All That Glitters Is Gold Cover Design: Christian Weststrate Printed By: W¨Ohrmann Print Service Isbn 978-94-6186-007-1 Copyright �C 2011, S

All that glitters is gold Cover design: Christian Weststrate Printed by: W¨ohrmann Print Service isbn 978-94-6186-007-1 Copyright c 2011, S. Brinkers, The Netherlands All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without the prior permission of the author. All that glitters is gold Nucleic acid detection using tethered gold

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magniﬁcus prof.ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op vrijdag 14 oktober 2011 om 12.30 uur door

Sanneke BRINKERS

natuurkundig ingenieur geboren te Gouda. Dit proefschrift is goedgekeurd door de promotor: Prof. dr. I.T. Young Copromotor: Dr. B. Rieger

Samenstelling promotiecommissie: Rector Magniﬁcus voorzitter Prof. dr. I.T. Young Technische Universiteit Delft, promotor Dr. B. Rieger Technische Universiteit Delft, copromotor Prof. dr. N.H. Dekker Technische Universiteit Delft Prof. dr. V. Subramaniam Universiteit Twente Prof. dr. ir. M.W.J. Prins Technische Universiteit Eindhoven Dr. A. van Amerongen Wageningen Universiteit Prof. N. Destainville Universit´e Paul Sabatier Prof. dr. ir. L.J. van Vliet Technische Universiteit Delft, reservelid

This work was partially supported by the BSIK program Microned, work package 2F

Advanced School for Computing and Imaging This work was carried out in the ASCI graduate school. ASCI dissertation series number 239.

http://www.library.tudelft.nl/dissertations

The printing of this thesis was sponsored by Olympus Nederland. Contents

1 Introduction 9 1.1Nucleicacids...... 9 1.1.1 Structure...... 10 1.1.2 Function...... 12 1.1.3 Single molecule methods to study and manipulate nucleic acids...... 15 1.1.4 Detectionofspecificnucleicacids...... 17 1.2DarkfieldTetheredParticleMotion...... 19 1.2.1 Lightscatteringbysmallparticles...... 20 1.2.2 Darkfieldmicroscopy...... 21 1.3Thesisobjectives...... 23

2 Mechanics of Tethered Particle Motion 27 2.1Introduction...... 28 2.2Theoreticalbackground...... 30 2.2.1 Worm-likechainmodel...... 30 2.2.2 Volumeexclusioneﬀect...... 31 2.3Experimentalmethods...... 33 2.3.1 MonteCarlosimulations...... 33 2.3.2 TPMexperiments...... 34

5 2.4Results...... 39 2.4.1 MonteCarlosimulations...... 39 2.4.2 TPMexperiments...... 42 2.5Discussion...... 44 2.6Conclusions...... 46

3 Three dimensional measurements of Tethered Particle Motion 49 3.1Introduction...... 50 3.2Materialsandmethods...... 51 3.2.1 Samplepreparation...... 51 3.2.2 Setupanddatacollection...... 52 3.2.3 Calibrationofthepositionmeasurements...... 52 3.2.4 Driftandpositioncorrection...... 55 3.2.5 Persistencelengthfromstatistics...... 55 3.2.6 Persistencelengthfromdynamics...... 56 3.3Results...... 57 3.3.1 Positionprecision...... 57 3.3.2 Persistencelengthfromstatistics...... 59 3.3.3 Persistencelengthfromdynamics...... 59 3.3.4 Overview...... 63 3.4Discussion...... 63 3.4.1 Extendingthestatisticssimulations...... 65 3.4.2 Stretching due to excluded volume in tethered particle motion...... 67 3.4.3 Hydrodynamicseﬀectsofthenearbysubstrate...... 67 3.4.4 Electrostatic repulsion between substrate and particle . . 67 3.4.5 Thermalbuoyancy...... 68 3.5Conclusions...... 69

4 Dynamics of Tethered Particle Motion 71 4.1Introduction...... 71 4.2Theoreticalbackground...... 72 4.2.1 Brownianmotionofsphericalparticles...... 72 4.2.2 DiffusionofDNA...... 74 4.2.3 Diffusioninaharmonicpotential...... 75 4.2.4 Diffusionofatetheredparticle...... 77 4.3Materialsandmethods...... 79 4.3.1 Samplepreparation...... 79 4.3.2 Setupanddatacollection...... 79 4.3.3 Dataanalysis...... 80 4.3.4 MSDplot...... 80 4.4Results...... 82 4.5Discussion...... 86 4.5.1 Persistencelength...... 86 4.5.2 Diffusioncoefficient...... 87 4.5.3 Dynamicalscaling...... 87 4.6Conclusion...... 88

5 Nucleic acid detection using Tethered Particle Motion 89 5.1Introduction...... 89 5.2Materialsandmethods...... 90 5.2.1 ssDNAfragmentpreparation...... 90 5.2.2 Samplepreparation...... 91 5.2.3 Datacollection...... 91 5.2.4 Analysis...... 93 5.2.5 Excursion...... 93 5.2.6 Verificationofthehybridization...... 96 5.3Results...... 98 5.3.1 Excursion...... 98 5.3.2 Verification...... 98 5.4Discussion...... 104 5.5Recommendations...... 104 5.5.1 Biochemistryandsurfacechemistry...... 104 5.5.2 Setup...... 105 5.5.3 Sensitivity and specificity ...... 106 5.6Conclusion...... 106

Summary and conclusions 107

Samenvatting en conclusies 111

A Underestimation of Brownian motion due to motion blur 115

B Diﬀusion near a substrate 119 B.1DLVOtheory...... 119 B.1.1Electrostaticinteraction...... 119 B.1.2VanderWaalsinteraction...... 120 B.2Gravity...... 120 B.3Hydrodynamicinteraction...... 121 B.4Discussion...... 122

C Drift correction 125

Bibliography 129

Curriculum Vitae 145

List of publications 147

Acknowledgements 151 1

Introduction

In the past molecular biologists could only look at bulk properties of molecular species to gain insight in biological processes. The development of many single-molecule methods has radically changed this. According to the ergod- icity hypothesis, the time-averaged properties of a single molecule are equiva- lent to the mean values from averaging over an ensemble of identical molecules. Single-molecule experiments can therefore provide the same information as bulk experiments but have the advantage that inter-molecular diﬀerences can be distinguished [1]. In molecular biology, the molecules of foremost interest are the nucleic acids (DNA and RNA) and proteins, as they are essential for the func- tioning of processes in living organisms. In the following sections we give a short introduction to what is known of nucleic acids, mostly from the textbook ”Molecular Cell Biology” [2]. The currently available methods to study and detect nucleic acids are explained. In this thesis dark ﬁeld tethered particle motion is utilized for the detection of nucleic acids at the single molecule level and therefore a short introduction to this method is given. This chapter concludes with an overview of the objectives of this thesis and an outline of its contents.

1.1 Nucleic acids

Nucleic acids are the genetic information carriers in cells. Deoxyribose nucleic acid (DNA) provides the genetic code, or information databank of a living or-

9 1 Introduction ganism. The genetic information encodes for functional proteins that govern the processes in living cells. In prokaryotes (bacteria and archaea) the DNA is stored in the cytoplasm, whereas the cells of eukaryotes (such as humans) contain a nucleus where the DNA is stored. RNA molecules can have several diﬀerent roles, but serve only as genetic code in RNA viruses. The most important role for RNA molecules lies in the process of gene expression.

1.1.1 Structure Primary structure The primary structure of a nucleic acid is its nucleotide sequence. A nucleic acid is a nucleotide polymer, a long linear chain of nucleotides. Each nucleotide consists of a five-carbon sugar (ribose in RNA and deoxyribose in DNA), a negatively charged phosphate group and a specific nitrogenous base. There are 5 different nitrogenous bases in two types: the purine bases adenine (A) and guanine (G), and the pyrimidine bases thymine (T), cytosine (C) and uracil (U). The base thymine occurs in DNA and corresponds to the uracil base occuring in RNA molecules. Each non-overlapping sequence of 3 bases in DNA or RNA is called a codon and each codon usually corresponds to one of 20 standard amino acids. The nucleotide sequence therefore provides the blueprint for a protein, which is a linear chain of amino acids. The nucleotides in the polymer chain are connected by bonds between the phosphate group and sugar group of successive nucleotides. These bonds are asymmetric. The phosphate group bonds to the third carbon atom of the sugar on one side and to the fifth carbon atom of the sugar at the other side. This results in the polymer having a direction and asymmetric ends, the 5’ and 3’ end. The directionality is important since, for instance, synthesis of a nucleic acid only proceeds in the 5’ to 3’ direction.

Secondary structure DNA molecules in living organisms natively consist of two antiparallel (the 5’ to 3’ directions are opposite to each other) and complementary strands: double stranded DNA. The base T is the complement to A and a C is the complement to a G (Watson-Crick base pairing). The complementary bases form hydrogen bonds. When two strands bond this is known as hybridization of the two strands. The hydrogen bonds can be broken by high temperature or alkaline pH conditions, causing the two strands to separate (usually called denaturing or melting). RNAs natively occur as single stranded molecules, although double stranded RNA can be found, e.g. as a genetic information carrier in RNA viruses. Single stranded DNA and RNA can contain self-complementary sequences, which can also form hydrogen bonds (base pairs).

10 1.1 Nucleic acids

RNA has an increased ability to form hydrogen bonds due to the fact that the ribose sugar group contains an extra hydroxyl (OH) group. Internal base pairing results in molecules with secondary structures such as stem-loops, hairpins or pseudo-knots (see e.g. ﬁgure 1.1a).

Tertiary structure The precise three-dimensional structure of a nucleic acid is its tertiary structure. The dominant tertiary structure for double stranded DNA is the famous double helix form (see ﬁgure 1.1b), ﬁrst described by Watson and Crick in 1953 [3].

(a) messenger RNA (b) Double stranded DNA

G C C A C G A U A U G G A U Sugar G G C U U A Phosphate U G G Backbone C G U

G U A

A U 1360 A T

Adenine C C C G U Base G G U A C Pair A A T A G A A C A Cytosine C U G A U Thymine G C Nitrogenous G C T A Base C

G G U Guanine A U G A

A T A U C C

A A

C G A A T G

A U

U U C A A A

Figure 1.1: a Part of the secondary structure of messenger RNA transcribed from the luciferase gene in ﬁreﬂies. b Tertiary structure of double stranded DNA: the double helix. Image from: “The Science Creative Quarterly”, http: // www. scq. ubc. ca/ , Jane Wang.

11 1 Introduction

Genomic DNA The entire human genome (hereditary information) is approximately 3 billion base pairs long. As one base pair is 0.34 nm long (and 2nmwide),thetotallengthoftheDNAineachhumancellisonemeter.The DNA must be highly compacted to ﬁt in the nucleus of the cell. Genomic DNA is tightly packed in three levels. The DNA is ﬁrst wrapped around histone proteins to form a bead-on-a string structure. The beads are called nucleo- somes. The entire DNA protein complex is called chromatin, which exists in an extended form, but can also be coiled into a 30 nm solenoid arrangement (condensed chromatin). The entire genome is contained in several chromosomes (46 for humans), with each chromosome consisting of one DNA molecule. In nondividing cells, the individual chromosomes are not visible. During cell divi- sion, the chromosomes condense and become visible in a light microscope. The condensation probably results from several orders of folding and supercoiling of the condensed chromatin.

Bare DNA Bare double stranded DNA is a semi-flexible polymer, which means that on short length scales the molecule behaves as a rigid rod. On long length scales the molecule appears flexible. The flexibility comes from the small freedom of rotation of the chemical bonds that adds up over long lengths. This results in the molecule being able to take up an enormous number of conformations. Even though these conformations can be very complex, there exist several very simple models to describe the statistical properties of the polymer [4]. The model that is especially suited for semi-flexible polymers such as DNA is the worm-like chain model. It describes a conformation as a continuous curve with a fixed total length, the contour length. The persistence length is the characteristic length over which the direction correlations over the curve die off. The persistence length for double stranded DNA is typically quoted to be about 50 nm. The entropy of conformations is reduced if the distance between the ends of the molecule is extended. A force must therefore be applied to stretch the molecule, which is the origin of the entropic spring constant of DNA [5].

1.1.2 Function The central dogma of molecular biology is a framework for understanding the transfer of sequence information between the nucleic acids and proteins. It states that sequence information can not be passed back from protein to either protein or nucleic acid (see ﬁgure 1.2). There is a distinction between general information transfers (DNA to DNA, DNA to RNA and RNA to protein, the

12 1.1 Nucleic acids solid lines in figure 1.2) that can occur in all cells, and special transfers (RNA to RNA, RNA to DNA and DNA to protein, the dashed lines in figure 1.2) that only occur under special circumstances. The last 3 information transfers (protein to DNA, protein to RNA and protein to protein) have never been observed and are believed not to occur as per the central dogma. The three general transfers are important for normal cellular processes. DNA replication is carried out when the cell is dividing, when the genetic code in the DNA has to be faithfully copied to the offspring cells. The other two general transfers have to do with gene expression. DNA replication

DNA translation Direct

TranscriptionReverse

transcription RNA Protein Translation RNA replication

Figure 1.2: Central dogma in molecular biology. Only certain information transfer processes between these biomolecules are possible (those with an arrow). The solid arrows are general transfers that can occur in all cells, whereas the dashed arrows are special transfers that only occur under special circumstances.

Gene expression Gene expression is the process where the information in a gene is used to form a functional protein. Figure 1.3 shows this process: The DNA is ﬁrst transcribed into messenger RNA (mRNA), which transfers the genetic information between the nucleus and ribosome. Double stranded DNA contains two complementary strands. The coding strand in double stranded

13 1 Introduction

DNA contains the genetic information, whereas the non-coding strand serves as thetemplatefortheproductionofthemRNA.ThemRNAthuscontainsacopy of the information in the DNA coding strand. The primary mRNA transcript is processed into its functional form, after which it travels to the ribosome where it is translated into the corresponding protein. Transfer RNA (tRNA) with the complementary sequence to a codon binds to the mRNA, delivering the associated amino acid to the growing protein chain. Ribosomal RNA (rRNA) is responsible for chaining the amino acids together to form a protein.

Cytoplasm

Nucleus

Growing Transcription protein chain Free amino DNA acids

mRNA Ribosome

Translation Figure 1.3: The process of gene expression in the cell. DNA gets transcribed into mRNA that brings the copied genetic information to the ribose. There the mRNA is translated into a protein. Image from: “The Science Creative Quarterly”, http: // www. scq. ubc. ca/ , Jane Wang

14 1.1 Nucleic acids

1.1.3 Single molecule methods to study and manipulate nucleic acids In the last two decades many methods have been developed to study nucleic acids at the single molecule level. The rise of scanning probe microscopy methods allowed researchers to study surfaces and molecules with (near) atomic resolution. In particular, atomic force microscopy (AFM) is often used to study the topography of biomolecules.

AFM In AFM (figure 1.4a), a cantilever with a sharp tip (radius of curvature 5-10 nm) at its end is scanned over a surface. The tip is brought in close proximity to the surface (from contact to a few tens of nanometers). Forces, such as mechanical contact force, van der Waals force and electrostatic force, either attract or repel the tip, causing the cantilever to deflect. The amount of deflection is recorded by observing the reflection of a laser spot on the cantilever. The resulting images thus provide a three-dimensional surface profile of the molecule. The drawback of AFM for the study of nucleic acids is the fact that the molecule is immobilized on a flat surface, preventing the molecule from adopting its natural 3D conformations. With the recently developed video rate AFM the speed of acquisition of AFM images has significantly increased. AFM images, however, are still acquired at speeds much slower than the kinetics of the molecules of interest [6]. The method does allow applying a force (1-1000 pN) to the molecule to study its mechanical properties [7].

Tethered particle methods Tethered particle methods (figure 1.4b) are popular methods where the molecule under study is not completely immobilized. The molecule under study is used to tether a particle to the substrate. In this manner the molecule is only immobilized at its ends, the rest of the molecule can adopt its natural conformations. In Tethered Particle Motion (TPM) [8] no force is applied to the particle. The particle’s Brownian motion, influenced by the tethering DNA, is followed over time. The motion reflects the contour length and persistence length of the tethering molecule and allows one to study conformational changes at the single molecule level. Often the particle is held in place by an optical tweezer. An optical tweezer is formed by focusing a laser beam with high NA optics. The beam waist (the narrowest point of the beam) forms an optical trap for micrometer sized dielectric particles due to the high electric field gradient. For a Gaussian shaped beam, the trap has a 3 dimensional harmonic potential. The trap allows the user to displace the particle and apply a force on the tethering molecule. The

15 1 Introduction magnitude of the force can be determined from, for instance, the Brownian ﬂuctuations of the particle position and usually ranges between 0.01 to 100 pN. This methods allows one to measure processes at a time scale on the order of 100 μs[7].

(a) Atomic force microscopy (b) Tethered particle methods

Tethered particle

Biomolecule

Substrate

Figure 1.4: a Atomic force microscopy: an atomically sharp tip is translated over the sample. The tip is mounted on a cantilever that deflects as a function of the force applied to the tip. The deflection is read out by reflecting a laser on the cantilever and reading the reflection angle on a quadrant photo detector. Source: http: // www. farmfak. uu. se/ farm/ farmfyskem-web/ instrumentation/ afm. shtml . b Tethered particle methods: A particle is tethered to a substrate using a biomolecule. The particle can be displaced or rotated using an optical or magenetic tweezer as to apply a force on the biomolecule, or the otherwise unconstrained Brownian motion of the tethered particle can be followed to determine the mechanical properties of the biomolecule.

When a magnetic particle is used, the tweezing can be done by a pair of magnets. The applied forces and time scale are on the same order of magnitude as with optical tweezers. In contrast to an optical tweezer, a magnetic tweezer can also rotate the particle to induce twist and supercoiling in the DNA tether. In a magnetic tweezer it is easy to control multiple particles in parallel [9], whereas with optical tweezers either the laser focus needs to be switched between particles or a holographic set of traps need to be created [7]. In addition to these methods, many single molecule imaging methods have been used to study nucleic acids. Examples are fluorescence microscopy, total internal reflection microscopy, Förster resonance energy transfer, fluorescence spectroscopy, electron microscopy [10] and surface plasmon resonance. Combinations of imaging and manipulating tools are also often used [11]. An exhaustive overview of these methods is beyond the scope of this work. The

16 1.1 Nucleic acids interested reader should start with the Springer Handbook of Single-Molecule Biophysics [12].

1.1.4 Detection of specific nucleic acids The detection of specific nucleic acids amounts to finding a specific sequence of nucleotides. Often used methods for nucleic acid detection in cells include FISH (fluorescence in situ hybridization), molecular beacons and the expression of fluorescent protein [13]. The two most common methods for the detection of gene expression are the real time quantitative polymerase chain reaction (real- time qPCR) [14] and microarrays [15]. Other methods are being developed, some of which are similar to the one we propose. The next section discusses real-time qPCR, microarrays and two methods methods that show some similarity to the work in this thesis.

Real-time qPCR The polymerase chain reaction was invented over 25 years ago and is now a widely used method to amplify the amount of a specific nucleic acid if the ends of the sequence are known. First the DNA is heat-denatured into both its single strands. Two synthetic oligonucleotides (short nucleotide sequences) are annealed (hybridized) to the ends of the target sequence. The hybridized oligonucleotides serve as the primers for DNA synthesis. Single nucleotides and a DNA polymerase enzyme are added to extend the complementary strands, starting at the primers. When the synthesis is complete, the double stranded products are heat-denatured again and the process repeats. Each cycle doubles the number of copies of the target sequence. To amplify RNA, it is first transcribed into its complementary DNA (cDNA), using reverse transcription. This reaction is called reverse-transcription PCR (RT-PCR). The amount of double stranded DNA product can be quantified by labeling the product with fluorescent probes. Quantification can either be done at the end of the reaction (qPCR) or during the reaction (real time qPCR). Most commonly the number of PCR cycles it takes to reach a certain amount of fluorescence is determined and compared to a control reaction. As the fluorescence signal increases linearly with the amount of fluorophores and the PCR doubles the amount of product in each cycle, the comparison gives the relative amount of target nucleic acid in the original sample with respect to the control nucleic acid [14].

Microarrays The use of microarrays is popular in the ﬁeld of gene expression analysis as the expression of many genes can be determined simultaneously [16].

17 1 Introduction

In general, a microarray consists of a glass slide with many robotically printed areas with specific probes consisting of oligonucleotides. The oligonucleotide probes have a nucleotide sequence corresponding to the gene(s) of interest. Mes- senger RNA is isolated from the sample and labeled with a specific fluorophore in a reverse transcription process. Usually the relative gene expression between a control and treated sample is determined by labeling the resulting cDNA from both species with a different fluorophore. The labeled cDNA is added to the glass slide and left to hybridize with the probes. The relative fluorescence of both fluorophores at the spot of each probe is determined using (confocal) fluorescence microscopy. This gives the relative gene expression between the control and treated sample of each gene. Housekeeping genes that should have the same gene expression in both samples are used to normalize the differences in fluorescence intensity of both fluorophores [17].

Similar methods to the work in this thesis Singh-Zocchi et al. [18] used 40-90 nucleotides long DNA oligonucleotides to tether 1 μmdiameter polystyrene particles to a glass substrate. Electrostatic repulsion between particle and substrate stretches the tether molecules. The height of the particles is monitored by using evanescent illumination and determining the scattered intensity. The nucleic acid detection scheme involves detecting either an increase or a decrease in the height of the particle, depending on the amount of tethers per particle. So far the method has been proven to be able to detect oligonucleotides at a length of only 40-90 nucleotides long. However, the evanescent height readout cannot distinguish between intensity ﬂuctuations of the illumination and a true change in eﬀective tether length upon hybridization. Maye et al. [19] constructed molecular devices from 11.5 nm diameter gold nanoparticles interconnected by DNA constructs. Part of the constructs were single stranded. The molecular devices were formed as either three dimensional bcc crystal-like structures or as dimers. The lattice constant of the 3D structure and the hydrodynamic radius of the dimers was shown to contract or extend upon hybridization of ssDNA using small-angle x-ray scattering and dynamic light scattering, respectively. This method could be used to detect small nucleic acid sequences (oligonucleotides with a length determined by the length of the lattice DNA construct). However, as stated in the paper by Maye et al., the re- use of the molecular devices is hampered by the fact that removing the detected nucleic acid results in double stranded DNA constructs to get stuck in the 3D crystal-like structure.

18 1.2 Dark ﬁeld Tethered Particle Motion

(a) quantitative PCR (b) Microarray

Figure 1.5: a Fluorescence intensity versus PCR cycle during qPCR. The amount of cycles necessary for a certain fluorescence signal is a marker for the number of molecules at the start of the reaction. Source: http: // www. hgbiochip. com/ eservices-3. html . b Principle of gene expression analysis using a microarray. mRNA from a control and treated sample is first translated into cDNA labeled with 2 different color fluorophores. The cDNA is left to hybridize with specific gene probes on the chip. The relative amount of gene expression for each gene is determined by the relative fluorescence intensity. Source: http: // www. fastol. com/ ~ renkwitz/ microarray_ chips. htm

1.2 Dark ﬁeld Tethered Particle Motion

In tethered particle motion the reporter particle that is tethered to the substrate is usually a (fluorescent) polystyrene particle. In dark field tethered particle motion (DF-TPM) highly scattering metallic nanoparticles are used as reporter particles. The scattering intensity and spectrum of those particles depends mainly on the material, size and shape of the particles and can be influenced by the surrounding medium. The particles are clearly visible against a dark background under dark field illumination.

19 1 Introduction

1.2.1 Light scattering by small particles

Rayleigh scattering The light impinging on a small spherical particle causes the electrons in the particle to oscillate at the same frequency. The electrons will then radiate photons with the same frequency as their oscillation. Rayleigh scattering describes this elastic light scattering by spherical particles much smaller (roughly 20 times) than the wavelength of the incident light, where the particle behaves as one large oscillating electric dipole. Lord Rayleigh deduced that the scattering intensity then depends on the wavelength of the incident light as I ∼ 1/λ4 [20]. He could thereby explain why the sky appears blue: The light from the sun is scattered by atoms and molecules in the atmosphere before reaching our eyes. Shorter wavelengths (blue light) are scattered much more strongly than longer wavelengths (red light). The Rayleigh scattering intensity from a particle illuminated by an unpolarized light source is given by [21]: 4 6 4 2 − 2 8π r nmedI0 m 1 2 I = 2 4 2 1+cos θ . (1.1) d λ0 m +2

I0 is the intensity of the incident light, r the radius of the particle, nmed the index of refraction of the surrounding medium, d the distance between the particle and detector, λ0 the wavelength of the incident light in vacuum, θ the angle between the incident light and detection and m =(nim + nreal)/nmed is the ratio between the particle and medium index of refraction. Equation 1.1 predicts that the light is not scattered isotropically: The intensity is twice as high in the forward direction (θ = 0) as in the direction perpendicular to the incident light. The intensity depends on the size and composition of the particle: It increases with the radius of the particle to the sixth power. The scattering does not change the wavelength of the light, however some wavelengths are scattered more intensely than others. The spectrum of the scattered light can be determined from the dependence of the index of refraction on the wavelength of the light. For many materials the scattering intensity decreases with wavelength, however for metallic nanoparticles there are certain wavelengths where resonance scattering occurs due to surface plasmon resonance [22]. Resonance occurs when the denominator of the second term in equation 1.1 approaches zero, i.e. when the real part of the particle index of√ refraction equals zero nreal = 0 and the relative imaginary part nim/nmed = 2. The peak scattering wavelength for gold Rayleigh scatterers lies around λ = 535 nm (green).

20 1.2 Dark ﬁeld Tethered Particle Motion

Mie scattering As particles get larger, the particle can no longer be approximated as an oscillating electric dipole. The electrons in different parts of the particle will oscillate with a different phase. Mie theory [23] describes the scattered light as a superposition of the influences of electric and magnetic multipoles of many orders. For small particles the Mie theory reduces to that of an electric dipole and is equal to the Rayleigh expression. The higher order multipoles broaden the scattering spectrum with respect to the Rayleigh scattering and add other resonance peaks to the spectrum [21]. The resonant peak of metallic nanoparticles experiences a red shift with increasing particle size [22]. Yguerabide and Yguerabide [21] determined the scattering cross section for metallic Rayleigh and Mie scatterers as a function of wavelength, both in theory and experiment. They determined that the scattering of gold nanoparticles up to a diameter of 30 nm can be described by Rayleigh scattering. Further- more, they determined that the peak scattering wavelength for 80 nm diameter gold nanoparticles lies at 555 nm. When illuminated by light with equal irra- diance, the scattering intensity of a single gold nanoparticle is approximately equal to the fluorescence intensity of 5 × 105 fluorescein molecules. Fluores- cein molecules, however, can only emit roughly 1 × 105 photons before they are photochemically destroyed under the influence of the incident light and oxygen (photobleached). Metallic nanoparticles do not photobleach. Thus, under the same imaging conditions, gold nanoparticles can be imaged for a much longer period of time than fluorophores such as fluorescein and with a very high signal compared to single fluorophores.

1.2.2 Dark field microscopy Dark field microscopy is a contrast method to distinguish scattering from non- scattering objects. In dark field microscopy, the sample is illuminated by rays with a higher angle of incidence than the imaging objective can accommo- date. Therefore direct transmitted or reflected light cannot enter the objective. This is ensured by using illumination with a higher NA (numerical aperture: NA = n sin(θ), with n the index of refraction of the immersion medium and θ the opening angle of the lens) than the imaging objective. Only light that is scattered or diffracted by the sample can enter the objective. In this manner even scatterers much smaller than the resolution limit of the imaging optics can be visualized. The simplest dark field illumination can be achieved using e.g. a fiber coupled light source and illuminating the sample under a high angle of incidence. This

21 1 Introduction method has the drawback that the sample is only illuminated from one side and therefore shadows occur [24]. Symmetric dark field illumination can be achieved by placing a light stop over the condenser such that the central part of the illumination is blocked. The sample will then be illuminated by a hollow cone of light. This method is suitable for objectives whose NA is smaller than 0.65, as the NA of the objective should be smaller than that of the illumination. For high NA objectives, specialized dark field condenser lenses for transmission imaging are used. The most popular type is a cardioid condenser, which uses glass mirrors and oil immersion for illumination with a typical NA of 1.2 to 1.4 [25]. Another method for dark field imaging is to only illuminate the outer ring of the imaging objective and block the directly reflected light in the image forming path using an annular block [26]. Specialized reflection dark field objectives are now readily available. They are mostly used in metallurgy, for the inspection of metallic surfaces, as surface micro-defects can be visualized clearly on a dark background [25].

Objective

Sample

Condenser

Figure 1.6: The light path in a transmission dark ﬁeld microscope. The sample is illuminated with oblique rays, light rays at a high angle of incidence, by placing a light stop in the center part of the condenser. The NA of the objective is smaller than the NA of the condenser, therefore direct light can not enter the objective. Only light that is diﬀracted or scattered by the sample can enter the objective.

22 1.3 Thesis objectives

1.3 Thesis objectives

The work in this thesis was carried out as part of the MicroNed program. Our industrial partners are looking for new methods for rapid and sensitive detection of nucleic acids for post-harvest quality assessment and production control in dairy products. Processes in living tissue of agro-products determine among other things the freshness and shelf-life of the products. These processes are regulated by proteins (enzymes). Post-harvest quality assessment relies on the fact that the mRNA content reports which genes are expressed and thus which proteins are being formed in the specimen. Bacteria play a large role in the fermentation process of cheese. For production control in dairy products, it is necessary to assess which bacterial strains are present in a fermentation mixture as well as to determine the gene expression of those bacteria. Other applications of rapid and sensitive nucleic acid detection can be found, e.g. in medical diagnostics. For instance, a newly developed method could be used to diagnose a tuberculosis infection by detecting nucleic acid sequences specific for the mycobacterium tuberculosis bacteria. As both the genome and the primary markers for the most important drug resistent forms of M. tuberculosis have recently been identified, the fast and sensitive nucleic acid detection would enable a true point-of-care test, which is currently lacking [27]. Real-time qPCR and microarrays, the current widely used methods for detection of nucleic acids, require the nucleic acid to be amplified and labeled before detection is possible. They can be very expensive and time consuming and often require dedicated clean laboratories and highly trained personnel [28]. The projects in the MicroNed work package FoaC are dedicated to develop- ing technologies for a lab-on-a-chip device for rapid, sensitive, high-throughput sensing of nucleic acids. Such a lab-on-a-chip device requires several processing steps to be done on-chip. Consider for instance the lysing of the cells containing the nucleic acid and purification of the nucleic acid. Each of the partners in the work package will develop new technologies that will support the complete device. Our role is to develop a method for the final detection of the nucleic acid, at the point where purified nucleic acid will reach the detection area. We propose using dark-field tethered particle motion. A single stranded DNA molecule with a sequence complementary to the target nucleic acid is used to tether a gold nanoparticle to the substrate. Upon hybridization of the target nucleic acid with the tether, the motion of the particle will change. The main advantage of this method would be that the nucleic acid can be added directly to the detection part of the chip. This method would be most suited for the

23 1 Introduction detectionofthepresence of the nucleic acid at low target concentrations. The pre-processing needs to involve extraction and purification of the nucleic acids; no further amplification and labeling is necessary. Furthermore, the scattering signal of gold nanoparticles does not bleach over time as do the commonly used fluorescence labels. The method could be multiplexed by tethering several particles to the substrate using DNA molecules with different sequences. A system where multiple particles are tethered using the same tether sequence might enable concentration measurements of the DNA molecules. A schematic view of how such a multiplexed system would look is presented in figure 1.7.

gene A gene B control

Figure 1.7: Multiplexing of Tethered Particle Motion.

This thesis describes theory, simulations and experiments to describe and characterize the dark ﬁeld tethered particle motion method for nucleic acid detection. The objectives of this thesis are to understand and characterize the method and setup, and to provide a proof-of-principle experiment. This does not comprise the design of a multiplexed system for the detection of multiple sequence or the concentration of a sequence. The rest of this thesis is structured as follows:

Chapter 2 The contour length and persistence length of the DNA largely determine the position distribution of the particle. Chapter 2 describes the statistics of the tethered particle’s motion and we show how the persistence length of the DNA can be determined when the contour length of the tethering DNA is known. We determine the 2D (projected) motion of the particle in a dark ﬁeld microscope and compare the position distribution to simulated ones.

Chapter 3 In chapter 3 the microscopy and analysis of the motion is expanded to the third dimension. A cylindrical lens is used to encode the height of the

24 1.3 Thesis objectives particle in the image.

Chapter 4 Tethered particle motion is often used to study the kinetics of DNA binding proteins. In chapter 4 we study the kinetics of the motion of the tethered particle itself, i.e. we study the relationship between the forces acting on the particle and its motion. To avoid confusion with the study of enzyme kinetics we call this the dynamics of tethered particle motion.

Chapter 5 In chapter 5 the experiments that should lead to a proof-of- principle are described. As we have not been able to obtain satisfying results, the chapter ends with several recommendations on how to proceed with further experiments.

The diﬀerent materials and methods used for the experiments in these four chapters are summarized in table 1.1.

25 Sub- Cou- Tether Measurement buffer R/T4 Imaging optics Cyl. Camera strate pling molecule lens5 Chapter 2 gold thiol2 dsDNA 25 mM Tris-HCl, 100 R 50x 0.8 dark field No Hamamatsu (λ-DNA) mM NaCl, pH 7.4 objective C8800 Chapter 3 glass DIG3 dsDNA 50mM sodium phos- T Oil immersion dark Yes Andor (λ-DNA) phate buffer, 50 mM field condenser, 60x iXon 897 NaCl, pH 7.4 0.7 air objective or 100x oil immersion objective with adjustable NA Chapter 41 shiitake BX glass DIG3 dsDNA 50 mM sodium phos- R 100x 0.9 dark field No Andor (shiitake) phate buffer, 100 objective iXon 897 mM NaCl, pH 7.4 lambda BX glass DIG3 dsDNA 50 mM sodium phos- R 100x 0.9 dark field No Andor (λ-DNA) phate buffer, 100 objective iXon 897 mM NaCl, pH 7.4 lambda IX glass DIG3 dsDNA 50 mM sodium phos- T Oil immersion dark Yes Andor (λ-DNA) phate buffer, 50 mM field condenser, 60x iXon 897 NaCl, pH 7.4 0.7 air objective or 100x oil immersion objective with adjustable NA Chapter 5 glass DIG3 ssDNA 1x SSC + 33% v/v T Oil immersion dark No Andor (lu- formamide, pH 7.4 field condenser, 60x iXon 897 ciferase) 0.7 air objective

Table 1.1: Overview of used (bio-)chemical materials and methods for the Tethered Particle Motion experiments per chapter. 1Three experiments; Experiment name as used in chapter 4. 2Disulﬁde (S-S) covalent binding. 3Digoxigenin (DIG) on one end of the DNA, antibody to DIG on substrate. 4R for imaging in reﬂection, T for imaging in transmission. 5Used for 3D imaging. 2

Mechanics of Tethered Particle Motion

The worm-like chain model describes the micromechanics of semi-flexible polymers by introducing the persistence length. We propose a method of measuring the persistence length of DNA in a controllable near-native environment. Using a dark field microscope, the projected positions of a gold nanoparticle under- going constrained Brownian motion are captured. The nanoparticle is tethered to a substrate using a single dsDNA molecule and immersed in buffer. No force is exerted on the DNA. We carried out Monte Carlo simulations of the experiment, that give insight into the micromechanics of the DNA and can be used to interpret the motion of the nanoparticle. Our simulations and experiments demonstrate that, unlike other similar experiments, the use of nano- instead of micro-meter sized particles causes particle-substrate and particle-DNA interactions to be of negligible effect on the position distribution of the particle. We also show that the persistence length of the tethering DNA can be estimated with a statistical error of 2 nm, by comparing the statistics of the projected position distribution of the nanoparticle to the Monte Carlo simulations. The persistence lengths of 45 single-molecules of four different lengths of dsDNA were measured under the same environmental conditions at high salt concentration. The persistence lengths we found had a mean value of 35 nm (standard error 2.8 nm), which compares well to previously found values using similar salt concentrations. Our method can be used to directly study the effect of

27 2 Mechanics of Tethered Particle Motion the environmental conditions (e.g. buﬀer and temperature) on the persistence length.

2.1 Introduction

Research into the properties of polymers such as double stranded DNA (dsDNA) has made a transition from bulk experiments to single-molecule experiments. Bulk experiments provide results averaged over the population, whilst single- molecule methods provide a clearer understanding of the mechanics of individual molecules. The micromechanics of dsDNA can be described by several models, the best known of which is the worm-like chain (WLC) model [29] for semi- flexible polymers. It describes dsDNA especially well if the forces exerted on the DNA are small (< 10 pN) [30]. The WLC model describes the conformations of the polymer as a curve with a certain correlation length in the direction along the contour. This correlation length is called the persistence length of the polymer and is the basis of the entropic elasticity of semi-flexible polymers. Many single-molecule experiments have been carried out to determine the persistence length of dsDNA. Optical [31, 32] or magnetic tweezers [33, 34, 35] have been used to apply a force to the DNA and obtain a force-extension curve. Fitting the WLC model to such a curve provides the persistence length of the dsDNA [36]. Other well-known methods include depositing the DNA onto a substrate and imaging its shape using either atomic force microscopy (AFM) [37, 38, 39] or electron microscopy (EM) [40, 41]. In the images collected using AFM or EM, the contours of the DNA are traced from which the persistence length can be determined. In this article, we describe a method for measuring the persistence length of dsDNA in a controllable environment. No force is exerted on the dsDNA and the molecules are not confined to a 2D surface, therefore they can adopt more natural 3D conformations. We use tethered particle motion (TPM), where a small reporter particle is tethered to a substrate using a single dsDNA molecule. The particle-molecule system is allowed to exhibit (confined) Brownian motion. The particle’s motion is influenced by the (micro-) mechanical properties of the tethering molecule and the environmental conditions (see figure 2.1). By following the motion of the particle, properties of the tether can be deduced. Using TPM the influence of different buffers and temperatures on the mechanical properties of dsDNA can be examined without applying any external forces on the DNA. TPM has been used for a number of applications, including studying DNA-

28 2.1 Introduction

Buﬀer Reporter particle

Tether molecule

Substrate

Figure 2.1: Principle of Tethered Particle Motion: a chain molecule is used to tether a reporter particle to a substrate. The reporter particle exhibits Brownian motion inﬂuenced by the mechanical properties of the tether.

protein interactions [42, 43], DNA and RNA transcription [44, 8], looping and supercoiling of DNA [45, 46, 47] and the determination of mechanical properties of DNA/RNA [48, 49, 50]. In these cases (except [48]) the reporter particle is a micrometer-sized polystyrene particle. The large size of the reporter particle compared to the DNA (lengths on the order of 100-2000 nm are generally used) causes the position distribution of the reporter particle to diﬀer from the Gaussian distribution that is characteristic of Brownian motion. According to Segall et al. [51] this is to be attributed to a volume-exclusion eﬀect due to steric hindrance of the particle near the substrate.

In contrast to the above mentioned methods, we use nanometer-sized gold particles (diameter 80 nm). In our case the dimensions of the particle are small enough such that volume-exclusion eﬀects caused by the particle’s proximity to the substrate do not inﬂuence the motion.

These highly scattering gold nanoparticles [52] are made visible using an (objective- type) dark ﬁeld microscope and imaged using a CCD camera. This combination (dark ﬁeld tethered particle motion, DF-TPM) produces images with high contrast and high signal-to-noise ratio, using a relatively simple setup [48]. The persistence length of the tethering dsDNA can be determined by statistically comparing the position distribution of the nanoparticle to computer simulations of the experiment where the dsDNA is modeled by the worm-like chain model.

29 2 Mechanics of Tethered Particle Motion

2.2 Theoretical background 2.2.1 Worm-like chain model

θ (ls; P )

DNA ts

Figure 2.2: Bending a semiﬂexible polymer over an angle θ between two tangents (t1 and t2) a distance l over the contour apart.

In the worm-like chain (WLC) model [29], semi-ﬂexible polymers are described by their bending rigidity. On short length scales it takes considerable energy to bend the polymers, whilst on longer length scales the molecule can be bent and curved much more easily. The characteristic bending length scale is called the persistence length. The persistence length (P ) is mathematically deﬁned as the decay length of tangent-tangent correlations of the polymer:

−|s−s | t(s) · t(s ) = e P . (2.1)

Here t(s)andt(s) are tangents to the polymer at two points a distance |s − s| apart on the contour of the polymer (see figure 2.2). The energy needed to bend a semi-flexible polymer over an angle θ over a length l depends on the temperature T and the persistence length P of the polymer: k TP E = B θ2. (2.2) WLC 2l Thermal fluctuations give rise to an entropic elasticity with an effective spring constant given in equation 2.3 for a dsDNA molecule of contour length L (ap-

30 2.2 Theoretical background proximation for small forces) [53]:

3k T k = B . (2.3) WLC 2PL The central moments of the end-to-end distance (R) distribution (see equation 2.4) have been analytically determined [54]. The second central moment for 2D and 3D conformations is the same, however the 2D persistence length is twice the 3D persistence length:

R =0, 2 2 − L − − P3D R3D =2P3DL 2P3D 1 e , 2 2 − L − − P2D R2D =2P2DL 2P2D 1 e ,

P2D =2P3D. (2.4)

Considerable effort has been made to analytically derive the complete end-to- end distance distribution of worm-like chains [55, 56, 57, 58]. Since in TPM experiments the dsDNA molecule is attached to a substrate at one end and the other end carries a reporter particle, the influence of these factors has to be taken into account. Although analytical approaches were used to determine the distribution for worm-like chains with constrained ends [56, 57], as of yet there is no simple analytical formula for the position distribution of tethered particles. We therefore take a different approach: We obtain the position distribution by sampling a large number of possible dsDNA and particle conformations using Monte Carlo simulations and determine the simulated position distribution of the particle.

2.2.2 Volume exclusion effect In our TPM experiments the observable is the (projected) motion of a particle attached to the free end of the DNA. Directly fitting the WLC model to our observations disregards the influence of interactions between the substrate, DNA and reporter particle. The influence of excluded volume by particle-substrate interactions was analyzed in a recent article by Segall et al. [51]. The particle- substrate interaction is modeled as a hard-wall interaction, which limits the conformations that the DNA can adopt and results in an effective stretching force on the DNA. Segall et al. define a dimensionless number, the excursion

31 2 Mechanics of Tethered Particle Motion

number NR, as a function of the particle radius Rp and the contour length L and persistence length P of the polymer chain:

Rp NR = . (2.5) PL/3

For situations where the excursion number is larger than 1, the volume exclusion effect is such that the DNA is effectively stretched. The Brownian motion of the particle is said to be “particle-dominated”. At excursion numbers < 1the motion is not significantly influenced by the particle and therefore the motion is “molecule-dominated”. According to equation 2.5 the motion of a particle with radius 40 nm is “molecule-dominated” for dsDNA tether lengths down to 137 nm or 400 bp. For ssDNA tethers, the tether length should be larger than 3 μm or 7000 nucleotides. Segall et al. go on to show the influence of the excursion number on the central moments of a freely-jointed chain (FJC), which is a more general model for flexible polymers. The end-to-end distance distribution of a freely jointed chain is Gaussian with a mean-square end-to-end 2 distance R3D =2PL [4], equal to the WLC model for polymers with a long contour length (L P ). The influence of the excursion number on the second central moments of the end-to-end distance for freely jointed chains is given in equation 2.6 (see [51] , eqn. 10): PL 4N R2 = 2+√ R , ⊥ 3 π erf(N ) R PL 4N 2 √ R 2 Rz = 2+ + NR . (2.6) 3 π erf(NR)

2 2 Here R⊥ and Rz are the second central moments of the projected radius and height of the position of the particle, respectively. Adding the height and projected radius (which can be done as they are independent of each other) gives the following equation for the 3D mean square end-to-end distance: PL 8N 2 √ R 2 R3D = 4+ + NR . (2.7) 3 π erf(NR)

In the limit of NR 0 equations 2.6 and 2.7 give the same results as the FJC model without adaptations.

32 2.3 Experimental methods

2.3 Experimental methods

2.3.1 Monte Carlo simulations

Monte Carlo simulations were carried out to determine the position distribution of the particles in TPM experiments. The WLC model was used to incorporate the mechanical properties of the tethering dsDNA. Apart from simulations of TPM experiments, we also simulated the end-to-end distance distribution of free DNA molecules, as well as the position distributions of the free end of DNA molecules attached to a substrate at one end. The simulations were carried out in Matlab and included the influence of the physical properties of the substrate and nanoparticle. Our implementation is based on an article and (Mathematica) code provided by Nelson et al. [49] For each conformation, the DNA molecule is built as a chain of segments with length ls P . Each segment has a certain (bending) angle with respect to the previous segment, that is randomly drawn from the statistical distribution of the bend angle given in the WLC model. This distribution is obtained from Boltzmann statistics of the energy needed for a certain bending angle (eqn 2.2) [39]: 2 P −Pθ 2 Pr(θ|ls,P)= e L . (2.8) 2πls In TPM experiments the DNA is attached to a substrate using a freely pivoting connection and we simulate it as such. The interactions of the DNA and nanoparticle with the substrate are modeled as hard-wall interactions. This is implemented in the simulations by taking the orientation of the first segment confined to the upper half space (z>0) and discarding any configurations where the chain or nanoparticle crosses the z = 0 plane. The nanoparticle attached at the free end of the DNA is freely pivoting around the end of the DNA. For each DNA configuration, the orientation of the nanoparticle is randomly drawn from a uniform distribution. If the nanoparticle intersects with the DNA or the substrate in any segment the conformation is discarded. The simulations are carried out for 81 different persistence lengths from 10 to 90 nm in steps of 1 nm. For each persistence length conformations are generated until a total of 105 allowed conformations have been obtained. This is done for each of the following three cases: 1) free molecules, 2) molecules attached to a substrate at one end, and 3) molecules attached to a substrate at one end and a reporter particle bound at the other end, as in our TPM experiments. Generating 105 allowed conformations for a 480 nm long DNA molecule with a

33 2 Mechanics of Tethered Particle Motion persistence length of 50 nm takes approximately half an hour on a modern PC.

2.3.2 TPM experiments TPM experiments (as opposed to simulations) were carried out on double- stranded DNA of 4 different contour lengths: 123 nm, 482 nm, 908 nm and 1660 nm (362, 1417 , 2672 and 4882 basepairs respectively). The DNA is coupled at one end to a gold substrate using thiol-thiol binding. At the other end a gold nanoparticle (diameter 80 nm) is bound using biotin-anti-biotin binding. The different lengths are all observed in the same environmental conditions (buffer, temperature). The excursion numbers as defined in equation 2.5 for the different DNA lengths are all below one (0.88, 0.45, 0.33 and 0.24 for the different contour lengths respectively, using a value of 50 nm for the persistence length). According to Segall et al. the motion of the nanoparticle is therefore not dominated by its proximity to the surface and there is no significant effective force stretching the DNA (see equation 12 in [51]: the force is 3-34 fN for these lengths). dsDNA fragment preparation The dsDNA fragments were synthesized from an unmethylated lambda DNA (Promega, NL) template using Expand Long Template PCR System (Roche, NL). dNTPs were bought from Promega, NL. The following primers (Isogen, NL) were used for the production of all fragments: 5’-Biotin-ATA GGC CAG TCA ACC AGC AGG-3’ (forward), 5’-disulfide-ATA GGT AAA GCG CCA CGC TCC-3’ (reverse), 5’-disulfide-GGG ATA ATC GGC GTG GCA GAT AAC-3’ (reverse, for 2672 bp fragments only). 5’-disulfide-GCA GCT TCT GAC CGC AGT TAG CG-3’ (reverse, for 1417 bp fragments only), 5’-disulfide-TCC AAG CTC CGG GTT GAT ATC AAC C-3’ (reverse, for 362 bp fragments only). The PCR product was purified according to the QIAquick PCR purification kit manual (Qiagen, NL).

TPM sample preparation All steps in the preparation of the TPM chips were carried out in a humidi- ﬁed surrounding. Gold supports (Arrandee, GER) were incubated with 1 mM hexanethiol (Fluka, NL) diluted in toluene (Sigma, NL) for approximately 60 minutes and subsequently washed with toluene and isopropanol for at least 30 minutes each. This step prevents the non-speciﬁc binding of DNA to the gold

34 2.3 Experimental methods surface. The hexanethiol chips were divided into 4 sections, one for each of the different DNA fragments. Onto each section 0.5 mg/ml biotin in TE buffer (10 mM Tris-HCl, 1 mM EDTA; pH 8.0 at 21◦ C) was applied for 15 minutes and subsequently washed with TE buffer. The immobilized biotin allowed the production of stationary beads as the gold nanoparticles are coated with anti-biotin antibodies. For each length, the purified dsDNA was diluted to a concentration of approximately 10 ng/μl in TE buffer, applied onto a separate section of the support and incubated over night at 4◦ C. Unbound material was washed away by thorough rinsing with TE buffer. Gold nanoparticles coated with anti-biotin antibodies (80 nm diameter, British Biocell, UK), diluted 200 times from stock in TE buffer, were applied onto the chip surface and incubated for 60 minutes. Unbound particles were washed off with TE buffer. The prepared gold slide was kept wet by TE buffer until usage, then it was placed on the lower part of a flow chamber, which was subsequently closed by a cover slip and filled with measurement buffer resembling physiological conditions (25 mM Tris-HCl, 100 mM NaCl; pH 7.4). This allowed observation of the sample over several hours.

TPM measurement

The flow chamber was placed on the specimen holder of an upright microscope (Olympus, NL). A darkfield objective (UMplan Fl BD 50x 0.80, Olympus) was used to image the nanoparticles on a frame transfer CCD camera (Hamamatsu C8800). In a darkfield objective, the illumination and imaging light paths are separated from each other. The sample is illuminated with a hollow cone of light under an oblique angle. Only scattered light can re-enter the imaging part of the objective, therefore objects that scatter light brightly are imaged against a dark background. Fields of view with several moving and stationary nanoparticles (the latter are used for drift correction) were chosen and 1500-2000 consecutive frames were captured for each field of view. The exposure was set to 10 ms per frame to collect enough photons for high signal-to-noise ratio images without a significant underestimation of the motion due to motion blur [59]. A short explanation of the motion blur effect is given in the supplementary material in appendix A. The sampling distance in x and y was Δx =Δy = 160 nm. The image of a 80 nm gold nanoparticle is given by the point-spread function (PSF) of the microscope, which can be approximated by a Gaussian [60]. Figure 2.3 shows a typical image of a gold nanoparticle attached to DNA, the peak signal

35 2 Mechanics of Tethered Particle Motion to noise ratio of which is 33 dB 1. The measured image of the nanoparticle is larger than the theoretical PSF due to imaging through 500 μm of buﬀer.

800 nm

Figure 2.3: The dark ﬁeld image of a gold nanoparticle (SNR is 33 dB).

Analysis The position distribution of the tethered nanoparticles was obtained by analyzing the image series. They were analyzed using in-house software based on the Matlab toolbox DIPimage (Scientific Image processing toolbox, www.diplib.org, Delft University of Technology, Delft, NL). The user manually selects the stationary and moving nanoparticles in the first frame of the image sequence via a graphical user interface. The remaining procedure is fully automated. The positions of all selected nanoparticles are tracked with sub-pixel precision using a maximum likelihood estimation of the position of the Gaussian image profile. Based on the relative averaged motion of the nanoparticles marked as stationary, the global drift is computed and subtracted from the motion of the moving nanoparticles. No rotation of the sample plane during the experiments has been found. Care has to be taken to only include correctly (singly) tethered particles in the subsequent analysis steps. Multiply tethered particles are identified by asym- metry of the position distribution [46, 50]. For this reason we visually inspected 2D histograms (see e.g. figure 2.7a) of the positions of the moving nanoparticles to verify an isotropic distribution. Blumberg et al. [46] and Pouget et al. [50] discard any position distribution with an anisotropy above 20 and 10 percent

1 max(I) I N Deﬁned as: 20 log10 std(N) . and are the intensities and noise in the image.

36 2.3 Experimental methods respectively. Visual inspection shows that an anisotropy of 10 percent is already clearly visible by eye, therefore we can safely assume that we kept only singly tethered particles.

Localization precision

The localization precision of our method was extensively tested. The theoretical 2 √σg limit to the localization precision of Gaussian image profiles is Δx = γAt, where σg denotes the size of the Gaussian profile and γAt the number of photons collected per particle [60]. We compared the localization precision of simulated Gaussian blobs to this limit, as well as the remaining detected motion of the stationary particles. Figure 2.4 shows some results. The localization algorithm has a precision comparable to the theoretical prediction in the absence of (Gaus- sian) read noise in the camera (data not shown). However, the CCD camera has considerable read noise (30 e− rms), therefore Gaussian noise was added to the simulated images resulting in a more realistic simulation and producing a slightly inferior localization precision. The detected remaining motion of stationary particles is larger than the localization precision as predicted by the simulated images. This indicates the presence of instrument vibrations or resid- ual motion of the stationary particles. In our experiments we used an exposure time of 10 ms, which typically resulted in 0.1-0.2x105 detected photons per bead per image. In that case the standard deviation of the x-position of the stationary particles was only on the order of 30 nm. This represents a minor influence on the obtained position distribution for the moving particles. Increasing the exposure time would result in a slightly better precision (25 nm), but would lead to a much larger underestimation of the distribution due to motion blur averaging of the positions [59] (and appendix A).

Persistence length Our method for determining the persistence length of the dsDNA makes use of statistically comparing the measured position distribution to the simulated ones. The simulations were carried out with diﬀerent persistence lengths ranging from 10 to 90 nm. The statistical test we use is the nonparametric two sample Kolmogorov-Smirnov (K-S) test [61]. This test compares the cumulative distribution functions (CDF) of the two distributions (Fn1 and Fn2 ). The test statistic D is the maximum vertical distance between the two CDFs:

| − | D =maxFn1 Fn2 . (2.9) x

37 2 Mechanics of Tethered Particle Motion

50 Theoretical limit Simulated images using camera model Experimental images of stationary particles 40

10 Standard deviation of X-position [nm]

0 00.20.40.60.811.21.41.61.82 ×105 Photons

Figure 2.4: Localization precision for Gaussian image profiles. The solid line represents the theoretical limit by Ober et al. [60] The diamond scatter plot is the precision obtained when analyzing simulated images with the same properties as experimentally obtained images. The circular scatter plots represent measurements of the position of 9 different stationary particles in TPM experiments. The difference between the simulated images and stationary particles is due to instrument vibrations and resid- ual motion of the particles. The resulting localization precision for our experimental conditions is 30 nm.

The probability of ﬁnding a certain D with sample size N is seen here as the statistical agreement between the measurement and simulation. A large value of D, taking into account sample size, leads to a low probability that the measurement of the stochastic process and the simulation of the process are in agreement. The persistence length of the dsDNA is determined by looking for the simulation with which the measured distribution has the highest statistical agreement. The persistence length used in that simulation is the measured persistence length.

38 2.4 Results

2.4 Results

2.4.1 Monte Carlo simulations

In figure 2.5 the results are shown for simulations of dsDNA molecules with a contour length of 4882 bp (∼ 1660 nm), persistence length of 50 nm and (where applicable) particle radius of 40 nm. In this case the excursion number is NR =0.24. The resulting position distributions for the three different cases (free molecules, molecules attached to a substrate and molecules in TPM experiments) are shown. The histogram in figure 2.5a represents the distribution of the end-to-end distance of simulated free molecules. Figures 2.5b and 2.5c show the distribution of the projected radius (R⊥ = x2 + y2) of the end point of the DNA and of the center of the attached nanoparticle respectively. We fitted the distributions with Gaussian distributions (solid lines) since for long molecules (L P ) the DNA should have a Gaussian position distribution according to both the FJC and WLC models (central limit theorem). The Gaussian distribution of the radius r in 2D and 3D is given in equation 2.10 [62]:

2 r −r Pr(r, σ, 2D)= e 2σ2 , for r > 0, σ2 2 2 1 2 r −r Pr(r, σ, 3D)= e 2σ2 , for r > 0. (2.10) σ π σ2 The fits show that our simulated distributions follow Gaussian distributions. If the particle-substrate interactions would have caused a significant volume exclusion effect, the distributions would not be Gaussian. This implies that the volume exclusion effect is negligible in our case, as predicted by the small excursion number. In figure 2.6 an overview of the central moments of the different simulations is given. The mean square radius is plotted as a function of the persistence length used in the simulations. In figure 2.6a we show the (3D) mean square end-to- end radius of free molecules and molecules attached to a substrate as well as the mean square radius of the position of the particle attached to molecules in TPM experiments. The DNA length used here is 4882 bp (∼ 1660 nm). Each data point represents the mean square radius of 105 conformations. The variation between 20 simulations of 5000 conformations each is less than 1.5 % for each data point, therefore no error bars are presented. As can be seen in this figure, attaching the molecules to a substrate causes a scaling of the mean square radius compared to free molecules. This scaling is

39 2 Mechanics of Tethered Particle Motion

(b) Molecule attached to a substrate, (a) Free molecule without a particle −3 ×10 ×10−3 3 3 Simulation Simulation 3D Gaussian ﬁt 2D Gaussian ﬁt 2.5 2.5

2 2

1.5 1.5

1 1

. Normalized count . 0 5 Normalized count 0 5

0 0 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 Radius (nm) Projected radius (nm)

×10−3 3 Simulation 2D Gaussian ﬁt 2.5

1.5

. Normalized count 0 5

0 0 200 400 600 800 1000 1200 Projected radius (nm)

Figure 2.5: The distribution of the (projected position) of the end point of the dsDNA (figures 2.5a and 2.5b) or the center of the nanoparticle (figure 2.5c) for simulated dsDNA configurations. Parameters: L = 1660 nm, P =50nm, Rp =40nm.

caused by an almost doubling (1.7 times) of the mean square height of the free end of molecules attached to a substrate compared to free molecules. For a freely jointed chain, DiMarzio [63] derived theoretically that the mean square height doubles when the chain is confined to a half-space. The fact that we find a factor of 1.7 might be due to the differences between the WLC model and the

40 2.4 Results

(b) Mean square radius from projected (a) Mean square radius (3D) as a func- position (2D) as a function of persis- tion of persistence length tence length ×105 ×105 6 2.5 Free molecules WLC model (projection) Molecules attached to a substrate Molecules in TPM experiments 5 Molecules in TPM experiments 2 Segall et al (projection)

Segall et al ) 2 )

2 4 1.5 (nm

(nm 3

2 1 2 proj

R 2 R

. 1 0 5

0 0 0 102030405060708090 100 01020304050607080 90 100 Persistence length (nm) Persistence length (nm)

Figure 2.6: Central moments of worm-like chains. Figure 2.6a shows the mean square radius of 105 simulated free molecules, molecules attached to a substrate and molecules in TPM experiments (dsDNA length: 4882 bp or 1660 nm, radius of the nanoparticle: 40 nm). The variation on each data point is less than 1.5%, therefore no error bars are plotted. The dashed line is the model proposed by Segall et al. In ﬁgure 2.6b the simulations of molecules in TPM experiments are compared to the WLC model and Segall et al. using only the projected position. The diﬀerences between the models and simulation is much less pronounced in that case.

FJC model. Attaching a nanoparticle to the free end of the molecules results in an additional offset of the mean square radius. The offset represents interactions of the nanoparticle with the DNA and the substrate, however the influence is much less pronounced than the model proposed by Segall et al. (equation 2.6) which is based on the scaling of the central moments with a dimensionless excursion number. Our simulations do not show the same scaling behavior as Segall et al. predict. In their article, however, they show that the model complies well with their own Monte Carlo simulations. These different behaviors can be explained by the fact that our nanoparticles are of a size that is on the order of the persistence length (diameter of 80 nm). Effectively, the DNA molecule will not ”feel” an extra segment that is on the same length scale as its own stiffness. We conclude that the scaling model proposed by Segall et al. does not hold in

41 2 Mechanics of Tethered Particle Motion the limit of small particle sizes [64]. 2 In figure 2.6b the mean square radius of the (x,y-)projection (R⊥) is plotted against the persistence length. In this figure we see that the differences between the WLC model (without taking into account the substrate and nanoparticle), the model proposed by Segall et al. and our simulations hardly differ within the measurement uncertainty if only the projected radius (2D) is used.

2.4.2 TPM experiments

Figure 2.7 shows some of the results for a nanoparticle tethered using 4882 bp long dsDNA molecule. A 2D histogram of the positions of that nanoparticle is shown in figure 2.7a. In figure 2.7b a histogram of the projected (radial) position is shown. The line represents a fit of a 2D Gaussian distribution to our data. The goodness of the fit denotes that our experiments too are not restricted by nanoparticle-substrate interactions. In figure 2.8 the results for the two-sample K-S tests with the simulations with different persistence lengths is shown. The measured persistence length here is 50 nm with an error (FWHM of the probability peak) of 2.0 nm.

(a) Isocontour histogram of 2D position (b) Radial position distribution −3 26.4 ×10 200 3 26.6 Experiment 2D Gaussian ﬁt 26.8 2.5 150 27 2 m 27.2 μ 1.5 y 27.4 100 1 27.6 . 27.8 0 5 50 Normalized count 28 0 13 13.413.814.2 14.6 0 200 400 600 800 1000 x μm Projected radius (nm)

Figure 2.7: Results for a gold nanoparticle (r = 40 nm) tethered to the surface using a 4882 bp dsDNA molecule. Figure 2.7a shows a 2D histogram of the positions of the nanoparticle during 2000 frames, while ﬁgure 2.7b shows the distribution of the projected radius of the particle positions. It can be ﬁtted well by a 2D Gaussian distribution.

42 2.4 Results

0.4 0.35 P=50nm 0.3 0.25 0.2 →←FWHM = 2.0 nm 0.15 Probability 0.1 0.05 0 02040 60 80 100 Persistence length (nm)

Figure 2.8: Results of two-sample K-S test, comparing experimentally obtained particle positions to simulations using diﬀerent persistence lengths. The ﬁgure shows that the best statistical agreement is with simulations using 50 nm. The error in this determination is only 2.0 nm.

In total 45 nanoparticles showing an isotropic position distribution were found for the four dsDNA lengths (6 for 123 nm, 18 for 482 nm, 12 for 908 nm and 9 for 1660 nm). The mean error in the determination of the persistence length for a single-molecule was 2 nm. In figure 2.9 the results of the 45 molecules are combined. In figure 2.9a the full distribution of the measured persistence lengths is shown in a histogram. The persistence lengths we found had a mean value of 34.8 nm (σ = 18.6 nm) with standard error 2.8 nm. The mean persistence length corresponds to what other researchers found under similar salt conditions (high Na+ concentration) [32, 65, 66]. In figure 2.9b the distribution of the mean-square radii for the different dsDNA lengths is visualized in box-plots. Overlayed on the box plots are the results of the simulations and the WLC model and influence of the volume exclusion, using 35 nm for the persistence length. Both models and the simulations fit the data very well: differences between these models and simulation are negligible compared to the measured variation between molecules.

43 2 Mechanics of Tethered Particle Motion

(a) Apparent persistence length distribution (b) Mean square projected radius 5 30 × Histogram 10

Mean value Simulations with P = 35 nm 25 2 WLC model (projection) with P = 35 nm Segall (projection) with P = 35 nm )

20 2 1.5 nm

15 (

1 10 2 proj

R .

0 5 5 Number of observations

0 0 0 10 20 30 40 50 60 70 80 90 100 0 500 1000 1500 2000 Measured persistence length (nm) DNA length (nm)

Figure 2.9: Results of the DNA experiments. (a) Distribution of the measured apparent persistence length of 45 dsDNA molecules. (b) Mean square projected position as a function of DNA length, experiments (in box-plots) compared to the simulations and theoretical models.

2.5 Discussion

In TPM experiments, the 2D projection of the position of the particle that is attached to the tether is imaged. The distribution of these positions should follow a Gaussian distribution, however other researchers (e.g. [49, 50]) show that their experimental data cannot be described by such a curve. This can be explained by taking into account excluded volume effects due to the presence of a large particle at the end of the DNA. Segall et al. have quantified this effect and defined a dimensionless excursion number to account for this effect [51]. In other TPM experiments (e.g. [49] and [50]), the bead radius is large compared to the persistence length and the contour length of the DNA; the excursion numbers are above one. In our case the use of dark field microscopy permits much smaller particle radii, since the scattering of these particles is quite visible against the dark background. The excursion number posed by Segall et al. is well below the critical value of one and the volume exclusion effect is therefore negligible. This is confirmed by the fact that a fit of a 2D Gaussian distribution to simulated (figure 2.5c) and experimental (figure 2.7b) data shows good agreement. This means that in our case there is no effective stretching force acting on the DNA

44 2.5 Discussion and the DNA is in an unaltered state. The excursion number was also used to predict a scaling of the central moments of the position distribution of freely jointed chains due to the volume exclusion effects. We have shown with our simulations that the behavior for worm-like chains differs from that model. If the tethered particle is small enough (Rp ∼ P ), that scaling behavior does not even hold. However, this has not been verified experimentally, since the simulations and models do not differ more than the variation between single molecule experiments if only the projected radius is collected (see figures 2.6b and 2.9b). If height information of the nanoparticle is also taken into account, the differences between the models and simulation are larger (see figure 2.10). Our measurements of the persistence length resulted in a mean value of 35 nm which is below the 50 nm value generally found in the literature. However, over the years many researchers have determined the persistence length at different salt concentrations and temperatures resulting in values ranging between 30 and 80 nm [65]. Notably, methods wherein the rotational relaxation time of the DNA is measured even generate different values depending on the model that is used to calculate the persistence length from the experimental results [67]. The general consensus is that at low salt concentrations, the self-interaction of the negatively charged DNA backbone results in a higher apparent persistence length. At higher salt concentrations this negative charge is screened by the positive ions in the buffer. Our measurements were done in a buffer with a relatively high salt concentration of 100mM and compare well to other results in this concentration range [32, 65, 66]. The large spread in the persistence lengths we measure resides in the fact that we have taken 45 individual, independent measurements: one for each molecule. Single-molecule measurements by AFM or EM, where the angle distribution or the end-to-end distance of the contour is used, are often analyzed by a slid- ing window approach over individual molecules, yielding a narrower persistence length distribution due to correlated evaluation. Furthermore, although it is common practice in TPM to discard any particle that exhibits significantly larger or smaller motion than is expected [46], we have taken into account all particles showing an isotropic position distribution to avoid biasing our measurements. In contrast to other single molecule methods such as AFM and EM where the environmental conditions are fixed, our method offers the possibility of measuring the influence of changing the temperature and buffer on the persistence length directly. Furthermore, it is possible to study the effect of interactions of the DNA tether with other molecules as for example proteins.

45 2 Mechanics of Tethered Particle Motion

×104 12 WLC model (free molecules) Simulations of TPM experiments )

2 10 Segall et al. m

2 Mean square radius (3D) (n

0 0 10 20 30 40 50 60 70 80 90 100 Persistence length (nm)

Figure 2.10: Second central moments of the (unaltered) worm-like chain model, simulated molecules in TPM experiments and the model predicted by Segall et al. [51] using 3D positional information for DNA with a contour length of 972 bp (330 nm).

2.6 Conclusions

We have described a method for sensitively determining the persistence length of DNA. By determining the motion of a gold nanoparticle tethered to a substrate using a DNA molecule and comparing the obtained position distribution to simulations we are able to estimate the persistence length of single molecules with a precision of 2 nm. The obtained projected position distributions have a Gaussian character, as expected from long polymers with negligible volume exclusion. The measured persistence length of 45 single molecules with 4 different lengths in the same environmental conditions had a mean value of 35 nm (standard deviation 18.6 nm) with standard error of the mean 2.8 nm. This complies with other results under the same salt conditions. Our method can also be used to directly measure the effect of environmental conditions on the persistence length, without additional external influences.

46 2.6 Conclusions

Acknowledgements

The authors would like to thank Philip Nelson for generously providing his (Mathematica) code for the Monte Carlo simulations and Keith Lidke for the CUDA code for the maximum likelihood estimation of the position of the Gaus- sian peaks. We would also like to thank Theo Odijk for numerous discussions.

Three dimensional measurements of Tethered Particle Motion

In this chapter the motion of gold nanoparticles tethered to a substrate using double stranded DNA is characterized in 3D, as opposed to the 2D measurements in chapter 2. The height information of the particle is captured using a cylindrical lens in the emission beam path of the dark ﬁeld microscope. This introduces astigmatism in the optical system, which allows us to determine the position of the particle with a precision of 6 nm in the lateral direction and 15 in the axial direction. We have measured the persistence length of double stranded DNA in all 3 dimensions separately by looking at both the statistics and dynamics of the motion of the tethered particle. In the lateral direction both statistics and dynamics measurements provide a persistence length of less than 30 nm, while the literature value lies around 50 nm. In the axial direction we see that the particle is on average further away from the substrate than expected from simulations. At the same time, the dynamics in z are much slower when compared to the expected behavior for a persistence length of 50 nm. This leads us to believe the particle is pushed upwards, resulting in a lateral motion reduced by the spring potential of the DNA. This would also explain the low measured persistence length in the lateral dimensions. We have estimated that this force would be a few fN. A likely candidate causing this upwards force is thermal buoyancy of water locally heated by the light source. The insights provided by the 3D measurements contribute to a better understanding of tethered

49 3 Three dimensional measurements of Tethered Particle Motion particle motion and the factors inﬂuencing it.

3.1 Introduction

Traditionally in TPM the particles are followed in a 2-dimensional projection as available with most microscopy techniques. In chapter 2 we have shown measurements of the persistence length of dsDNA in 2D. As was pointed out in section 2.5, 3D positions should enable us to describe the position distribution of a tethered particle more precisely. There exist a number of methods for the 3D tracking of single particles. Some researchers have used Total Internal Re- flection microscopy [46, 68, 69] for TPM experiments. However, this method only works in the range determined by the penetration depth of the evanescent field. The penetration depth depends on the wavelength and angle of incidence of the light and the index of the refraction of the immersion media and reflecting substrate. Van Ommering et al. [68] report a penetration depth of 95 nm in their experiments, while Blumberg et al. [46] determine a penetration depth of 200 nm for their setup, thus limiting the length of the DNA that can be studied to a few hundred nanometers. Two other frequently used methods for 3D particle tracking are based on the shape of the point spread function (PSF) as a function of the axial position of the particle. In defocused imaging the radius of the central peak and diffraction rings of the 3D PSF are used to determine the z-position of the particle [70, 71]. The precision of the z measurement is problematic when the particle is in focus and is best for moderate defocus, when the diffraction rings are clearly visible [72]. For larger defocus, the image becomes too blurred and the resulting drop in signal-to-noise ratio limits the precision. The lateral position can be determined from the 2D location in the image. The precision in x and y, however, is best if the particle is in focus. Fur- thermore, in the absence of spherical aberrations the PSF is symmetric around the focal plane, thus it is not possible to determine if the particle is above or below focus. This method was therefore expanded to multifocal plane imaging where either multiple focal planes are imaged on one camera side by side [73] or sequentially [74], or multiple detectors are placed to image the different focal planes [75, 76, 77]. The combined information of different focal planes then gives good resolution in all dimensions. In astigmatic imaging [78, 79, 80] a cylindrical lens is introduced in the imaging beam path of the microscope, splitting the focal plane into two axially separated planes for perpendicular rays. The particle will be imaged as an ellipse and the axial position with respect to the focal planes can be determined by fitting an

50 3.2 Materials and methods elliptical point spread function to the image. Astigmatic imaging allows position determination in a range defined by the depth of field of the objective with a precision that is best around focus [81]. There is no need to image multiple focal planes, since the height of the particle can be determined unambiguously from the principle axis of the elliptical image. Recently Smith et al. [81] published a paper and code for fast localization software running on the GPU. The software uses an iterative algorithm that con- verges to the maximum likelihood estimate of the position of a Gaussian PSF. It has been expanded to include 3D position estimation for astigmatic images. If the PSF of the system can be approximated as a 2D (elliptic) Gaussian peak, there is no need to use an experimentally measured PSF. In that case the software allows position estimation at the theoretical minimum uncertainty. We have applied this astigmatic imaging method to our dark field tethered particle motion setup in order to measure the persistence length of double stranded DNA in 3D. We will show that we can estimate the particle position between -500 and +500 nm of the focal plane with a precision of 6 and 15 nm in the lateral and axial directions, respectively. This has allowed us to determine for the first time the full 3D position distribution of particles tethered by dsDNA between 2000 and 5000 basepairs long.

3.2 Materials and methods

3.2.1 Sample preparation Double stranded DNA fragments of 3 different lengths are synthesized from an unmethylated lambda DNA template (Promega, NL) using the GoTaq PCR Core System (Promega, NL). The fragments are labeled by using a biotin modified forward primer and 3 different digoxigenin modified reverse primers. The resulting products are 2190, 3202 and 4899 basepairs long, containing a biotin label at one end and a digoxigenin label at the other end. A microscope object glass and cover glass are cleaned in isopropanol in a sonic bath for 20 minutes. A microfluidic cell is constructed by placing a sheet of parafilm or double sided tape between the glasses. This cell is incubated with 5 mg/ml blotting-grade blocker (Bio-Rad, NL) in PBS (50mM sodium phosphate buffer pH 7.4, containing 50mM NaCl) for 30 minutes. The cell is then washed with PBS and incubated with 50 μg/ml anti-digoxigenin (AbD Serotec, DE) in PBS buffer for 45 minutes. After washing with PBS, approximately 3-4 ng/μl of DNA in PBS buffer is incubated for 45 minutes. At this point, the anti-biotin coated gold

51 3 Three dimensional measurements of Tethered Particle Motion nanoparticles (BBInternational, UK) are suitably diluted in PBS and incubated for 45 minutes. In a ﬁnal washing step with PBS the unattached nanoparticles are ﬂushed away.

3.2.2 Setup and data collection The sample is placed in a holder on the stage of an Olympus inverted microscope (IX71, Olympus Nederland, NL). An oil immersion dark field condenser is used to illuminate the nanoparticles with a high angle of incidence. The light scattered by the nanoparticles can enter the objective (60x NA 0.7 air objective or 100x oil immersion with adjustable NA, Olympus). Direct light is rejected by ensuring that the NA of the objective is smaller than the NA of the condenser, the prerequisite for dark field microscopy. The NA of the dark field condenser is 1.2-1.4 as indicated on the condenser diaphragm. We have observed that an NA of the objective smaller than 0.9 gives satisfactory (good contrast) dark field images. A 500 mm cylindrical lens (Thorlabs, DE) is placed in the emission light path after the tube lens and the resulting images are captured using a cooled, back-illuminated EM-CCD camera (iXon 897, Andor Technology, UK). The EM-CCD camera ensures very fast readout times and virtually eliminates readout noise. A schematic of the setup can be found in figure 3.1. A region of interest (ROI) containing one or a few nanoparticles is selected on the camera. We collect 1500 time frames for each ROI at maximum framerate, which is between 100 and 300 fps depending on the size of the ROI (between 160x160 and 26x26 pixels respectively), and with an exposure time of 1 ms. This results in a photon count of 1 × 104 to 2 × 104 photons per nanoparticle per image. Note that this is a much higher photon count than can typically be achieved in fluorescence measurements.

3.2.3 Calibration of the position measurements The particles are tracked offline using CUDA code (C like programming lan- guage for the GPU, Nvidia Corporation, USA) based on the paper by Smith et al. [81] and using the DIPimage toolbox (Scientific image processing toolbox, www.diplib.org, Delft University of Technology, NL). The algorithm iteratively fits a 2D elliptical Gaussian to the data using parameters calibrated from a calibration set. The calibration set is obtained by imaging particles immobilized on the cover glass at different focal planes. A piezo nanofocusing system (PIFOC, Physik Instrumente, DE) lifts the objective in steps of 50 nm from -1 μmto+1 μm around the approximate focus. At each z-position 10 images are taken. Im-

52 3.2 Materials and methods

Dark ﬁeld ray path Mirror Light source

Dark ﬁeld condensor

Microﬂuidic cell Objective Cylindrical lens

CCD Computer Mirror

Figure 3.1: Schematic view of the 3D dark ﬁeld microscope setup. The inset shows the ray path for dark ﬁeld imaging: Direct light can not enter the objective, only scattered light.

ages are corrected for gain and offset to produce photon counts and then fed into the algorithm to fit the standard deviation (size) σ in the x-andy-direction as a function of z. The theoretical relation between z and the standard deviations in x and y is given in equation 3.2. The standard deviations found are fitted to the theoretical relation simultaneously to obtain the calibration parameters γ (astigmatism), d (depth of field), A and B (relative contributions of third and fourth orders).

(z − γ)2 (z − γ)3 (z − γ)4 σx(z)=σ0 1+ 2 + A 2 + B 2 , (3.1) d d d (z + γ)2 (z + γ)3 (z + γ)4 σ (z)=σ 1+ + A + B . (3.2) y 0 d2 d2 d2 An example of the measured and fitted standard deviations can be found in figure 3.2, where the fit parameters are: σ0 =1.03 pixels, γ = −1.00 μm, d = 0.6916 μm, A =0.02 and B = −0.04. After calibration of the parameters, the position of the particle in each image is found by maximum likelihood estimation of the x, y and z-position of a digitized 2 dimensional Gaussian with intensity I set against a background of mean intensity b. The digitized Gaussian is obtained

53 3 Three dimensional measurements of Tethered Particle Motion by integrating the following PSF over each pixel:

θ (x − θ )2 (y − θ )2 I0 − x − y PSF(x, y)= exp 2 2 + θbg. (3.3) 2πσx(θz)σy(θz) 2σx(θz) 2σy(θz)

Here x and y are the positions in the image and θx, θy, θz, θI0 and θbg are the estimated position, intensity and background.

4 Measured σx

3.5 Measured σy σ x Fitted σ 3 x σy Fitted σy 2.5 [pixels]

σ 2

1.5

1 −1.5 −1 −0.5 0 0.51 Piezo setting of objective [μm]

Figure 3.2: Calibration data for 60x 0.7 air objective. Note that the x and y direction are aligned with the pixel directions in the image.

Axial scaling Since there is a mismatch between the index of refraction of the medium in which the objective moves (either oil or air) and the sample medium (water) the measured z-position needs to be scaled. This axial scaling factor (ASF ) can be derived from geometrical optics. The paraxial value [82] is given in equation 3.4: z n ASF = 2 = 2 . (3.4) z1 n1

Here z2 is the z-position in the sample (in water), z1 the z-displacement of the objective, n2 is the index of refraction of water and n1 the index of refraction of

54 3.2 Materials and methods the immersion medium. Wave optics analysis shows that the true ASF diﬀers signiﬁcantly from the paraxial value (3 to 7.5% in our case) [83]. The true ASF for the 60x air objective is ASF =1.43 and for the 100x oil immersion it is ASF =0.85.

3.2.4 Drift and position correction In TPM, the measured positions are usually corrected for microscope stage drift using either the motion of stationary particles in the same ROI [48] or the low pass filtered moving particle positions [49]. Drift correction using low pass filtering of the particle positions can result in an artificial reduction of the apparent motion. Since in our case the observed drift (estimated from the data) is less than 15 nm in the few seconds of the measurement, we do not apply drift correction (see appendix C). In the case of a singly attached particle, the mean x and y position signify the anchor point of the tethering DNA and are therefore subtracted from the measurements. The measured z-position is a value relative to the focal plane. The absolute height is determined by finding the relative height at which the number of observations shows a steep increase. This point is found by plotting the empirical cumulative distribution (ECDF) of the z-positions and finding the height at which the slope of the ECDF increases above a certain threshold (1 × 10−3, see figure 3.3). That height is then set to z =40nm,theradiusofthe particle and minimum achievable height. Outliers below this height are caused by noise in the position determination and are discarded in further analysis (typically between 1-4 % of the position measurements). The data is then visually inspected for anomalies such as multiply tethered particles. Only singly tethered particles are included in subsequent analysis steps. (see also chapter 2 of this thesis).

3.2.5 Persistence length from statistics In our previous paper [84], we proposed a method to determine the persistence length of a DNA tether by comparing the measured 2D position distribution to simulated ones. This method is expanded here for 3D measurements. Instead of comparing the radial distribution as in our previous paper, we now compare the x-, y-andz-positions separately to the simulations and determine the persistence length in each of the 3 dimensions. Brieﬂy: the position distribution is compared to simulations of Tethered Particle Motion using diﬀerent values for the persistence length of the tether. The simulation with the highest statistical

55 3 Three dimensional measurements of Tethered Particle Motion

×10−3

1 ECDF 7 Slope of ECDF Found z =40nm 6 . 0 8 Found z =0nm 5

0.6 4

3 Slope 0.4

umulative distribution 0.2 C 1

0 0 0 100 200 300 Measured height with respect to focal plane [nm]

Figure 3.3: Empirical cumulative distribution of measured heights of the motion of TPM using a 4899 bp long dsDNA tether. The absolute minimum height is determined by ﬁnding the height at which the slope of the ECDF increases above the threshold value 1 × 10−3. This is set to 40 nm since that is the minimum achievable height of the center of the nanoparticle.

agreement (measured using the Kolmogorov-Smirnov test) to the measured data determines the value for the persistence length that best ﬁts the measured data.

3.2.6 Persistence length from dynamics

The persistence length of the DNA can also be determined by looking at the dynamic behavior of the system. For that we look at the mean squared displacement (MSD) of the particle as a function of time. The motion of the tethered particle can be modeled as Brownian motion in a harmonic potential. This means that for short time differences (shorter than the relaxation time of the motion, see below), the displacement resembles free diffusion and is therefore linear with time. For long time differences (Δt →∞) the motion is confined due to the elasticity and finite length of the DNA. The mean squared displacement

56 3.3 Results is then dominated by the harmonic potential posed by the elasticity of the DNA: 2 2kBT MSDx = Δx (∞) = . (3.5) kDNA Here we use the spring constant of dsDNA as determined from the Worm-Like- Chain model in the case of a small stretching force [53]:

3 k T k = B , (3.6) DNA 2 PL with P the persistence length and L the contour length of the DNA. Note that this equation does not take into account the tethered particle and nearby substrate. Furthermore, due to the ﬁnite exposure time used in the experiments, the MSD is underestimated [59]. As long as the exposure time W is less than kB T 3 times the relaxation time of the motion τ = Dk , the approximation given in appendix D of the paper by Wong and Halvorsen [59] can be used to determine thetruevalueofk to within 3%. They measure the position variance whereas we determine the displacement, therefore we repeated their calculations for the displacement (see appendix A). In the case of 900-5000 basepairs long DNA, the exposure time should be lower than 5.7 and 31.8 ms respectively. All our measurements are done using an exposure time of 1 ms, thus we can use equation A.3 and equation 3.6 to determine the estimated true persistence length. Here we only use the long time dynamics, but in chapter 4 the dynamics of TPM will be explained more extensively, including the short time behavior.

3.3 Results 3.3.1 Position precision The precision with which the lateral and axial positions could be estimated was tested by collecting a second calibration set of stationary particles. In each of the 10 images, the lateral and axial positions of the particles were determined. The standard deviation of those values is a measure for the position precision. These numbers are presented in ﬁgure 3.4. If the particle stays between -500 nm and +500 nm of the focal plane, the precision is 6 and 15 nm in the lateral and axial direction, respectively. Outside this range, aberrations such as coma and spherical aberration present in the optics system deteriorate the performance of the ﬁtting procedure (see [81] supplementary section 3.2.2). Figure 3.5 is an example of an image of a gold nanoparticle at defocus 1 μm,takeninoursetup

57 3 Three dimensional measurements of Tethered Particle Motion without the cylindrical lens. At this defocus, the image is clearly affected by optical abberations. The abberations are also present at smaller defocus, but it is easier to perceive them at this defocus. The shape of the PSF is rotationally asymmetric and the central peak is displaced from the center, flowing into the first diffraction ring. Images taken at a defocus between 500 nm and 1 μmshow the same abberations.

(a) Lateral precision (b) Axial precision

20 30 X-position Y-position 25 15 20

10 15

10 5 5 Std of 10 msrmts [nm] Std of 10 msrmts [nm] 0 0 −1 −0.500.51 −1 −0.500.51 Piezo setting [μm] Piezo setting [μm]

Figure 3.4: Precision of lateral and axial position estimation as a function of the z-position.

Figure 3.5: Image of a single gold nanoparticle at a defocus of 1 μm without the cylindrical lens. Abberations in the optical system cause the shape to deviate from the theoretical Airy shape.

58 3.3 Results

DNA length N xyz 2190 bp 10 26 nm 30 nm 73 nm 3202 bp 72 23 nm 27 nm 57 nm 4899 bp 40 26 nm 31 nm 65 nm

Table 3.1: Mean measured (apparent) persistence length from statistics for diﬀerent dsDNA lengths. The second column shows the total number N of analyzed particles per DNA length.

3.3.2 Persistence length from statistics In total we analyzed 10, 72 and 40 measured particles for the 2190, 3202 and 4899 bp fragments respectively. The mean measured persistence lengths from the statistics of the position distributions are summarized in table 3.1. In literature the general consensus on the persistence length of double stranded DNA lies around 50 nm for common salt and pH conditions [85]. On the one hand we measure a mean persistence length in the x and y position (26.2 nm) that is significantly lower than this value, while on the other hand the mean measured value in z (65.0 nm) is higher. In figure 3.6 the results are shown for a single particle. Here the measured persistence length in z (fig. 3.6f) is 68 nm, which is higher than the value determined from the x and y positions (figs. 3.6b and d), 29 and 23 nm respectively. To understand the discrepancy between the axial and lateral measurements let us look at the distribution of the x, y and z position, together with the simulated ones using a value of P = 50 nm for the persistence length (figs. 3.6a, c and e). The average measured height of the particle is higher than expected from simulations, while the lateral distribution is narrower than expected. It seems the particle is pushed upwards, restricting the distribution in the axial direction. Every 3D position distribution we measured showed this behavior.

3.3.3 Persistence length from dynamics Table 3.2 gives an overview of the mean measured persistence length from the dynamics of the motion. Here we measure values for the persistence length in x and y similar to the ones obtained from statistics, however, the value in z is now lower than from lateral positions. Figure 3.7 gives an example of the dynamic measurements for a single particle (the same particle as before), again for the three dimensions separately.

59 (b) Apparent persistence length from x- (a) Position distribution in x positions

×10−3 0.25 3.5 Measurements Simulations with P = 50 nm . 3 0 2 2.5 0.15 2 1.5 0.1 Probability

Histogram 1 0.05 0.5

0 0 −1000 −500 0 500 1000 0 20 40 60 80 100 X-position [nm] Persistence length [nm]

(d) Apparent persistence length from y- (c) Position distribution in y positions

×10−3 0.25 3.5 Measurements Simulations with P = 50 nm . 3 0 2

2.5 0.15 2

1.5 0.1 Probability

Histogram 1 0.05 0.5

0 0 −1000 −500 0 500 1000 0 20 40 60 80 100 Y-position [nm] Persistence length [nm]

(f) Apparent persistence length from z- (e) Position distribution in z positions

×10−3 1 3.5 Measurements )

Simulations with P = 50 nm 5 . 3 0 8 − 2.5 0.6 2 1.5 0.4

Histogram 1 0.2

0.5 Probability (x10

0 0 0 200 400 600 800 1000 02040 60 80 100 Height [nm] Persistence length [nm]

Figure 3.6: a, c, e: 3D position distribution for a single particle tethered to the substrate by a 4899 bp dsDNA molecule. The measured distribution is compared to the simulated position distribution using a persistence length of 50 nm. b, d, f:De- termination of the apparent persistence length by comparing position distribution to simulations. DNA length N xyz 2190 bp 10 32 nm 33 nm 17 nm 3202 bp 72 27 nm 31 nm 15 nm 4899 bp 40 30 nm 33 nm 15 nm

Table 3.2: Mean measured (apparent) persistence length from dynamics for different dsDNA lengths. The second column shows the total number N of analyzed particles per DNA length. (a) MSD of x-positions (b) MSD of y-positions ×105 ×105 2 2 Experiment Experiment Linear fit Linear fit Fitted P = 30.1 [nm] Fitted P = 31.8 [nm] 1.5 1.5 ] ] 2 2

1 1 MSD [nm MSD [nm 0.5 0.5

0 0 00.20.40.60.81 00.20.40.60.81 Δt [s] Δt [s]

5 MSD [nm 2.5

0 0 0.2 0.40.60.81 Δt [s]

Figure 3.7: Determination of the apparent persistence length from dynamics for a single particle tethered to the substrate using a 4899 bp dsDNA molecule. Notice the diﬀerence in the scaling of the MSD axis in c. 3.4 Discussion

3.3.4 Overview Figure 3.8 combines the results in table 3.1 and 3.2 and shows the measured persistence length for all singly tethered particles from statistics and dynamics. The measured persistence length in the lateral direction from statistics and dynamics are in agreement, while the measurements in z result in a higher value for the persistence length when looking at the statistics and a lower value when looking at the dynamics.

] 60 m From x statistics 50 From y statistics From z statistics 40 From x dynamics From y dynamics 30 From z dynamics

20 Persistence length [n

0 0 1000 2000 3000 4000 5000 6000 DNA length [bp]

Figure 3.8: Determination of the apparent persistence length for all singly tethered particles. Error bars represent the standard error of the mean.

3.4 Discussion

The results in ﬁgure 3.8 show a slightly higher value of the persistence length from the y measurements than from the x measurements. This is an artefact of the astigmatic imaging. Due to a small misalignment of the cylindrical lens with respect to the optical axis of the microscope, the center of mass of the spot is shifted (see section 3.2.2 of the supplementary material of the paper by Smith et al. [81]). Since this is not taken into account in the calibration of

63 3 Three dimensional measurements of Tethered Particle Motion the localization procedure, the y position is somewhat exaggerated compared to an underestimated x position.Forthedynamicsmeasurementswehavenot taken into account the effect of the nearby substrate and the particle on the conformations the DNA tether can adopt. In chapter 2 we have shown (see figure 2.6b) that the mean squared radius of the particle motion is larger than the mean squared end-to-end distance of a free DNA molecule. Not taking the particle and substrate into account therefore results in a higher apparent value for the persistence length of the DNA. In the statistics measurements the effect is included in the simulations, however for the dynamics measurements we have not taken that into account. Therefore the measured persistence length is slightly higher in the lateral dynamics measurements compared to the statistics measurements. In z, however, the measured persistence length is significantly lower as determined from the dynamics, while the value measured from the statistics is significantly higher than the lateral measurements. We see in our experiments that the average measured height of the tethered particle is much larger than expected from the x and y-position distribution. The dynamics in z, however, produce a much lower value for the persistence length, indicating that the particle moves even less in the z direction than in x and y. The dynamics in z are partly slowed down due to hindered diffusion (see B.3). This, however, does not explain the higher average height in the statistics of the motion. A possible explanation can be found by postulating a force that pushes the particle upwards. The motion would then also be limited in the lateral direction by the DNA tether. In fact Fan et al. [86] specifically apply a stretching force on a DNA tether to reduce the motion in the direction perpendicular to the force. The magnitude of this force is estimated by determining how much the position distribution is stretched in z and applying Hooke’s law. F = kΔz is the force 3 kB T necessary to stretch dsDNA with spring constant k = 2 PL (valid for F<0.5 pN [87]). The spring constant of the dsDNA depends on its contour length L and persistence length P . The stretching Δz is found by determining by which amount the particle’s average height should be reduced to obtain the height distribution corresponding to the lateral position distribution. In figure 3.9 the necessary stretching Δz and the corresponding force are plotted for all measured particles as a function of the tether contour length. Clearly the amount of stretching depends on the length of the tether (figure 3.9a), but the average force causing the stretching is between 0.5 and 1 fN for each tether length (figure 3.9b). In force-extension measurements [36, 53] forces in the order of pN are usually applied to extend the DNA to a fraction of its contour length, therefore this 0.5 fN is relatively small. It is in the same order of magnitude as

64 3.4 Discussion the attractive van der Waals potential between the substrate and the particle (see appendix B).

(a) Amount of stretching in z (b) Corresponding force 200 2 [fN] z

150 Δ . k 1 5 = F

[nm] 100 1 z Δ

50 0.5

0 0 0 1000 2000 3000 4000 5000 6000 Stretching force 0 1000 2000 3000 4000 5000 6000 DNA length [bp] DNA length [bp]

Figure 3.9: Determination of stretching in z and corresponding force. To find the stretching Δz, first the simulation that corresponds best with the x and y position distribution is found. The difference between the average z position in that simulation and the average measured z position is then the amount of stretching. The corresponding force is F = kΔz, the force necessary to stretch the DNA conformations, with k the spring constant of the DNA. Error bars represent the 25 and 75 percentile of the measurements.

3.4.1 Extending the statistics simulations

From the many force-extension measurements on DNA (see [33] for an overview) we know that a stretching force in the z direction leads to stretching in z and reduced motion in x and y of the particle position. We want to quantify this in our Monte Carlo simulations of the statistics of TPM (see chapter 2). As a first approximation of the influence of the stretching force, we take the previously obtained simulation results and adjust the particle positions using the net force in the directions parallel and perpendicular to the the stretching. The effective ∂F rigidity of the DNA in the z direction, parallel to the stretching force, is k = ∂z . F The effective rigidity in x and y of the stretched molecule is k⊥ = l with l = x2 + y2 + z2 the total amount of stretching [87]. Therefore each obtained

65 3 Three dimensional measurements of Tethered Particle Motion particle position is adjusted according to: F x Δx = − , (3.7) kDNA l F y Δy = − , (3.8) kDNA l F Δz = . (3.9) kDNA Afterwards the new position distributions are fed into the algorithm for determining the persistence length. As a result of the stretching force, the measured persistence length is now underestimated in x and y and overestimated in z. The over- and underestimation of the persistence length are approximately linear with the applied force (see ﬁgure 3.10). For the overestimation in z the slope also linearly increases with the true persistence length.

(a) Underestimation of P in x and y (b) Overestimation of P in z

16 45 P=35nm P=35nm 14 Linear fit 40 Linear fit P=40nm P=40nm 35 12 Linear fit Linear fit P=45nm 30 P=45nm 10 Linear fit Linear fit P=50nm 25 P=50nm 8 Linear fit 20 Linear fit 6 15 4 10 2 5 Overestimation of P [nm] Underestimation of P0 [nm] 0 012 345 6 0123 456 Applied axial force [fN] Applied axial force [fN]

Figure 3.10: a Underestimation of P in x and y as a function of applied axial force and true persistence length from simulated position distributions. b Overestimation of Pinz as a function of applied axial force and true persistence length from simulated distributions.

Figure 3.10 shows that a small stretching force of a few fN reduces the measured persistence length in x and y and increases the value measured in z. Qualitatively, our experimental results best ﬁt these simple simulations with a true persistence length of 37 nm and stretching force of 5.8 fN. A more in

66 3.4 Discussion depth realization of simulations of stretched DNA should include the eﬀect of 3kB T the stretching force on each segment in the DNA chain, using k = P 2 for the elasticity of a single segment [4]. The goal of TPM experiments is to study biopolymers like DNA and RNA in the absence of any external forces other than those caused by molecules (proteins, other nucleic acids) interacting with the tether. Our observations show that this absence of external forces might be hard to achieve. We comment on possible causes for the axial stretching in the next few paragraphs.

3.4.2 Stretching due to excluded volume in tethered particle motion Segall et al. [51] pose an eﬀective out-of-plane stretching force due to volume exclusion of the particle and substrate in tethered particle motion experiments. When their equation 12 is applied to our experiments, the stretching force is between 4 and 20 fN, depending on the tether length. We, however, determined a constant force, independent of tether length. Furthermore, the inﬂuence of the particle and substrate are included in the simulations used for the statistics measurements. The upwards force we see is therefore an additional factor and one that is relatively small compared to the inherent stretching in tethered particle motion.

3.4.3 Hydrodynamics effects of the nearby substrate The reduced freedom of motion near a substrate slows down diffusion near the substrate. This is called hindered diffusion [88, 89]. This effect, however, would cause the particle to be trapped near the substrate, reducing the motion in all directions and causing a lower average height of the particle.

3.4.4 Electrostatic repulsion between substrate and particle Iftheparticleandsubstratehaveasurfacechargeofequalsign,theparticle would be electrostatically repelled from the substrate. We, however, use a measurement buﬀer with a relatively high ion concentration (50 mM NaCl), which would shield the surface charge. The characteristic length over which the elec- −1 f 0kB T trostatic force acts is given by the Debye length: κ = 2ce2 ,with f the

67 3 Three dimensional measurements of Tethered Particle Motion

relative permittivity of water, 0 the permittivity of free space, c the concentration of monovalent ions and e the elementary charge [90]. For the 50 mM NaCl buﬀer we use, the Debye length is in the order of 1 nm. According to our simulations the particle would be closer to the substrate than the Debye length less than 0.5% of the time in the case of no substrate interaction.

3.4.5 Thermal buoyancy According to Stoke’s law the flow necessary to exert a certain force on a body is F v = =0.24 μm/s. (3.10) vert ζ Here ζ =6πηR is the friction coefficient for a complex with radius r and η the viscosity of water. The radius√ of the complex is roughly R = RDNA + Rp = 448 nm, with RDNA ∼ 2PL the radius of a 4899 bp dsDNA molecule and Rp = 40 nm the radius of the tethered particle. This amounts to an upwards 2 2 flow rate of Qvert = Avvert =0.9nl/sforaheatedareaofA = πr =3.8mm given by the approximate radius r =1.1 mm of the illumination light spot (estimated from the completely illuminated field of view of the 10x objective). This upwards flow has to be provided by a horizontal flow from each side (left and right) of the microfluidic cell. This means that the flow rate in the bottom half of the cell is 1/2Qvert vhor = =1.7 μm/s, (3.11) 1/2tcellwcell with wcell = 4 mm the width of the microfluidic flow cell. The pressure gradient from steady 1D laminar flow between parallel plates is obtained from the Navier-Stokes equation using the no-slip condition at the boundaries [91]:

dP − Qvert 12 = η 3 , (3.12) dx 1/2wcell tcell − 12 = η2vhor 2 . tcell

dP The pressure drop over a horizontal flow of 1.1 mm is then ΔP = dx lflow = 2.9mPa Local heating of the buffer in the focal spot of the illumination would cause a local reduction in the density of the buffer. The heated water would rise, taking

68 3.5 Conclusions the particle with it. Buoyancy pressure is given by:

ΔP =Δρgtcell , (3.13) with Δρ the change in density of the heated water, g the gravitation constant and tcell = 127 μm the depth of the microfluidic cell (determined by the thick- ness of the parafilm). For a buoyancy pressure equal to the pressure drop of 2.9 mPa, the water would have to be locally heated approximately 9 K above the surrounding water at room temperature. Values for the thermal density variation of water were downloaded from http://webbook.nist.gov/chemistry/fluid/. We tried measuring the local heating of the water by means of a thermocouple. Although we could not fit the thermocouple in a microfluidic cell having the same size as the ones used in the TPM experiments, we did see an increase in temperature of 2 degrees in a somewhat larger cell. As thermal buoyancy seems the most likely cause of the axial stretching force in our experiments, future experiments should include an infrared filter in the illumination to reduce heating of the buffer.

3.5 Conclusions

In the previous chapter, we showed measurements of the persistence length of DNA using only 2D projected data. We determined a mean value of 37 nm for double stranded DNA, which is significantly lower than the 50 nm generally reported in literature. In this chapter measurements of the 3D positions of gold particles and results from both statistics and dynamics analysis were presented. We found similar values for the persistence length in x and y, but the persistence length from the statistics in z was higher than expected. A possible explanation for the apparent contradiction between the measured persistence length in x and y with the value measured in z, and also for the lower values of the persistence length, is an upwards force acting on the DNA-particle complex. These 3D measurements suggest the existence of such a force. We estimate it to be on the order of a few fN to make the observations consistent. The most probable candidate for the upwards force is thermally driven buoyancy pressure from locally heated water. Future experiments should include an IR filter to reduce heating of the liquid through the illumination light source. These 3D measurements have provided insight into the factors influencing observations in tethered particle motion and are essential for a complete understanding of the method.

Dynamics of Tethered Particle Motion

The dynamics of Tethered Particle Motion have not been studied extensively before. In this chapter we explain our observations of the diffusion of gold nanoparticles tethered to the substrate using double stranded DNA molecules of several different lengths and from 2 different species. We compare our observations to existing theories and find that in time regimes longer than the relaxation time of the system (a few milliseconds), the diffusion is dominated by the flexibility of the tether. For time scales shorter than the relaxation time, the mathematical model by Qian describes our measurements well. Using this model we could determine the exponent in the scaling laws that describe how the observable quantities of DNA are scaled with length. We measure a relatively low value of the scaling exponent γ =1.58. This corresponds to a situation where there is minimal swelling of the polymer due to long range self-interactions. Our findings are consistent with the expectation for short semi-flexible DNA molecules.

4.1 Introduction

Tethered Particle Motion (TPM) is often used for studying interactions of the tether molecule with (looping) proteins [8, 45, 47, 92, 93, 94, 95, 96, 97] and with other nucleic acids [18, 98]. Before an accurate assay can be developed, it is ﬁrst necessary to understand how the moving particle and tethering molecule aﬀect the observed dynamics. Although the mechanics of TPM have been stud-

71 4 Dynamics of Tethered Particle Motion ied extensively [48, 49, 50, 84, 99], not many researchers have done an in-depth analysis of the dynamics. Beausang et al. [100] proposed a simplified dynamics simulation of TPM using a random walk in a harmonic potential. Recently, Manghi et al. [101] reported measurements and simulations of the relaxation time of the TPM system, a quantity determining the time resolution with which conformational changes of the tether can be detected. Long before those papers were published, Qian and Elson published several papers containing mathematical analyses of the dynamics of TPM [102, 103, 104]. In this chapter we combine knowledge of Brownian motion of spherical particles and of diffusion of free DNA molecules with Qian’s mathematical model to characterize the mean squared displacement (MSD) of 80 nm gold nanoparticles tethered to the substrate using double stranded DNA. We relate the observed MSD in our experiments at long and short time scales (with respect to the relaxation time of the system, a few milliseconds) to the mechanical properties of the DNA and particle. The MSD in the long-time limit is dominated by the effective spring constant of the tether. This allows us to determine the persistence length of DNA from the dynamic measurements. The short-time diffusion has been mathematically described by Qian [103] and we show that our experimental data fit this model. Further- more, measurements of the apparent diffusion constant of the particle enabled us to determine the scaling exponent γ. This scaling exponent is associated with scaling laws that define how observable quantities of polymers relate to their mechanical properties (contour length, persistence length). The first part of this chapter is devoted to an overview of existing theories on diffusion and the characteristic mean squared displacement.

4.2 Theoretical background

4.2.1 Brownian motion of spherical particles In 1827 the botanist Robert Brown discovered that pollen suspended in water exhibited a random motion that did not originate from currents in the fluid or from the living origin of the pollen [105]. This phenomenon was named Brownian motion and had to be explained by physics. Almost a century later, Albert Einstein showed that the motion of the particles could be accounted for by the molecular-kinetic theory of heat [106]. Historically this was an important finding supporting the atomistic world model. Einstein deduced that the mean squared displacement of the diffusing particle grows linearly with time. The proportionality constant was the diffusion coefficient of the particle. Marian

72 4.2 Theoretical background von Smoluchowski independently showed the same relation using a kinetic model based on collisions of hard spheres [107].

The equation of motion (Langevin equation) for a diffusing particle is the sum of the forces acting on the particle. The force from collisions with the molecules in the surrounding fluid is separated into a systematic friction force F = −ζv, which depends on the velocity of the particle v and the viscosity of the fluid ζ, and a stochastic, fluctuating force F (t): F = m · a = F (t) − ζv. (4.1)

The random force is considered a Gaussian stochastic process with zero mean and has a delta function autocorrelation [108]. The magnitude of the autocorrelation is determined from the ﬂuctuation dissipation theorem [109]:

F (t) =0, (4.2)

F (t)F (t + τ) =2kBTζδ(τ). (4.3)

Einstein deduced that the mean squared displacement of a diffusing particle Δx2 grows linearly with the time difference Δt and the number of observed dimensions n [106]: Δx2 =2nDΔt. (4.4) The proportionality constant D is the diffusion coefficient given by the Stokes- Einstein relation: k T D = B , (4.5) ζ where kBT is the thermal energy and ζ is the Stokes friction coefficient. For an ideal spherical particle ζp =6πηr,withη the shear viscosity of the medium and r the radius of the particle. These equations hold for a particle diffusing in an infinite thermal bath. For diffusion near a wall several interactions come into play. In appendix B an overview of the most important ones is given: the electrostatic, gravity and van der Waals forces and hindered diffusion. The conclusions are that in our experiments the effects of the electrostatic and gravity forces are negligible. The attractive van der Waals force is on the same order of magnitude as a possible upwards force we proposed in chapter 3. The hindered diffusion caused by hydrodynamic drag of the substrate is moderate in the x and y direction, but has greater impact on the diffusion in the z direction.

73 4 Dynamics of Tethered Particle Motion

4.2.2 Diﬀusion of DNA

In the 1950s Rouse [110] provided an exact solution for the diffusion coefficient of linear polymers (e.g. linear DNA) in liquid by treating the molecules as chains of beads connected by segments with a Gaussian distributed length. He showed that the diffusion coefficient is given by: k T D = B , (4.6) Nζs where N isthenumberofsegmentsandζs is the friction coefficient of one segment. Not long after that Zimm [111] published an analytical theory for polymer diffusion in the presence of hydrodynamic interactions between the segments of the polymer (mediated by the inertia of the solvent):

k T D =0.192 B , (4.7) N 1/2bη with b the rms segment length. This diffusion coefficient depends on the radius 1/2 of gyration Rg = N b of the molecules. In so-called Θ conditions linear polymers behave as ideal chains with this radius of gyration. This equation, however, only takes into account short-range interactions between segments. In good solvents the molecules behave as real chains and swell due to long-range interactions (volume exclusion). The range is here the distance along the chain between segments and not the spatial separation of the segments. These long- range interactions include e.g. steric effects (the segments cannot occupy the same volume) and van der Waals attraction. The effect is known as volume exclusion and should not be confused with the volume exclusion caused by particle-substrate interactions in TPM as defined in [51]. The volume exclusion effect can be quantified by realizing that observable physical quantities such as the radius of gyration of the molecule should not depend on the local description of the polymer. The size of the polymer must be invariant to a transformation of the parameters, e.g. of the rms segment length. Many observable static properties of polymers therefore show a scaling relation with the parameters used. The radius of gyration is for instance given by [4]:

ν Rg = N b, (4.8) with ν the scaling power. Flory calculated that in a Θ solvent ν =1/2(no volume exclusion) and in a good solvent ν =3/5 (volume exclusion), while

74 4.2 Theoretical background perturbation theory resulted in a value of ν =0.588 in good solvents [4]. The consequence is that in the presence of volume exclusion, the size of the polymer depends more heavily on the number of segments (or its contour length) than in the absence of volume exclusion. De Gennes [112, 113] proposed that these scaling laws could be extended to the dynamics of the polymers. Subsequently, researchers have investigated the dynamical scaling in bulk experiments using rheology, light scattering and birefringence (see the references in [114]) and later on in single molecule experiments using e.g. the strain relaxation time [114] or the free diffusion of single DNA molecules [115]. We combine equations 4.7 and 4.8 and substitute the number of segments N and rms segment length b with the parameters used in the worm-like chain (WLC) model (which for L P corresponds to the Gaussian model given above): the length of the polymer (L = Nb) and the persistence length (P =1/2b). This results in the following scaling relation for the diffusion coefficient of linear DNA:

kBT DDNA = , ζDNA γ−1 2−γ ζDNA = CL P , (4.9) with C a constant. Theoretically γ =3ν lies between 1.5 for Θ solvents (no volume exclusion) and 1.8 for good solvents (volume exclusion) [114]. In the absence of volume exclusion, when γ =1.5, both P and L contribute equally to the friction coefficient. The friction coefficient increases with the square root of both lengths. In the presence of volume exclusion, γ increases and the contour length of the DNA has a larger impact than the persistence length. This means the long range interactions between the segments outweigh the impact of the stiffness of the polymer.

4.2.3 Diﬀusion in a harmonic potential

The next type of diffusion we are interested in is diffusion of a spherical particle in a harmonic potential. As in our TPM experiments the DNA behaves as a Hookean spring [53, 100], the motion of the particle can be approximated by this kind of diffusion. The equation of motion for a particle diffusing in a harmonic potential incorporates the spring force Fs = −kx: F = m · a = F (t) − ζv − kx. (4.10)

75 4 Dynamics of Tethered Particle Motion

The mean squared displacement has been solved by Uhlenbeck [116] in the 1930s. Clercx and Schram [117] have investigated the mean squared displacement of Brownian motion in a harmonic potential including hydrodynamic memory effects. Lukic et al. [118] used their results to describe the motion of a colloidal particle in an optical trap and defined the ”free diffusion” time of such a particle (i.e. the time scale on which the particle does not feel the harmonic potential and exhibits free diffusion). The sources of hydrodynamic memory effects are the inertia of the particle and surrounding fluid. Lukic et al. [118] defined three time constants: τp related to the inertia of the particle, τf related to the inertia of the fluid displaced by the particle and τk related to the relaxation in the harmonic potential:

m r2ρ 6πηr τ = ,τ= f ,τ= . (4.11) p 6πηr f η k k

Here m is the mass of the particle and ρf the density of the fluid. The harmonic potential relaxation time is related to the free diffusion time scale τfree,which Lukic et al. measure to be τfree = τk/20. The mean squared displacement of a particle diffusing in a harmonic potential without inertial effects in n observed dimensions is given by [118]: 2nkBT − Δx2(Δt) = 1 − e Δt/τk . (4.12) k For Δt → 0 the relation for free diffusion returns (see equation 4.4) and the long time limit gives: 2nk T Δx2(∞) = B . (4.13) k In our experiments we use 80 nm diameter particles diffusing in water. The inertial time constants are on the order of a few nanoseconds. Since the time scale on which we probe the motion of the tethered particle is in the millisecond range, we do not observe the inertial effects. For a particle with radius r =40 nm tethered by double stranded DNA of lengths between 900 and 5000 basepairs and persistence length 50 nm, the harmonic relaxation time τk lies between 1.9 and 10.6 ms. The bandwidth of this exponential relaxation is between 83 and 15 Hz, therefore we can probe the harmonic relaxation if the particles are tracked with a framerate at least twice as high (Nyquist theorem).

76 4.2 Theoretical background

4.2.4 Diﬀusion of a tethered particle

Manghi et al. [101] have studied the dynamics of TPM extensively in simulation and experiment. They provide an equation for the MSD in TPM similar to equation 4.12. They neither give a model nor an estimate of the apparent (measured) diffusion coefficient in the short-time domain. They indicate, however, that the apparent diffusion coefficient is not equal to the diffusion coefficient of the particle-DNA complex:

Dm = Dp+DNA = kBT/(ζp + ζDNA) . (4.14)

Qian [103] provides a mathematical analysis for the dynamics in TPM. He shows that for semiflexible polymers the short-time (limΔt→0) mean squared displacement is given by: 2nk Tσ Δx2∼ B Δt. (4.15) ζ 1+2/σL ζ˜ ˜ Qian used ζ = limΔs→0 Δs ,whereζ is the frictional coefficient of one segment of the DNA and NΔs = L is the contour length of the DNA divided into ζ˜ N segments of length Δs.Furthermore,σ = limΔs→0 ,whereζp is the ζpΔs frictional coefficient of the tethered particle. Then σ/ζ =1/ζp relates to the friction coefficient of the particle, and we conclude that σL = ζDNA/ζp contains the relative influence of the friction of the DNA. Equation 4.15 can then be rewritten to: 2nk T Δx2∼ B Δt. (4.16) ζp 1+2ζp/ζDNA Compare equations 4.16 and 4.4. Apparently the following relation exists between the measured diffusion coefficient and the friction coefficient for the DNA and particle: kBT Dm = . (4.17) ζp 1+2ζp/ζDNA In figure 4.1 the diffusion coefficient of the particle-DNA complex (equation 4.14) and the apparent diffusion coefficient from the equation provided by Qian (equation 4.17) are plotted as a function of DNA contour length. The particle is 80 nm in diameter and it is diffusing in a water medium with viscosity of 1 mPas. We consider the persistence length of the DNA to be 35 nm. The reader is referred to chapters 2 and 3 for a discussion of this value. Figure 4.1 clearly shows that both models are in complete disagreement.

77 4 Dynamics of Tethered Particle Motion

×106

5 /s] 2 4 Particle 4.5 3 Qian 4.17 Particle-DNA complex 4.14 2

Apparent D [nm 1

0 0 1000 2000 3000 4000 5000 6000 DNA length [bp]

Figure 4.1: Comparison of the diffusion coefficient of the particle-DNA complex, the diffusion coefficient from the mathematical analysis of Qian [103] and the diffusion coefficient of the particle, for a particle of radius 40 nm and dsDNA with a persistence length of 35 nm. The medium in which the diffusion takes place is water with viscosity 1 mPas and temperature 293 K.

The measured friction coeﬃcient ζm = kBT/Dm can be rewritten using equation 4.9. The squared measured friction coeﬃcient is then:

3 2 2 2ζp ζm = ζp + , (4.18) ζDNA = ζ2 +2ζ3CL1−γ P γ−2, p p L P γ = ζ2 +2ζ3C . p p P 2 L

Furthermore, if we also measure the persistence length P of the DNA tether and know the contour length L, the scaling exponent γ can be determined from the following relation: ζ2 − ζ2 P 2 P log m p = logC + γ log , (4.19) L L with C a constant.

78 4.3 Materials and methods

4.3 Materials and methods

4.3.1 Sample preparation Double stranded DNA fragments of different lengths were synthesized from either an unmethylated lambda DNA template (Promega, NL) using the GoTaq PCR Core System (Promega, NL) or from cDNA from the exg2 gene for exo- beta-1,3-glucanase in Lentinus endodes (Shiitake mushrooms). The DNA constructs are referred to as lambda DNA and shiitake DNA respectively. The fragments were end-labeled by using a biotin modified forward primer and 3 different digoxigenin modified reverse primers. The resulting products were 2190, 3202 and 4899 basepairs (bp) long for the lambda DNA and 854, 973 and 2205 bp long for the shiitake DNA. A microscope object glass and cover glass were cleaned in isopropanol in a sonic bath for 20 minutes. A microfluidic cell was constructed by placing a sheet of parafilm or double sided tape between the glasses. This cell was incubated with 5 mg/ml blotting-grade blocker (Bio- Rad, NL) in PBS detergent (50mM sodium phosphate buffer pH 7.4, containing 50 mM NaCl and 0.02 % Tween) for 30 minutes. The cell was then washed with PBS detergent and incubated with 0.5 mg/ml biotinylated BSA (Pierce Biotech- nology, BE) for 30 minutes. Then the cell was washed again with PBS detergent and subsequently incubated with 50 μg/ml anti-digoxigenin (AbD Serotec, DE) in PBS buffer for 45 minutes. After washing with PBS detergent, approximately 30 μlof3-4ng/μl of DNA in PBS buffer was incubated for 45 minutes. Then the anti-biotin coated gold nanoparticles (BBInternational, UK) were suitably diluted in PBS detergent and incubated for 45 minutes. In a final washing step with PBS detergent, the unattached nanoparticles were flushed away. Af- terwards the buffer was exchanged to PBS buffer (50 mM sodium phosphate buffer pH 7.4, containing 50 mM or 100 mM NaCl). In some cases Tween was omitted from the preparation buffer, but this did not give any differing results. The coating with biotinylated BSA was introduced to capture some stationary particles on the substrate for drift correction. In some samples this step was omitted and no significant differences were found between data sets with and without biotinylated BSA (compare the results for the lambda BX and lambda IX experiments in the results figures 4.3).

4.3.2 Setup and data collection Three sets of experiments were carried out, which we call shiitake BX, lambda BX and lambda IX. The experiments denoted BX were carried out by placing

79 4 Dynamics of Tethered Particle Motion the microfluidic cell in a holder on the stage of an Olympus upright darkfield microscope (BX51, Olympus Nederland, NL). A 100x 0.9 dark field objective (Olympus) was used to image the scattering of the gold nanoparticles. For the experiments denoted IX, the microfluidic cell was placed in a holder on the stage of an Olympus inverted microscope (IX71, Olympus Nederland, NL). An oil immersion dark field condenser was used to illuminate the nanoparticles and the scattered light was imaged by either a 60x NA 0.7 air objective or a 100x oil immersion objective with adjustable NA (both from Olympus). For a schematic view of the latter setup see figure 3.1 in chapter 3. The images were collected using a cooled, back-illuminated EM-CCD camera (iXon 897, Andor Technology, UK). The EM-CCD camera ensured very fast readout times with achieved framerates ranging from 100 to 300 frames per second, depending on the size of the readout area (between 160x160 and 26x26 pixels) and the exposure time (1-2 ms). For each particle 1500 frames were captured at this framerate, therefore the measurement time was 5-15 seconds per particle.

4.3.3 Data analysis The particle images in the data sets denoted BX were processed by ﬁtting a 2 dimensional Gaussian point spread function to collect the x and y position of the particle. The procedure is as explained in section 2.3.2 in chapter 2. We did not apply drift correction here since there was no signiﬁcant drift during the few seconds of data collection (see also section 3.2.4). The analysis of the IX data was carried out as explained in section 3.2, resulting in 3D position measurements of the particles.

4.3.4 MSD plot The dynamics of the motion are visualized in a so called MSD plot, where the mean square displacement (MSD) of the particle position is plotted against the time between the observations. Each value of the MSD is determined by averaging over pairs of points with a given time difference. For free diffusion, the diffusion coefficient is found by fitting the diffusion equation (equation 4.4) to the data. In [119] the effects of different averaging and fitting strategies on the measured diffusion coefficient are examined. We conclude that averaging over independent pairs of points is necessary to avoid correlated values. For the fitting procedure it is appropriate to use weighted fitting as there are more pairs for short time differences than for long time differences. The weights should be inversely proportional to the variance of each value of the mean squared

80 4.3 Materials and methods deviation. The inherent variance for linear diﬀusion is [119]:

VarΔx2 =(2nDΔt)2. (4.20)

For averaged measurements this variance is scaled by the number of independent pairs NI : 2 2 VarΔx =(2nDΔt) /NI . (4.21) 2 In our fitting we therefore use WI = NI /Δt as the weight function. For an extensive overview of the different types of diffusion that can be found in biological samples and methods for the extraction of relevant parameters from the MSD plot, see [120] and [121]. In our case the diffusion resembles diffusion in a harmonic potential, therefore the MSD will show a linear part for approximately the duration of τk and will then level off to a value determined by the spring constant of the harmonic potential (equation 4.12). We determine the apparent diffusion coefficient in each dimension (x, y and if available z) separately by a weighted linear least squares fit to the first few values in the MSD plot. Next, we determine the mean value of the long time MSD for the determination of the spring constant of the DNA, again for each dimension separately. Due to the finite exposure time used in the experiment the measured value of k is an underestimate of the true value. Since the exposure time is less than 3 times the relaxation time of the system, we can use equation A.3 to get the correct value for k . Afterwards we calculate the persistence length P of the DNA using [53]:

3 k T P = B , (4.22) 2 kDNAL with L the contour length of the DNA. Figure 4.2 contains an example of such an MSD plot and reports the ﬁtted values for this particle.

81 4 Dynamics of Tethered Particle Motion

×105 3.5 Experiment Linear ﬁt, D = 2.2 × 106 [nm2/s] 3 Fitted P = 56.7 [nm]

2.5 ] 2 2

1.5 MSD [nm 1

0.5

0 00.10.20.30.40.5 0.6 0.7 Δt [s]

Figure 4.2: Example of an MSD plot for a single tethered particle. The particle is tethered to a glass substrate using lambda DNA with a length of 4899 basepairs.

4.4 Results

In total we analyzed the diffusion of 253 particles (47 in the shiitake BX experiments, 127 in the lambda BX experiments and 122 in the lambda IX experiments). Table 4.1 shows the summary of all measured values and they are visualized in figure 4.3. Each data point in the figure represents the average measurement of all tethered particles in one experiment and the error bars represent the 25 and 75 percentile of the data. Figures 4.3 a, c, e show the measured diffusion coefficient as a function of DNA length in the x, y and z dimension respectively. They indeed show that the diffusion coefficient is not simply that of the particle-DNA complex (compare to figure 4.1). The measurements do show behavior similar to the theory by Qian [103]. In figures 4.3 b, d, f the measured persistence lengths from the long time MSD are shown. On average, the shiitake dsDNA molecules have a higher persistence length than the lambda dsDNA molecules. This will be discussed later in this chapter. With the known contour length of the DNA tether, the measured persistence 2 2 − length and measured diffusion coefficient we can plot the logarithm of P (ζm 2 ζp )/L as a function of the logarithm of P/L. We have used for ζp the Stokes friction coefficient for spherical particles with a radius of 40 nm and a medium with viscosity 1 mPas (water). In practice, colloidal particles diffuse at a rate

82 4.4 Results

Experiment DNA N D [μm2/s] P [nm] length in x in y in z in x in y in z shiitake BX 854 bp 8 0.6 0.6 - 57 57 - 973 bp 34 0.8 0.8 - 61 61 - 2205 bp 23 1.2 1.2 - 57 55 - lambda BX 2190 bp 31 1.1 1.1 - 37 36 - 3202 bp 54 1.1 1.1 - 32 32 - 4899 bp 80 1.3 1.3 - 34 34 - lambda IX 2190 bp 10 1.0 1.1 0.9 32 33 17 3202 bp 72 0.9 1.0 0.7 27 31 15 4899 bp 40 1.3 1.4 1.2 30 33 15

Table 4.1: Summary of the measurements for each experiment and tether length. N is the number of particles that were analyzed. The values in the next columns are the mean measured diffusion coefficient (D) and persistence length (P )inx, y and z. determined by their effective (hydrodynamic) radius that is slightly larger than the physical radius (see e.g. [101], where the measured hydrodynamic radius of 100 nm particles is 120 nm). Since the measured friction coefficient in our measurements is much larger than that of the particle, this does not produce a significant error. The results are shown in figure 4.4. The x and y data can be fitted by a linear relation over 4 decades with good correlation (R2 ∼ 0.8). The slope gives the scaling factor γ. We measure a mean value of γ =1.58±0.02 from the x and y measurements. The measurements in z do not produce a well defined linear relation (R2 is only 0.17) and the slope gives an uncharacteristically low value of γ =0.73.

83 (a) Diﬀusion coeﬃcient in x (b) Persistence length from MSD in x

2 100 Shiitake dsDNA BX Shiitake dsDNA BX /s]

2 Lambda dsDNA BX Lambda dsDNA BX Lambda dsDNA IX 80 Lambda dsDNA IX

nm 1.5 6 60 1 40

0.5

Measured P [nm] 20

Measured D [x 10 0 0 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 DNA length [bp] DNA length [bp]

2 100 Shiitake dsDNA BX Shiitake dsDNA BX /s]

2 Lambda dsDNA BX Lambda dsDNA BX Lambda dsDNA IX 80 Lambda dsDNA IX

nm 1.5 6 60 1 40

0.5

Measured P [nm] 20

Measured D [x 10 0 0 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 DNA length [bp] DNA length [bp]

(e) Diﬀusion coeﬃcient in z (f) Persistence length from MSD in z

2 30 /s]

2 Lambda dsDNA IX Lambda dsDNA IX 25

nm 1.5

6 20

1 15

10 0.5

Measured P [nm] 5

Measured D [x 10 0 0 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 DNA length [bp] DNA length [bp]

Figure 4.3: a, c, e: Diffusion coefficient measured from the linear part of the MSD plots. b, d, f: Measured persistence length from long time MSD behavior. The error bars represent the median value and 25 and 75 percentile of the data. Notice the difference in the scaling of the P axis in f. (a) Measurements in x

−32 Shiitake dsDNA BX Lambda dsDNA BX ) −34 Lambda dsDNA IX

/L Linear ﬁt ) 2 P γ ζ −36 =1.56 (conf: 1.48 - 1.64) − R2 =0.81 2

ζ − ( 38 2 P −40 log(

−42 −5 −4 −3 −2 −1 log(P/L)

(b) Measurements in y

−32 Shiitake dsDNA BX Lambda dsDNA BX ) −34 Lambda dsDNA IX

/L Linear ﬁt ) 2 P γ ζ −36 =1.59 (conf: 1.50 - 1.67) − R2 =0.80 2

ζ − ( 38 2 P −40 log(

−42 −5 −4 −3 −2 −1 log(P/L)

−32 Lambda dsDNA IX Linear ﬁt ) −34

/L γ =0.73 ) 2

P (conf: 0.44 - 1.01)

ζ −36

− R2 =0.17 2

ζ − ( 38 2 P −40 log(

−42 −7 −6 −5 −4 −3 −2 −1 log(P/L)

Figure 4.4: Measurements of the apparent friction coefficient with respect to measured DNA properties. Each symbol represents one single molecule measurement. The linear fit gives the measured value of γ (see equation 4.19) and its confidence interval. 4 Dynamics of Tethered Particle Motion

4.5 Discussion

We have seen from the measurements in chapter 3 that the particles might be influenced by an upwards force, which could have an effect on the dynamics in z as well. This would also be consistent with these observations, since the observed MSD in z is approximately halved with respect to the measurements in x and y. This means that the relaxation time of the harmonic potential is halved as well. The underestimation of the MSD due to motion blur is in many cases too severe to use the approximation for the true value of the spring constant. Furthermore, theoretical predictions of the hindered diffusion of a particle near a substrate also predict a significant influence on the dynamics in z (see appendix B). Correctly accounting for this effect is not trivial. A solution could be to use the height information in the 3D measurements and scale the MSD with the observed height using equation B.6. As the particle’s displacement also occurs in the z direction between observations, the scaling should be weighed over the true particle track, which is unknown. A better option is to incorporate the hydrodynamic coupling into the model, as Qian himself suggests at the end of his paper [103]. The measurements in x and y do produce meaningful results. The following sections are a discussion of those results.

4.5.1 Persistence length The measured persistence length of our shiitake dsDNA is more than 25 nm longer than that of the lambda dsDNA. This might be due to differences in the (nucleotide) sequence of the DNA. It has been shown that the persistence length of dsDNA depends on the dinucleotide steps in the chain [122]. The persistence length between different nucleotide steps can be as large as 13.6 nm, with GG/CC steps having the shortest persistence length. Our lambda dsDNA constructs contain more GGCC steps (almost 15% of the steps) than the shiitake dsDNA constructs (13% of the steps). Molecules with high GC content are also known to have shorter persistence length [122]. The GC content of our lambda dsDNA constructs (57%) is higher than that of the shiitake dsDNA (49%). According to the supplementary material of [122], however, this should not reduce the persistence length more than 0.5 nm. The contributions of the GGCC steps and high GC content do not come close to the 25 nm difference, therefore additional sources for the discrepancy must be present. For instance, it could be that our lambda dsDNA constructs contain more intrinsic bending

86 4.5 Discussion than the shiitake dsDNA.

4.5.2 Diﬀusion coeﬃcient

The mathematical model for the short time dynamics in TPM by Qian [103] shows a counterintuitive relation between the length of the DNA tether and the apparent diffusion coefficient of the tethered particle. If the radius of the particle goes to zero, the diffusion coefficient goes to infinity when it should reflect the diffusion of the free end of the DNA tether. In the limit of long DNA, Qians model results in an apparent diffusion coefficient which is that of the particle alone. Intuitively, however, the diffusion should be slower for a longer tether, since a larger structure diffuses at a slower rate than a smaller structure. Furthermore, the relaxation time of the DNA increases with increasing length, which also slows down the diffusion. The solution should be found by looking at the influence of attaching one end of the DNA to a substrate. A possible explanation was in fact given and dismissed in Qians paper: the dynamics of the free end of the DNA could be much faster, therefore the motion is dominated by the diffusion of the particle. In the lower limit of L ↓ 0, Qian predicts that the diffusion coefficient goes to 0. This could be valid, since an infinitely short tether would inhibit any motion of the particle. Qian described the dynamics of a tethered particle, which is fundamentally different from the diffusion of a (free) particle-DNA complex. Even though the model is counterintuitive, it does describe our measurements of the apparent diffusion coefficient well and we are able to extract physically realistic and meaningful values from the data.

4.5.3 Dynamical scaling

We measure a value of the scaling exponent ν = γ/3=0.53 that is close to ν =0.5, the value in Θ conditions where no excluded volume occurs. This is consistent with the remark in the paper by Smith et al. [123] that for DNA with a length of less than 40 persistence lengths (6 kbp), the polymer becomes semiﬂexible and non-scaling. For longer DNA molecules the scaling does persist and Robertson et al. indeed determined a scaling exponent of ν =0.571 for linear DNA with lengths of 6 to 290 kbp. Volume exclusion by self repulsion of the negatively charged DNA [124] probably does not occur in our experiments, since the concentration of monovalent ions in our buﬀer is such that the negative charges on the DNA are screened.

87 4 Dynamics of Tethered Particle Motion

4.6 Conclusion

We have been able to relate the dynamics of gold nanoparticles tethered to a substrate using double stranded DNA molecules of several lengths to properties of the particle and DNA. We have shown measurements of the persistence length of double stranded DNA from the mean squared displacement in the long-time regime. Furthermore, to our knowledge this is the ﬁrst time the short-time diﬀusion properties have been experimentally characterized. A good agreement with existing mathematical models has been found. Using our methodology, we have found a value for the scaling exponent γ =1.58 that is comparable to other measurements. The value is in the low range indicating that there is only a limited amount of swelling of the polymer due to long-range self-interactions.

88 5

Nucleic acid detection using Tethered Particle Motion

In this chapter, the first steps towards the application of Tethered Particle Mo- tion to nucleic acid detection are described. Experiments were carried out on a model hybridization system, consisting of ssDNA from luciferase and commercially available complementary mRNA. Although we were unable to verify it using a fluorescent marker, in the Tethered Particle Motion experiments we did see indications of successful hybridization of the mRNA with the ssDNA tethers. Therefore TPM seems to be a promising candidate for nucleic acid detection, although it is more suited for the detection of the presence of the specific sequence than for concentration measurements. TPM could also be used to study the kinetics of hybridization reactions. The knowledge and experience gained with these experiments is translated into recommendations for future steps and experiments in the development of the method.

5.1 Introduction

In the previous chapters, experiments have been described that characterize our dark ﬁeld tethered particle motion method. The relation between the observed motion of the tethered particle and the properties of the tether is now largely understood. The next step in the development of a nucleic acid detection method is a proof-of-principle experiment. As a model system we have

89 5 Nucleic acid detection using Tethered Particle Motion chosen ssDNA and mRNA from luciferase, as the DNA template and mRNA are readily available from commercial sources. Single stranded DNA fragments with biotin and digoxigenin (DIG) labeled ends are made from the DNA template. The fragments are used to tether the 80 nm gold nanoparticles to the substrate. The motion of the nanoparticles is then followed for a few minutes as a baseline measurement. Next, the mRNA is added to the cell and the particles are followed over a period of several hours to allow hybridization of the mRNA to the ssDNA tethers to occur. The excursion of the particle is plotted as a function of time and motion characteristic of hybridization of the mRNA to the tether is sought. Previously, experiments were carried out on an upright dark field microscope from Olympus (BX51). This microscope can be used with a dark field objective, that combines the illumination and imaging light path. Consequently, the microfluidic cell can be held in an opaque holder, which leaves ample room for a temperature control system on the underside of the cell. The drawback of that setup was that the dark field objectives were not corrected for looking through a coverslip at a sample in water. This meant that the nanoparticle images were seriously degraded due to spherical aberrations and that particle tracking was done with suboptimal precision. The inverted microscope setup from the 3D experiments in chapter 3 uses a dark field condenser to illuminate the particles. Objectives with cover glass correction can therefore be used to image the gold nanoparticles. For this reason, the experiments in this chapter have been carried out on the inverted microscope. In this setup the cell needs to be clamped between the objective and condenser, leaving little room for the temperature control. Thus all experiments were done at room temperature. This should not pose a problem for the proof-of-principle detection, as the hybridization reaction can also occur at room temperature. In further experiments an elevated temperature would be necessary to increase the specificity of the reaction.

5.2 Materials and methods

5.2.1 ssDNA fragment preparation The single stranded DNA fragments were prepared from the pGEM-luc template (Promega, NL) using the GoTaq PCR Core system (Promega, NL). The reverse primer (5’ DIG AAGACCTTTCGGTACTTCGTCCACAAACACAACTCC 3’) contained a digoxigenin (DIG) label. The resulting 746 bp dsDNA construct was puriﬁed using the Nucleospin Extract II kit from Machery-Nagel (Bioke, NL).

90 5.2 Materials and methods

At this point the fragment had a 5’ DIG label at one end. The 3’ end of the same strand was labeled with biotin by first cleaving the dsDNA with HindIII (New England Biolabs) at the site incorporated in the forward primer (5’ AG- GATTACAAGCTTCAAAGTGCGTTGCTAGTACC 3’). After that the 3’ end was filled in using a Klenow fragment (3’-5’ exo-, New England Biolabs) with biotin-11-dUTP (Fermentas) and otherwise unlabeled nucleotides (Invitro- gen). The complementary strand was then nicked using NtAlwI (New England Biolabs) before separating the strands using alkaline agarose gel electrophoresis. Finally, the 737 nucleotides (nt) single stranded fragment containing a DIG label at one end and a biotin label at the other end was purified using the Nucleospin Extract II kit.

5.2.2 Sample preparation The sample preparation is largely the same as described in chapters 3 and 4. As in these experiments mRNA is used, the sample preparation is carried out entirely in a RNAse free environment (a separate workbench that is frequently cleansed with RNase decontamination solution (RNaseZAp, Ambion) and using only RNase free pipette tips and tubes). A microfluidic cell is constructed by placing a sheet of parafilm between a cleaned object glass and cover glass. The cell is incubated with 5 mg/ml blotting-grade blocker (Bio-Rad, NL) in PBS (50mM sodium phosphate buffer pH 7.4, containing 50mM NaCl) for 30 minutes. The cell is then washed with PBS and incubated with 50 μg/ml anti-digoxigenin (AbD Serotec, DE) in PBS buffer for 45 minutes. After washing with PBS, approximately 3-4 ng/μl of the ssDNA construct in PBS buffer is incubated for 45 minutes. The anti-biotin coated gold nanoparticles (BBInternational, UK) are then diluted 200 times from stock in PBS and incubated for 45 minutes. In a final washing step with PBS, unattached nanoparticles are flushed away. Afterwards the buffer is exchanged to hybridization buffer (1x SSC + 33% v/v formamide pH7.4).

5.2.3 Data collection The microfluidic cell is placed in a holder containing an inlet and outlet for fluids as shown in figures 5.1a and b. The holder is placed on the stage of an Olympus inverted microscope (IX71, Olympus Nederland, NL) as shown in figure 5.1c. An oil immersion dark field condenser is used to illuminate the nanoparticles and a 60x NA 0.7 air objective (Olympus, NL) images the particles on a cooled, back- illuminated EM-CCD camera (iXon 897, Andor Technology, UK). A region of

91 5 Nucleic acid detection using Tethered Particle Motion

(a) (b)

(c)

Figure 5.1: a Picture of the microfluidic flow cell in its holder. b Holder with Hamilton syringe and regular syringe in the inlets. The outlet is visible in the back. c Holder in the microscope setup with the condenser on the top and objective on the bottom of the microfluidic cell. interest (ROI) is selected, which contains as many particles as possible. There were usually 30-50 particles in one field of view as shown in the example in figure 5.2. As a baseline measurement 1500 time frames with an exposure time of 1 ms at a framerate of 2 fps are collected. Next, the complementary mRNA (0.1 mg/ml 1803 nt luciferase control RNA (Promega,NL) in hybridization buffer containing 0.02 mg/ml DNA from fish sperm (Sigma, NL) and 1 U/μl RNase inhibitor (Ambion, Applied Biosystems, NL)) is injected through a Hamilton

92 5.2 Materials and methods

12 μm

Figure 5.2: Example image of a region of interest (136 by 54 μm) containing many gold nanoparticles tethered to the substrate using ssDNA. syringe. The motion of the particles is then followed for 3 hours by collecting 21600 images at a framerate of 2 fps. Motion blur is minimized by taking the images at an exposure time of 1 ms. As hybridization can take several hours (see e.g. [125]), the framerate at which the images are taken can be very low.

5.2.4 Analysis The particles are tracked offline using CUDA code (C like programming lan- guage for the GPU, Nvidia Corporation, USA) based on the paper by Smith et al. [81] and using the DIPimage toolbox (Scientific image processing toolbox, www.diplib.org, Delft University of Technology, NL). The algorithm iteratively fits a 2D Gaussian to the data to estimate the x and y position, intensity and background. The positions are corrected for drift by subtracting the low-pass filtered positions (filter size 25s or 50 frames, see appendix C). Unattached particles were not completely removed by the washing step. They often traverse the field of view of a tethered particle, causing outliers in the tracked positions. Outlier removal is therefore applied to get rid of these faulty positions. A running average of the standard deviation of the positions is estimated and positions > 3σ from the mean are removed from the dataset.

5.2.5 Excursion The anchorpoint of the DNA is estimated from the mean position of the particle. The excursion, i.e. the Euclidian distance between the projected particle posi-

93 5 Nucleic acid detection using Tethered Particle Motion

200 150

Z 100 50 0 Excursion 0 100 −100 50 0 Y −200 −50 X

Figure 5.3: The excursion is defined as the (projected) distance from the center of the nanoparticle to the anchorpoint of the DNA. tion and the DNA anchorpoint, is used as a measure for the freedom of motion of the particle (see figure 5.3). The excursion is limited by the length and persistence length of the tethering DNA. For single stranded DNA the persistence length is on the order of 1 nm [126, 127]. Simulations, as described in chapter 2, result in a value of 42 nm for the 2D root-mean-square excursion when the tether is 737 nt single stranded DNA. After hybridization of the mRNA with the complementary ssDNA the tether should have a higher persistence length equal to that of double stranded DNA (30-35 nm in our experiments, see chapters 2 and 3). The simulations then result in a 2D rms excursion of 107 nm. Figure 5.4 shows plots of the simulated excursion for single and double stranded DNA tethers. The rms excursion is estimated from the square root of the smoothed squared excursion of 40 (simulated) particle positions, i.e. averaged over 20 s in the experiments. The 5 and 95 percentile of the excursion are estimated in a similar fashion and indicated in the plots as well. As mentioned in section 2.2.2 the ssDNA tether should be longer than 7000 nucleotides for the motion of the particle to be “molecule-dominated”. If the ssDNA is shorter the proximity of the particle to the substrate will influence the motion and effectively stretch the ssDNA. In this force range, the contour of the ssDNA is not stretched, rather the molecule adopts more stretched out configurations. An order of magnitude estimate of the stretching force on the 737 nt ssDNA we use here is found by applying equation 12 in the paper by Segall et al. [51]. This

94 5.2 Materials and methods results in a stretching force of 220 fN, which will stretch the molecule’s configurations by about 11 nm (applying Hooke’s law and using equation 2.3 for the spring constant of the ssDNA). This is less than 4% of the contour length of the DNA, however it is more than 20% of the excursion of the particle. The effects of this stretching are taken into account in the simulations, therefore the 2D rms excursion of 42 nm is still correct. The stretching force could influence the hybridization process as it increases the accessibility of the ssDNA molecule to the mRNA.

(a) Single stranded DNA 200 Excursion ]

m 150 RMS excursion 5 and 95 percentile 100

50 Excursion [n 0 0 2000 4000 6000 8000 10000 Conformation

(b) Double stranded DNA 200

] 150 m

100

50 Excursion [n 0 0 2000 4000 6000 8000 10000 Conformation Figure 5.4: Simulated excursion of a 80 nm diameter gold nanoparticle tethered to the substrate using a a 737 nt single stranded DNA molecule and b a 737 bp double stranded DNA molecule.

95 5 Nucleic acid detection using Tethered Particle Motion

5.2.6 Verification of the hybridization We added picogreen (Invitrogen, NL) to the microfluidic cell afterwards to verify the hybridization. Picogreen binds to dsDNA as well as to RNA-DNA hybridization products [128]. It does bind to ssDNA and RNA, but the fluorescence is only a fraction of the signal from the dsDNA [129]. We tested this by adding picogreen to microfluidic cells in which either only dsDNA or only ssDNA was used to tether gold nanoparticles to the substrate. Picogreen (Invitrogen, NL) diluted 200 times in TE buffer (Invitrogen, NL) was added to the microfluidic cell and left to incubate. A 100x oil immersion objective with adjustable NA (Olympus, NL) was used to image the nanoparticles on the EM-CCD. Setting the NA to its minimum (0.6) made it possible to image the gold nanoparticles via dark field imaging. For the imaging of the picogreen labeled DNA, it was necessary to set the NA to its maximum (1.3) to collect enough photons. The halogen light source was exchanged for a mercury arc lamp and a suitable filter cube was selected (exciter: 480/40 nm, dichroic: 505LP, emitter: 535/50 nm, Chroma Technology Corp, Bellows Falls, VT, USA) for the fluorescence images. After the incubation time of 30 minutes, a fluorescence image followed by a dark field image was taken of the same field of view. Figure 5.5 shows the results. The images on the left are of a sample containing only dsDNA tethers. Many picogreen fluorescent spots are visible and many of them can be overlayed with gold nanoparticles. The fact that there are more fluorescent spots than gold nanoparticles indicates that the dsDNA was added in excess of the particles. The images on the right are of a sample with only ssDNA tethers. Less particles are present in the field of view and no fluorescent spots are discernable. In experiments where no DNA (either single or double stranded) was added, no picogreen fluorescent spots could be found either. The same procedure was followed after the TPM hybridization measurements.

96 (a) Dark ﬁeld dsDNA (d) Dark ﬁeld ssDNA

(b) Fluorescence dsDNA (e) Fluorescence ssDNA

4 μm 4 μm

Figure 5.5: Dark field (a, d) and picogreen fluorescence (b, e) images of the same field of view. In c and f an overlay of both images is shown, in which the red channel is the dark field image and the green channel, the picogreen image. The images are corrected to photon counts and show the maximum projection of 10 collected frames. The images on the left (a, b, c) were taken of samples containing dsDNA tethers, the ones on the right (d, e, f) of samples containing ssDNA tethers. 5 Nucleic acid detection using Tethered Particle Motion

5.3 Results

5.3.1 Excursion In total 231 nanoparticles were followed in 7 microfluidic cells. Of those, 53 were immediately discarded due to irregular motion. They were either tethered using more than one DNA molecule or exhibited Brownian motion in a confinement area much larger than expected for this tether length. Another 34 particles were discarded since they almost immediately detached from their previous location. Some 30 of the observed particles had an excursion similar to that of stationary particles, thus it is likely they were permanently stuck to the substrate. Of the remaining 114, it seems 45 were tethered to the substrate using a double stranded DNA molecule. Their rms excursion was larger than 80 nm, twice the value expected for a single stranded DNA tether. The presence of dsDNA molecules could have been caused by incomplete separation in the alkaline gel electrophoresis. Most of these particles detached during the course of the observation. This left 69 particles that were presumably attached to single stranded DNA molecules. A large portion of those, 27 particles, did not stay attached for the entire duration of the experiment. In 7 of the remaining cases, the particle had a constant rms excursion, consistent with the expected value for a single stranded tether (see figure 5.6). Ten particles temporarily had a much smaller excursion, which indicates they stuck to the substrate and came off again. That left 25 cases for which it was possible that hybridization of the tether with the mRNA occurred. In 15 cases the excursion of the particle started to increase towards the double stranded DNA level, only to go back to its previous level a little later. An example of this is shown in figure 5.7a. For 4 particles the excursion showed a step-like transition as displayed in figure 5.7b. In total 6 particles showed a slow transition between the expected excursion for a single stranded and a double stranded tether (figure 5.7c). A summary of these numbers can be found in table 5.1.

5.3.2 Verification Unfortunately, we could only obtain fluorescence images of the same field of view as the TPM measurements in one of the experiments. In other experiments the picogreen was bleached before the focus was properly adjusted. Images of the field of view corresponding to the TPM field of view are shown in figure 5.8. No

98 5.3 Results

ssDNA dsDNA Irregular Detached Perma- tether tether motion imme- nently diately stuck Particles6945533430 Defects - Detached later 27 33 - - - - Temporarily stuck 10 3 - - - Transitions -Partialtransition15---- -Step-liketransition4---- -Slowtransition7----

Table 5.1: Overview of observed particle behavior. Shown are the number of particles showing an excursion consistent with a ssDNA or dsDNA tether, particles that showed irregular motion, detached immediately from their previous location or showed motion in the same order of magnitude as stationary particles.

200 Excursion

150 RMS excursion RNA injection 5 and 95 percentile 100 ↓

50 Excursion 2D [nm] 0 0 2000 4000 6000 8000 10000 12000 Time [s]

Figure 5.6: Measured excursion of a 80 nm diameter gold nanoparticle tethered to the substrate using a 737 nt single stranded DNA molecule. The excursion stays at the level expected for a single stranded DNA tether (42 nm rms). The increase in excursion before injection of the RNA is caused by a sudden drop of the microscope stage. The particle went out of focus and this resulted in a large position tracking error. picogreen fluorescent spots could be found that overlayed with the particles. We could only overlay picogreen spots with very large, highly scattering structures. Other fields of view could be imaged and some fluorescent spots were visible,

99 5 Nucleic acid detection using Tethered Particle Motion but they were also much larger than expected (see figure 5.8 and the left images in figure 5.9). Those large spots were most likely of the DNA from fish sperm in the hybridization buffer. In only 8 cases could an overlay of a gold nanoparticle with a fluorescent spot be found (see e.g. the images in figure 5.9). In those cases it appears hybridization did take place, however there was no cross-validation with the TPM results.

100 (a) Partial transition 200 RNA injection 150 ↓ 100

50 Excursion 2D [nm] 0 0 2000 4000 6000 8000 10000 12000 Time [s]

(b) Step-like transition 200 RNA injection 150 ↓ 100

50 Excursion 2D [nm] 0 0 2000 4000 6000 8000 10000 12000 Time [s]

Figure 5.7: Measured excursion of a 80 nm diameter gold nanoparticle tethered to the substrate using a 737 nt single stranded DNA molecule. a The excursion increases for a while but then levels oﬀ again to the excursion expected for a single stranded DNA tether. b The excursion shows a sharp increase to a level near the expected excursion for a double stranded DNA tether (107 nm rms). c The excursion slowly increases to a level expected for a double stranded DNA tether. (a) Dark ﬁeld

(b) Fluorescence

4 μm

Figure 5.8: Dark field (a) and picogreen fluorescence (b) images of the same field of view. In c an overlay of both images is shown. The images are corrected to photon counts and show the maximum projection of 10 collected frames. The small bright spots in a are gold nanoparticles. A few picogreen fluorescent spots can be seen in b, however they are overlayed with large scattering structures and not with the particles that were followed in the TPM experiment. (a) Dark field (d) Dark field

(b) Fluorescence (e) Fluorescence

4 μm 4 μm

Figure 5.9: Dark field (a, d) and picogreen fluorescence (b, e) images of the same field of view. In c and f an overlay of both images is shown. The images are corrected to photon counts and show the maximum projection of 10 collected frames. In the left images, a very large, highly scattering structure can be seen. Some of it is overlayed with fluorescent spots. In both the left and right image set, one gold nanoparticle is overlayed with a fluorescent spot. In the images on the right, the fluorescent image was not focused properly, therefore the size of the fluorescent spot is exaggerated. 5 Nucleic acid detection using Tethered Particle Motion

5.4 Discussion

Before carrying out these experiments, our hypothesis was that the tethered particles would first exhibit confined Brownian motion in a range limited by the single stranded DNA tether. After injection, the complementary mRNA would travel by diffusion to the single stranded DNA. This could take some time as it would take a single mRNA molecule approximately an hour to diffuse from the top of the cell to the bottom where the ssDNA was (the height of the cell is about 100 μm, which is the rms distance an RNA molecule of 1800 nucleotides travels by diffusion in an hour). Probably the hybridization would start at a point where a small part of the mRNA came randomly in the vicinity of the complementary sequence on the ssDNA. After this initial step it could still take some time before the mRNA was fully hybridized to the tether. After that, the particle’s excursion would have increased to a level corresponding to a double stranded tether. Even though the mRNA was added in excess to the single stranded DNA in the microfluidic chip, only a little over 10% of the observed particles exhibited motion resembling the above process. The largest share of those particles showed the behavior as in figure 5.7a. It seems that there the mRNA did partially hybridize to the tether, as indicated by a slow increase of the (rms) excursion over time. The process then reversed, however, as the excursion dropped back to a level consistent with ssDNA. This is consistent with association and dissociation of the mRNA as mentioned in [130]. There were also a few cases where the excursion showed a step-like increase, which happened within a few seconds. This indicates that once the mRNA is near the ssDNA, the actual bond formation could be very fast. Only in 7 cases did we observe the exact behavior as hypothesized. Unfortunately we were unable to verify these results with fluorescence images of the same field of view.

5.5 Recommendations

5.5.1 Biochemistry and surface chemistry Judging by the low amount of plausible hybridizations it appears the conditions for hybridization were not optimal in these experiments. To improve this, conditions as buﬀer, concentrations and temperature should be tested and optimized before further TPM experiments are sensible. The most suitable conditions can be selected by determining which give the best hybridization results in gel electrophoresis experiments.

104 5.5 Recommendations

Many of the particles detach from their previous position, which indicates that the tethering system is not stable. It could be that the single stranded DNA gets nicked by free radical oxidation, thereby severing the tether. This could be inhibited by adding EDTA and ethanol to the buffer [131]. Another cause could be that the bonds break, that connect the particle to the tether and the tether to the substrate. We used antibody coated particles and substrates that bind to proteins at the ends of the tether. It could be that this type of binding is not stable enough. The thermal stability of this bond will probably be an issue when the microfluidic cell is heated for a more specific hybridization reaction. A better option is to design surface chemistry that allows the DNA to be covalently bonded to the substrate and particle. This should be done before experiments at elevated temperatures are carried out.

5.5.2 Setup Hybridization experiments are usually carried out at elevated temperatures (60- 90◦ C). This is done to reduce secondary structure (caused by self-hybridization), giving the mRNA better access to the full sequence of the ssDNA. The reaction is then also more specific since the heat will melt bonded molecules with an incomplete match in sequence. For the experiments described in this chapter, the microfluidic cell was squeezed between the condenser and objective, leaving little room for a heating stage (see figure 5.1). The low amount of observed hybridizations could thus be inhibited by the secondary structure of the mRNA and ssDNA. One solution is to heat the mRNA to 60◦ C and then quickly put it on ice to preserve the state of the molecules until injection in the cell. This was done for one of the experiments described in this chapter, but did not result in more detected hybridizations. Heating just the mRNA therefore does not prove sufficient. In future experiments some kind of heating should be used, possibly a box that includes the condenser and objective. Care should be taken to stabilize the microscope system in the z-direction. The objective turret slowly drops (about a micron per hour) during the 3 hours of particle observation. The precision with which the positions of the particles can be tracked depends on their height relative to the focal plane. Even a drop of a few hundred nanometers decreases the precision significantly (see e.g. section 3.3.1) and this hampers the sensitivity of the detection. The focus could be manually adjusted, but an automatic feedback system would keep the focus more stable over time. The speed of our nucleic acid detection system is limited by the hybridization time of the mRNA and ssDNA tether. This time depends mainly on the time it

105 5 Nucleic acid detection using Tethered Particle Motion takes the mRNA to reach a ssDNA molecule by diffusion. There are several ways to reduce that time. For instance, the buffer containing mRNA can be pumped back and forth through the cell. Another possibility is to steer the negatively charged mRNA towards the ssDNA on the substrate using an electric field. Fixe et al. [132] reduced the hybridization time in their experiments from 16 hours to a few microseconds using electric field pulses.

5.5.3 Sensitivity and specificity If proof-of-principle of the detection method with TPM experiments is successful, there are several ways to proceed in the optimization of the method. The sensitivity could be enhanced by optimizing the surface coverage by the ssDNA tethers. The surface coverage should not be too high, as the spacing between the tethers should be large enough to avoid influencing each other. As this results in a much lower density of probes than is possible with untethered probes, this method is more suited for the detection of the presence of nucleic acid than for concentration measurements. Sensitivity and specificity also depend on the length of the tether [133], which could be varied to obtain the best results. The current model system of luciferase ssDNA and mRNA is a good choice for proof-of-principle experiments, since it is readily commercially available. For the detection of another gene of interest it will be necessary to use a different tether. The tether could be designed in such a way that a hairpin loop is formed at the most crucial sequence in the gene. In that case the loop would only be opened by hybridization with the specified RNA. This could be investigated to see if single nucleotide polymorphisms (SNPs) of the gene can be distinguished using our method.

5.6 Conclusion

If the above mentioned technical diﬃculties can be overcome, Tethered Particle Motion should be an excellent candidate for rapid and sensitive nucleic acid detection. We have already seen clues for diﬀerent types of hybridization behavior in our experiments. Thus, on a more fundamental level, TPM could also be used to study the kinetics of the hybridization reaction.

106 Summary and conclusions

Dark ﬁeld tethered particle motion (DF-TPM) is a single-molecule method that can be used to study DNA in a near-native environment. We propose to use DF-TPM for the rapid and sensitive detection of nucleic acids (DNA, RNA). This thesis describes theory and computer simulations of the motion of a gold nanoparticle tethered to a substrate using a single DNA molecule. Furthermore, physical experiments to validate the theory and simulations and to provide insight into the method and experimental setup are reported. Experiments leading towards a proof-of-principle of the method for nucleic acid detection are reported. Recommendations for future steps to reach this goal are given.

In DF-TPM a gold nanoparticle is tethered to a substrate using a single DNA molecule inside a microfluidic cell. The DNA and particle are immersed in a water buffer. Thermal energy causes the molecules in the buffer to collide with the particle and DNA. This results in a random motion of the particle and DNA, a phenomenon which is called Brownian motion. The gold nanoparticles scatter light intensely, thus using a dark field microscope they are clearly visible against a dark background.

Chapter 2 We investigated how the position distribution of the particle depends on the properties of the DNA and the proximity of the particle to the substrate. As an analytical description of the behavior of a tethered particle

107 Summary and conclusions was unavailable, we used Monte Carlo simulations to obtain simulated position distributions of the particle. The DNA was simulated using the Worm-Like Chain (WLC) model, which needs only two parameters (the contour length and persistence length of the DNA) to fully describe the conformations the DNA can adopt. We compared the computer simulations to physical experiments where the 2D (projected) position of the particle was imaged using a dark field microscope. The double stranded DNA (dsDNA) tethers we used were produced using PCR, therefore the contour length was known. By statistically comparing the simulated position distributions to the experimentally obtained ones, we were able to determine the persistence length of each single dsDNA molecule with a precision of 2 nm. The average persistence length of 45 dsDNA molecules of four different lengths was 35 nm (standard error 3 nm), a value other researchers have found under the same buffer conditions (high salt concentration of 100 mM NaCl).

Chapter 3 The DF-TPM method was further investigated by expanding the 2D position measurements to 3D. By adding a cylindrical lens to the imaging light path in the microscope, an optical aberration called astigmatism is introduced. This causes the particles to be imaged as ellipses. The orientation and size of the ellipse provide the third dimension of the particle position. We were able to determine the particle position in 3D with a precision of 6 nm in the lateral and 15 nm in the axial direction. The statistics (position distribution) and dynamics (mean squared displacement, MSD, as a function of time difference, Δt) were analyzed in each dimension separately. In the lateral dimensions (x and y) the measured persistence lengths agreed well with each other, resulting in an average value around 30 nm. In the axial dimension (z) the statistics measurements resulted in a much higher average persistence length (65 nm) than the dynamics measurements (16 nm). A closer look at the data showed that, on the one hand, the axial positions were on average much further away from the substrate than expected from the lateral position distributions of the particles. On the other hand, the axial mean squared displacements were much lower than the lateral ones. This suggested that the particle is pushed upwards (away from the substrate), thus limiting the statistics and dynamics in the lateral dimension and the dynamics in the axial dimension. We estimated that the magnitude of the responsible force should be on the order of a few fN. The most likely cause we found was thermal buoyancy due to local heating of the buffer by the illumination light source of the microscope. Qualitatively, our experimental results best fit simple simulations incorporating an upwards force with a true

108 Summary and conclusions persistence length of 37 nm and stretching force of 5.8 fN as input.

Chapter 4 We studied the dynamics in more detail by looking at the MSD on short and longer time scales. For large Δt (longer than the relaxation time of the system, which is on the order of a few milliseconds) the MSD is constant and determined by the spring constant of the tethering DNA. The behavior for small Δt depends on the diffusion properties of the particle and DNA, combined with the influence of the nearby substrate. Gold nanoparticles were tethered to the substrate using dsDNA of several different lengths and of two different species. The motion of the nanoparticles was imaged with an EM-CCD camera that could achieve frame rates high enough to observe the short-time regime of the motion. We compared our experimental observations with a mathematical model by Qian and found good agreement. The mathematical model allowed us to determine the friction coefficient of the DNA. The friction coefficient follows a scaling law with the contour length and persistence length of the DNA. The scaling exponent reflects the amount of swelling of the molecule due to long- range interactions (volume exclusion). We determined a value of the scaling exponent close to 0.5, indicating there is only a minimal amount of volume exclusion consistent with expectations for semi-flexible polymers such as dsDNA. This is also consistent with the high salt concentration (100 mM NaCl) used in the buffer; the salt screens the negative charge of the dsDNA, preventing swelling due to electrostatic self-repulsion.

Chapter 5 To use DF-TPM for the fast and sensitive detection of nucleic acids, a single stranded DNA (ssDNA) molecule instead of a dsDNA molecule is used as tether. The tethering ssDNA has a nucleotide sequence that is complementary to the nucleic acid to be detected, therefore both molecules can hybridize. The detection principle amounts to observing the tethered particle’s motion before and after adding an unknown sample. If the target nucleic acid is present in the sample, the motion of the particle should change from a level consistent with a single stranded DNA tether to a level consistent with a double stranded DNA tether. We carried out experiments on a model system of ssDNA obtained from a luciferase RNA template and commercially available mRNA that is complementary to the ssDNA. The motion of gold nanoparticles tethered to the substrate using the luciferase ssDNA was followed over several hours. A few minutes after starting the observation, the complementary mRNA was added. The motion was analyzed oﬄine and the rms excursion (distance to estimated anchor point of the ssDNA) was plotted as a function of time.

109 Summary and conclusions

We found that 10% of the particles showed motion that is consistent with partial or full hybridization and even association and dissociation of the mRNA molecule. To increase the rapidity and sensitivity, several modiﬁcations to the biochemistry, surface chemistry and experimental setup are necessary and recommendations for these are given. Ultimately, the DF-TPM method showed promise as a new method for nucleic acid detection and can even be used to study the kinetics of hybridization reactions.

110 Samenvatting en conclusies

Donkerveld tethered particle motion (de beweging van een getuierd deeltje) is een single-molecule methode, die kan worden gebruikt om DNA in zijn zo goed als natuurlijke toestand te bestuderen. Wij stellen hier voor deze methode te gebruiken voor snelle en gevoelige detectie van nucle¨ıne zuren (DNA, RNA). Dit proefschrift beschrijft theorie en computer simulaties van de beweging van gouden nanodeeltjes, die door een enkel DNA molecuul getuierd zijn aan een oppervlak. Om de theorie en simulaties te valideren en om meer inzicht in de methode en experimentele opstelling te krijgen, zijn fysische experimenten uitgevoerd. Die experimenten worden hier gerapporteerd, samen met experimenten die zouden moeten leiden tot een proof-of-principle van de methode voor nucle¨ıne zuren. Daarnaast worden aanbevelingen gedaan voor de volgende stappen die daarvoor nodig zijn.

Een gouden nanodeeltje is getuierd aan een substraat met behulp van een enkel DNA molecuul, binnen in een micro vloeistof cel. Het deeltje en het DNA zijn ondergedompeld in een water buﬀer. Thermische energie zorgt ervoor dat de moleculen in de buﬀer botsen met het deeltje en het DNA. Dit zorgt ervoor dat het deeltje en DNA een willekeurige beweging gaan uitvoeren, die de Brownse beweging wordt genoemd. De gouden nanodeeltjes verstrooien opvallend licht zeer sterk, daarom kun je ze goed zichtbaar maken in een donkerveld microscoop.

111 Samenvatting en conclusies

Hoofdstuk 2 We hebben onderzocht hoe de positie verdeling van het gouden nanodeeltje afhangt van de eigenschappen van het DNA molecuul en van zijn nabijheid tot het substraat. Een analytisch model van het gedrag van het deeltje was niet beschikbaar, daarom hebben we Monte Carlo simulaties gebruikt om gesimuleerde positie verdelingen van het deeltje te verkrijgen. Het DNA wordt omschreven door het Worm-Like Chain model (het worm-vormige keten model). Dat model gebruikt maar twee parameters om de conformaties die het DNA kan aannemen volledig te omschrijven. Die parameters zijn de contour lengte en persistentie lengte van het DNA. We hebben de resultaten van de computer simulaties vergeleken met fysische experimenten van de 2D (geprojecteerde) posities van een getuierd deeltje, die we met een donkerveld microsccop hadden afgebeeld. De dubbelstrengs DNA (dsDNA) moleculen die we daarvoor gebruikten, waren gemaakt met een PCR reactie, daarom wisten we de contour lengte. Door de posities uit de fysische experimenten te vergelijken met die uit de computer simulaties, konden we de persistentie lengte van elk dsDNA molecuul met een precisie van 2 nm bepalen. De gemiddelde persistentie lengte van 45 dsDNA moleculen met vier verschillende lengtes was 35 nm (standaard fout 3 nm). Deze waarde hebben andere wetenschappers ook gevonden met gebruikmaking van dezelfde buﬀer condities (hoge zout concentratie van 100 mM NaCl).

Hoofdstuk 3 We hebben de donkerveld methode uitgebreid met 3D in plaats van 2D metingen van de positie van de gouden nanodeeltjes. Door een cylin- drische lens in het afbeeldingspad van de microscoop te plaatsen, hebben we een optische aberratie, die astigmatisme heet, geintroduceerd. De deeltjes worden dan afgebeeld met een elliptische vorm. De ori¨entatie en afmetingen van de ellips geven de derde dimensie van de positie van het deeltje. Op deze manier konden we de positie van gouden nanodeeltjes bepalen met een precisie van 6 nm in de laterale en 15 nm in de axiale richting. De statistiek (positie verdeling) en dynamiek (kwadraat van de afgelegde afstand als functie van de verstreken tijd) zijn voor iedere dimensie apart geanalyseerd. In de laterale dimensies (x en y) kwamen de metingen van de persistentie lengte goed overeen. We kwamen uit op een gemiddelde van 30 nm. In de axiale dimensie (z) gaven de statistiek metingen een veel hogere persistentie lengte (65 nm) dan de dynamiek metingen (16 nm). Bij nader onderzoek bleek dat aan de ene kant de axiale posities veel verder weg lagen van het substraat dan we zouden verwachten bij het bekijken van de laterale posities. Aan de andere kant bleken de axiale gekwadrateerde afgelegde afstanden veel lager dan de laterale. Dit suggereert dat het deeltje omhoog (weg van het substraat) geduwd wordt. Daarbij wordt dan in de laterale

112 Samenvatting en conclusies richting de statistiek en dynamiek, en in de axiale richting de dynamiek beperkt. De grootte van de kracht die daarvoor verantwoordelijk is, zou orde grootte een paar fN moeten zijn. Lokale opwarming van de buﬀer door de lichtbron in de microscoop is de meest waarschijnlijke oorzaak die we konden vinden. Kwali- tatief gezien kwamen onze fysische metingen het best overeen met een simulatie waarin een opwaartse kracht is toegevoegd van 5.8 fN en DNA moleculen met een persistentie lengte van 37 nm.

Hoofdstuk 4 We hebben de dynamiek meer gedetailleerd bestudeerd, door de gekwadrateerde afgelegde afstand (MSD) op korte en lange tijdsschaal te bekijken. De MSD voor grote tijdsverschillen (langer dan de relaxatie tijd van het systeem, ongeveer een paar milliseconden) is constant en wordt bepaald door de veer constante van het DNA molecuul. Het gedrag voor korte tijdsverschillen hangt af van de diffusie eigenschappen van het deeltje en het DNA, en van de invloed van het substraat. We hebben de beweging bestudeerd van gouden nanodeeltjes, getuierd door dsDNA met verschillende lengtes en van twee verschillende soorten dsDNA. De beweging van de deeltjes is opgenomen met een EM-CCD camera die met een zo hoge beeldsnelheid beelden kon verw- erken, dat we het bewegingsgedrag op korte tijdsschaal konden bestuderen. We hebben onze observaties vergeleken met het wiskundig model van Qian en vonden daarbij goede overeenkomst. Het wiskundige model zorgde ervoor dat we de frictie coefficient van het DNA konden bepalen. Dat frictie coefficient volgt een schalingswet met de contour lengte en persistentie lengte van het DNA. De schalingsfactor zegt iets over hoe het molecuul opzwelt door interacties met zichzelf over lange afstanden. Onze meetresulaten gaven een waarde voor de schalingsfactor dicht bij de 0.5. Dit duidt op een minimale opzwelling van het DNA molecuul en dat is consistent met wat verwacht wordt voor semi-flexibele polymeren zoals dsDNA. De waarde is ook consistent met de hoge zout concentratie die we gebruikten (100 mM NaCl), aangezien het zout de negatieve lading van het dsDNA afschermt, waardoor geen electrostatische zelf-afstoting plaats vindt.

Hoofdstuk 5 Om onze donkerveld tethered particle motion methode te gebruiken voor de snelle en gevoelige detectie van nucle¨ıne zuren, moeten we een enkelstrengs in plaats van een dubbelstrengs DNA molecuul gebruiken om het deeltje te tuieren. Dit enkelstrengs DNA (ssDNA) molecuul heeft een nucleotide sequentie die complementair is aan het te detecteren nucle¨ıne zuur. De beide moleculen kunnen dus met elkaar hybridizeren. Het principe van detectie is

113 Samenvatting en conclusies dan als volgt: bekijk de beweging van het getuierde nanodeeltje voor en na de toevoeging van je onbekende monster. Als het te detecteren nucle¨ıne zuur aanwezig was in het monster, zou de beweging moeten zijn veranderd van een niveau consistent met een enkelstrengs DNA tuier, naar een niveau consistent met een dubbelstrengs DNA tuier. We hebben experimenten uitgevoerd op een model systeem met ssDNA gemaakt van een luciferase RNA sjabloon en com- mercieel verkrijgbaar mRNA dat complementair is aan het ssDNA. De beweging van gouden nanodeeltjes, die met het luciferase ssDNA getuierd waren aan een substraat, is gevolgd gedurende enkele uren. Het complementaire mRNA is een paar minuten na het starten van de meting toegevoegd. De beweging van de deeltjes is later uit de opgenomen beelden gehaald en de rms excursie (de wortel van de gekwadrateerde afstand tot het geschatte aanhechtingspunt van het ss- DNA molecuul aan het substraat) geplot als functie van de tijd. Bij 10% van de deeltjes vonden we een bewegingskarakteristiek die consistent is met de gedeel- telijke of volledige hybridizatie van het mRNA met het ssDNA. Bij sommige van die deeltjes konden we zelfs de associatie en disassociatie van het mRNA aan het ssDNA herkennen. Om de snelheid en gevoeligheid van de detectie te verbeteren zijn enkele aanpassingen aan de biochemie, oppervlakte chemie en experimentele opstelling nodig. We hebben hiervoor aanbevelingen gegeven. Desalniettemin is de donkerveld tethered particle motion methode veelbelovend alsnieuwemethodevoornucle¨ıne zuur detectie en kan de methode zelfs gebruikt worden om de kinetiek van de hybridizatie reactie te bestuderen.

114 A

Underestimation of Brownian motion due to motion blur

At long exposure times with respect to the time it takes for a particle to traverse its confined range by Brownian motion, motion blur causes an underestimation of the variance of the measured position distribution. Wong and Halvorsen [59] have determined the factor with which the variance is underestimated when a particle is exhibiting Brownian motion in a harmonic potential, as a function of exposure time: 2 2 S(α)= − 1 − e−α . (A.1) α α2 The dimensionless parameter α is defined as the ratio of the exposure time kB T W and the relaxation time of the harmonic potential τ = Dk : α = W/τ = (WDk) / (kBT ), where D is the diffusion coefficient of the particle with radius r and k is the spring constant of the harmonic potential. We have applied their findings to our measurements by taking the theoretical (entropic) spring constant of the DNA for the harmonic potential, k = 3kBT/2PL with P the persistence length and L the contour length, and the theoretical diffusion coefficient, D = kBT/6πηr,ofar=40 nm spherical particle. In chapter 4 we have found that the observed diffusion of the particle is described by the diffusion coefficient in equation 4.17. If we use equation 4.17 in the definition of the relaxation time, the relaxation time is only 15-25% longer than using the theoretical diffusion coefficient of a spherical particle.

115 A Underestimation of Brownian motion due to motion blur

Depicted in figure A.1 is a plot of the motion blur underestimation factor as a function of exposure time, using typical values for the length of the DNA and the diffusion coefficient of the tethered particle. At an exposure time of 10 ms the underestimation due to motion blur is less than 10 %, while at exposure times of 1-2 ms, the underestimation is between 1 and 2%. Destainville and Salomé [134] also investigated the effect of time averaging in single particle tracking. Their equation 8 provides the same result as Wong and Halvorsen for diffusion in a harmonic potential. In a later paper [101] they showed that using the harmonic potential approximation for the relaxation time underestimates the relaxation time in Tethered Particle Motion. Manghi et al. [101] determined the relaxation time from simulations and gave an alterna- tive theoretical relation for the relaxation time using the diffusion coefficient of the DNA-particle complex (see equation 4.14). We have seen in chapter 4 that our experiments do not show the same relation between observed diffusion coefficient and DNA properties, therefore we keep the above approximation for the relaxation time τ. In appendix D of [59], Wong and Halvorsen give an approximate analytical expression for the true spring constant k as a function of the measured position variance. This approximation gives the true value to within 3% as long as the exposure time W is less than 3 times the relaxation time of the motion τ.Our measurements of the dynamics of TPM contain the mean squared displacement instead of the position variance. The two are related in the following way:

2 2 2 Δx = (xi − xj) =2x , (A.2) since the mean position x =0.FollowingthesamemethodasWongand Halvorsen, the true spring constant can then be found by applying the following equation: 2 2 2 2 2 2 kBT 4DW +15Δx − −44D W + 480Δx DW + 225 (Δx ) k ≈ . DW (DW − 6Δx2) (A.3) 2kB T ↓ This equation returns k = Δx2 in the limit for W 0.

116 1 A.1: Figure ihalnt f48 padapritnelnt f3 nm. 35 of length persistence a and bp 4882 of length a with . 07 × 10 − 12 n oinbu neetmto atrfrapril ihdﬀso constant diﬀusion with particle a for factor underestimation blur Motion m Underestimation due to motion blur [%] 2 /s 15 30 35 10 20 25 5 0 nahroi oeta ie rmtesrn osato dsDNA of constant spring the from given potential harmonic a in 0 510 15 xoueti Exposure 20 530 25 m e[ m s] 35 40 550 45

Diﬀusion near a substrate

When a particle is diﬀusing close to a substrate, a number of interactions between them inﬂuence the motion. Here we cover the most important ones. The interactions are described in the following sections, after which a graphic overview of all of them is given and discussed.

B.1 DLVO theory

In the 1940s Derjaguin and Landau [135] and separately Verwey and Over- beek [136] provided a theory for the stability and instability of colloidal disper- sions, which is now called the DLVO theory. The theory combines the inﬂuence of the van der Waals attraction and the repulsive electrical potential from electrostatic charging of the substrate and particles.

B.1.1 Electrostatic interaction Charged bodies that are submersed in an ionic solution are covered with an ionic double layer (the electrical double layer, EDL). When two charged bodies come close to each other, they exert an electrostatic force on each other. The characteristic length scale for this is the Debye length [137]:

k T κ−1 = f 0 B , (B.1) 2ce2

119 B Diﬀusion near a substrate

where 0 is the permittivity of free space, f the relative permittivity of the ﬂuid, c is the concentration of ions in the solution and e is the elementary charge of an electron. The electrostatic potential energy between a sphere and a plane is:

−κ(z−r) Uel(z)=Be . (B.2)

B is the magnitude of the electrostatic potential and can be calculated from the surface charges of the sphere and the plane [138]. Common values that are used are between 25 and 100 mV, but it seems the surface charges are fairly difficult to measure. The higher the concentration of ions the more screening occurs. For the 100 mM NaCl solution we generally use, the Debye length is only 0.7 nm. From the simulations in chapter 2 we know that the particle is less than 0.5% of the time this close to the substrate. Therefore this interaction does not play a significant role in the dynamics of our tethered particle (see also figure B.1).

B.1.2 Van der Waals interaction When the particle is close to the substrate (z<2r) there is an attractive potential due to the van der Waals force. The van der Waals potential energy for the interaction between a sphere and a plate is [90]: A r r z − r U (z)=− + + ln , (B.3) vdw 6 z − r z + r z + r with A the Hamaker constant, which is on the order of 10−20 J [139].

B.2 Gravity

Gravitational force plays a role for density mismatched particles. The gravitational potential of the particle rises with its height above the substrate: 3 Ug = mgh = 4/3πr (ρp − ρf )g(z − r), (B.4) where m is the net mass of the particle and ρp and ρf are the density of the particle and the ﬂuid, respectively. Gravity force is constant for all heights and equal to 0.05 fN. The inﬂuence is smaller than the thermal energy when the particle is closer to the substrate than z =7.8μ m for our 80 nm diameter gold nanoparticles.

120 B.3 Hydrodynamic interaction

B.3 Hydrodynamic interaction

The diffusion of particles near a substrate is significantly hindered due to an increase in the hydrodynamic drag. The fluid surrounding the particle has less opportunity to make room for the particle, therefore there is an increase in drag force. This alters the apparent diffusion coefficient. The relative diffusion parallel to the substrate has been determined by the ”method of reflections” and works well for heights z/r > 2 [140]: D 9 z −1 1 z −2 45 z −4 1 z −5 z −6 x =1− + − − + O . (B.5) D0 10 r 8 r 256 r 16 r r The diffusion perpendicular to the wall has been described by Brenner [88]. Bevan and Prieve [141] have given a computationally more convenient approximation: z − 2 z − Dz 6 r 1 +2 r 1 = 2 . (B.6) D0 z − z − 6 r 1 +9 r 1 +2 An indication of the total effect of this hindered diffusion is determined by integrating the amount of hindered diffusion (equations B.5 and B.6) multiplied by the simulated height distribution of the particle. For the different lengths of tether molecules we use, this relative hindered diffusion factor is given in table B.1. As the tether molecule becomes shorter, the influence of hindered diffusion increases. For our relatively long tether lengths with respect to particle radius, the effect is still significant.

DNA tether length total Dx/D0 total Dz/D0 972 bp 0.77 0.56 2205 bp 0.83 0.67 2698 bp 0.84 0.70 4882 bp 0.88 0.76

Table B.1: Total relative hindered diﬀusion factor for tethered particles: the inte- gral of the hindered diﬀusion factor weighed by the height distribution of the tethered particle.

121 B Diﬀusion near a substrate

B.4 Discussion

As we have shown in the previous sections, the motion of the tethered particle is influenced by the nearby substrate. The magnitude of the electrostatic, van der Waals and gravitation potential are plotted in figure B.1. In the same figure, simulated height distributions of the gold nanoparticle tethered to a substrate using DNA molecules of different lengths are plotted. The simulations have been described in chapter 2. The shorter the tethering DNA molecule, the more the particle is influenced by these potentials. The particle is closer to the substrate than the Debye length typically 0.5% of the time, thus it does not influence the motion significantly. As can be seen in a plot of the force associated with the potentials (figure B.1b), the repulsive electrostatic force and gravitational force are very small, especially when compared to the upwards force of 2 fN mentioned in chapter 3. The attractive van der Waals force, however, is in the same range as the suggested upwards force. As we have approximated the net upwards force from the measurements, any upwards force itself must then be larger. In figure B.2 the relative diffusion in the lateral and axial direction due to hydrodynamic drag is plotted. The influence on the diffusion in the direction parallel to the wall is moderate. In contrast, the diffusion in z is significantly influenced. The measurements in chapters 3 and 4 confirm this phenomenon.

122 (a) Potential energy ×10−21 7 1 Electrostatic 6 Van der Waals 10x Gravitation 0.8 Thermal energy 5

0.6 4

3 0.4

Potential energy [J] 0.2 1

0 0 0 200 400 600 800 Height above surface [nm]

(b) Interaction force ×10−15 1 Electrostatic

5 Van der Waals 0.8 Gravitation 4 0.6 3 0.4 Force [N] 2

0.2 1

0 0 0 200 400 600800 Height above surface [nm]

Figure B.1: a Magnitude of potential energies near the substrate. The electrostatic potential is repulsive, while the van der Waals potential is attractive. The gravitation potential is upscaled 10 times, otherwise it would not have been visible. b Magnitude of interaction forces near the substrate. In the ﬁgure also the relative height distributions of a particle tethered to the substrate using a 972 (×), 2205 (◦), 3202 () and 4899 () bp dsDNA molecule are plotted. 1

0.8 Dx/D0

Dz /D0

0.6

0.4

0.2

0 0 200 400 600 800 Height above surface [nm]

Figure B.2: Hindered diﬀusion in the direction parallel and perpendicular to the substrate. The relative height distribution of a particle tethered to the substrate using a 972 (×), 2205 (◦), 3202 () and 4899 () bp dsDNA molecule. C

Drift correction

The stage containing the sample on a microscope can slowly drift during long measurements. The tracked positions of the particle in Tethered Particle Motion need to be corrected for this. There are two methods mainly in use in TPM. One is to track stationary particles in the field of view and use their averaged observable motion as drift coordinates. This method is applied for the measurements described in chapter 2. The substrate is coated with biotinylated BSA and the anti-biotin coated gold nanoparticles bond to that, producing stationary particles. This method has the drawback that tethered particles can also stick to the substrate. The second method is to apply a low-pass filter (in time) to the tracked positions (x(t)andy(t)) of the tethered particle. Drift is usually a slow process, that is why the very low frequencies should be filtered. We use a Gaussian low-pass filter to estimate the drift. The found drift is then subtracted from the tracked positions. In this method, filter size is the crucial factor. The power spectrum of the motion of the tethered particle should be similar to that of Brownian motion in a harmonic potential, which is given in equation C.1 [142].

2kBTζ Sx(ω)= (C.1) (k − mω2)2 + ζ2ω2

This power spectrum has its maximum at the zero frequency and then slowly drops to zero. If the filter size is small as in figure C.1a, much of the diffusive motion in the lower frequencies is filtered out (figure C.1b). The filter size

125 C Drift correction should be larger, e.g. much longer than the relaxation time of the harmonic potential. This is done for the same particle and the results are shown in ﬁgures C.1c and C.1d. The resulting drift is less than 15 nm during the 5 seconds of observation, which is typical for the measurements in chapters 3 and 4. There is so little drift in these measurements (less than 15 nm), that no drift correction is deemed necessary. The measurements in chapter 5 take several hours and do need drift correction. We use a ﬁlter size of 50 frames (25 seconds). Figure C.1e shows an example of the x-position of the tracked particle and the results of the drift correction.

126 (a) Filter size 33 ms (b) Measured spectrum

X-position 1600 300 Original signal Low-pass ﬁltered positions Drift corrected signal 200 1200

100 800 0

− 400 100 PSD [W/Hz] X-position [nm] − 200 0 0 123 45 0 50 100 150 Time [s] Frequency [Hz]

X-position 1600 300 Low-pass ﬁltered positions Original signal 15 nm Drift corrected signal 200 1200

100 800 0 400 −100 PSD [W/Hz] X-position [nm] − 200 0 0 123 45 0 50 100 150 Time [s] Frequency [Hz]

(e) Filter size 25 s (f) Measured spectrum

2000 Original signal X-position 6 Low-pass ﬁltered positions 10 Drift corrected signal 1000 104 0

102

−1000 PSD [W/Hz] X-position [nm] 0 10 −2000 . . . . 0 1000 2000 3000 4000 5000 0 0 2 0 406081 Time [s] Frequency [Hz]

Figure C.1: a, c:Measuredx-position of a single gold nanoparticle tethered using a 2 kbp dsDNA molecule. The black line constitutes the low-pass filtered positions using a filter size of a: 10 frames (33 ms) and c: 150 frames (495 ms). e:Measuredx-position of a single gold nanoparticle tethered using a 737 nt ssDNA molecule. The black line constitutes the low-pass filtered positions using a filter size of 50 frames (25 s). The sharp spikes are outliers caused by unattached beads traversing the field of view (see section 5.2.4). Notice the difference in the time and position scale with figures a and c. b, d, f: Measured power spectral density (PSD) of the same particle with and without drift correction using the low-pass filtered positions from a, c and e respectively.

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144 Curriculum Vitae

Sanneke Brinkers was born on October 23, 1981 in Gouda. She graduated in 1999 from the Philips van Horne scholengemeenschap (secondary school) in Weert. Sanneke then started her university education in Applied Physics at the University of Twente in Enschede. She spent four months at Immunicon Corporation in Philadelphia, USA for her internship, working on an automated time resolved ﬂuorescence microscope for circulating tumor cell detection. In 2006 she received her ”ingenieurs diploma” (M.Sc) cum laude with a thesis ti- tled ”AIDS in Africa, Aﬀordable HIV staging: Innovations in CD4 enumeration instrumentation”. The thesis work was supervised by prof. dr. J. Greve.

In 2006 she started her PhD work in the Quantitative Imaging group at the Delft University of Technology on the development of the dark ﬁeld tethered particle motion method for rapid and sensitive nucleic acid detection. She was supervised by prof. dr. I.T. Young and dr. B. Rieger and worked in close col- laboration with dr. H.R.C. Dietrich. In the third year of her PhD she worked part-time (1 day per week) at the Medical Delta research consortium as project leader for the ”Medical Delta Caf´e”.

In 2011 she started working as a research scientist for the Optics department at TNO in Delft. She continues her fascination with optical instrumentation for medical applications.

145

List of publications

Papers

S. Brinkers, H.R.C. Dietrich, S. Stallinga, J.J. Mes, I.T. Young and B. Rieger, Single Molecule Detection of Tuberculosis Nucleic Acid Using Dark Field Tethered Particle Motion. 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Rotterdam, The Netherlands (2010), 1269-1272.

S. Brinkers, H.R.C. Dietrich, F.H. de Groote, I.T. Young, and B. Rieger, The persistence length of double stranded DNA determined using dark ﬁeld tethered particle motion, Journal of Chemical Physics, Vol. 130:22 (2009), 215105.

Oral presentations

S. Brinkers, H.R.C. Dietrich, B. Rieger and I. T. Young, Fast, Sensitive De- termination of Gene Expression, Awards Ceremony at the International Society for Analytical Cytology XXVI International Congress, Budapest, Hungary, 19 May 2008. (Nominee for the President’s Award for Excellence)

S. Brinkers, H.R.C. Dietrich, B. Rieger and I. T. Young, Lab-on-a-Chip for Rapid Determination of Gene Expression, National Micro Nano conference,

147 List of publications

MicroNed and MinacNed, Wageningen, The Netherlands, 16 November 2007. (Best Presentation Award)

S. Brinkers, H.R.C. Dietrich, B. Rieger and I.T. Young, Lab-on-a-chip for rapidly determining gene expression, Annual Dutch meeting on Molecular and Cellular Biophysics, Veldhoven, The Netherlands, 1 October 2007.

S. Brinkers, H.R.C. Dietrich, B. Rieger and I.T. Young, Detection of DNA Hybridization Events Using the Diﬀusion Constant in TPM Experiments, Focus on Microscopy conference, Valencia, Spain, 13 April 2007.

Poster presentations

S. Brinkers, H.R.C. Dietrich, J.J. Mes, I.T. Young and B. Rieger, A 3 dimensional dance of gold: Three dimensional characterization of Tethered Particle Motion, Annual Dutch meeting on Molecular and Cellular Biophysics, Veld- hoven, The Netherlands, 4 October 2010.

S. Brinkers, H.R.C. Dietrich, S. Stallinga, J.J. Mes, I.T. Young and B.Rieger, Single Molecule Detection of Tuberculosis Nucleic Acid Using Dark Field Teth- ered Particle Motion, IEEE International Symposium on Biomedical Imaging, Rotterdam, The Netherlands, 14 April 2010.

S. Brinkers, H.R.C. Dietrich, J.J. Mes, S. Stallinga and B. Rieger, Dynamics in Tethered Particle Motion: Interpreting the Observations, Biophysical Society 54th Annual Meeting, San Francisco, CA, USA, 23 February 2010.

H.R.C. Dietrich and S. Brinkers, J.J. Mes, B. Rieger, Genomics for Fresh- ness: BioChips for Rapid Quality Assesment of Fresh Agro-Products, Nether- lands MicroNano Conference ’09, Delft, The Netherlands, 5 November 2009

S. Brinkers, H.R.C. Dietrich, J.J. Mes, S.Stallinga and B.Rieger, The Dy- namics of Tethered Particle Motion: How to design your experiment, Annual Dutch meeting on Molecular and Cellular Biophysics, Veldhoven, The Nether- lands, 28 September 2009.

148 List of publications

S. Brinkers, H.R.C. Dietrich, I.T. Young and B.Rieger, 3D Characteriza- tion of Tethered Particle Motion Using Bifocal Imaging, Focus on Microscopy Conference, Krakow, Poland, 5 April 2009.

S. Brinkers, H.R.C. Dietrich, B. Rieger and I.T. Young, Single Molecule RNA Detection: Fast and Sensitive Gene Proﬁling, Netherlands MicroNano Conference ’08, Ede, The Netherlands, 17 November 2008.

S. Brinkers, H.R.C. Dietrich, B. Rieger and I.T. Young, Fast, Sensitive Determination of Gene Expression, Annual Dutch meeting on Molecular and Cellular Biophysics, Veldhoven, The Netherlands, 29 September 2008.

S. Brinkers, H.R.C. Dietrich, B. Rieger and I. T. Young, Fast, Sensitive De- termination of Gene Expression, International Society for Analytical Cytology XXVI International Congress, Budapest, Hungary, 19 May 2008. (Outstanding Poster Award)

S. Brinkers, B. Rieger and I.T. Young, Lab-on-a-Chip for Rapid Deter- mination of Gene Expression, Interdisciplinary Summer School on Bio-medical Imaging, Z¨urich, Switzerland, June 2007.

149

Acknowledgements

So many people contributed to my work and life as a PhD student. I want to thank all of you for your support. Some people I want to give some extra credit. Bernd, without you I would have never been able to come this far. Thank you so much for supervising and supporting me in every step of the way, both in PhD related and personal matters. Ted, thank you for having faith in my abilities as a researcher and for giving me the opportunity to broaden my horizon at Medi- cal Delta. Lucas, I enjoyed our numerous discussions about anything that came across our minds. Heidi, even though sometimes the road was rocky, I enjoyed working together with you and learning from you. Sjoerd, you have made a big difference for the group QI and I appreciate very much all the times you were willing to help out with my project. Yuval, thanks for your interest in my work, even though you were already on your way back to Israel. Jurriaan, bedankt voor je hulp bij het vinden van mijn weg in de wondere wereld van qPCR en microarrays. Mandy, Ronald en Wim, jullie hebben een speciaal plekje in mijn hart, bedankt voor al jullie hulp en vriendschap. Thanks also to all the PhD students at QI and also CPO for the good times in and outside the office. Spe- cial thanks go to all the people with which I have shared F262: Bart, Milos, Maya, Qiaole and of course to Vincent, Vincenzo and Alexander for sharing beers and conversations about the important things in life. Thanks also go to all other members of QI for the good conversations and work atmosphere. Aan iedereen die betrokken was bij de Medical Delta cafés: bedankt voor de kans

151 Acknowledgements om iets compleet anders en zeer inspirerends te doen naast mijn promotie. Ook mijn huidige collega’s bij de afdelingen Space en Optics van TNO dank voor de steun tijdens het laatste, soms erg zware, deel van mijn promotie. Alles werd een hoop lichter gemaakt door de niet aﬂatende gezelligheid, steun en gedeelde levenservaring van de vrienden en vriendinnen uit mijn favorietste borrel com- missie (Janneke, Joost, Joris, Lieuwe, Maarten, Martijn, Merel, Michel, Roel, Wouter). Alle ooms, tantes, neven en nicht en natuurlijk oma, jullie steun en interesse betekenen veel voor mij. Broertje, ik vind het leuk dat we, sinds we ”volwassen” zijn, elkaar toch wel mogen en elkaar wat vaker opzoeken. Mama, ook al beweer je vaak niet te begrijpen wat ik doe, het is zo ﬁjn dat je altijd je trotsheid toont en naast een liever moeder ook een echte vriendin voor me bent. Ik ben ontzettend trots en blij dat de twee belangrijkste mannen in mijn leven tijdens de verdediging van mijn proefschrift naast me willen staan als paranim- fen. Papa: je bent mijn rots in de branding, bedankt dat je er altijd voor me bent. Erik: jij maakt me gelukkig, daardoor en door jouw hulp en steun kan ik de hele wereld aan.

152