACF was measured to be approximately 5.2 pixels, which was equivalent to 0.26 µm. This value matched the manufacturer’s information about the speciﬁc objective that was used for green excitation [162]. Since the emission of the ﬂuorescence microspheres was in the green-yellow spectrum (500-550 nm), and because the evaluation of the PSF is actually from the emission rather the excitation, it was decided to use this beam waist for all RICS measurements. It is important to note, that small variations in the laser beam radius are common, and that it was better to determined at the start of each day the exact value of the beam radius. Therefore, it is pointed out that inaccuracy can be contributed to the following measurements. 5.2. Validation of RICS with Microspheres 98

5.2.3 Effect of viscosity on the ACF of diffusing microspheres

Figure 5.3 shows representative images of the diffusing ﬂuorescence microspheres in three different glycerol concentrations (0%, 50% and 75% w/w). The higher the glycerol concentration, the higher the viscosity of the solution as predicted by the Dorsey table [145]. Therefore, the smallest diffusion coefﬁcient is expected in the 75% w/w glycerol solution. Although the microsphere concentration in all of the images in Figure 5.3 is the same, there are distinguishable differences in the patterns visible in the images. The difference in the patterns is caused by the different diffusion rates of the microspheres in the solutions. When diffusion is faster, individual microspheres appear more elongated because they move larger distances as a single frame is being acquired. This is reminiscent of the ”smudging” that occurs in photographs of rapidly moving objects. There is an asymmetry in the apparent elongation of the microspheres because horizontal 5.2. Validation of RICS with Microspheres 99

lines are scanned faster than vertical lines.

(a) 0% Glycerol (b) 50% Glycerol (c) 75% Glycerol

Figure 5.3: Diffusing microspheres in glycerol/water solutions. Images were collected using the parameters : Laser power (Multi-ion Argon, visible): 20%. AOTF ((λexcitation=488 nm): 15% [7 mW]. Emission collected:500-550 nm . Detector gain was set to: 1193 V. Pinhole diameter: 103 µm. Objective: 63× 1.3 NA. Images size: 128 × 128 pixels [6.3 µm×6.3 µm]. Pixel dwell time, τ p=39 µs and Line time, τ l=5 ms [scanning speed: 200 Hz]. Moving Average subtraction: 0/200. Total time: 139.3 s. Resolution: 8 bits.

Each image out of the image series above was processed to give its corresponding ACF. The ACFs were averaged for 0%, 50%, 75% w/w glycerol to give the dominant correlation for each viscosity. Figure 5.4 shows the average ACF for each solution. 5.2. Validation of RICS with Microspheres 100

Figure 5.4: ACF of diffusing microspheres in glycerol/water solutions The ACFs were derived from Figure 5.3

From Figure 5.4 it can be seen that the shape of the experimental ACF changes as the diffusion coefﬁcient of the beads changes as predicted by the RICS equation. In order to compare more precisely the dependence of the ACF on viscosity, the central horizontal normalized ACF vector, g(ξ,0), and the vertical ACF vector, g(0,ψ), were plotted. Figure 5.5 shows that the normalized ACF curves decline slower with increases in the glycerol concentration. 5.2. Validation of RICS with Microspheres 101

(a) Horizontal ACF

(b) Vertical ACF

Figure 5.5: Horizontal and vertical ACF curves of diffusing microspheres in glycerol/water mixtures. The dependency of the ACF in the viscosity shown at the horizontal and vertical ACF proﬁles: (a) Horizontal ACF; (b) Vertical ACF. 5.2. Validation of RICS with Microspheres 102

This is in agreement with the RICS theory that assumes that a decrease in the rate of Brownian motion of the particles causes a reduction in the number of correlated pixels, particularly in the vertical direction. The ACFs were fitted to the standard RICS equation, and were compared with the expected diffusion coefficients as defined by Stokes-Einstein relation (Equation (2.3)). The obtained values are presented in Table 5.1.

The experimental diffusion coefﬁcient values were between ±7% and ±23% of the theoretical values. The experimental error as estimated from the standard deviation of the measurements was of the order of between ±15% and ±0.027%. The higher deviations of the experimental measurements from the theory were observed in the low percentage glycerol mixtures. This is most likely because of a mismatch in refractive index between the non-glycerol solutions (n≈1.33), and the glycerol solution in the objective immersion solution which was 80% w/w (n≈1.45).

The refractive index mismatch induces spherical aberrations on the focused beam, altering its PSF. There are reports that such aberrations can affect FCS measurement and can lead to an increased diffusion time and thus to a decreased apparent diffusion coefﬁcients [163]. Similar to FCS, RICS may also be affected since the spherical aberrations might cause the experimental ACF of a source point

Table 5.1: Effect of viscosity on the diffusion coefﬁcient of diffusing microspheres. a Calculated by Stokes-Einstein relation. b Uncertainties are reported as standard errors.

Experimental D compared with theoreticala b Glycerol Concentration ν DT heoretical DExperimental (w/w) (Centipoises/mPa·s) (µm2/s) (µm2/s) 0% 0.7 3.2 2.15±0.34 50% 3.4 0.66 0.52±0.04 75% 16 0.14 0.15±0.004 5.2. Validation of RICS with Microspheres 103

(in this case, the microspheres) to appear axially elongated or compressed [164] and may result impreciseness in RICS measurments.

Although this objective has a correction ring to correct focus changes due to the thickness of the cover slip or due to small changes in the NA as a result of different concentrations of glycerol/dH2O in the immersion solution [162], turning the correction ring can compensate for index variations between 1.447 and 1.455 [162]. These values are still far above the 1.33 refractive index of water. However, it is important to note that the objective that was used for these measurements has a refractive index speciﬁc for microscopy of living cells, as the aim of this study is to implement RICS for cell biology research. Therefore, the refractive index mismatch is less of a problem in living cells as the refractive index within cells is closer to glycerol than water, and common mounting media have refractive indices of about 1.45 [154].

To summarize, these measurements demonstrate the potential of RICS not only to biology but also to other research areas, such as the capability to measure viscosities of very small samples (in µm scale) can be extremely useful in rheological studies as shown by Raub et al. (2008) who studied the viscosity of Collagen by using CLSM [153]. 5.2. Validation of RICS with Microspheres 104

5.2.4 Effect of scanning speed on the ACF of diffusing microspheres

The basis for RICS is that the shape of the ACF in confocal images is influenced by the diffusion coefficient of the particle being imaged. In particular, the horizontal and vertical slopes of the ACF change in a systematic manner, which is indicative of the diffusion coefficient. The same effects in the ACF can be obtained by imaging a sample at different scan rates. Figure 5.6 shows the horizontal and vertical central ACF curves of images of a microsphere solution obtained at different scanning speeds.

It can be seen that increasing the scanning speed resulted in a slower decay in both in the horizontal and vertical curves of the ACF, with a faster decay in the vertical ACF, as predicted by the RICS equation. As the laser beam scans the sample faster, the relative motion of the diffusing particles is reduced relative to the movement of the laser beam.

As expected, higher scanning modes showed experimental ACFs that are equivalent to slower diffusion. In fact if the scan rate is too fast relative to the diffusion coefﬁcient, then the ACF will resemble the ACF of a ﬁxed particle, and it will be impossible to derive quantitative information about diffusion from the images. Similarly, if the scan rate is too slow, then the decay rate along the horizontal axis will approach zero, and derivation of information through the RICS procedure will not be possible. This leads to the conclusion that there must be an optimal range of scanning speeds with which to perform RICS. How to identify this range will be discussed in section 5.3.2 (with PVPON), and in section 6.3.3 with living cells. 5.2. Validation of RICS with Microspheres 105

(a) Horizontal ACF

(b) Vertical ACF

Figure 5.6: Horizontal and vertical ACF curves of diffusing microspheres imaged using various scanning speeds The dependency of the ACF in the scanning speed shown at the horizontal and vertical ACF proﬁles: (a) Horizontal ACF; (b) Vertical ACF 5.3. ACF Studies by Using PVPON Solutions 106

5.3 ACF Studies by Using PVPON Solutions

In section 5.2 we showed that the SP5 could be used to measure the diffusion coefficients of microspheres in solution. However, microspheres are large relative to the proteins that we aim to characterize. Furthermore, their fluorescence is bright and the S/N in the resulting images is high. Hence, the fact that our system can be used for accurate RICS measurements on microspheres solutions might not be indicative of its capability to measure diffusion of proteins in solutions. In order to test and characterize the performance of our system under more challenging conditions, we chose to measure the diffusion coefficients of PVPON in solution.

Poly(N-vinyl pyrrolidone) (called also PVP, or PVPON) is a water-soluble, non-toxic, non-charged, biocompatible and FDA approved polymer, which is made from monomer N-vinylpyrrolidone [165]. PVPON was especially selected for the following measurements because it has two covalent attachment sites that can bind two Alexa R Fluor dye molecules for each polymer chain, as shown in section 3.8. This provides PVPON the ability to be attached to two different dyes with different emission spectra, and therefore to be used in future work to develop cc-RICS protocols using the promising multispectral characteristics of the Leica SP5. Moreover, it is possible that PVPON may be employed in other emerging applications, as FRET, due its capability to be linked with both the acceptor and donor of each polymer molecule. The next sections show an investigation of the ACF obtained from diffusing PVPON and how the ACF is affected by different imaging conditions, and support the theory that quantitative information about rate of diffusion can be extracted from the ACF. 5.3. ACF Studies by Using PVPON Solutions 107

5.3.1 Effect of laser power

To study the effect of the excitation intensity on the ACF, images of freely diffusing PVPON polymer in aqueous isotropic solutions were collected at several different excitation intensities ranging from 15 mW to 160 mW. To compensate for changes in detection efﬁciency at different illumination intensities the PMT gain was adjusted manually to 1210, 1129, 977, 925, and 918 V. These gain values gave relatively close values of intensity histograms for all samples. Figure 5.7a shows the horizontal vector curve of the normalized ACF, g(ξ,0), at different excitation intensities. Figure 5.7a shows the distribution of the pixels intensities as a function of excitation intensity.

Increasing the laser power output results in a slower decline of g(ξ,0). There are several factors that could contribute to the consistent relationship between the laser power and the ACF, including photobleaching and non-linear response of the detectors. In addition, it is possible that the effects on the ACF are due to photobleaching. It is also important to note that above 100 mW, instability of the measured laser excitation was observed. Inconsistency in the laser intensity may cause an artifact in the RICS measurements. However, since we performed RICS within living cells in less than 100 mW, and since the aim was not to show quantitative measurements with PVPON, this limitation is acceptable.

In order to determinate whether photobleaching might affect the ACF, we ﬁrst aimed to establish that photobleaching does occur in our samples and that the rate of photobleaching is inﬂuenced by diffusion. This was done by plotting the change in the average intensities in time-sequences of the same images that were used in Figure 5.3.1. Figure 5.8 shows the photobleaching curves as a function of laser power versus the frame number according to the acquisition order. 5.3. ACF Studies by Using PVPON Solutions 108

(a)

(b)

Figure 5.7: The effect of laser power on the ACF measured with PVPON.

(a) The effect of various laser powers on the intensity distribution histogram were checked with: Laser power (Multi-ion Argon, visible): λexcitation=488 nm. Laser power: 15, 24, 75, 130, and 160 mW. Subsequently, the PMT gain was adjusted manually to 1210, 1129, 977, 925, and 918 V, respectively with the laser power. The histograms describe the distribution of the pixels intensities of the average image for each series, binned by a vector from 0 to 512. (b) The corresponding horizontal ACF curve, g(ξ,0), is affected by the change in the illumination intensity. Images were collected using the parameters : Emission collected:505-565 nm. Pinhole diameter: 130 µm. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 32 nm×32 nm [zoom factor of 15]. Images size: 512×512 pixels [16.4 µm×16.4 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. Moving Average subtraction: 0/30. Total time: 152 s. Resolution: 16 bits. 5.3. ACF Studies by Using PVPON Solutions 109

Figure 5.8: Photobleaching of PVPON-Alexa at different laser power. The normalized intensity is given on an arbitrary scale between 1 (the intensity before photobleaching) and 0.945 (94.5% of the maximum intensity before photobleaching) in arbitrary units (a.u.).

It can be seen that higher laser power yields a faster decline in the normalized intensity. The most likely reason is that higher laser power raises the probability of each ﬂuorophore in the focal volume to be bleached. Thus, photobleaching does occur in this system and is inﬂuenced by laser power.

The next parameter that was studied in this thesis was the effect of scanning speed on the rate of photobleaching. Since higher excitation intensity is required to photobleach a photostable molecule like the Alexa-488 (up to 500 mW, while photobleaching of GFP can be achieved in 25 mW [76]) high laser power was applied in this experiment.

Figure 5.9 shows the average intensity over time in sequences of images of PVPON acquired at several different scanning speeds. The excitation time is determined by the scanning speed of the laser beam. Thus higher scanning speeds result in shorter effective excitation times, which lead to less photobleaching ([137, 166]). However, since there is a recovery of unbleached particles during the 5.3. ACF Studies by Using PVPON Solutions 110

scan, the recovery of the fluorescence is less at high higher scanning speed. The net effect is a faster photobleaching decay as demonstrated in the figure. Hence, the principle of fluorescence recovery while the laser raster scans the sample was demonstrated.

Figure 5.9: Photobleaching of PVPON-Alexa at different scanning speeds. 5.3. ACF Studies by Using PVPON Solutions 111

Finally, we examined whether diffusion rates could inﬂuence the rate of photobleaching within images. Figure 5.10 shows the average intensity over time in sequences of images of PVPON solutions with different viscosities. It can be seen that when the diffusion was predicted to be fast (in low concentrations of glycerol), the photobleaching decay is slow. Hence, this proves that the dynamic property of the PVPON is reﬂected by the dynamics of the photobleaching. The most likely reason for this effect is that fast diffusion allows fast recovery and a compensation of the photobleached molecules by new molecules. In addition, because fast diffusing molecules spend less time within a focal volume than slow diffusing particles, they will be exposed to smaller doses of light. Hence, individual molecules will be less likely to undergo photobleaching.

To summarize, we have shown that in confocal microscopy the rate of photobleaching is influenced by diffusion. Thus, it might be possible to use the rate of photobleaching in confocal images to quantitatively measure diffusion. Since the diffusion of particles is reflected in photobleaching kinetics, it is likely that photobleaching will also affect the ACF, and hence influence RICS measurements when high intensity illumination is used. 5.3. ACF Studies by Using PVPON Solutions 112

Figure 5.10 shows the photobleaching curve of PVPON solutions contained different glycerol concentrations imaged at same scan speeds. Clearly, the viscosity of the solutions affects the photobleaching curve exactly the opposite as described for Figure 5.9. This demonstrates the rule that fast diffusion and fast scan is equivalent to slow diffusion and slow scan, and therefore scanning speed has to be adjusted to the diffusion coefﬁcient of the particles.

Figure 5.10: Photobleaching of PVPON-Alexa at different viscosities.

5.3.2 Effect of scan speed

In order to validate that this is not an artifact of a potential relationship between the intensity distribution histogram and the ACF, the gain was manually adjusted (as in Figure 5.14a). Comparison between Figure 5.11a and Figure 5.12a shows the gain was successfully adjusted and the intensity histograms for different scanning speeds are approximately the same range.

Figure 5.12b shows that the ACF was not sensitive to the gain adjustment and therefore the relationship between the ACF and the scan speed was validated to be an important parameter that has to be considered during RICS measurements. 5.3. ACF Studies by Using PVPON Solutions 113

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Figure 5.11: The effect of scanning speed on the ACF measured with PVPON. (a) The effect of various scanning speeds on the intensity histogram were checked with: [100, 200, 400 and 700 Hz, which are equivalent to Pixel dwell time of 19.5, 9.75, 4.8 and 2.44 µs, and line time of 10, 5, 2.5 and 1.25 ms, respectively]. The total experiment time was: 152, 76, 38.14 and 21.8 s, respectively with the scanning speed. (b) The corresponding horizontal ACF curves. Images were collected using the parameters : Laser power (Multi-ion Argon, visible): 50%. AOTF ((λexcitation=488 nm): 100% [130 mW]. Emission collected:505-565 nm. Detector gain was set to: 850 V. Pinhole diameter: 130 µm. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 32 nm×32 nm [zoom factor of 15]. Images size: 512 × 512 pixels [16.4 µm×16.4 µm]. Moving average subtraction: 0/30. Resolution: 16 bits. 5.3. ACF Studies by Using PVPON Solutions 114

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Figure 5.12: The effect of scanning speed on the ACF measured with adjustable gain. (a) The effect of various scanning speed on the intensity distribution histogram were checked with: 100, 200, 400, and 700 Hz. The PMT gain was adjusted manually to values between 925 and 940 V. (b) The corresponding horizontal ACF curves. Images were collected using the parameters : Laser power (Multi-ion Argon, visible): 50%. AOTF ((λexcitation=488 nm): 100% [130 mW]. Emission collected:505-565 nm. Pinhole diameter: 130 µm. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 32 nm× 32 nm [zoom factor of 15]. Images size: 512 × 512 pixels [16.4 µm×16.4 µm]. Moving Average subtraction: 0/30. Resolution: 16 bits. 5.3. ACF Studies by Using PVPON Solutions 115

5.3.3 Effect of pinhole

We now continue to characterize the effect of the pinhole diameter on the ACF. When the pinhole size is optimal, background ﬂuorescence and scattered laser light out of the confocal volume cannot pass through the pinhole. In the absence of adequate pinhole adjustment, most of the desired signal will be rejected, leading to a low S/N ratio. In contrast, if the pinhole diameter is widely opened, the emission outside the focal plane will be correlated, and the ACF will be noisier and less deﬁned.

To study the effect of pinhole diameter on the ACF, a series of images of freely diffusing PVPON in aqueous solution was imaged under different pinhole diameters. Figure 5.13b shows the g(ξ,0) at different pinhole diameters. Figure 5.13a shows the distribution of ﬂuorescence intensity under different pinhole settings. It can be seen that increasing the pinhole diameter shifts the histogram of intensity distribution to higher values as a result of additional photons that pass through the pinhole. The corresponding ACF shows that increasing the pinhole diameter results in a slower decay of the ACF curve. We offer three theoretical explanations for the dependence of the ACF on the pinhole diameter:

1. Opening the pinhole may lead to over-saturation of the detector. However, since the peaks of intensity histograms were around the middle of the number of greyscales that was used, this explanation is unlikely.

2. The detection volume depends on the pinhole diameter. Since the ACF is strongly dependent on the detection proﬁle, the corresponding ACF changes. This effect is well known to be an acceptable limitation in the FCS literature. For example, for speciﬁc FCS systems different pinhole settings can give up to 25% deviation in the apparent diffusion time [167]. 5.3. ACF Studies by Using PVPON Solutions 116

3. Increasing the pinhole diameter may be translated into less pixel variations in the image. Since the decay of the ACF curve indicates the frequency of the ﬂuctuations in the collected intensity (as illustrated in Appendix A), it might be suggested that increasing the pinhole diameter consequently affects the ACF

The last explanation would be a major concern. If the distribution of the pixel intensities has a strong effect on the ACF, it can cause severe artifact in any measurements. In order to check this explanation, the gain was manually adjusted for achieving relatively constant intensity histograms (Figure 5.14a).

As can be seen in Figure 5.14b, there was not a signiﬁcant change in the ACF with and without gain adjustments, indicating that the effect of the pinhole is not an artifact, but a real physical phenomena probably related to the increase in the size of the PSF caused by opening the pinhole. Hence, as is the case for FCS, we must accept a potential deviation in measurement from the absolute diffusion coefﬁcient when the pinhole diameter is not optimal. Thus, adjusting the pinhole diameter by using a well-known standard is essential for obtaining reliable RICS measurements in cells, as will shown in section 6.3.5. 5.3. ACF Studies by Using PVPON Solutions 117

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Figure 5.13: The effect of pinhole diameter on the ACF measured with PVPON. (a) The effect of various pinhole diameters on the intensity distribution histogram were checked with: 70, 100, 130, 160, and 190 µm. (b) The corresponding horizontal ACF curve. Images were collected using the parameters: Laser power (Multi-ion Argon, visible): 50%. AOTF (λexcitation=488 nm): 100% [130 mW]. Emission collected:505-565 nm. Detector gain was set to: 850 V. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 32 nm×32 nm [zoom factor of 15]. Images size: 512 × 512 pixels [16.4 µm×16.4 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. Moving Average subtraction: 0/30. Total time: 152 s. Resolution: 16 bits. 5.3. ACF Studies by Using PVPON Solutions 118

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Figure 5.14: The effect of pinhole diameter on the ACF measured with adjustable gain. (a) The effect of different pinhole diameters on the intensity distribution histogram were checked with: 70, 100, 130, 160, and 190 µm. The PMT gain was adjusted manually: [1250, 1047.5, 926, 871, and 825 V] respectively with Pinhole diameters. (b) The corresponding horizontal ACF curves. Images were collected using the parameters: Laser power (Multi-ion Argon, visible): 50%. AOTF (λexcitation=488 nm): 100% [130 mW]. Emission collected:505-565 nm. Objective: 63×, 1.3 NA Glycerol. Pixel resolution x and y, δr= 32 nm× 32 nm [zoom factor of 15]. Images size: 512 × 512 pixels [16.4 µm×16.4 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. Moving Average subtraction: 0/30. Total time: 152 s. Resolution: 16 bits. 5.3. ACF Studies by Using PVPON Solutions 119

Once the complexity of measuring the diffusion coefﬁcient was demonstrated, and some of the imaging parameters that inﬂuence the ACF were studied, the next step was to prove that such measurements could be obtained. This will be achieved in the next section by using the same strategy that was shown in section 5.2.3 of using different glycerol concentrations with diffusing PVPON.

5.3.4 Effect of viscosity

In order to study the inﬂuence of viscosity on the ACF, a series of different glycerol concentrations with PVPON was visualized. To compare between the widths of the different intensity distribution histograms, accumulated histograms were plotted from the normalized histogram. Figure 5.15 shows the accumulated histograms as a function of different glycerol concentration. Slight differences in the gradients can be noticed, with a consistency with the glycerol concentrations. The relationship between the intensity distribution histogram and the diffusion coefﬁcient is described by Vukojevic et al. (2008) who developed an alternative method to RICS based on statistical analysis of the intensity distribution [151].

Figure 5.15: Effect of glycerol concentration on the accumulating intensity distribution histogram.

Figure 5.16a shows the intensity histograms several solution viscosities. 5.3. ACF Studies by Using PVPON Solutions 120

Figure 5.16b shows the corresponding horizontal ACF curves. Since faster estimated diffusion coefficients gave faster decline ACF, as predicted by the theory, we conclude that although our system does not always enable quantitative measurement of diffusion coefficients, comparing decline rates of the ACFs of different samples under the same imaging conditions can be used to determine the relationship of rates of diffusion between samples. Comparison between Figure 5.16b and Figure 5.5a shows exactly the opposite trend in that the horizontal ACF decays faster for high glycerol concentrations using the microspheres (5.5a) but slower for high glycerol concentrations when using PVPON (Figure 5.16b). We offer that two distinct types of RICS experiments are possible: In the first case we consider bright and large particles (but still smaller than the PSF), as sub- resolution beads or receptor aggregations. We offer that in such a case, RICS measurements should be more robust, as shown in section 5.2. The second case describes many fluorescent proteins or dyes in solution or within cells, where the contribution of each particle to the over fluctuation in the recorded intensity is important. In this case, the results are more sensetive to changes in the experimental system. As mentioned in section 5.3, we noticed that high excitation intensity gives more correlated pixels. This technique was used to enhance the ACF for the second case, which is actually the case that this thesis deals with. A more detailed theoretical explanation about how the use of high excitation intensity can possibly enhance the ACF is discussed later in this chapter. 5.3. ACF Studies by Using PVPON Solutions 121

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Figure 5.16: The effect of viscosity on the ACF measured with PVPON. (a) The effect of various solution viscosities on the intensity distribution histogram were checked with: [0, 5, 10, 15, and 20% glycerol solution, which are equivalent to approximated viscosity of 0.7, 0.8, 0.9, 1, and 1.15 Centipoises, respectively]. (b) The corresponding horizontal ACF curve. Images were collected using the parameters : Laser power (Multi-ion Argon, visible,λexcitation=488 nm): 130 mW. Emission collected:505-565 nm. Detector gain was set to: 850 V. Pinhole diameter: 130 µm. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 32 nm× 32nm. Images size: 512 × 512 pixels [16.4 µm×16.4 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. Moving Average subtraction: 0/30. Total time: 152 s. Resolution: 16 bits. 5.4. ACF of Diffusing GFP in Isotropic Solutions 122

5.4 ACF of Diffusing GFP in Isotropic Solutions

To show the principle that RICS can be applied to analyse diffusion of ﬂuorescent proteins, GFP in PBS and in solution of 40% w/w glycerol-PBS were visualized. Figure 5.17 shows the horizontal curve of the ACF, g(ξ,0). It can be seen that the g(ξ,0) of GFP in only PBS declined faster, indicating faster diffusion, as expected.

Figure 5.17: Horizontal ACF of diffusing GFP in PBS and glycerol. Images were collected using the parameters: Laser power (Multi-ion Argon, visible): 50%. AOTF (λexcitation=488 nm): 70% [100 mW]. Emission collected:494-571 nm. Detector gain was set to: 1100 V. Pinhole diameter: 130 µm. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 68 nm × 68 nm [zoom factor of 8]. Images size: 512 × 512 pixels [35.2 µm × 35.2 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. Moving Average subtraction: 0/100. Total time: 519 s. Resolution: 16 bits.

Trials to fit the corresponding ACF of both PVPON and GFP to the RICS equation were unsuccessful. The obtained results were above the upper boundary of the fit and gave significant residuals. Figure 5.18 shows unsuccessful fitting of ACF corresponding to freely diffusing PVPON where the fitted diffusion coefficient crossed the upper boundary of the fit. The upper boundary was determined to be 300 µm2/s, which is larger than the measured diffusion coefficient of diffusing Alexa-488 when it is not conjugated to PVPON (274 µm2/s [63]), therefore the 5.4. ACF of Diffusing GFP in Isotropic Solutions 123

diffusion coefﬁcient could not been resolved. A possible explanation for this failure is that the fast diffusion of PVPON in solution crossed the sensitivity limit of our system.

Figure 5.18: Unsuccessful ﬁtting of ACF describing PVPON.

In summary, although we were not always able to obtain quantitative measurements of diffusion coefficients, we were always able to identify trends and compare diffusion coefficients in samples imaged under the same conditions. Such comparisons, rather than measurement of absolute values of diffusion are the goal of our cellular studies, so these findings confirmed the likely utility of our approach. Although further work involving production of more viscous samples is required to determine the parameter limit for RICS measurements of GFP in solution, these data indicate that a high diffusion coefficient gives correlation only in the horizontal ACF vector. Fitting only the horizontal pixels along the line of the ACF to the theoretical RICS equation was found to be much less accurate then full-surface ACF. This indicates that there is an upper limit of diffusion coefficient possible to quantitative measure with our system. However, the diffusion coefficients of cytoplasmic proteins in living cells are estimates in range from 1 to 30 µm2/s, and even smaller diffusion coefficients as 0.1 - 1 µm2/s 5.4. ACF of Diffusing GFP in Isotropic Solutions 124

are expected for membrane proteins such as integrins [135]. Therefore, this upper limit should not affect measurements within living cells.

5.4.1 Effect of the scanning direction in RICS

Many microscopes can perform more than one scanning mode. For this thesis, the horizontal scan along the X-axis was used. The connection between the scanning direction (vertically/horizontally raster scan) and the ACF is considered in Equation 2.35, where ξ is multiplied with τ p, and ψ is multiplied with τ l. In order to demonstrate this connection, the average ACF was calculated from a series of images describing diffusing sub-resolution microspheres in water. The whole stack was then rotated 90◦, and the average ACF was calculated again.

Figure 5.19 shows a representative image from the stack before and after rotation, and the corresponding ACFs. It can be clearly seen that the central line of the ACF before rotation is along the X-axis due to the horizontal scanning direction, and after rotating the images, the ACF was rotated. This indicates that the calculated ACF is an experimental result, and not an artifact due to data manipulation. Insigniﬁcant difference is observed between Figure 5.19c and 5.19d indicates that the ACF is appropriately calculated. In addition, it demonstrates the dependency of the ACF on the scanning mode as a parameter for RICS equation.

The reason the ACF becomes narrower along the X-axis direction is due to the direction of the raster scanning, supporting the theory of RICS as shown in Chapter 2. 5.4. ACF of Diffusing GFP in Isotropic Solutions 125

(a) Before rotation. (b) After rotating 90◦ right.

Figure 5.19: The effect of scanning direction on the ACF in RICS. The ACF of diffusing microspheres in water were calculated before and after rotating the images. (a) representative frame out of a series of images before rotation; (b) representative frame out of a series of images after all stack was rotated.; (c) ACF before rotation with a horizontal dominant ACF; and, (d) dominant vertical ACF correspond with the rotation. Images were collected using the parameters : Laser power (Multi-ion Argon, visible): 20%. AOTF (λexcitation=488 nm): 15% [7mW]. Emission collected:494-571 nm. Detector gain was set to: 1193 V. Pinhole diameter: 103 µm. Objective: 63× 1.3 NA Glycerol. Pixel resolution x and y, δr= 50 nm×50 nm [zoom factor of 39]. Images size: 128 × 128 pixels [6.3 µm×6.3 µm]. Pixel dwell time, τ p=39 µs and Line time, τ l=5 ms [scanning speed: 200 Hz]. Moving Average subtraction: 0/200. Total time: 139.3 s. Resolution: 8 bits. 5.5. The Effect of Immobile Fraction Removal on RICS measurements 126

5.5 The Effect of Immobile Fraction Removal on RICS measurements

Once we showed that our system could be used to perform RICS measurements in isotropic solutions, the next step was to apply RICS measurements to living cells, and to try to identify trends in diffusion during biological activity. As explained in Chapter 4, working with cells is more complicated than working with solutions because of the lower signal to noise ratio, the heterogeneity in cell structure and in types of motion, and because of the presence of a large immobile fraction.

One of the methods we used for removing the immobile fraction from images, was to apply a high pass filter to the images with a cut-off frequency determined from the power spectrum (see section 4.2). To determine if the new RICS modification can enhance the accuracy of RICS measurements in living cells and to study the influence of the cut-off frequency on the ACF, we performed RICS measurements in diffusing EGFP-EGFR in living BaF3 cells. During the analysis, we applied high pass filters to the images with different cut-off frequencies using the procedure described in section 4.3 and evaluated their effects on the apparent diffusion coefficients.

The BaF3 cell line had been characterized by Clayton et al., who used ICS to count EGFR-EGFP clusters and demonstrated that in the absence of EGF in the media, EGFR had an average of 2.2 receptors per cluster, and after activation with EGF the average number of receptors per cluster increased to 3.7 [168]. The proposed model is that the activation induces dimerization or oligomerization of receptors at the cell surface [168]. By using ﬂow cytometry it was also demonstrated that the ﬂuorescent intensity of the cells was constant, indicating that the total number of receptors remains relatively constant [168]. Using FCS, 5.5. The Effect of Immobile Fraction Removal on RICS measurements 127

the diffusion coefficient of EGFP-EGFR was measured to be approximately 0.25 µm2/s in CHO cells [169]. Since the hydrodynamic radius of the dimer is larger than the monomer, it is predicted that the diffusion coefficient of EGFR should be smaller in activated cells than it is in non-activated cells [170]. Therefore, comparison of activated and un-activated EGFR-EGFP is a perfect candidate for RICS calibration and validation. In addition, the fact that the spatial correlation of EGF receptor in fixed cells (where the diffusion coefficient can be regarded as zero) was measured by ICS [133, 168, 171] gives a good opportunity to study how this spatial correlation can be eliminated by using the high pass filter.

The standard technique to activate the cells is by adding EGF to the media. However, due to the difficulty of preventing receptor internalization and at the same time performing RICS on relatively immobile cells, this technique proved impractical. As an alternative, two populations of BaF3 cells were cultured under different conditions: the first group was cultured in RPMI containing 10% FBS and 10% conditioned medium, while the second group was starved without FBS and conditioned medium to create conditions in which EGF is absent, therefore a different state of activation might be expected. Validating any differences in activation between the samples was beyond the scope of this thesis, but might involve assessment of receptor phosphorylation. Further work might also test whether inhibition of the internalization by using Phenylarsine oxide (PAO) as reported by Clayton et al. (2008) [172] can significantly reduce the obtained diffusion coefficient. 5.5. The Effect of Immobile Fraction Removal on RICS measurements 128

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Figure 5.20: Starved BaF3 cells expressing EGFP-EGFR. (a): Starved BaF3 cells expressing EGFR-EGFP in micro grids. (b): Cross section of starved BaF3 cell expressing EGFR-EGFP in soft agarose. Images were collected using the parameters : Laser power (Multi-ion Argon, visible): 50%. AOTF (λexcitation=488 nm): 10% [5m W]. Emission collected:505-565 nm. Detector gain was set to: 1250 V. Pinhole diameter: 160 µm. Objective: 63× 1.3 NA. Pixel resolution in the x and y size, δr= 32 nm×32 nm [zoom factor of 15]. Images size: 512× 512 pixels [16.4 µm×16.4 µm]. Scanning speed: 10 Hz. Resolution: 16 bits. 5.5. The Effect of Immobile Fraction Removal on RICS measurements 129

To accommodate the slow diffusion of the receptors we tried to minimize the movement of the cell as much as possible. The best scanning mode for such a slow diffusion is 10Hz, which is the slowest scanning mode in the Leica SP5. At scan speed of 10 Hz, the time taken to scan one frame is 51.2 s. Since the BaF3 cells are not adherent cells, individual cells starved in micro-grids (Figure 5.20a) were shown to move significantly (up to approximately 3 µm/min). In order to immobilize the cells in such a way that the viability was not affected, the soft agarose method was applied. Very briefly, soft agarose is a method to culture eukaryotic cells in a viscous gel environment that holds the cells in their position, while enabling cell viability. The viscosity of the soft agarose rises with the increasing concentration of the agarose. The optimal agarose concentration was determined to be approximately 0.8% w/v, whereas higher concentrations lead to deformation of cells. Individual cells were randomly selected, and were imaged at a magnification that allowed the entire cell to be fitted into the image frame.

The diameter of the receptor aggregations has an important effect in any ICS-based measurements. Ideally, the diameter of the aggregation would be homogeneous and smaller then ωxy. ICS measurements of the BaF3 are out of the scope of this thesis, but importantly, we did see a large variance in the diameter of the receptor (as indicated by variation in the intensity and size of receptor aggregates).

Receptor aggregates were seen to move relatively fast at the surface of the cells, possibly because of the rotational motion of the cells within the gel. In order to minimize any inaccuracy in RICS measurements that may be caused either by the heterogeneity in the diameter or the movement of the aggregation, the optical section was focused on an interior plane of the cell, where ﬂuorescence at the cortex was visible as a ”cell ring”. Receptor aggregations were observed 5.5. The Effect of Immobile Fraction Removal on RICS measurements 130

as bright spots on the ”cell ring” and within the cells, potentially as a result of internalization. Since most ﬂuorescence is at the cell membrane, it is assumed that the contribution of the internalization to the apparent diffusion coefﬁcient is negligible.

Sets of time-lapse images from 15 living cells were obtained for both starved and non-starved cells and the average ACFs for each series were calculated. In order to quantify the effect of the cut-off frequency and to determine the optimal cut-off frequency value, the vertical ACF vector from each cell was ﬁtted to the RICS equation under different cut-off frequency values. Figure 5.21a shows the values of the apparent diffusion coefﬁcients versus the number of points eliminated from the PSD.

As explained in section 5.5, the effect of the immobile fraction filtering is to eliminate cellular components and immobile structures from the apparent diffusion coefficient. Proportions between the graphs that quantify the effects of the immobile fraction removal on the diffusion coefficients for the three cell lines were found to be almost constant. However, the scales of the apparent diffusion values were different, suggesting that it is hard to neglect all the other parameters while testing a specific parameter because of the complex relationship between them. Yet, it clearly demonstrates the effects of the immobile filtering on the apparent diffusion coefficient. Since the apparent diffusion coefficient of the EYFP cells was close to the reference when the cut-off frequency was between 400 and 600 pixels, it was decided to adjust the cut-off frequency to this range of values. 5.5. The Effect of Immobile Fraction Removal on RICS measurements 131

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Figure 5.21: Measuring Diffusion of EGFP-EGFR in BaF3 cells with RICS. (a) Dynamic measurements of the apparent diffusion coefficient versus the number of points eliminated by the high pass filter. (b) R-square of the fitting. The R-square parameter gives an indication of the goodness of the fit. 5.5. The Effect of Immobile Fraction Removal on RICS measurements 132

In order to determine which cut-off frequency should be used, the R-squares of the fitting were returned as an output from the fitting procedure. Figure 5.21b shows the R-square (the square of the correlation between the response values and the predicted response values [161]) of the fitting. A small R-square indicates that the theoretical ACF describes the experimental ACF well, while a large R- square indicates a large deviation between the experimental and the theoretical ACF. This deviation can be characterized by two properties: Firstly, the shape of the experimental ACF has to be Gaussian, or at least Gaussian-like. Secondly, the waist of the ACF has to be at the same size of the XY-waist of the PSF,

ωxy. Since the spatial correlation of the EGF receptor is expected to dominate the low frequencies of the ACF, it is expected that the R-square will decrease with the deletion of this spatial correlation up to an optimal point, whereas the experimental ACF is due to the spatial-temporal correlation as predicted by the RICS theory. Once an optimum R-square is achieved, it is expected that the R- square will increase again because of over-elimination by the high pass ﬁlter.

Based on this technique, it was found that when the cut-off frequency value was set to 3,000 pixels, the optimal R-square was acheived, indicating for an optimal cut-off frequency value. The apparent diffusion coefficients were found to be 0.252 µm2/s and 0.264 µm2/s for the un-starved and starved cells, respectively. The fact that this value is close to that reported previously (0.25µm2/s, [169] suggests that our system can give a good approximation of the absolute diffusion coefficient of EGFP-EGFR under several simplifications. For example, the diffusion inside the cells should be different from diffusion at the cell membrane. Since we scanned across the ”cell ring”, 2-D diffusion or even anomalous diffusion should be considered. Additionally, other RICS models that assume that the PSF is oriented with the axial waist in parallel to the membrane would need to be developed. 5.5. The Effect of Immobile Fraction Removal on RICS measurements 133

Figure 5.22: Graphical illustration of the effect of the cut-off frequency of high pass filter on the ACF. The effect of the immobile fraction filtering on the horizontal vector of the normalized ACF. As more immobile fraction is removed, the horizontal ACF projection becomes narrower, with a diameter closer to the diameter of the PSF. However, at some point over-elimination will lead to over- estimation of the diffusion coefficient. This effect was quantified using the automated RICS approach.

Here we determined semi-quantitatively the effect of the high pass filter on the apparent diffusion time: higher cut-off frequency values give higher apparent diffusion coefficients. A full analysis involving additional strategies and complementary techniques such as ICS and FCS is not within the scope of this thesis but would confirm the obtained results. Meanwhile, these measurements show that the establishment of the high pass filter methodology can separate between the spatial correlation due to the cell structure and the faster fluctuation due to the dynamic properties of the proteins. Once again, it is important to note that this parameter is only one from a full list of parameters that needs to be optimized in order to perform accurate RICS measurements of cells. Since the focus of this thesis is in βPIX-Scribble interaction and not the EGFR, in-depth analysis of EYFP-βPIX expressed in 3T3 cells will be presented in section 6.3. 5.6. Discussion 134

5.6 Discussion

RICS measurements were validated by using microspheres in glycerol solutions with different viscosities. However, when the particles were much smaller than microspheres (PVPON, ﬂuorescence proteins) it was found that the experimental ACF did not entirely match the theoretical ACF predicted by the standard RICS equation, and ﬁtting the experimental ACF to the theoretical ACF gave a characteristic residual. This effect was probably caused by using high laser intensity to overcome the sensitivity limitation of the Leica SP5 that was reported previously [152].

The mechanism by which high intensity illumination enhanced our RICS measurements is not clear. One possible mechanism by which this could occur is photobleaching, the rate of which we showed to be influenced by the diffusion coefficient in section 5.3. Currently we lack a mathematical model to describe this effect. Therefore, we cannot fully validate this hypothesis. We propose two ways in which photobleaching could influence the ACF:

1. Short-term photobleaching: Since fluorophores that spend a large time in the beam are bleached, then the probability of measuring specific fluorophores at two points will decrease with the distance between them. Therefore, high laser intensities might give a faster decline in both g(ξ,0) and g(0,ψ). Since there is a connection between the diffusion time (the average time the fluorophore stays in the effective volume) and the probability of each individual fluorophore to be photobleached, it is theoretically possible to derive information about the diffusion coefficient from the experimental ACF.

2. Long-term photobleaching: If the scanning speed is slower then the critical 5.6. Discussion 135

velocity Vc =2D/ωxy, high excitation intensity can create a progressive decrease in the total number of fluorescent particles (termed ”photobleaching hole”), and create a non-uniform concentration of fluorophores [173]. The spatial-temporal correlation of the distribution of photobleached fluorophores in the sample describes the average photobleaching rate for the detection volume, the scanning speed, and the diffusion coefficient of the fluorophores.

We assume that a correction factor for RICS under short term photobleaching should be easier to derive than for long term photobleaching. For example, Satsoura et al. 2007 [173] introduced a modiﬁed expression for ACF under short term photobleaching in a case of line scan. Since the transition between the short-term and long-term photobleaching is dependent on the scanning speed, it would be useful to adjust the scanning speed up to a point where only short-term photobleaching occurs.

A similar effect of high laser intensity on the ACF was reported during FCS of rhodamine 6G in aqueous solutions [174]. Moreover, Widengren et al demonstrated that in order to obtain optimal conditions during FCS it is necessary to apply excitation intensities that lead to photophysical alterations in the fluorophore [174]. In the case of rhodamine 6G, the mechanism that is responsible for this effect is a contribution to fluctuations from the triplet state (blinking). In such a system, the fluctuations in intensity are caused both by the dynamic properties of the fluorophores and by the kinetic rates of its triplet state. More recently, a system that combines FCS with photophysical processes was reported, in addition to modelling and formulations that consider blinking in the fitting procedure [166].

Since the laser illumination that was used in this thesis was strong enough 5.6. Discussion 136

for photobleaching (as seen in Figure 5.8), it is suggested that increasing the excitation intensity increases the weight of the photobleaching effect in the ACF in RICS. This effect had an indirect inﬂuence on the apparent diffusion time and the diffusion coefﬁcient values, and should be considered.

The principle that the ACF is sensitive to photobleaching is also well characterized in the FCS literature, and is expressed in FCS correction models [175, 176]. Moreover, this effect can be also exploited, as demonstrated by Wachsmuth et al. [177], and by Delon et al. [178, 179]. In such a system, the ACF contains correlations due to the probability of detection of the fluorophores, the probability to photobleach each single fluorophore and the dynamic movement of the fluorophores. The probability of each single fluorophore to be photobleached is also complex and dependent on the number of photons striking the fluorophore and the sensitivity of the fluorophore to photobleaching, which in some cases can also be dependent on the conditions of the surrounding environment.

The concept of using photobleaching with a laser scanning confocal microscope was recently described by Braeckmans et al. who showed accurate measurements of diffusion coefficients by scanning rapidly along a line segment with a scanning laser beam while allowing continuous recovery of fluorescence throughout the photobleached line [97]. This recovery resulted from diffusion of surrounding non-bleached fluorophores into the bleached area while the laser beam was continuously changing its position. Hence, the distribution of the bleached and un-bleached fluorophores in the surrounding bulk is dependent on the rate of recovery, which is characterized by the dynamic property of the fluorophores, for instance the diffusion coefficient (long-term photobleaching). It is worth mentioning that integrating the advantage of the photobleaching effect was also demonstrated in FRET by Zal et al. who developed a photobleaching correction factor for FRET and used this technique to study protein-protein 5.6. Discussion 137

interactions in the immunological synapse in living T-cells by analysing time-lapse imaging [180].

All these data support the idea that photophysical effects, and photobleaching in particular, can be exploited to improve current technologies in the biophysics field. As a new member of the FFS family, RICS is still open for new improvements and modifications. We propose that our data on photobleaching in RICS presents both a problem and an opportunity. It presents a problem since it suggests that the ACF contains not only correlations due to fluctuations in the temporal change in the concentration (as assumed in the original RICS equation), but also fluctuations due to photobleaching. A correction model is required to account for these effects to allow more quantified interpretation of the ACF. However, there is currently no available RICS model that considers photobleaching, therefore fitting the experimental ACF to the original RICS equation creates a dominant residual that interferes with the RICS analysis. Conversely, it also presents an opportunity since performing RICS with high intensity excitation might provide a method to enhance the ACF by giving more correlated pixels, and to overcome the sensitivity problem of the SP5. A simple calculation reveals that even the slowest scanning speed in the Leica software (10Hz), is above the critical velocity, indicating that short-term bleaching is the mechanism we deal with. Yet, the validity of this assumption should be investigated as part of any RICS work in the future.

As with FCS, better physical equations are required in RICS to increase the sensitivity of the ﬁtting. Moreover, our measurements show that a number of parameters, which are not easy to formulate into a single biophysical model, inﬂuence RICS analysis. Since RICS is such a novel technique, it is still not clear if some of the effects we measured are exclusive to the Leica SP5 system, or whether they are generic to all RICS measurement systems. Future work involving 5.6. Discussion 138

other optical settings and other confocal microscopes is necessary to answer this critical question. Nevertheless, our measurements showed the establishment of new strategies to handle effectively some of these factors, including qualitative measurements and theoretical suggestions that can explain these very important issues in any FCS based techniques, and in particular in RICS.

Since the phenomena of photobleaching is much more established in FCS then in RICS, and since the Leica SP5 microscope is commercial available with integrated FCS system, we offer that future work should correlate the information derived from both our RICS modiﬁcation with FCS measurements. This can give extremely important information about our system, for instance, to quantify the effect of photobleaching in RICS, to enhance the sensitivity of the SP5 for RICS measurements, and to create standard solution curve by using series of solutions with increasing viscosities to optimize the precision of our measurements. Chapter 6

RICS Measurements in 3T3 Cells

6.1 Introduction

Chapter 5 showed that RICS measurements are influenced by a variety of parameters, which significantly affect the apparent diffusion time (Figure 5.5), or caused a characteristic residual in the fitting procedure (Figures 4.3 and 5.18). Since the original RICS equation does not consider these effects, and in the absence of available correction models, it can be hard to interpolate the ACF precisely. Hence, careful control of acquisition and analysis parameters throughout the ACF analysis are required. Thus, it is important to develop a standardized methodology that enables consistent calibration of the system. This methodology is presented in this chapter, in addition to more precise measurements of diffusion coefficients of EYFP-βPIX and EYFP-βPIX∆CT within 3T3 cells once the system setup is achieved.

139 6.1. Introduction 140

Originally, RICS was shown to give absolute diffusion coefficients without the use of well-known standards for calibration. However, the consequence of the photobleaching modification to overcome the sensitivity problem in the SP5 is that the use of well-known standard is a requirement. Ideally, it would be better to have a ”standard solution” with well-known diffusion coefficients. However, solutions can not mimic the diffusion of protein within cells. The interior of the cell is very heterogeneous, and the environment of the cell cytoplasm is very different from dilute solution for several biophysical properties such as pH, concentrations, type of diffusion, viscosity. The following measurements in this chapter were calibrated by using freely diffusing EYFP within living cells as a standard to compare the apparent diffusion coefficients under identical experimental and post acquisition analysis parameters as EYFP-βPIX and EYFP-βPIX∆CT.

Previous RICS analysis that were held in CHO cells expressing EGFP, showed that EGFP is uniformly distributed as a monomer with a large variety in the measured diffusion coefficient [155], and with an average value of approximately 20 µm2/s [60]. In addition, diffusion coefficients of enhanced cyan mutant of green fluorescent protein (ECFP) were shown to give close values [181]. Since the molecular structure of EGFP, ECFP and EYFP is very similar [83, 182], it is assumed that EYFP is also freely diffusing in 3T3 cells with a diffusion coefficient in the same range.

The hypothesis to be tested is that the binding of βPIX to partner-proteins during biological activities has a strong effect on its diffusion coefﬁcient. Since the (-TNL) motif responsible for the interactions between βPIX and Scribble, and the absence of the (-TNL) motif in βPIX∆CT abrogates its interaction with Scribble, the hypothesis is that the diffusion coefﬁcient of EYFP-βPIX and EYFP- βPIX∆CT will be different. 6.2. Validation of Cell Lines 141

To test this hypothesis, 3T3 fibroblast cell lines expressing EYFP, EYFP-βPIX and EYFP-βPIX∆CT were generated and the averaged diffusion coefficients within these cells were measured by RICS. Validation of these cell lines is shown in section 6.2. Section 6.3 shows several effects that can influence the experimental ACF, as shown in Chapter 5 and determines the optimal framework for this analysis. Based on these measurements, section 6.4 describes the comparison of diffusion coefficients of EYFP, EYFP-βPIX and EYFP-βPIX∆CT within living cells, and shows diffusion maps of these proteins in living cells.

6.2 Validation of Cell Lines

Cell lysates from the transfected cells were assessed for EYFP, EYFP-βPIX and EYFP-βPIX∆CT expression by western blot (Figure 6.2 ). The membranes were incubated with antibodies speciﬁc for the detection of endogenous and transfected βPIX (A), and GFP (detects EYFP) (B). The two membranes were also probed with antibody speciﬁc for tubulin to control for protein loading.

The ﬁrst lane was loaded with untransfected (UT) cells for negative control. The second lane was loaded with EYFP-expressing cells as positive control. The third and forth lanes are 3T3 cells expressing EYFP-βPIX and EYFP-βPIX∆CT, respectively. Band are detected at approximately 98 kDa by antibodies to GFP and βPIX only in the third and forth lanes. These bands indicates a stable expression of EYFP-βPIX and EYFP-βPIX∆C in the transfected cells. Bands above 148 kDa are shown in the third and forth lanes. These bands are likely to represent dimerized βPIX. The only band at approximately 27 kDa was detected in the cells expressing EYFP alone, indicating that the only free EYFP can be found in the control cells. Approximately equal bands were detected at 64 kDa in all lanes by βPIX antibodies, indicating equal expression of endogenous βPIX. 6.2. Validation of Cell Lines 142

Figure 6.1: EYFP-βPIX and EYFP-βPIX∆CT FACS proﬁle.

To confirm the western blot results, the cell lines were checked by FACS for YFP fluorosence. Figure 6.1 shows the FACS analysis. It can be seen that there are significant percentages of positive transfected populations, indicating that the transfections were successful, and stable cell lines were achieved. Future studies will assess populations with varying expression levels, but these cell lines provided a suitable stable population on which to apply RICS. 6.2. Validation of Cell Lines 143

Primary 3T3 EYFP EYFP- EYFP- Abs: UT βPIX βPIXΔCT anti Tubulin anti GFP

148kDa

98kDa EYFP-βPIX

50kDa Tubulin 36kDa EYFP

(a) anti GFP and anti tubulin

Primary 3T3 EYFP EYFP- EYFP- Abs: UT βPIX βPIXΔCT anti Tubulin anti βPIX

148kDa

98kDa EYFP-βPIX 64kDa βPIX 50kDa Tubulin

(b) anti βPIX and anti tubulin

Figure 6.2: EYFP-βPIX and EYFP-βPIX∆CT are expressed in the transfected 3T3 cell lines (a) Anti GFP and anti tubulin. The only band around 36 kDa ( 27 kDa) is in the EYFP cells. (b) Anti βPIX and anti tubulin. The bands at 50 kDa indicate tubulin protein and show that approximately equal amounts of protein was loaded in each lane. 6.3. Calibration of RICS to 3T3 Cells 144

6.3 Calibration of RICS to 3T3 Cells

6.3.1 RICS measurements in Fixed Cells

As a validation procedure, cells expressing EYFP-βPIX∆CT and EYFP were fixed with fixation solution (Appendix B), and the diffusion coefficient of EYFP and EYFP-βPIX∆CT were measured. It is assumed that fixation of the cells reduces dramatically the diffusion of the protein within the cells, causing the difference in the molecular weight between EYFP-βPIX∆CT and EYFP (as shown in Figure 6.2) to have an insignificant effect on the diffusion coefficient. Figure 6.3 shows the averaged normalized ACF for each cell. As can be seen, there is no distinguishable difference between the ACF of EYFP-βPIX∆CT and EYFP, supporting the hypothesis that fixing the cells results in equal diffusion coefficients (very close to zero).

Comparing Figure 6.3 with Figure A.5a (Appendix A) shows that the obtained ACFs for the fixed cells are different from theoretical ACF when the diffusion coefficient is equal to zero. As discussed before, the optimal framework for RICS is a combination of parameters. One example for a possible factor that can affect the ACF is photobleaching of the fluorophores due to high laser excitation intensity. Several additional effects that were shown with PVPON, and factors that are specific to living cells all have to be characterized. In order to define the optimal setup for RICS measurements under the Leica SP5 microscope, and to obtain the best analysis parameters to use, RICS measurements were performed in 3T3 cells expressing EYFP as a control under changeable image acquisition and analysis settings. 6.3. Calibration of RICS to 3T3 Cells 145

Figure 6.3: ACF of ﬁxed ﬁbroblast cells expressing EYFP-βPIX∆CT and EYFP. Images were collected using the parameters : Laser power (Multi- ion Argon, visible): 50%. AOTF (λexcitation=514 nm): 40% [90 mW]. Emission collected: 537-595 nm. Detector gain was set to: 1250 V. Pinhole diameter: 160 µm. Objective: 63×, 1.3 NA. Pixels resolution in the x and y directions size, δr= 60 nm×60 nm [zoom factor of 8]. Images size: 512 × 512 pixels [30.8 µm×30.8 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. MA subtraction: 3/5 as there is no cell movement. Total time: 21 s. Resolution: 16 bits.

6.3.2 Workﬂow of RICS experiments

3T3 cells were plated at 5×103 cells/well on 35 mm optic glass bottom dishes (Matek, MA) and were cultured for 24 or 48 hours before each experiment as in 3.1. The environmental chamber of the Leica SP5 enabled constant temperature

◦ of 37 C, humidity, and a constant concentration of CO2/O2 gas mixture. To select the optimal conditions for imaging the cells, our approach was first to adjust the experimental conditions, and later the post acquisition parameters. The first experimental condition is the scanning speed, which is proportional to the movement of the cell and to the expected diffusion coefficient of the protein of interest. Next, the pixel size has to be adjusted according to the size of the cell. 6.3. Calibration of RICS to 3T3 Cells 146

Once the scan speed and pixel size is adjusted, the laser power has to be adjusted. Since high laser has to be applied, the next parameter to be determined is the pinhole diameter to prevent saturation. Next, the post-acquisition parameters have to be adjusted: the size of the ROI, the number of data points eliminated before fitting the ACF (”jumping pixels”), and the immobile subtraction filtering. The order of adjustment of the post-acquisition parameters is less important, but since there is a complex relationship between them, we found that this adjustment is not a simple matter. In fact this was one of the reasons that we developed the automated RICS approach, to systematically scan for the optimal combinations that give a good approximation between the apparent diffusion coefficients of the standard.

6.3.3 Adjustment of the scanning speed

It has been reported that when high scanning speeds are applied, the detector cannot reset itself properly and can result in false correlation between successive pixels [61, 65]. This bleed-through noise caused by the limitation of detector electronics was found to be a major problem in other confocal microscopes [61, 65]. Therefore, it was decided to work with a slow detection mode.

A scanning speed of 10 Hz under the specific magnification and objective used here was shown to be too slow for RICS measurements (data not shown). This was because of significant 3T3 cell movement, especially at the cellular edge and cell protrusions. Scanning speeds faster than 100 Hz gave a low S/N ratio, and pixelated corresponding ACF (very few correlated pixels) so they were not ideal for quantitative analysis. Therefore, it was decided to use a scanning speed of 100

Hz. This scanning speed is equivalent to a pixel dwell time, τ p, of 19.5 µs and

Line scan time τ l, of 10 ms when the size of the image is 512 × 512 pixels. 6.3. Calibration of RICS to 3T3 Cells 147

6.3.4 Determination of the optimal pixel size

This is important to have enough correlated pixels in the ACF for accurate fitting of the data [61]. Although the average size and shape of 3T3 cells is varied, the average 3T3 cell can generally fit within a frame size of 50 µm × 50 µm. Since the size of the images is 512 × 512 pixels, this equals a pixel size of 0.08 µm. However, such a pixel size gives small insufficient number of correlated pixels, which is equal to the beam waist divided by the pixel size. Therefore, it was decided to finding a pixel size that allows over-sampling of the confocal PSF so that that it contains enough detail to enable easy analysis. At the same time, the chosen pixel size allows a maximum cell part to be fitted into the image frame. Therefore, the optimal pixel size was found to be between 0.06 and 0.065 µm.

6.3.5 Determination of the pinhole diameter and laser power

As demonstrated with PVPON in sections 5.3.3 and 5.3.1, the intensity of the laser excitation and the pinhole diameter alter the ACF. In addition, increasing the laser illumination power and the pinhole size gives higher S/N ratios and fewer images are required. Figure 6.4a shows the apparent diffusion coefficients for different combinations of pinhole and laser power settings. The average ACFs of three cells from each cell line were calculated, and the diffusion coefficient values were obtained by fitting the ACFs to the RICS equation. The images were captured using different pinhole and laser intensity. The Cut-off frequency was set to 500 pixels, the total time was 73.4 s, and the resolution was 16 bit. To avoid the negative effect of saturation during image acquisition the histograms of image intensity were used to assess the level of saturation, as shown with PVPON. 6.3. Calibration of RICS to 3T3 Cells 148

(a)

(b) Figure 6.4: The effect of pinhole and laser on the diffusion values. (a) Apparent diffusion coefficient versus the number of points eliminated by the high pass filter. (b) Each measurement describe the average apparent diffusion coefficient for each cells. The error bars correspond to the standard deviation of the three cells analysed for each cell line. The laser power was 33 mW and pinhole diameter was 130 µm. λexcitation=514 nm. Emission: 531-591 nm. Gain: 1200 V. δr= 60 nm×60 nm. Images size: 512 × 512 pixels. τ p=19.5 µs, τ l=10 ms. MA: 13/15. 6.3. Calibration of RICS to 3T3 Cells 149

Figure 6.4a shows that when the laser power was set to 60 mW under these settings, the ACF cannot be fitted properly. One possible explanation why strong excitation intensity gives an over estimation of the diffusion coefficient is that the contribution of the correlated fluctuations results partly from photobleaching and the recovery of diffusing fluorophores. As the photobleaching process is stronger, the ACF will contain more information about the photobleaching process and describe the effect of diffusion less, and therefore the standard RICS equation can not be used anymore. Another possible explanation is the effect of oversaturation in the detection. In addition, the optical relation between the pinhole diameter and the PSF diameter is a complex matter. Future work should thoroughly investigate the affects above in addition to generating more accurate measurements. Despite the issues described above, the average ACF for the EYFP cell line gave reasonable apparent diffusion coefficients (when the pinhole was adjusted to 130 µm (approximately 1.3 airy disks by the Leica LAS AF software) and the laser power 33 mW), indicating that under specific pinhole and laser power settings, a good experimental framework exists. The deviation of this result is shown in Figure 6.4b. Once the acquisition settings were adjusted, the cells were imaged under these settings, and the next post acquisition parameters were adjusted by using RICSIM software:

6.3.6 The effect of the ROI Size on the ACF

The ROI size is an important factor that inﬂuences the accuracy of the RICS analysis. A larger ROI gives an ACF that contains more information with a higher S/N ratio. Conversely, larger ROI also describes a larger averaged space and therefore the overall size of the cell can be divided into a smaller number of grids. Thus, the resolution of the analysis within the cell decreases as the ROI size increases. Brown et al. ([61] previously showed that a ROI with a size of 32 × 32 6.3. Calibration of RICS to 3T3 Cells 150

pixels, where the pixel size is approximately 65 nm × 65 nm (2 × 2 µm2), is the smallest ROI size that gives sufﬁcient statistical accuracy for their RICS system.

To demonstrate the principle that the ROI size has an strong effect on the ACF, ACFs were calculated from several different ROI sizes. It can be seen that as the lower g∞ decreases as the size of the ROI increases, with more correlated pixels along the g(ξ,0). Therefore, the corresponding ACF is better deﬁned, and with higher SNR.

Figure 6.5: Effect of ROI size. ACF were calculated from ROIs taken from same location but with different sizes: a. 16 × 16 pixels. b. 32 × 32 pixels c. 64 × 64 pixels. d. 128 × 128 pixels. The axes symbolize the pixels coordinates in the ACF, g(ξ,ψ). Applying size of 128 × 128 pixels provide sharper image, while ROI with a size of 16×16 leads in losing information. Axes symbolize the pixels along g(ξ,ψ). 6.3. Calibration of RICS to 3T3 Cells 151

6.3.7 Effect of removing data points before ﬁtting the ACF

As discussed in the beggining of Chapter 4.1, in some CLSM systems, under certain conditions the detector does not completely reset itself before new data points arrive. As a result, there is a residual signal from the previous data points that contributes correlated shot-noise to the ACF [65]. This noise can lower the S/N ratio and damage the accuracy of the ﬁtting.

Collecting images while the microscope is set to the eyepiece and no light can go through to the PMTs, and calculating the corresponding ACF from these images was reported by Brown et al. as a standard procedure to estimate this effect on the ACF [61]. The shot-noise was found to be dependent on the digitization rate of the detector (i.e. scanning speed, gain and offset), and does not depend on the objective configuration, focusing, pixels resolution in the x and y directions and laser intensity [61]. Thus, sensitive consideration in choosing the optimal number of pixels to ignore is required. The standard procedure to overcome this unwanted correlation was simply not to use the first correlated pixels to the fit [61, 135].

In our system, we noticed that the central pixel in the ACF matrix, the g(0,0), is very dominant and it has to be removed before ﬁtting the ACF to the RICS equation. Possible reasons for the large value of g(0,0) in the ACF matrix is that the ACF contains much un-correlated shot noise, in addition to possible contributions of spatial correlation and other noise factors. To eliminate these effects, it was decided to ignore this pixel in the ﬁtting procedures, and the ACF was normalized with the value of g(1,0). It can be seen that by ignoring more pixels in the x direction, the weight of the values in the sides of the ACF rises. However, over-elimination of the central pixels can be also a problem as the noise around the ACF sides can dominate the ACF. Therefore, it was decided to eliminate the central pixel, g(0,0), and to normalize the ACF to g(1,0). 6.3. Calibration of RICS to 3T3 Cells 152

Figure 6.6: ACF under different numbers of ignored pixels.

A. Selected ROI from 3T3 express EYFP. B. ACF of the ROI. The ACF is normalized with g(0,0). C. ACF after ignoring the ﬁrst central peak. The ACF is normalized with g(1,0). D. ACF after ignoring the three central peaks. The axes symbolize the pixels coordinates in the ACF, g(ξ,ψ)

6.3.8 Adjustment of the MA subtraction

As explained in Chapter 4, the Moving Average (MA) subtraction has to be adjusted correspondingly to the movement of the cells. To quantify the effect of the immobile fraction filtering on the apparent diffusion coefficients, the corresponding ACFs were averaged for each cell line, and then were fitted to the standard RICS equation. Figure 6.7 shows a graph of the dependence of the apparent diffusion coefficient on the MA value. It can be seen that there 6.3. Calibration of RICS to 3T3 Cells 153

is an increase in the apparent diffusion coefﬁcient with the increasing MA value. This might be a result of the elimination of cellular components and immobile structures. However, it suggests that the MA value should be chosen carefully, as over subtraction could add artifacts due to elimination of correlated information that truly describes the dynamic property of the proteins. When the MA subtraction value was above 10, the apparent diffusion coefﬁcient of EYFP was close to the reference, indicating a good range.

In addition, it can be seen that when the total number of images in the series was 15, there was a well-defined corresponding ACF. This number of images is smaller than the minimal number of images that was reported for the original RICS by Gielen et al. who reported just recently that a number of 15 images is insufficient to give accurate results [65]. At this point, it is still not clear if the small number of images required here is due to the high laser intensities that were used. In addition it is important to note that although high laser illumination can cause phototoxicity to the cells [74], it is assumed that in this short experiment time (around 70 seconds), it is unlikely that phototoxicity can influence cell activity. Whether high laser intensities can increase the detection efficiency and minimize noise in the ACF, and if there is a phototoxicity process during this short experiment time, should be verified in the future. Determination of cell viability can be achieved, for example, by using mitochondrial staining [183]. Nevertheless, these observations combined indicate that, with the appropriate settings reasonably accurate diffusion values can be obtained.

6.3.9 Adjustment of the cut-off frequency of high pass ﬁlter

The role of the high pass ﬁlter in reducing the contribution of cell components was explained in section 4.2. Figure 6.8 demonstrates the effect of the high pass ﬁlter on the ACF. While a cut-off frequency of zero gives ACF of the entire cell structure 6.3. Calibration of RICS to 3T3 Cells 154

Figure 6.7: Effect of Moving average subtraction on the diffusion values. Diffusion coefficient values were calculated from the average ACF for three cells for the three cell lines. The ACFs were calculated by using different MA subtraction values, in units of the number of frames in a window over which averaging is performed. An increment in the apparent diffusion coefficient as function of the MA value was observed. Images were collected using the parameters : Laser power (Multi-ion Argon, visible): 20%. AOTF (λexcitation=514 nm): 60% [60 mW]. Emission collected: 531-591 nm. Detector gain was set to: 1200 V. Pinhole diameter: 160 µm. Objective: 63× 1.3 NA. Pixels resolution in the x and y directions size, δr= 60 nm×60 nm [zoom factor of 8]. Images size: 512 × 512 pixels [30.8 µm × 30.8 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. Cut-off filter:500 pixels. Total time: 73.4 s. Resolution: 16 bits. that cannot be resolved, applying a cut-off frequency of 500 pixels gives ACF only due to the fast fluctuations representing the dynamics of the fluorophores.

To formally test the effect of the cut-off frequency of the spatial filter on RICS measurements quantitatively, the apparent diffusion coefficients were calculated after the high pass filter was applied with various cut-off frequencies. The graphs that quantify the effect of the high pass filter on the apparent diffusion coefficients 6.3. Calibration of RICS to 3T3 Cells 155

Figure 6.8: Effect of high pass filter on the ACF. A. 3T3 cell express EYFP. B. ACF for the cell. The cut-off frequency was set to: 0. C. ACF with dominant correlation in the horizontal axis but still very noisy. The cut-off frequency was set to: 100 pixels. D. Very clean ACF. (The cut-off frequency was set to: 500 pixels.) In order to filter out cellular structures from the ACF there is a requirement that approximately 500 central pixels will be masked out from the power spectrum. Images were collected using the parameters : Laser power (Multi-ion Argon, visible): 20%. AOTF (λexcitation=514 nm): 60% [60 mW]. Detector gain was set to: 1200 V. Emission collected: 531- 591 nm. Pinhole diameter: 160 µm. Objective: 63× 1.3 NA. Pixels resolution in the x and y directions size, δr= 60 nm×60 nm [zoom factor of 8]. Images size: 512 × 512 pixels [30.8 µm × 30.8 µm]. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. MA subtraction: 13/15. Total time: 73.4 s. Resolution: 16 bits were generated in the same manner as for Figure 6.7. The corresponding ACFs for three cells from each cell line were averaged for each cell line, and then were fitted to the standard RICS equation. The ROI was defined as the total size of the image (512 × 512 pixels), as shown in Figure 6.8. For each point in the graph, the cut-off frequency value was adjusted in RICSIM prior to the ACF calculation. As shown in section 5.5, there is a consistent increment in the calculated diffusion coefficients as a function of the cut-off frequency.

We offer that the effect of the immobile fraction ﬁltering eliminate cellular 6.3. Calibration of RICS to 3T3 Cells 156

Figure 6.9: Effect of high pass filter on the calculated diffusion coefficients.The average ACF for three cells from each cell line were calculate using different cut-off frequencies. The ACFs were fitted into RICS equation to give the diffusion coefficient values. components and immobile structures. In addition, it is suggested that both the MA value and the cut-off frequency should be chosen carefully, as over subtraction could add artifacts due to elimination of correlated information that truly describes the dynamic property of the proteins. The proportions between the diffusion coefficients of the three cell lines were found to be almost constant but show different scale of diffusion coefficients, suggesting that it is hard to neglect all the other parameters while testing the effect of specific parameter due to the complex relationship between them. Yet, it clearly demonstrates the effects of the immobile filtering on the apparent diffusion coefficient as explained in sections 4.2 and 5.5. Since the apparent diffusion coefficient of the EYFP cells was close to the reference when the cut-off frequency was between 400 and 600 pixels, it was decided to adjust the cut-off frequency to this range of values. 6.4. Measurements Under Optimal Conditions 157

6.3.10 Summary

In summary, it is suggested that once the scanning speed is adjusted according to the estimated diffusion coefficient of the fluorophores, the next parameter that should be determined is the laser power. The laser power should be adjusted corresponding to the concentration of the fluorophores and the sensitivity of the fluorophores to photobleaching. Next, there is a requirement to adjust the recorded intensity to avoid over-saturation. As can be seen in Figure 6.4a, adjustment of the pinhole size affects the apparent diffusion coefficient. This can be explained by the fact that changing the pinhole size also affects the PSF. Therefore, our data indicates an advantage in adjusting the recorded intensity using the PMT gain. Finally, the automated RICS approach should be used to adjust the cut- off frequency of the high pass filter and the MA subtraction under the selected ROI size. This combination of parameters is not easy, especially since there is complex relationship between them. This complexity and the hard work involving this adjustment is one of the major limitations that our system suffers from. Yet, once this process is complete and the optimal settings is achieved, measurements in sub-resolution scale within living cells can be achieved, as demonstrated in the following section.

6.4 Measurements Under Optimal Conditions

6.4.1 Spatial Diffusivity of βPIX in living cells

Fitting the ACF from images that describe EYFP diffusing in living cells gave a characteristic residual that could not be eliminated. However, in the previous section it was shown that the characteristic residual could be minimized under a certain combination of parameters, and the calculated diffusion coefﬁcient gave 6.4. Measurements Under Optimal Conditions 158

reasonable values. This means that the optimal setup was successfully established. The next section shows precise diffusion coefﬁcient measurements that were obtained using this optimal framework.

The fluorescence intensity of EYFP-βPIX was shown by fast time-lapse fluorescence microscopy to distribute homogeneously within the cytoplasm and that EYFP-βPIX was excluded from the nucleus. To determine whether intracellular localization influenced diffusion, the cell images were divided into small grids, with a size of 32 × 32 pixels as explained in section 6.3.6. The diffusion coefficient of each grid was calculated as explained in section 4.3. The upper limit of the fitting procedure was set in perspective to the measured diffusion coefficients to threshold outer values. Finally, the diffusion map is smoothed as explained in section 4.3.

Figure 6.10 shows spatial-temporal diffusion maps in a living EYFP cell, which was used as validation for the diffusion maps of EYFP-βPIX (Figure 6.11) and for EYFP-βPIX∆CT (Figure 6.12) under similar conditions . 6.4. Measurements Under Optimal Conditions 159

(a) Fluorescence image

(b) Diffusion map Figure 6.10: Interpolated detailed Diffusion maps for EYFP cell.

Laser power:90 mW. λexcitation=514 nm. λemission=:523-537 nm. Gain: 1000 V. Pinhole: 130 µm. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 60 nm × 60 nm. Images size: 512 × 512 pixels. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. MA:10/15. Time: 73.4 s. Resolution: 16 bits. a. Fluorescence image. The colour bar maps the intensity. b. Colour bar maps the diffusion coefﬁcients. Grids: 32 × 32 pixels with an overlap of 8 pixels. 6.4. Measurements Under Optimal Conditions 160

(a) Fluorescence image

(b) Diffusion map Figure 6.11: Interpolated detailed Diffusion maps for EYFP-βPIX cell. The cells was cultured and imaged at the same conditions as in Figure 6.10 6.4. Measurements Under Optimal Conditions 161

(a) Fluorescence image

(b) Diffusion map Figure 6.12: Interpolated detailed Diffusion maps for EYFP-βPIX∆CT cell. The cells was cultured and imaged at the same conditions as in Figure 6.10. 6.4. Measurements Under Optimal Conditions 162

It was reported previously that possible artifacts are expected to give higher diffusion coefficients near bright spots or at the cell perimeter [65]. However, we found that near the cell perimeter the obtained diffusion coefficients are actually slower than expected due to the dominant structure of the cell edges. Although it is possible to eliminate the spatial correlation of the cell edges by applying an immobile filter for each grid, determination of the cut-off frequency caused a difficulty for such a calculation. Since there is no available method to determine automatically the cut-off frequency for each grid, and because the cut- off frequency is currently constant for all the grids once the user of RICSIM selects it, we chose simply to eliminate the cell edges from the diffusion maps. Therefore, a space with a size of 8 × 8 pixels in the border between the edge of the cell and the media background was thresholded out before generation of the diffusion map. Future work can investigate how it is possible to overcome this kind of data loss by developing a method to determinate the cut-off frequency automatically for each grid. An example of the dominant structure of the cell edges is shown in Appendix F.

The overall similarity between Figure 6.10 and the diffusion maps published by Dross et al. (2009) [155] confirming the diffusion values shown in our diffusion maps. The fact that there is no correlation between the fluorescence intensity and the diffusion coefficient supporting that our measurements are not artifacts due to intensity changes within the images. In addition, the variability in the measured diffusion coefficient between different cell regions probably reflects different biological activities at the sub-cellular level with different viscosities, and providing proof of principle that RICS can indicate the influence of intracellular localization on protein diffusion.

The diffusion maps for each cell line were uniformly thresholded, and the mean diffusion coefﬁcient per pixel squared was calculated for each diffusion map. 6.4. Measurements Under Optimal Conditions 163

Figure 6.13 shows the diffusion coefﬁcients distribution histogram from Figures 6.10, 6.11, and 6.12 before the smoothing operation.

Figure 6.13: Histograms of diffusion maps.

As can be seen in Figure 6.13, there is a significant difference between the histograms and the mean diffusion coefficients of EYFP and both EYFP-βPIX and EYFP-βPIX∆CT. However, considering that even the accuracy of RICS measurements that have been taken under perfect conditions is still not ideal (a large variance as 30% for measurements within cells and between 80 to 90 % accuracy [135]), the accuracy of these maps needs to be improved. Furthermore, we note that the following simplifications contribute to the inaccuracy of our diffusion maps: Firstly, the photobleaching of EYFP has some dependency on 6.4. Measurements Under Optimal Conditions 164

the pH and concentration [184]. Next, it is important to consider the possibility of anomalous diffusion. For instance, the diffusion of GFP in the nucleus can be described as anomalous, while normal diffusion is observed in the cytosol [185]. Finally, the presence of potential quenchers can be also heterogeneously distributed.

Improving the accuracy of these maps is out of the scope of this thesis, but it is clear that trends do exist, suggesting that this approach will yield relevant diffusion maps of EYFP-βPIX and EYFP-βPIX∆CT in the near future. Since we aim to get data for a large population, this future work should give the average diffusion coefﬁcient per sub-region per cell line.

One important question relates to whether the differences in localization between EYFP-βPIX and EYFP-βPIX∆CT can affect their diffusion behaviour. As mentioned in section 6.1, the intracellular bulk has heterogeneous spatial features, such as pH, concentrations of the fluorophores, type of diffusion and viscosity. These features can significantly alter the diffusion coefficients of proteins within the cells. For instance, if the WT and the mutant are localized in different concentrations, reduced diffusion might be found as a consequence of molecular crowding [186]. In brief, molecular crowding is a phenomenon by which the diffusion of the particles exhibits different diffusion properties when the concentration of the particles becomes high, and the diffusion due to the Brownian motion is transformed to anomalous diffusion as the molecules collide with each other and affect each others trajectories [187] . In addition, different distribution patterns have a strong effect on the binding properties of the protein. For example, when paxillin localizes in the cytoplasm close to adhesions, its diffusion coefficient was measured be much slower than in the general cytosol as a result of binding to larger complexes [60]. 6.4. Measurements Under Optimal Conditions 165

In order to investigate this important question we suggest an approach to quantify the correlation between the differences in localization and diffusion coefﬁcient. This solution is based on the ability of RICS to generate diffusion maps, and the multispectral ability of the Leica SP5. Firstly, a new cell line expressing both the WT conjugated to ECFP and the mutant conjugated to EYFP has to be generated. Next, the diffusion map of each species has to be generated by RICS. Finally, the diffusion coefﬁcients of each species have to be characterized for each distinct cellular compartment

6.4.2 Measurements of diffusion coefﬁcients for a large population

Preliminary data (Figure 6.4b) showed that EYFP-βPIX∆CT has smaller diffusion coefficient then EYFP-βPIX. In order to perform precise measurements of diffusion coefficients with better statistics for the three cell lines, the average diffusion coefficient for a population of 12 cells from each cell line was measured. Each cell was subdivided into 64 × 64 pixel grids (total area size of 17.3 µm2), and the corresponding ACF for all the grids were averaged. The reason for this selection was to eliminate the contribution of the cell edges, and to apply a cut-off frequency that considers the size of the cell in the image, rather than using the same cut-off frequency to the entire grids in the diffusion map. To determine the spatial filter cut-off frequency for each grid, EYFP was used for calibration. Figure 6.14a shows the difference between the corresponding horizontal ACF curve, g(ξ,0) and 6.14b the vertical ACF curve, g(0,ψ). 6.4. Measurements Under Optimal Conditions 166

(a) [Horizontal ACF for large population of cells

(b) Vertical ACF for large population of cells

Figure 6.14: Horizontal and vertical ACF vectors for large population of cells Horizontal and vertical of the average ACF for 12 cells from each line. Images were collected using the parameters: Laser power:90 mW. λexcitation=514 nm. λemission=:523-537 nm. Gain: 1000 V. Pinhole: 130 µm. Objective: 63× 1.3 NA. Pixel resolution x and y, δr= 60 nm × 60 nm. Images size: 512 × 512 pixels. Pixel dwell time, τ p=19.5 µs and Line time, τ l=10 ms [scanning speed: 100 Hz]. MA:10/15. Time: 73.4 s. Resolution: 16 bits. Grids size of 64×64 pixels with no overlap between the grids. 6.4. Measurements Under Optimal Conditions 167

There was a distinguishable difference in the vertical and horizontal ACF curves of the three cell lines. The ACF declined fastest for EYFP diffusing alone, indicating faster diffusing coefficient of EYFP, while the diffusion coefficient of EYFP-βPIX∆CT was the lowest. The average ACFs from each cell was fitted to give the representative diffusion coefficient of each cell line.

Balanced one-way Analysis Of Variance (ANOVA test) was performed by Matlab ANOVA1 function to show the mean diffusion coefficients for each cell line and to determine whether the differences in the diffusion coefficients between EYFP, EYFP-βPIX and EYFP-βPIX∆CT were statistically significant. The p- value gives the probability that the average diffusion coefficient of the cell lines is significantly different. Common significance levels are under p<0.05 [161].

The ratio between the measured diffusion coefficient of both EYFP-βPIX and EYFP-βPIX∆CT and the measured diffusion coefficient of EYFP was ap- 1 proximately . EYFP-βPIX and EYFP-βPIX∆CT were both clearly shown to 4.5 diffuse differently than EYFP alone (p=1×10−12), but there was not a convincing difference between EYFP-βPIX and EYFP-βPIX∆ (p=0.05). As can be seen from Equation (6.1), in the case of free diffusion resulted by Brownian motion (Eq. 2.3) without any binding interactions the ratio in diffusion coefficients between proteins with different molecular weight should be proportional to the cube root of the ratio in their molecular weights. Since the molecular weight EYFP-βPIX and EYFP-βPIX∆CT is approximately 98kDa, the theoretical ratio between the diffusion coefficient of both EYFP-βPIX and EYFP-βPIX∆CT with EYFP should 1 be approximately , which is about 3 times larger than the measured ratios. 1.5

One explanation for this result is that the biological activity of proteins can alter their diffusion coefﬁcient [54–56]. Therefore, the signiﬁcant difference between the expected and experimental ratio is probably resulted from the 6.4. Measurements Under Optimal Conditions 168

biological activity of both WT and the mutant. Since the relationship between the hydrodynamic radius and the diffusion is linear in case of pure Brownian motion of (Eq. 2.3), this proportion should be constant for the measured diffusion coefﬁcient ((6.1)): r Mw 3 ( Na ) Rh = 0.75 π·ρ Mw − Molecular weight Na − Avogadro number (6.02 · 1023 mol−1) (6.1) gr ρ − 1.2 cm3 for protein q ⇒ D1 ∝= 3 Mw1 D2 Mw2 Farther work is required to characterize even larger populations and to interpret the biological aspect of these results. 6.4. Measurements Under Optimal Conditions 169

(a) Diffusion coefﬁcients for the three cell lines

(b) ANOVA plot

Figure 6.15: Diffusion coefﬁcients of cell populations.

(a) shows diffusion coefficients for a group of cells. shows ANOVA box- plot for comparison of the diffusion coefficients of the three cell lines. Each the median diffusion coefficients and the standard deviation for each cell are mention for each cell line. The edges of the boxes ensemble the 25th and 75th percentiles. The whiskers extend to the most extreme data points not considered outer values, which appeared only for the EYFP cell line. 6.5. Summary 170

6.5 Summary

In summary, when RICS is applied, it is important to work in a suitable framework that gives extractable ACF. By using EYFP as a well-known standard, the optimal framework for RICS within living cells was shown to be determined by the microscopy acquisition settings adjustment, and by the post-acquisition settings adjustment. While working at the optimal framework, the ACF provides precise measure of the diffusion coefﬁcient. By using the automatic RICS approach, we showed an effective way to analyse a full list of different factors that have an effect on the ACF. In addition, more advantages are derived for using the automated RICS approach. From the biological aspect, statistical data are required for characterization of biological phenomena. From the physical aspect, the accuracy of the ACF analysis increases with the number of repeats. This approach may be useful to investigate the limitations of different LCSM setups, and to test concentration limits of different ﬂuorophores for RICS measurements.

Once this optimal framework was achieved, RICS measurements were applied to measure the diffusion coefﬁcients of EYFP-βPIX and EYFP-βPIX∆CT, both were clearly shown to diffuse differently than EYFP (p<1×10−12), but there was not a signiﬁcant difference between EYFP-βPIX and EYFP-βPIX∆CT. Given that βPIX∆CT is different in only four out of 646 amino acids [188], it is not surprising that the diffusion characteristics are comparable.

Whether the subtle differences in diffusion between EYFP-βPIX and EYFP- βPIX∆CT (p=0.05) are biologically relevant will require future investigation. This result might indicate that Scribble has a negligible effect on βPIX diffusion, or might indicate that more complex analyse are required to elucidate the effect of Scribble binding to βPIX. For example, it is possible that the diffusion of βPIX is mostly determined by associated proteins other than Scribble. Since interactions 6.5. Summary 171

of proteins with large complexes can slow their diffusion [56], the absence of the (- TNL) motif in EYFP-βPIX∆CT may be insigniﬁcant. Alternatively, it is possible that over expression of EYFP-βPIX and EYFP-βPIX∆CT may cause artifacts in localization or diffusion that obscure the effect of the absence of the (-TNL) motif in EYFP-βPIX∆CT. If the number of EYFP-βPIX bound by Scribble is small relative to the total number of EYFP-βPIX molecules in the cytoplasm, there will be a small effect on the average diffusion coefﬁcient measured for the all EYFP- βPIX∆CT pool.

The last two assumptions can be checked by, for instance, comparing the diffusion coefﬁcient of EYFP-βPIX to EYFP-βPIX∆CT only in regions where Scribble is present. This can be achieved by generating cells that overexpress Scribble, and to activate the recruitment of βPIX to the plasma membrane and the leading edge by adding EGF to the media as shown previously [20, 34]. Chapter 7

Conclusions and Future Work

This thesis studies new RICS applications and brings original data that extends the RICS frontier. By applying a new RICS modiﬁcation, this thesis overcomes the sensitivity barrier and succeeds to measure diffusion coefﬁcients of proteins in living cells by using the Leica SP5. The achievements that have been accomplished in this thesis can be divided into three parts:

The creation of the RICSIM program

Much work has gone into designing the interface of RICSIM to be a stable and efﬁcient platform. RICSIM provides a number of advantages over other publically available software as described earlier, and can be used in the future for the application of RICS measurements to many biological questions.

Offering a new avenue for RICS measurements

This thesis highlights the potential of performing RICS analysis with high intensity laser excitation, which was shown to enhance the measured ACF. 172 7.1. Conclusions and Outlook 173

It is unclear why high intensity enhances the ACF, but it is possible that this is due to photobleaching effects. This improvement was applied to enhance the sensitivity of the Leica SP5 to RICS, and to allow accurate quantitative measurements under deﬁned settings. Furthermore, by using high intensity excitation, we showed that fewer images are required in comparison to the original RICS in isotropic solutions and living cells. However, one limitation for every FRAP based technique that should be considered is that overexposure to excitation light can manipulate the biological behaviour of the sample and to cause phototoxicity [189].

Measurements of diffusion coefﬁcient in living cells

This thesis describes preparation of stable cell lines expressing EYFP- βPIX and EYFP-βPIX∆PIX, and preliminary measurements of diffusion coefficient within these cells. Although the accuracy of these RICS measurements have to be validated by complementary techniques, by using EYFP as a standard trends of small difference in the apparent diffusion coefficient were identified. These results bring new and original information about the dynamic properties of βPIX in living cells, and have the potential to improve our understanding of how βPIX and Scribble interact with each other in the future. A quantitative description of the spatial-temporal behaviour of βPIX in living cells demonstrates the ability of RICS to detect the dynamics of protein within living cells, and promise a wide range of opportunities in cell biology research.

7.1 Conclusions and Outlook

The ACF was found to depend on a combination of different experimental parameters such as the excitation intensity, the pinhole diameter, and the scanning 7.1. Conclusions and Outlook 174

speed. The precision of the ﬁtting procedure was also found to be dynamic, and its dependence on the experimental setup was demonstrated. These effects were found to be signiﬁcant, and required careful optimization through the ACF analysis. At this point, it is still not clear if these effects are exclusive to the Leica SP5 system, or can be found in any standard RICS measurement with other systems. Future work should continue to characterize more potential effects that were partly shown in this thesis. In addition, characterization experiments involving other optical settings and other confocal microscopes are necessary to answer this critical question.

Nevertheless, trends in the ACF of solutions with different viscosities were consistent. This consistency suggests that it can be possible to give the absolute physical values of the diffusion coefficient by considering the effects mentioned above. This can be achieved for each RICS experiment in two steps: The first step is to adjust the experimental setup to an optimum point by which the residual is minimized (and therefore can be neglected in the fitting procedure). The second step is to use well-characterized samples as a standard for each experiment, and to calibrate the system setup to a point that gives its accurate diffusion coefficients, which were found to be 6.7±0.8 µm2 for EYFP-βPIX and 5.5±1.8 µm2 for EYFP- βPIX∆CT, when the diffusion coefficient of EYFP was used as a calibration standard with a measured value of 28.5±6.1 µm2.

Since more complex biophysical processes such as photobleaching can contribute to the shape of the ACF, it is advisable to use a transfected fluorescence protein (i.e. - EGFP, EYFP) with well known diffusion coefficients in the same cells as the proteins of interest. This, in addition to the use of other complimentary techniques as FCS (as described previously) and FRAP should be used in future work to validate our RICS modification. Although our measurements lack this important validation, with the approach of using EYFP as standard, 7.2. Recommendations for Future Work 175

our measurements reveal that the diffusion coefficient of both than EYFP- βPIX and EYFP-βPIX∆CT were lower than expected when simple Brownian motion is assumed. This suggests that their biological function and protein- protein interactions impede their diffusion. In addition, EYFP-βPIX gave slightly higher diffusion coefficients than EYFP-βPIX∆CT. Once again, the significant variance with these results suggests that further measurements and the use of complimentary techniques such as FRET, FCS and FRAP, in addition to more biomolecular techniques are necessary to understand these results.

Overall, although our RICS modification contains limitations, such as sensitivity issues, possible phototoxicity derived from photobleaching, and the lack of proper fitting models, it also contains major advantages over existing techniques. In addition, by using RICS we demonstrated the ability to generate non-invasive diffusion maps of proteins in living cells. We anticipate that this extraordinary ability will be used in future in protein-protein interaction studies within living cells, and possible publications about our RICS modification and about the biological aspect of our study.

7.2 Recommendations for Future Work

Future work should focus on:

• Improving RICS models- Formulating new RICS correction factors that account for the effects that were described in this thesis work, in addition to further investigation for possible unknown biophysical/biological/experimental effects.

• Further validation- To continue to study the effect of the photobleaching in RICS by using complementary techniques such as FRAP, FRET and FCS 7.2. Recommendations for Future Work 176

to provide full information about the studied system.

• Scrambling technique in RICS- Investigating another RICS modification that may allow to measure diffusion at the focal adhesions and cell edges. This potential RICS-modification is based on the scrambling technique that was described previously in the ICCS literature [144]. The idea of the scrambling technique is that by collecting a large number of smaller grids close to edges and scrambling the order of these grids to form a new rectangular larger grid, the ACF close to cell edges can be estimated. The ACF of the reconstructed grid may be fitted to a modified and suitable RICS equation, to give the diffusion coefficient for sub-cellular close to cell protrusions and edges, which currently cannot be calculated.

• Cross-Correlation-RICS - The diffusion coefﬁcient measurements of EYFP-Scribble are essential to complete the data about βPIX and Scribble interaction. Although a cell line of 3T3 expressing the EYFP-Scribble construct was generated and validated as part of this thesis, due to insufﬁcient time no RICS measurements were performed. In addition, by exploiting the spectroscopic features of the Leica SP5 to perform cc-RICS measurements between βPIX and Scribble, extremely useful information may be gained. Bibliography

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Theoretical Studies of the ACF

This appendix presents theoretical studies of the ACF that were performed using computer simulations. These simulations demonstrate the relationship between the fluctuations in the collected emission intensity and the ACF. Studying physical effects using computational approaches is standard in the FFS field. For example- simulations of ICS have been used to show the absolute value of the relative error in ICS analysis [190]. Simulations of the ACF dependence on experimental effects were shown for STICS measurements [191], simulations of the effect of anomalous diffusion in living cells on the ACF in FCS [56], and simulations that describe the dependence of the two-dimensional ACF on the anisotropic diffusion coefficient according to RICS theory [63] have also been performed.

A.1 Simulation of diffusion

Simulations of two-dimensional diffusion were generated to demonstrate effects in FCS that can inﬂuence the ACF. The particles were simulated as dots with a negligible size that do not collide. Therefore, the diffusion can be assumed

203 A.1. Simulation of diffusion 204

as a free diffusion resulting from Brownian motion, and there is no correlation between the trajectories of individual particles.

MATLAB code for Monte-Carlo simulation of branching Brownian motion in the XY-plane was adopted from multibbm.m by I. Kaj and R. Gaigalas [192], and was modiﬁed for FCS simulation. To simulate the erratic motion of diffusing particles, the trajectories of each individual particle at time t were calculated by [192, 193]:

√ X(t) = X(t − 1) + cos(2π · randn(1)) · 4 · D · t √ (A.1.1) Y (t) = Y (t − 1) + sin(2π · randn(1)) · 4 · D · t

(A.1.1) shows stochastic movement in each direction of the local Cartesian frame. The trajectories of individual particles ∆(X(t) − X(t − 1)) were governed by the diffusion coefﬁcient according to the Einstein-Smoluchowski equation. Each increment was generated randomly from a Gaussian distribution by using the Matlab command RANDN [161], and increments over displacement intervals were independent [192]. Figure A.1 shows an example of the trajectories of a single particle undergoing Brownian motion over time in a planar surface.

Since the change in the position of the particle in X direction during time interval ∆t is ∆X, and similarly for Y:

h(∆X)2i+h(∆Y )2i D = 4·∆t Where : (A.1.2) ∆X = X(t) − X(t − 1) ∆Y = Y (t) − Y (t − 1) where ∆t is the time increments (s), ∆X and ∆Y, and the angle brackets denote time averaging over the sample trajectory, sectioned into bins of size ∆t [195]. A.2. The effect of the number of particles on the statistical distribution 205

Figure A.1: Trajectories of a single diffusing particle over time. Random movement of an individual particle in space and time. The average distance the particle travelled from its starting point (the displacement), is proportional to the square root of the time and its diffusion coefﬁcient. The position of the particle at each time point was marked in black dots and the path between 2,000 time points was colored in different colors to emphasize the particle progress over time. This computer simulation was performed in the same manner as shown by Weeks [194].

A.2 The effect of the number of particles on the statistical distribution

According to the Einstein-Smoluchowski equation for Brownian motion, the MSD increases linearly with the diffusion coefﬁcient. Therefore, the radius of the particle‘s distribution increases with the diffusion coefﬁcient. In section 2.2 the solution of Fick’s 2nd law (Equation (2.16)) gave the gaussian probability that a particle originally located at r=0 and t=0 can be found in location r at time t (Equation (2.17)). This gaussian probability is also equivalent to the particles distribution in space and time, and is usually referred as Green’s function for A.2. The effect of the number of particles on the statistical distribution 206

diffusion [121, 122, 196]. Since both FCS and RICS consider the gaussian shape of Green’s shape, it is important to validate that the simulations behave as predicted by this law.

In order to simulate Green’s function for diffusion, the distribution of the particle trajectories was visualized as a two-dimensional matrix. To examine the inﬂuence of the number of particles on the particle distribution, the number of the particles in the matrix was changed, as can be seen in Figure A.2.

Figure A.2: Distribution of diffusing particles as function of particles number. The trajectories of the particles were summed and normalized to the maximum value of each matrix to form a distribution image of the particles. The particles were diffused in a blocked area for 2,000 time intervals. A. Distribution of only one particle. There is not any deﬁned shape. B. Averaged distribution of 100 particles. A deﬁned shape is starting to form. C. Averaged distribution of 10,000 particles with a symmetric Gaussian shape. As the number of the particles increases, the distribution of the particles is more statistically accurate and therefore more symmetric.

It can be seen that a perfect geometric distribution was achieved when the number of the diffusing particles was 10,000, and there were 2,000 time intervals, while for smaller numbers of particles, the distribution was not gaussian. This A.3. Effect of number of particles on the ACF 207

means that when performing FCS or RICS experiments there is a requirement for a minimal number of particles that will give sufﬁcient statistical accuracy to be measured.

A.3 Effect of number of particles on the ACF

Simulations of FCS were generated to study the inﬂuence of the number of particles in the focal volume on the ﬂuctuations. FCS simulations were generated by counting the diffusing particles in each time interval weighted with the gaussian geometry of the PSF located at the centre of the XY-plane. The XY-plane resembles the sample bulk, and particles initially are distributed according to a Poisson probability by using the Matlab function POISSRND [161, 192]. The gaussian geometry was modeled as a 2-D matrix, where each pixel gives its value.

The simulation assumes that the intensity of the particles is equal and constant, and that the particles are diffusing in a Brownian fashion. The number of particles in the sample was statistically proportional to the number of particles in the focal volume, which is equivalent to the concentration in the case of an isotropic solution. The collected intensity at each time interval was the sum of all the weighted particles inside the circle of the focal volume. Therefore, the contribution of intensity from each particle is dependent only on its planar coordinates. Such dynamics occur, for example, in thin solutions and membranes [118].

Several simulations were performed for different numbers of particles. For each simulation, the total intensity was normalized by dividing it with its average. Figure A.3a shows the normalized intensities plotted as a function of time. Figure A.3b shows the corresponding ACFs plotted as a function of the number of particles in the sample. A.3. Effect of number of particles on the ACF 208

(a) Normalized collected intensity.

(b) ACF curve.

Figure A.3: FCS simulation of various particles number. (a) The simulated intensity for a various particles numbers in the sample at the first 300 s of the total simulation time, normalized and given on an arbitrary scale. (a) The corresponding ACF. Simulations were created using the next parameters : Defined area size: 512 × 512 pixels. Pixel resolution in x and y: 0.06 µm, ωxy: 0.26 µm, total time: 1000 s. Diffusion coefficient: 2 µm2/s A.3. Effect of number of particles on the ACF 209

Figure A.3a shows that there is an observable connection between the simulated intensity and the number of particles in the sample. The relative fluctuations in the signal increases with a decreasing average number of particles. When the total number of the particles in the defined area was 20,000, there were very little fluctuations in intensity whilst when the number of particles was 1,000 the intensity fluctuated very rapidly.

Quantification of the fluctuations was achieved by using the ACF to give a statistical analysis of the frequencies of the fluctuating signal. Figure A.3b shows that the normalized ACF declines slower with the increase in the number of particles in the defined area. The reason for this behavior is that the contributed signal from each individual diffusing particle is minor in comparison to the overall super-position of total contribution from all the particles.

Such an outcome means that there is a sensitivity limit for the number of particles in the focal volume, and therefore a limit on the dynamic range of concentrations that can be measured with FCS. Having a small number of particles per focal volume increases the required measurement time for accurate data with sufficient S/N ratio, while increasing the concentration of molecules will decrease the detected relative fluctuations up to a saturation level that cannot provide a satisficatory ACF. A.4. ACF of FCS Change as function of diffusion 210

It is important to note, that this simulation neglects the Poisson probability for each single photon out of the emission to be detected. In addition, it neglects the contribution of random noise to the fluctuations. These factors have to be considered in more accurate simulations,along with other factors such as instrumental counting efficiency, excitation efficiency, quantum yield of the molecules and real excitation intensity [118, 197, 198]. Therefore, this simulation cannot provide the dynamic range of particles in the focal volume that is required for accurate FCS measurements. Nevertheless, it points out that such a range exist, and can affect the ACF in FCS systems.

ICS simulations that were held by Sergeev et al. support this conclusion [196]. Based on their simulations, the optimal range of particles in the focal volume for accurate ICS observation were shown to be between 0.1 and 1000, when the focal volume is measured in ﬂ scale. Schwille et al. also prescribed similar values for FCS [114].

A.4 ACF of FCS Change as function of diffusion

In order to study the influence of the diffusion coefficient value on the sensitivity of FCS measurements, a series of simulations were generated with different diffusion coefficients. The simulated emission intensity was normalized and plotted. Figure A.4a shows the normalized intensities for various diffusion coefficients. Figure A.4b shows the dependence of the corresponding ACF on the diffusion coefficient. A.4. ACF of FCS Change as function of diffusion 211

(a) Normalized collected intensity

(b) ACF

Figure A.4: FCS simulation for a various diffusion coefficients. (a) shows the collected intensity for a various diffusion coefficients at the first 200 s of the simulation time, normalized and given on an arbitrary scale. (a) shows the normalized ACF for (a). Simulations were created using the next parameters: Area size:512 × 512 pixels. Pixel resolution in x and y: 0.06µm, ωxy: 0.26µm, total time: 2,000 s. Number of particles: 5,000. A.5. ACF of RICS Change as function of diffusion 212

Figure A.4a shows that the ACF curve declines faster with increasing diffusion coefﬁcient of the particles. Therefore, the simulated ACF successfully described the dynamic properties of the simulated particles and supports the use of the autocorrelation approach to investigate the diffusion coefﬁcient of diffusing particles.

A.5 ACF of RICS Change as function of diffusion

Matlab code describing the RICS equations illustrate the ACF behavior and the dependence of the ACF shape on the diffusion, beam waist, scanning speed and pixel resolution in the X and Y directions. This Matlab code was connected with the GUI of RICSIM, to give the user convenient accessibility to modify the input parameters from 4.3.5.

To validate the RICS equation that is used for the fitting in RICSIM, the theoretical ACF was compared when the diffusion coefficient was set to zero, and when the diffusion coefficient was larger than 0. Figure A.5 shows the theoretical ACF according the RICS equation.

It can be seen that for D=0 the ACF has a perfect gaussian shape, which is similar to the ACF in ICS, and for D>0 the ACF became less gaussian-elliptical and narrower with faster decay as a result of more rapidly ﬂuctuations as a result of the diffusion of the particles. Similar to FCS, demonstration of the dependence of the ACF in RICS exhibits the same effect as in the FCS simulations that are shown in Appendix A.4. A.5. ACF of RICS Change as function of diffusion 213

(a) D=0

(b) D>0

Figure A.5: Theoretical ACF according RICS equation. The theoretical ACF was simulated using the next parameters : Deﬁned area size: 512 × 512 pixels. Pixel resolution in x and y , δr= 37nm × 37nm , Wxy: 0.26µm Appendix B

List of lab recipes

Standard NETN buffer pH 8.0

Reagent Concentration Provider NP40 0.5% v/v Amresco, Denver, Colorado EDTA 1mM Amresco Tris-Cl 20mM Amresco NaCl 100mM Amresco

Permeabilisation solution

Reagent Concentration Provider TritonX-100 0.1% v/v Sigma BSA 0.5% w/v Sigma in PBS

214 Appendix B. List of lab recipes 215

Materials for separating SDS PAGE (1 gel)

Reagent Concentration Provider Information Acryl-40 1800µl Amresco 40% w/v pure Acry-

lamide in H2O Bis-2 360µl Amresco 2% w/v Bis-Acrylamid

in H2O Temed 30µl Amresco TetraMethyl Ethylene Diamine APS 60µl Amresco 10% w/v Ammonium

Persulfate in H2O Separating buffer 2000µl dH20 4000µl

Materials for stacking SDS PAGE (1 gel)

Reagent Concentration Provider Information Acryl-40 4800µl Amresco 40% w/v pure Acry-

lamide in H2O Bis-2 280µl Amresco 2% w/v Bis-Acrylamid

in H2O Temed 30µl Amresco TetraMethyl Ethylene Diamine APS 80µl Amresco 10% w/v Ammonium

Persulfate in H2O Separating buffer 500µl dH20 2600µl Appendix B. List of lab recipes 216

5xloading buffer (In H2O) Reagent Concentration Provider Information 2-ME 0.1% v/v Sigma 2-Mercaptoethanol 14M Bromophenol 0.25% v/v Sigma blue SDS 10% v/v Amresco Sodium Dodecyl Sulfate Glycerol 50% v/v Biolab,Clyton, VIC Tris 250mM Amresco

Transfer buffer(In H2O) Reagent Concentration Provider Methanol 10% v/v Amresco Glycine 1.74% w/v Amresco Tris 0.58% w/v Amresco

PEMED buffer pH 7 (in PBS)

Reagent Concentration Provider PIPES 100mM Sigma EGTA 10mM Sigma MgSO4 5mM Sigma DTT 2mM Sigma

Fixation solution

Reagent Concentration Provider Paraformaldehyde 3.7% w/v BDH Analar, Biolab in PEMED buffer Appendix C

Classes in RICSIM

Class Name Description

load tiff Import .Tiff into the listbox Load selected file Read selected file Thresh background Set the background of the cell to zero Moving Average Perform moving average subtruction Choose ROI Define the ROI ACF of ROI up/ down Present ACF of ROI in upper/bottom axes ACF for ROI Calculate ACF map from grids for ROI ACF for multi files Calculate ACF maps for a list of files stack threshed filter Thresh stack file based on cells filter cells filter In house threshold filter of cells stack bleaching correction Perform bleaching correction to stack Calculate ACF map Calculate ACF map from stack/matrix magnifyrecttofig3 Modified imagnifyrecttofig from [199] for ROI

217 Appendix D

RICSIM GUI

Figure D.1: Screen Shot of RICSIM GUI- a. Data windows.

218 Appendix D. RICSIM GUI 219

Figure D.2: Screen Shot of RICSIM GUI- b. User controls. Appendix E

Photobleaching curve for a ROI

Figure E.1: Photobleaching curve for a ROI. The intensity for the ROI from Figure 4.1a was collected over the total frames in the series and is represented by the plotted triangles. The photobleaching curve was ﬁtted to a bi-exponential decay and plotted as the upper curve. The lower curve is the residual between the experimental photobleaching curve and the ﬁtting equation. This plot also supports the hypothesis that there was a photobleaching effect during the RICS measurements.

220 Appendix F

Spatial correlation at the cell edges

221 Appendix F. Spatial correlation at the cell edges 222

(a) Fluorescence intensity

(b) Corresponding ACF map

Figure F.1: ACF map of freely diffusing EYFP expressed in 3T3 cell reveals additional spatial correlation at cell edges that is created by the dominant structure of the cell edges. The immobile ﬁltering was not applied intentionally.