optical tweezers and their applications …braslavs/honorthesis/honors_thesis...optical tweezers and...

OPTICAL TWEEZERS AND THEIR APPLICATIONS IN

BIOPHYSICS RESEARCH AND EDUCATION

____________

A Thesis

Presented to

The College of Arts and Sciences

Ohio University

____________

In Partial Fulfillment

of the Requirements for Graduation

with Honors in Physics

____________

by

Paul Francis Ingram

June 2008

This thesis has been approved by the

Department of Physics and Astronomy and the College of Arts and Sciences

_______Dr. Ido Braslavsky_______ Assistant Professor of Physics

_________Dr. Benjamin M. Ogles_________ Dean, College of Arts and Sciences

Abstract In recent years optical trapping, a technique developed from the use of lasers to trap atoms, has become widespread. Optical tweezers have been used in physics and biology to manipulate objects and measure forces. This thesis is divided into three parts which explore the use and application of trapping in biophysics. This includes their use as a tool in undergraduate and graduate lab courses, in single molecule DNA research, and in for ice research experiments that require local changes in temperature. Optical tweezers can be calibrated to measure forces using trapped microspheres as force transducers. This makes an ideal experiment for an undergraduate biophysics lab, the development of which is the first part of this thesis. Studying the diffusion of the beads in the potential well of the trap allows students to explore optics, statistical mechanics and electromagnetic field gradients in a single application. As part of this thesis a lab manual with detailed protocols for the use of an optical tweezer was developed. The second part of this thesis is a single molecule experiment using the optical tweezer. A more recent development in optical tweezing is the use of spatial light modulators for holographic optical trapping (HOT). This allows for the creation and manipulation of multiple traps from the same laser beam. The high degree of control makes it ideal for experiments involving manipulating single molecules like DNA. This requires that the DNA be attached to microspheres which are used as handles. Several steps necessary to conduct such single molecule experiment were completed as part of the thesis. Using a focused laser for local control of temperature in ice crystals is the third part of this thesis. Laser light will be absorbed in water to different degrees depending on the wavelength. The steep gradient of the laser light in the trap allows for a highly localized raise in temperature. This makes optical tweezers ideal for use in precision temperature control in ice experiments. Manipulation of ice crystals within a small area is a challenging task. Melting ice with micrometer precision can be achieved with the focused light in the optical tweezers. We designed and built an optical tweezer into a temperature control stage to assist in this investigation. While optical trapping can be considered a mature technology it continues to find new and novel applications in research. The three sections of this thesis explore current and possible future uses for optical tweezers in biophysics research and education.

Acknowledgments

I would first like to acknowledge the support of Biomimetics Nanoscience and NanoTechnology Initiative at Ohio University, BNNT, in their generous funding of the Biophysics lab development. Their contribution will continue to be felt by students who get the opportunity to work in the Biophysics Lab. I would also like to thank Dr. David Tees for assistance in creating the lab manual and Yeliz Celik for assistance with the ice melting experiment. Throughout the course of this project I received a great amount of help and encouragement from my advisor Dr Braslavsky. I truly appreciate the amount of time, support and guidance he was able to give me. This experience has made a great deal of difference to my development as a physics student. I would also like to thank Dr Hicks and the other involved faculty and staff of the Physics department for their role in organizing and expanding the opportunities for undergraduate research, from which I have benefited greatly. Most of all I would like to thank my wife for her loving support and understanding. Her support has been critical to my success at the university and in this project.

TABLE OF CONTENTS

1 INTRODUCTION..................................................................................................... 1

2 UNDERGRADUATE BIOPHYSICS LAB AND HOLOGRAPHIC OPTICAL TRAPPING........................................................................................................................ 5

2.1 Brownian motion and Boltzmann’s constant............................................................................... 5

2.2 Methods for calibrating optical trap strength ............................................................................. 6

2.3 Flexibility of Holographic Optical Trapping ............................................................................... 7

3 STEPS TOWARDS SINGLE MOLECULE INVESTIGATION OF PROTEIN DNA INTERACTION USING OPTICAL TWEEZERS.............................................. 9

3.1 Labeling Lambda DNA for attachment to microspheres ........................................................... 9

3.2 Dying DNA on microspheres....................................................................................................... 10

3.3 Looking for DNA dumbbells ....................................................................................................... 12

3.4 Improving yield and observation technique............................................................................... 13

4 MELTING ICE ....................................................................................................... 14

4.1 Laser Precision Temperature Control........................................................................................ 14

4.2 Melted Ice...................................................................................................................................... 16

5 CONCLUSION ....................................................................................................... 16

6 REFERENCES........................................................................................................ 17

7 APPENDIX A: POSTER FOR UNDERGRADUATE LAB COURSE ............. 19

8 APPENDIX B: BIOPHYSICS LAB MANUAL................................................... 20

9 APPENDIX C: PROTOCOL FOR LABELING LAMBDA DNA...................... 37

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1 Introduction Optical trapping of μm size objects grew out of the trapping of atoms1 and dielectric objects smaller than the wavelength of the laser being used.2 This regime is called the Rayleigh regime. Particles in the Rayleigh regime are subject to a scattering force due to radiation pressure and a gradient force due to the Lorentz force on a dipole.3

The following derivation of the scattering and gradient forces is distilled from an excellent explanation given by Harada et al. (1996). Radiation is absorbed and reemitted by the particle, but the emission is isotropic and so the net effect is in the direction of the incident photon flux. The scattering force in the direction of light propagations z is:

( )22 ˆs

S nF n I r z

c c

σσ⎛ ⎞= = ⎜ ⎟

⎝ ⎠ (1)

where n2 is the refractive index of the surrounding medium, σ is the scattering cross section of the particle and S is the intensity I from the time averaged Poynting vector.4 For a spherical particle of radius a the scattering cross section is:

22

4 62

8 13 2

mk am

σ π⎛ ⎞−

= ⎜ ⎟+⎝ ⎠ (2)

where 1

2

nmn

= is the relative refractive index of the particle and k is the wave number of

the light used. To have a stable three dimensional trap this scattering force must be overcome by

the gradient force. The induced dipole moment of a dipole with polarizability α in the field E of the laser is: ( , ) ( , )p r t E r tα= (3) The gradient force on this induced dipole is: ( , ) ( , ) ( , )F r t p r t E r t⎡ ⎤= ∇⎣ ⎦ (4) Using the vector identity:

21 ( ) ( )

2E E E E E∇ = ∇ + × ∇× (5)

and from Maxwell’s equations: 0E∇× = (6) the gradient force on a dipole reduces to:

21( , ) ( , )2

F r t E r tα= ∇ (7)

2

The gradient force on a particle is the time averaged version of the force on a dipole. Using the relation:

22 1( , ) ( )

2TE r t E r= (8)

we find:

221 1( ) ( , ) ( , ) ( )

2 4g

T TF r F r t E r t E rα α= = ∇ = ∇ (9)

The intensity I is defined by:

22 0( ) ( )

2n cI r E rε

= (10)

We can use this to relate the force to the intensity gradient by:

2 0

1( ) ( )2

gF r I rn c

αε

= ∇ (11)

From this we can see that the force will be in the direction of the highest intensity.5 In the case of a focused Gaussian laser beam it will result in a force towards the focus, where the intensity is highest. When the particle being trapped is larger than the wavelength of the light being used it is called the Mie regime and a ray optics argument can be used. When light crosses from into a bead with a higher index of refraction it will bend towards the optical axis. This results in a change in momentum in the light which must be accounted for in the bead.

Figure 1. Ray optics argument for trapping. As the light is bent towards the optical axis of the bead the change in momentum results in a force on the bead. In the left hand diagram the bead is displaced slightly from the center of the beam intensity and so experiences a restoring force into the center of the beam. On the right the bead is in the trap and experiences a net force back into the beam.

1 2

F1

1 2

F2 F2 F1

3

If the light rays are focused tightly then the net force perpendicular to the rays, the gradient force, overcomes any scattering force in the original direction of propagation. In the ray optics argument both the scattering and gradient forces come from the change in momentum as the light crosses into the new medium. An illustration of the ray optics argument is provided in figure 1.6

A steep gradient can be created by shining a laser through the objective lens of a microscope. To get a steep enough gradient to overcome the scattering force requires a very high numerical aperture (NA) objective lens. A lens with a higher NA will have a stronger trap, but this will also reduce the depth in which a trap can be created. Our optical trapping system consists of an inverted microscope with a system of dichroics and filters allowing the tweezer to be combined with fluorescent microscopy. Shown in Figure 2, the optical train first expands the beam so that it will overfill the back aperture of the objective and then guides it to a spatial light modulator (SLM) which can split and manipulate the beam. In simpler setups a mirror on a gimble mount can be used to manipulate a single beam trap.

Between the SLM and the back aperture of the objective lens are two identical lenses which allow the direction of the beam and thus the location of the trap to be altered

laser

Figure 2. Optical tweeezer schematic from the lab manual. The beam is first expanded and then guided to the SLM where it is controlled by the computer. The telescope configuration of lenses 3 and 4 allow the trap to be manipulated without it leaving the back aperture of the objective lens.

SLM

4

without shifting it from the back aperture of the objective lens. This is called a 4f setup, because the SLM mirror is four focal lengths from the back aperture. Lens 4 is one focal length from the back aperture and lens 3 is 3 focal lengths away.

The distance between lenses 3 and 4 can be adjusted to change the depth of the trap, but this will cause a problem when the trap is steered. To change the depth of the trap in the focal length it is best to move lenses 1 and 2 closer or further apart. This can be easily accomplished if the lenses are mounted in a cage system which would ensure they remain on the same axis and parallel.7 Moving lenses 1 and 2 has also been shown to have a more significant effect. Moving lens 3 a distance of 10mm results in a change in depth of just 1 micrometer. Moving lens 1 a distance of 10mm closer or away from lens 2 will change the focal plane of the trap by 17 micrometers.8 A dichroic mirror (z900dcsp Chroma Technology Inc) reflects the beam up through the objective lens without interrupting the view of the sample. The lens itself focuses the laser, creating a trap just short of the focus.

In recent years optical tweezers have been used by physicists in a wide range of experiments in biology. The ability to trap micrometer size objects and use them as handles for even smaller objects makes optical tweezing ideal for investigating biological systems. Being able to manipulate small objects has allowed new techniques for cell fusion. Cell fusion using optical tweezers can be used to create hybrid cells with different properties and to introduce genetic material and molecules into cells.9 Optical tweezers have been used in microsurgery to hold fragments of chromosomes during mitosis suggesting that they would be a useful tool in studying chromosome movement and cell genetics.10 In plant biology tweezers have been used to study gravity sensing in plants.11

The ability to apply and measure forces on the order of piconewtons has been used in studying DNA and its properties. Using optical tweezers DNA has been unzipped12, tied in a knot13, and stretched to take precise measurements of its mechanical properties.14 To measure mechanical forces the trap is modeled as a potential well with displacement corresponding to external force applied. Important investigations into the kinetics of motor proteins like RNA polymerase have also been made possible by optical trapping.15

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2 Undergraduate Biophysics lab and holographic optical trapping

The novelty of the trapping mechanism and the fact that it can be easily modeled using ray optics makes it ideal for undergraduate advanced labs. The trap in itself demonstrates basic physics concepts such as conservation of momentum and optics. The system as a whole can be used to demonstrate how a physics tool could be so useful in biology at a level appropriate for undergraduates. To create the lab it was necessary to piece together information from literature, state of the art HOT software and hardware, and existing video analysis software. The poster presenting the course is attached as appendix A. The detailed lab manual is attached as appendix B. By the end of the lab students should:

• Have a basic understanding of the fundamentals of optical trapping. • Have a basic understanding of the fundamentals of particle tracking by video

analysis. • Be able to explain Brownian motion and Diffusion. • Measure Boltzmann’s constant using the Einstein equation. • Be able to explain trap stiffness and to calculate it. • Be able to use basic programs in IDL.

2.1 Brownian motion and Boltzmann’s constant To measure Boltzmann’s using Brownian motion it is necessary to follow a

particles position vs time. To take these measurements with the system a suitable particle tracking routine had to be found. Particle tracking is commonly used in biological and colloidal studies. The IDL based routine called Rytrack, which has a graphical user interface and was developed by Ryan Smith was ideal16. Rytrack was developed from particle tracking routines developed by John Crocker and David Grier using the intensity maxima approach17. Rytrack allows video to be analyzed to give the position vs time of multiple particles. Now available is a newer particle tracking routine in Labview written by Graham Milne called the St Andrews Tracker or StAT which in the future might be more accurate and easier to use.18

The first part of the experiment for undergrads involves using Rytrack to track microspheres undergoing Brownian motion under the tweezers microscope. After the position vs time of the beads has been extracted by Rytrack the students use original IDL routines to help them analyze the data they have. In addition to helping them calculate the root means squared displacement the routines also make adjustments for any drift in the slide. This can be a significant problem, especially if the slide is not properly constructed. In previous research data that indicated drift would be discarded, but due to the limited time students have in the lab this is not practical.19

The diffusion of the particles allows students to derive Boltzmann’s constant. This is of course similar, but less time consuming, to the experiment done by Jean Baptiste Perrin in 1908 to determine Avogadro’s number. Perrin, a physicist working at the Sorbonne in Paris, did experiments that measured Brownian motion of particles. Perrin observed 2-dimensional Brownian motion of particles with a radius of 0.37 μm in water at 20°C under a microscope. Perrin observed the position of a particle, waited 30

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seconds, then observed again and plotted the net displacement in that time interval. He collected 500 data points in this way.20 This result independently confirmed results of experiments by Einstein and verified the atomic hypothesis.

Students track the particles and then analyze the data to extract the root means squared displacement in two dimensions and derive the displacement D as:

2

4r

Dt

= (12)

Plotting this allows them to use Einstein’s theory to derive Boltzmann’s constant kb using:

(6 )

B

p

k TDrπη

= (13)

Where η is the viscosity and rp is the radius of the particle. Figure 3shows a graph of the mean squared displacement <r²> vs time t of thirty-one 2µm beads. Video was taken through the 40x air objective. For this value of the diffusion coefficient D we get 1.3x10-23 ± .1 J K-1 for Bolzmann’s constant. The accepted value is 1.38 × 10-23 J K-1.

2.2 Methods for calibrating optical trap strength The next part of the lab experiment is to study particle diffusion in an optical trap. To take measurements of forces on the order of piconewtons it is necessary to determine how strong the trap is. One can think of the trap as a potential well with a stiffness k. For small displacements the trap can be modeled using Hookes Law Fx=-kx(x-x0). We imagine we have three springs for our trap with kx, ky, and kz . This is important because by attaching things to beads we can use them as force transducers to take measurements. There are a number of ways to measure trap stiffness.

One can measure the displacement of a trapped bead when the fluid is moving with respect to it, creating a drag which we can calculate given the viscosity of the fluid and the size of the sphere.21 At low speeds the drag on a bead is: drag 6F rvπη= (14) η is the viscosity, r is the radius of the sphere and v is its velocity with respect to the medium.

MSD = 0.8098t

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8time (s)

MSD

(µm

²)

Figure 3. This graph shows the mean squared displacement <r²> vs time t of thirty-one 2µm beads. The video of this sample was taken through the 40x air objective which allowed for a wider field of view. For this value of the diffusion coefficient D we get 1.3x10-23 ± .1 J K-1 for Bolzmann’s constant.

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Another method looks at the power spectrum of position fluctuations from the Brownian motion, the frequency with which the particle moves. To use this method systems use a quadrant detector to detect bead movement in the trap. This is because while accurate, this method requires tracking at very high frequency, on the order of kilohertz.6 The method we will is less accurate but simpler and also uses statistical analysis of the beads position. From the equipartition theorem we know that the energy will be ½kBT times the number of degrees of freedom, which is one degree in our case as we are breaking it down into components. Therefore since we are assuming a harmonic potential we can say:22

20

1 1( ) ( )2 2x BU x k x x k T⟨ ⟩ = ⟨ − ⟩ = (15)

Where U(x) is the potential energy and x0 is taken as the center of the trap. This is the method students use to calibrate a trap to give kx and ky.

2.3 Flexibility of Holographic Optical Trapping The addition of the Spatial Light Modulator (SLM) (Boulder Nonlinear Systems, Lafayette, CO) to our optical tweezer allows computer control of the trap. The SLM is shown in the center the image in figure 4, both in visible light and infrared. SLM’s are devices which, as the name suggests, modulate light in a spatial pattern. They do this by controlling the phase of an incident beam on a pixel by pixel basis, generating a hologram. Other uses for SLM’s include holographic data storage and beam steering.23

Computer control of the trap means that users can create additional traps from the same laser beam and manipulate each trap independently. The two sets of software to control the SLM with our system are HOTGUI and LABRyx (Aryyx, Chicago, IL). The

software allows 200 individual traps to be created from one laser, though with our setup and 800 milliwatt laser we start to see severe degradation after the beam is split 10 times. In addition to being able to create multiple traps with preprogrammed movements we can create optical vortices. An optical vortex creates a circular spinning trap. While the

Figure 4. The state of the art SLM in the center of the left hand image with Arryx HOTGui allows creation and manipulation of multiple traps from a computer workstation. The infrared image on the right shows the overfilling of the SLM mirror by the expanded laser beam which is otherwise invisible.

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practical use for such a trap configuration may not be obvious, it is an interesting demonstration for the undergraduate labs. Creating and manipulating traps gives students an intuition of the capabilities of holographic optical trapping. Figure 5 illustrates the capabilities of the SLM. Students also attempt to trap different size polystyrene beads ranging from 1 to 5 micrometers with the Tweezer. Also available are silica and magnetic beads. Results show that by far 2 micrometer polystyrene beads are the easiest to trap. Students also experiment with different objectives to note the effect of numerical aperture on the trap. They will note that while it is easier to trap with a high numerical aperture lens, they are unable to see or trap so deep into the sample. As important as aligning the optics is setting the parameters for the SLM to make correct calculations. As the laser is reflected at an angle through the SLM the pixels on its surface are not exactly square. To adjust for this and other aberrations Arryx has created a program called HOTUtility to aid in calibrating the trap. The user makes real time adjustments to the trapping parameters and views the results on a mirror slide.

Figure 5. The top two slides are images taken using a mirror to better show the laser. On the left is the beam without any manipulation and on the right is a ring trap or optical vortex created by the SLM. In the bottom left image the two lower beads are trapped. In the bottom right image beads are trapped in an optical vortex. The vortex can be made to spin the beads clockwise or counterclockwise.

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3 Steps towards single molecule investigation of protein DNA interaction using optical tweezers

Optical tweezers have proven to be a useful tool in investigating the interactions

between DNA and proteins at the single molecule level.24 An interesting problem is how a protein called Topoisomerase alters the topography of DNA. Topoisomerase can disentangle knotted DNA and are and important part of cell replication.25 We aim to investigate the interaction between Topoisomerase and DNA by creating an artificial entanglement between two DNA molecules, here are described the first steps towards this goal. To investigate single molecules of DNA using optical trapping it is first necessary to attach the single molecules to microspheres which can be trapped. This can be accomplished by labeling the DNA on one end with biotin and the other with digoxigenin. The biotin labels will attach to streptavadin coated beads and the digoxigenin to anti-digoxigenin beads creating a dumbbell shaped object.26 Having the DNA in dumbbells allows them to be knotted and tension to be applied so that the effects of Topoisomerase enzymes can be examined.

3.1 Labeling Lambda DNA for attachment to microspheres The DNA we chose to use is called Lambda DNA (New England Biolabs, Ipswich, MA), it is the genome for Enterobacteria phage λ which is a virus that attacks E. coli. Lambda DNA is double stranded with overhanging ends.27 Figure 6 is an excellent representation of the technique of attaching biotin and digoxigenin labels. To attach different labels to each end we fill up the base pairs withholding the

Figure 6. This figure is taken directly from an article by R. Zimmermann and E. Cox. It is an excellent representation of the process of labeling lambda DNA. First the cytosine and thiamine bases are matched until a biotin dUTP label is added to the first available adenosine base. The solution is filtered of everything but the DNA and then more dNTPs are added until another adenosine base becomes available to be filled with a DIG dUTP. The solution is filtered again to leave just the labeled DNA.27

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deoxynucleoside triphosphates (dNTPs) cytosine (dCTP) and thiamine (dTTP) on both ends until we reach adenosine (dATP) which is then labeled with biotin attached to uracil (dUTP). The dNTPs are from New England Biolabs and the biotin and digoxigenin labels are from Roche Applied Science (Mannheim, Germany).

The mix is filtered using a QIAprep Spin Miniprep Kit (Qiagen, Valencia, CA) to remove any excess nucleotides. Then more dNTPs are added, withholding dATP, to fill in until a digoxigenin attached to dUTP can be added. The base pairs are attached by klenow fragments which are from DNA polymerase I. Again the solution is filtered to remove excess nucleotides and the resulting solution contains labeled DNA suitable for attachment to microspheres. The protocols are attached as appendix C. To attach the DNA they are first mixed with the streptavidin coated beads. Before labeling and filtering the DNA is at 16 nano-molar concentration and according to QIAprep about 36% should remain after filtering twice. The streptavidin beads come at a concentration of 1.0% w/v which for polystyrene corresponds to a concentration on the order of picomoles. This indicates when mixing equal volumes of we should have 1000 times as many DNA as beads. After incubating for one hour the mix is then diluted by a factor of 10 and anti-digoxigenin beads at .1% w/v are added.

To reduce the bead concentration to a workable level they are diluted by a factor of ten. This brings the concentration down to about 0.01% w/v which provides enough beads that it isn’t difficult to find one and few enough that they are not constantly knocking one another out of the trap. Again it is incubated and then injected into a viewing chamber constructed of two microscope slides and two strips of double contact tape which create a channel approximately 50 micrometers deep and 1 mm across.

The ends of the chamber are sealed with SylGuard (Dow Corning, Midland, MI) to prevent drying. While nail polish works better and dries faster, the acetone destroys the glue on the tape and probably affects the DNA as well. SylGuard is adequate but does not dry immediately increasing the potential for leaks.

At this point the sample is usable for about thirty minutes to one hour, when the majority of the beads will have sunk to the bottom of the slide. Coated beads tend to sink much faster than plain polystyrene beads and stick firmly. To increase the buoyancy of the beads, and thus the time that they can be used before sticking sugar can be added to the solution containing the beads. Polystyrene has a density of 1.05g/mL, slightly denser than water.

3.2 Dying DNA on microspheres After the labeled DNA is mixed with streptavidin and anti-digoxigenin coated beads a dye solution is needed to see if there is DNA sticking to the beads. DNA cannot be directly seen without a dye. The dye used was PicoGreen (Invitrogen Corporation, Carlsbad CA). It proved to be an ideal dye to use, designed for double stranded DNA it does not glow unless it is trapped between the strands. Even then it is often difficult to see as the dye will bleach rapidly.

Free oxygen contributes to the bleaching of the dye and so to reduce bleaching an oxygen scavenger was added to the solution. The top two images in figure 7 show dyed DNA being viewed without oxygen scavenger at zero and 13 seconds. At thirteen

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seconds the dye is entirely bleached. The bottom two images in figure 7 show DNA dyed

with a scavenger in solution at zero and 15 seconds. There are different ways to reduce oxygen levels in the solution. Our scavenger

cocktail consists of glucose oxidase, catalase, and D-glucose. In addition trolox was added as a triplet state quencher.28 The glucose oxidase reduces O2 in the sample H2O2. The catalase converts two H2O2 into two H2O and one O2, reducing the total amount of O2 in solution. A problem discovered with the mix was that the reaction makes the solution more acidic. In the first runs it went from an acceptable pH of 8 to 3, which destroyed the sample. Once noted this was easily fixed by increasing the molarity of the buffer. The oxygen scavenger greatly increased the stability of the dye allowing it to be viewed for minutes rather than seconds. Unfortunately the DNA was still bleaching due to the high power of the fluorescence necessary for the camera on our optical tweezer system. Using a better camera (Cascade 512B, Photometrics, Tuscon, AZ) allowed the DNA to be viewed under much lower light and allowed the observation that the labeled DNA appeared to stick to the beads much more than the unlabeled control DNA.

Figure 7. The upper two images show DNA in PicoGreen dye without an oxygen scavenger in solution at 0 and 13 seconds. The lower two images show DNA and two beads in solution with PicoGreen dye and oxygen scavenger at 0 and 15 seconds. Despite a much higher illumination the DNA in the scavenger cocktail continues to fluoresce. With lower levels of illumination the DNA can be seen for minutes. The DNA are coiled tightly and at very high concentration giving the soup like appearance.

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The unlabeled DNA was used at 1.6nM and .16nM strength and mixed with varying concentrations of beads. The vast majority of the beads did not fluoresce and the few that did were the ones stuck to the surface of the slide. The beads in solution with the labeled DNA did glow. Unfortunately the better camera does not work with the optical tracking software and so it had to be switched back. It did indicate that the labeled DNA was sticking to the beads with a much higher affinity than the unlabeled DNA. The top left image in figure 8 is of streptavidin beads in a dye solution with no DNA. The green circle indicates the location of a bead. The top right image shows streptavidin beads in solution with DNA and dye. The bead is inside the circle and does not glow significantly. The bottom left image shows DNA in solution with labeled DNA. The three beads are easily identified. Their appearance ranges from hairy to an even glow. Though the Lambda DNA are around 10 micrometers long they are thin and can smooth themselves out over the surface of the beads.

3.3 Looking for DNA dumbbells The first runs compared beads in solution with labeled DNA to those in solution

with unlabelled DNA. The samples indicated that there was an increase in the amount of beads stuck together when labeled DNA were present, but this is not conclusive and could also be a result of different handling of the beads. Once the beads are mixed with DNA they cannot be vortexed, sonicated or otherwise rough handled as it will shred the DNA. This means they have more chance to settle and the dispersion is no longer so

Figure 8. The top left image is SA beads in solution with PicoGreen dye. The green circle is the location of a bead, which does not glow. The top right image is control DNA in solution with SA beads. The blue circle is the location of a bead and as can be noted it does not glow significantly. The solution in the bottom left image contained labeled DNA and SA coated beads which fluoresced, indicating that they were coated with DNA.

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even. To conclusively show tethered DNA it is necessary to demonstrate one bead being pulled by another. Grabbing the beads and trying to stick them together was the first approach. Unfortunately the beads did not attach when held closely and stuck too firmly when touched together. Also it was shown that beads with no DNA stick together so strongly when touched together that the tweezer cannot separate them. Adding a soap like material called tween-20 to the solution did not stop the beads from sticking to one another. This effect is noted in figure 9. The two beads in the circles were touched together but then could not be separated.

Looking at the ratio of beads to the estimated yield of labeled DNA indicates that there are 103 times as many DNA as beads. If there are too many DNA on each bead then the tweezers will not be strong enough to separate them. While some videos after review did indicate possible tethered beads, none were conclusively shown by tugging on one end. From this observation it appears that rather than too many complete tethers there were too few indicating a problem with the labeling protocol.

3.4 Improving yield and observation technique Initially the yield of labeled DNA was not of great concern. The assumption was that as the concentration of DNA was much greater than that of the beads this would not be an issue. When the DNA shown by dyeing to be attached to the beads this confirmed that the yields of labeled DNA were sufficient. However with the search for DNA dumbbells it can be noted that having a reasonable percentage of DNA labeled on both ends is critical. Without a significant number of DNA with both labels it would take a huge amount of time to seek out and find the beads attached as dumbbells in a view that is less than 100 micrometers across. One step that should be added to increase the yield is heating the DNA to 65°C and then rapidly cooling before adding the dNTPs. Lambda DNA has sticky ends at room temperature. Also increasing the incubation time should increase the percent of DNA that receive both labels. The protocol from Roche labs mentions that increasing the incubation time to 20hrs can increase yields. Another difficulty was in distinguishing the streptavidin beads from the Anti-digoxigenin beads. Beads of diameter 2 micrometers are most easily trapped, and so are

Figure 9. Inside the circle are two microspheres in two separate traps. Force is being applied to separate them but they are bonded too strongly. Labeled DNA were in the solution when this image was taken, but a similar result is noted when just beads are in solution.

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preferable. The first set of streptavidin beads were .3 micrometers larger, but this turned out not to be enough to distinguish the beads and so another set of diameter 1 micrometer were purchased. This made it considerably easier to match bead pairs without being concerned that time was being wasted trying to stick two of the same type of bead together.

4 Melting Ice Of the many organisms that live in very cold climates some have evolved the ability to produce antifreeze proteins (AFPs). AFPs prevent ice crystals which would cause fatal cell membrane injuries. Recent experimental data shows that AFPs from Antarctic bacteria can protect against melting, in addition to inhibiting ice crystals from forming. To study this further it is necessary to superheat small crystals of ice with antifreeze proteins. This requires precisely located temperature control, which the focus of an optical tweezer is ideal for. Studies have already been done to investigate the effect of laser induced heating in optical traps. This is important to trap calibration using Brownian motion in the trap. As the bead is heated its thermal motion increases and the viscosity of the medium in decreased. Not only has it been shown that the most significant heating occurs in the solvent, but that it can have a non-negligible effect on calibration especially of systems using lasers over 100mW.29 Controlling the intensity of the optical trap by adding a filter to the setup makes it ideal for precise temperature control in water. Efforts to use lasers for global temperature control in a sample found it problematic. When heating fluid the temperature difference decreased logarithmically towards the periphery of the laser beam, creating convection currents.30 This should not cause a problem when the laser is highly focused to make small changes of temperature in specific locations. The absorbance of water varies greatly with the wavelength of light used. While our laser is at 1064nm and puts out 800mW, a laser at 1450nm would be absorbed over 100 times more by water.31 This means a much smaller power could be used. On the other hand an 800 nm laser would be barely absorbed and thus unsuitable for heating water.

4.1 Laser Precision Temperature Control The optical setup for the Laser Precision Temperature Control (LPTC) device is

roughly the same as that for the optical tweezer. The biggest difference is that instead of an very expensive SLM it uses a much less expensive gimble mounted mirror to control just one beam. The LPTC is custom built into a microfluidics system already in place.

To control the intensity of the laser light the LPTC uses a round continuously variable metallic neutral density (ND) filter (Thorlabs, Newton, NJ). The filter is placed in the optical train immediately before the 1064nm beam is expanded by two achromatic doublets of focal lengths 35mm and 200mm. The expanded beam continues to be directed towards a gimble mounted mirror. Between the gimble and the back aperture of the objective are two planoconvex lenses. As in the optical tweezer setup these are two

15

focal lengths apart, the first one focal length from the gimble and the second one focal length from the back aperture. This allows adjustments to the gimble to be projected onto the image plane in the sample while the beam stays on the back aperture. A dichroic mirror (z900dcsp Chroma Technology Inc) reflects the laser up into the sample without blocking the image from the viewer. The microscope objective used has a low NA and so is the only component not suited to optical trapping.

Figure 10 The top left image shows a sheet of ice about 20 µm thick, the image is about 150 µm across. The ice contains TmAFP-GFP at a concentration of 20 µM. The black dots are air bubbles and the temperature is -0.97 Celsius. The top right image shows the reflection of the focused laser used in the LPTC. After a short pulse from the laser the hexagonal hole appears in the ice crystal seen in the bottom left image. In the bottom right image an ice crystal has formed in the pool of water, if no AFP was present the pool would freeze over almost instantaneously.

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4.2 Melted Ice When correctly tuned, the LPTC can create very small pools of water in an ice

crystal. This allows microfluidics research to be conducted with the kind of precise temperature adjustments necessary to keep small pieces of ice and water together. The adjustments can be made instantaneously and without affecting the rest of the sample. Figure 10 shows an ice crystal being melted by the laser. Once the device has been calibrated it can be used to raise the temperature in an ice crystal to determine if AFPs protect the crystal from melting.

AFPs are generally divided into two groups; hyperactive AFPs and moderate AFPs. Hyperactive AFPs are more active with respect to the level to which they depress the freezing point.32 While much research has been done it is not clear how AFPs function at the water/ice interface. Combining microfluidics with fluorescence microscopy could assist in revealing the mechanisms controlling AFP activity at the interface. Direct visualization of AFPs on the ice surface gives insight into the kinetics of attachment of these proteins. Controlling the ice growth within microfluidics devices could be a challenging task. The ability to melt ice with micrometer precision within the experimental setup is desired, and the LPTC is suitable for this task. The use of a laser to control ice crystal growth is novel and new to the research field.

5 Conclusion

After 20 years optical trapping as a technique can be considered a mature technology. Despite this new applications and effects are frequently being developed and discovered. This thesis has examined optical tweezing as an educational tool, a single molecule research tool, and using its focused energy to expand research on antifreeze proteins.

The development of a Biophysics Lab course required piecing together existing research, equipment, and programming. At the start of the research the optical tweezer setup was only capable of creating 2 dimensional traps against the glass of the sample slide. At the end students in the Physics 372 lab course were able to create multiple stable 3 dimensional traps, vortex traps, and use video analysis to measure Boltzmann’s constant and the strength of an individual trap.

The first steps in conducting single molecule experiments were the second part of this research. Through control experiments with dye it was shown that DNA was successfully labeled and attached to coated microspheres. While attempting to find microspheres that were physically tethered was unsuccessful, it is probable that increasing the yield of DNA labeled on both ends will improve the chances of creating a DNA dumbbell. Increasing the yield is possible and several steps which should do this have been identified and will be used in further studies.

Designing and building a focused laser setup in the optical tweezer model has been successful precision growth control in ice crystals. It opens exciting new opportunities in Biophysics research into hyperactive antifreeze proteins.

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6 References 1 Chu, S., Bjorkholm, Ashkin, A., and Cable, A. (1986). Experimental observation of optically trapped atoms. Physical Review Letters, 57(3):314-317. 2 Ashkin, A. (1997). History of optical trapping and manipulation of neutral particles using lasers. PNAS, 94(10):4853-4860. 3 Fällman, E. and Axner, O. (1997). Design for fully steerable dual-trap optical tweezers. Appl. Opt., 36(10):2107-2113. 4 Griffiths, D. J. (1998). Introduction to Electrodynamics (3rd Edition). Prentice Hall, Upper Saddle River NJ. 5 Harada, Y. and Asakura, T. (1996). Radiation forces on a dielectric sphere in the rayleigh scattering regime. Optics Communications, 124(5-6):529-541. 6 Svoboda, K. and Block, S. M. (1994). Biological applications of optical forces. Annu Rev Biophys Biomol Struct, 23:247-285. 7 Lee, W.M., Reece, P.J., Marchington, R.F., Metzger, N.K., Dholakia, K. (2007). Construction and calibration of an optical trap on a fluorescence optical microscope. Nature Protocols, 2(12):3226-3238. 8 Fällman, E. and Axner, O. (1997). Design for fully steerable dual-trap optical tweezers. Appl. Opt., 36(10):2107-2113. 9 Steubing, R. W., Cheng, S., Wright, W. H., Numajiri, Y., and Berns, M. W. (1991). Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap. Cytometry, 12(6):505-510. 10 Liang, H., Wright, W. H., Cheng, S., He, W., and Berns, M. W. (1993). Micromanipulation of chromosomes in ptk2 cells using laser microsurgery (optical scalpel) in combination with laser-induced optical force (optical tweezers). Exp Cell Res, 204(1):110-120. 11 Leitz, G., Schnepf, E., Greulich, K.O., (1995). Micromanipulation of statoliths in gravity-sensing Chara rhizioids by optical tweezers. Planta, 197(2):278-88. 12 Koch, S. J., Shundrovsky, A., Jantzen, B. C., and Wang, M. D. (2002). Probing protein-dna interactions by unzipping a single dna double helix. Biophys J, 83(2):1098-1105. 13 Bao, X. R., Lee, H. J., and Quake, S. R. (2003). Behavior of complex knots in single dna molecules. Physical Review Letters, 91(26). 14 Bustamante, C., Bryant, Z., and Smith, S. B. (2003). Ten years of tension: single-molecule dna mechanics. Nature, 421(6921):423-427. 15 Bai, L., Santangelo, T. J., and Wang, M. D. (2006). Single-molecule analysis of rna polymerase transcription. Annu Rev Biophys Biomol Struct, 35:343-360. 16 Weeks, E., Rytrack http://titan.iwu.edu/~gspaldin/rytrack.html 17 Crocker, J. C. and Grier, D. G. (1996). Methods of digital video microscopy for colloidal studies. Journal of Colloid and Interface Science, 179(1):298-310. 18 Milne, G., St Andrews Tracker http://faculty.washington.edu/gmilne/tracker.htm 19 Nakroshis, P., Amoroso, M., Legere, J., and Smith, C. (2003). Measuring boltzmann's constant using video microscopy of brownian motion. American Journal of Physics, 71:568-573. 20 Perrin, J. (2005). Brownian Movement and Molecular Reality. Dover Publications. 21 Malagnino, N., Pesce, G., Sasso, A., and Arimondo, E. (2002). Measurements of trapping efficiency and stiffness in optical tweezers. Optics Communications, 214:15-24. 22 Phillips, R. Senior Engineering Lab Course, Caltech, http://www.rpgroup.caltech.edu/~natsirt/ME96/labs/tweezer.pdf 23 Boulder Nonlinear Systems, http://www.bnonlinear.com/products/XYphase/XYphase.htm 24 Kimura, Y. and Bianco, P. R. (2006). Single molecule studies of dna binding proteins using optical tweezers. Analyst, 131(8):868-874. 25 Uemura, T., Ohkura, H., Adachi, Y., Morino, K., Shiozaki, K., and Yanagida, M. (1987). Dna topoisomerase ii is required for condensation and separation of mitotic chromosomes in s. pombe. Cell, 50(6):917-925. 26 Fuller, D. N. N., Gemmen, G. J. J., Rickgauer, J. P. P., Dupont, A., Millin, R., Recouvreux, P., and Smith, D. E. E. (2006). A general method for manipulating dna sequences from any organism with optical tweezers. Nucleic Acids Res, 34(2). 27 Zimmermann, R. M., Cox, E.C. (1994). DNA stretching on functionalized gold surfaces. Nucleic Acids Res, 22(3):492-497.

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28 Rasnik, I., Mckinney, S. A., and Ha, T. (2006). Nonblinking and long-lasting single-molecule fluorescence imaging. Nature Methods, 3(11):891-893. 29 Peterman, E. J., Gittes, F., and Schmidt, C. F. (2003). Laser-induced heating in optical traps. Biophys. J., 84(2):1308-1316. 30 Mao, H., Arias-Gonzalez, R. J., Smith, S. B., Tinoco, I., and Bustamante, C. (2005). Temperature control methods in a laser tweezers system. Biophys. J., 89(2):1308-1316. 31Irvine, M.B., Pollack, J.B. (1968). "Infrared optical properties of water and ice spheres," Icarus 8, 324-360. 32 Pertaya, N., Marshall, C. B.,Celik, Y.Davies, PL.Braslavsky, I. (2008). Direct visualization of spruce budworm antifreeze protein interactions with an ice crystal: basal plane binding confers hyperactivity. Biophys. J., doi:10.1529/biophysj.107.125328.

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Appendix A

7 Appendix A: Poster for undergraduate lab course This poster presents the lab course developed and its learning objectives. The poster was presented at the 2007 BNNT undergraduate research poster competition where it received 3rd place. The poster can be downloaded from: http://www.phy.ohiou.edu/~braslavs/Presentations/Optical_Tweezer_Poster.ppt

Using Optical Tweezers as a Tool in Undergraduate Labs. Paul Ingram, Ido Braslavsky and David F. J. Tees

Dept of Physics and Astronomy, Ohio University, Athens OH 45701

Fig 5. IDL based particle tracking software. The upper image shows the unfiltered video with red dots on particles that the input parameters identify. The lower screen shows the filtered image as the program sees it.

Results and Conclusions At the end of the lab students have used the Optical Tweezer setup to: • Gain a basic understanding of the fundamentals of optical trapping. • Gain a basic understanding of the fundamentals of particle tracking. • Calculate Boltzmann’s constant. • Explain trap stiffness and calculate it. • Learn how to operate basic programs in IDL.

• Svoboda, K., et al., Direct observation of kinesin stepping by optical trapping interferometry. Nature. 365:721-727, 1993.

• Wang, M.D., et al. Stretching DNA with optical tweezers.Biophysical J. 72:1335-1346, 1997.

Citations

•Students first observe the Brownian motion of 2µm beads under the microscope to familiarize them with the equipment, programs and principles required to calculate the trap stiffness later on. •Students then manipulate the beads to gain a basic understanding of the fundamentals of optical trapping. •Students create multiple traps and can use different concentrations and types of beads such as silica, magnetic or polystyrene.

Methods

• Optical trapping using a device called Optical Tweezers was developed in the 1980s from work on laser trapping of atoms.

• It was realized that a focused laser could be used to trap and manipulate micrometer-sized particles, such as latex beads.

• Researchers have used optical tweezers to study molecular motors1 and the physical properties of DNA2.

• Beads can be attached to either end of a strand of DNA allowing it to be manipulated with the tweezers.

• Trap is made by directing a laser through the objective lens of a microscope.

• In our Tweezer the beam is split into multiple traps and manipulated using a Holographic Optical Trap (HOT) plate made by Arryx Inc.

Optical Tweezers

Fig 1. For objects larger than the laser wavelength the trap can be explained using ray optics. From Newton’s 3rd law the change in momentum as the ray enters and exits the bead forces it back to the center of the beam. Kind of like the Star Trek tractor beam, just without the optional photon torpedoes.

Beam

Forc

i

ou

chang

Beam

Forc

y = 0.8098x

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8

seconds

mic

rom

eter

s^2

Fig 6. Graph of the mean squared displacement <r²> vs time t of thirty-one 2µm beads. Video was taken through the 40x air objective. For this value of the diffusion coefficient D we get 1.3x10-23 ± .1 for Bolzmann’s constant.

2 4r Dt=

•Analysis of trap videos is done with Rytrack, one of several freely available particle tracking routines. •The routine outputs the x and y position in pixels and the frame number for each particle. •This data is used to calculate the diffusion coefficient and then Boltzmann’s constant from video of untrapped beads. • Students calculate the trap stiffness using statistical analysis of the beads position.

Analysis

Fig 4. Sequential images of magnetic streptavidin coated bead burning in the laser. A gas bubble appears and rapidly expands. In the last image the stage is being moved and a path is burnt into the slide. The beads had settled to the surface of the slide.

Fig 2. 2µm beads in buffer solution. The bead in the lower center of the screen is trapped.

Fig 3. Multiple traps of 2µm polystyrene beads. The bottom two beads are trapped, the dichroic used in this image does not allow the student to see glare from the laser.

•HOT plate software allows students to move traps manually, create preprogrammed trap movements, change the depth of traps relative to the focus of the microscope and take distance measurements.

6Bk TD

Rπη=

Eqn 1. Equation relates the diffusion coefficient D to Boltzmann’s constant kB by the temperature T, radius R and viscosity η.

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1 1( ) ( )2 2x BU x k x x k T⟨ ⟩ = ⟨ − ⟩ =

Eqn 2. Modeling the trap as a potential well we calculate the stiffness of the trap as spring constant kx. The right side is the energy from the equipartition theorem.

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PHYS 372 – Optical Tweezers Appendix B

8 Appendix B: Biophysics lab manual This lab manual was developed from a preliminary manual written by Professor David F.J. Tees and Professor Ido Braslavsky. The portions retained consist mostly of the theory and experimental setup sections. 1. Introduction to Optical Trapping Optical trapping using a device called Optical Tweezers or Laser Tweezers was developed in the 1980s from work on laser trapping of atoms. It was realized that a focused laser could be used to trap and manipulate micrometer-sized particles (dielectric objects) with index of refraction different from their surrounding medium (e.g. cells, latex beads in water). These trapped particles can then be used as handles to stretch DNA, control molecular motors or study adhesion molecules.

In this lab you will be learning to use an Optical Tweezer system and particle tracking software. You will measure the diffusion from the Brownian motion of 2 µm beads in a liquid and use this to calculate Boltzmann’s constant. Then you will measure the strength, or stiffness, of a trap made by the Optical Tweezer. By the end of this lab you should:

• Have a basic understanding of the fundamentals of optical trapping. • Have a basic understanding of the fundamentals of particle tracking. • Be able to explain Brownian motion and Diffusion. • Calculate Boltzmann’s constant. • Be able to explain trap stiffness and to calculate it. • Be able to use basic programs in IDL.

2. Theory 2.1 Brownian Motion Before you can use the laser trap, you must familiarize yourself with the use of the optical microscope. You will do this by observing the Brownian motion of 2 µm beads in water. This motion was observed by microscopist Robert Brown in the 1820s when he was observing pollen grains and he managed to demonstrate that this motion was not the result of the particles being alive. It was observed for any small particle.

The origin of this motion remained mysterious until 1905 when Albert Einstein (as part of a project to identify practical consequences of the atomic hypothesis, which was at that time still unproven) predicted that micrometer-sized particles should move significantly when viewed under the microscope thanks to random atomic collisions that change the direction of travel. These collisions can be thought of as a random walk. At each step in the walk, the molecule travels in a new random direction. Einstein was apparently unaware that Brownian motion had been observed by biologists but from general arguments he predicted it should exist for both small molecules and larger particles.

By analyzing the random walk he found that for diffusion in one dimension (i.e. back and forth along a line or inside a pipe), the mean square displacement of dye molecules or small

21


particles, <r2>, as a function of time was related to the diffusion coefficient, D (from Fick’s Law for diffusion; the units of D are m2/s) by the relation:

<x2> = 2Dt. For a random walk in 2-dimensions (which is what we see under the microscope, we note that r2= x2 + y2, and when we take averages (indicated by angle brackets), <r2> = <x2> + <y2>. But since x and y are independent 1-D axes, <x2> = <y2>, so <r2> = 2<x2> = 2(2Dt). We thus have that:

2 4r Dt= You will observe 2-D diffusion under the microscope.

Einstein’s analysis of the random walk also led to a relation between the diffusion constant and Boltzmann’s constant:

6Bk TD

Rπη=

Here, kB is Boltmann’s constant, T is the absolute temperature (in Kelvin), η is the viscosity (the viscosity of water at room temperature is 0.001 Pa s) of the fluid surrounding the particle and R is the radius of the diffusing particles (this can range from nanometers for molecules to a few micrometers for small dust particles or cells).

In 1908, Jean Baptiste Perrin, a physicist working at the Sorbonne in Paris did experiments that measured Brownian Motion of particles and used Einstein’s random walk theory to find a value for Avogadro’s number (the number of atoms in a mole, a term Perrin evidently coined). Perrin observed 2-dimensional Brownian motion of tiny latex particles in water at 20°C under a microscope. The particles had a radius of 0.37 μm. Perrin observed the position of a particle, waited 30 s, then observed again and plotted the net displacement in that time interval. He collected 500 data points in this way and found that for these particles, the root mean square displacement √<r2> was 7.84 µm after 30 s. Using this data, there are three steps to the estimate of Navogadro

• For 2-D diffusion, <r2> = 4Dt, so the diffusion constant can be calculated from D = <r2>/4t = (7.84 x 10-6 m)2/(4 * 30 s) = 5.12 x 10-13 m2/s.

• Once D is known, Einstein’s theory says that D = kBT/(6πηR). We can rearrange this to

find an estimate of Boltzmann’s constant kB = 6πηRD/T, so kB = 6π(0.001 Pa s)(0.37 x 10-6 m)(5.12 x 10-13 m2/s)/(293 K) = 1.22 x 10-23 J/K.

• Recall that the kinetic theory version of the general gas law constant requires that R =

Navogadro kB (R had been measured long before through the General Gas Law, pV = nRT). One can thus calculate Avogadro’s number from Navogadro = R/kB. Putting numbers in, we get Navogadro = (8.314 J/mol/K)/(1.22 x 10-23 J/K)= 6.81 x 1023 molecules/mol.

The value that Perrin found for Avogadro’s number (published under the title “Brownian

Movement and Molecular Reality”) was surprisingly close to the values measured using completely independent techniques suggested by Einstein and other pioneers of quantum mechanics. The concordance of the different independent values for this important number sealed the case for the atomic hypothesis, which had up until then been considered an unproven (if useful) hypothesis.

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The Perrin value was refined using similar methods to 6.02 x 1023 by 1914. This is close to the modern value based on extremely precise experiments using the atomic structure and spacing from X-ray crystallography to calculate the number of atoms in samples of known volume and mass (6.0221415 x 1023 ± 0.000 0010 x 1023 mol-1). In 1926 Perrin won the Nobel Prize for Physics for his “work on the discontinuous structure of matter” (i.e. the confirmation of the reality of the atomic hypothesis). 2.2 Optical Trapping Dielectric particles are affected by both scattering and gradient force. The scattering component is the photons pushing on the object. The gradient force is a force experienced by dielectric objects in an inhomogenous electric field in the direction of the field gradient, which points towards the direction of maximum increase (Neuman Block 2004).

A full treatment of trapping mechanism is complex, but a simplified argument for objects larger than the wavelength using ray optics and momentum transfer is shown in Fig. 1. Light momentum before and after refraction leads to a force toward the center of a beam, focused to make a 3 dimensional gradient. In addition an in-line restoring force returns particle to the focus of the laser beam if it displaced from the highest intensity region at the center of the beam.

To get a large gradient in intensity, an infrared laser beam is directed through the objective

lens of a microscope. One needs to use a high Numerical Aperture (NA) lens (NA = n sin θ where n is index of refraction between sample and objective lens and θ is half angle of light captured by objective lens). If there is not a large enough gradient the scattering forces will push the object out of the trap.

Fig 1. For objects larger than the laser wavelength the trap can be explained using ray optics. From Newton’s 3rd law the change in momentum as the ray enters and exits the bead forces it back to the center of the beam.

Beam Intensity

Force in

out

change

Beam Intensity

Force

23


You can think of the trap as a potential well with a stiffness k. For small displacements we can model our trap with Hookes Law Fx=-kx(x-x0). We imagine we have three springs for our trap with kx, ky, and kz. If our optics were perfectly aligned then kx and ky would be the same. There are a number of ways to measure trap stiffness.

• One can measure the displacement of a trapped bead when the fluid is moving with

respect to it, creating a drag which we can calculate given the viscosity of the fluid and the size of the sphere. At low speeds the drag on a bead is Fdrag = 6πηrv. η is the viscosity, r is the radius of the sphere and v is its velocity with respect to the medium.

• Another method looks at the power spectrum of position fluctuations from the Brownian

motion. Basically the frequency that it moves. To understand this method we look at the equation for a particle in one dimension in a viscous fluid while combined to a potential well ( xk x ) which is:

( )random xF t x k xγ= + We have left out the inertial term ( mx ) because the drag term (γ) dominates. Because Frandom(t), the fluctuating force on the bead (Brownian motion), averages to zero we must solve this using the Fourier transform and we get:

2 2 2( )( )

B

c

k TS ff fγπ

=+

Where T is the temperature, f is the frequency, kB is Boltzmann’s constant and γ is the drag coefficient (= 6πηr). fc is the corner frequency and is defined as:

2xc

kfπγ

= .

From the corner frequency we get the spring constant. The advantage to this method is that we get a precise value for the trap stiffness from the frequency of the position fluctuations. All you need is a very fast and accurate way to track the position of the beads.

• The method we will use is less accurate but simpler and also uses statistical analysis of

the beads position. From the equipartition theorem we know that the energy will be ½kBT times the number of degrees of freedom, which is one degree in our case as we are breaking it down into components. Therefore since we are assuming a harmonic potential we can say:

20

1 1( ) ( )2 2x BU x k x x k T⟨ ⟩ = ⟨ − ⟩ =

Where U(x) is the potential energy and x0 is taken as the center of the trap.

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3. Experimental Setup

3.1 Laser The laser you will use is an infrared diode laser with a power of 800 mW. When the beam is aligned, protective eyewear is not required. During alignment, however, you must wear the protective eyewear provided. NEVER LOOK DIRECTLY INTO THE LASER BEAM. The infrared light is not visible to your eyes so damage could occur without your being aware of it. Serious damage to your eyesight or blindness could occur! If you wish to trace the beam path, use the sensor strip that makes the infrared light visible

3.2 Filters You can control the strength of the trap by changing the laser intensity with filters. You may start out with no filter and then try the two filters to see how they affect your trap. When the IR laser beam passes through a filter it reduces its intensity (by factor of 10ND, where ND = 0.6 or 2). 3.3 Beam Expander The narrow, collimated beam that comes out of the laser is reflected by mirror M1 towards lens L1 (f = 35 mm) and lens L2 (f = 200 mm) that together expand the diameter of the beam by a factor of 200/35. This allows the laser to fill up the square window you see on the HOT plate. Mirrors M2, M3a and M3b direct the beam towards the HOT plate, which serves as mirror M4.

Lens1

IR Laser

Camera

Filter

IMAGE1

SLM

25


3.4 HOT Plate Multiple laser traps can be created and manipulated using a state-of-the-art Holographic Optical Trap plate made by Arryx Inc. (www.arryx.com/PDFdocs/optical_trapping.pdf). This plate contains a material whose refractive index can be modified so that it acts as a localized mirror at a number of spots. This sophisticated mirror can make multiple output beams from a single input laser beam. 3.5 Telescope The beam is reflected from the HOT plate (M4) towards Lens L3. The light is focused into the plane labeled IMAGE1. This plane is imaged into the sample by lenses L4 and the objective L5. In earlier optical tweezer setups Lens 3 was moved to control the movement of the actual trap instead of using a HOT plate.

3.6 Dichroics A dichroic mirror will reflect some light wavelengths and pass others. Here reflecting IR and passing visible light.

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3.7 Microscope and Illumination An essential component of the Optical Tweezers setup is the optical microscope. This is used to focus the laser beam into the specimen plane where a bead sample is placed for viewing. A traditional upright microscope is shown in Fig. 3b. Light from a lamp below the stage passes upwards through the sample (where differences in index of refraction in the specimen create contrast). An objective lens then creates an image that becomes the object for the eyepieces.

Most modern microscopes, however, now use the inverted geometry shown in Fig. 3a. Light is generated by a lamp above the specimen plane and then passed downward through the specimen before being collected by the objective lens. The image from the objective is then used as the object for the eyepieces.

Figure 3a. Inverted optical microscope Figure 3b. Upright optical microscope

The microscope you will be using is an inverted microscope. There are two ways to bring in the light. In trans-illumination (Fig. 4a), the light passes through the sample. In epi-illumination (Fig. 4b), light comes in from below the sample and is focused up through it using a dichroic mirror that reflects light of a range of wavelengths (e.g. infrared light) but allows other wavelengths (e.g. visible light) to pass through. In this experiment, the visualization will be done using trans-illumination, but the laser beam for the trap will be brought in using epi-illumination.

lamp

27


Figure 4a. Trans-illumination Figure 4b. Epi-illumination

The important parts of the microscope are shown in the figure below. The microscope lamp is

turned on using the button on the lamp control box (off the table). The viewing chamber is placed on the stage of the microscope. The objective lens (there are several of these mounted in a turret) can be moved up and down using the coaxial coarse focus and the fine focus control knobs. These controls are used to produce a sharply focused image of particles in the viewing chamber. The viewing chamber can moved by moving the stage top using the coaxial x-y stage control knob so that objects can be moved into the center of the field of view. The controls above are the major ones that you will use. Several other controls are also important. 1) The output selector switch controls whether light goes to the eyepieces (so that you can see the sample directly) or to the video camera (so that images can be captured to the computer). For reasons of safety, it is better to not look through the eyepieces when the laser is on. 2) Condenser lens adjustment. The position of the condenser lens has a significant effect on image quality. In general, it should be set by the instructor and not moved. It is set correctly when the image of the field aperture diaphragm is in focus in the image at the stage.

lamp

Field aperture diaphragm

28


Figure 5. Nikon TE200 inverted optical research microscope.

4. Methods 4.1 Prepare Sample Your first sample will be 2 µm-diameter polystyrene beads suspended in a “buffer” at a .01% by volume concentration. A buffer is a solution of a number of different salts dissolved in water. The salts mimic those that are present in biological tissues and they are chosen so that they can absorb small amounts of acids or bases without changing the overall pH of the solution (hence the term “buffer”).

The beads are made by Bangs Labs or Polysciences, two of the major manufacturers of high quality monodisperse micro particles. They come from the factory at high concentration. If these beads were place directly into the viewing chamber they would be far too concentrated (1% by volume) and it would be hard to see anything. The beads first need to be diluted

A dilution is normally done in two steps. In the first you take out a sample of beads from the bottle that came from the factory. This first dilution will have been done for you already. 5 µl of the original bead suspension has been pipetted into 45 µl of buffer to do a 10 fold dilution. This suspension will be in a 1.5 ml Eppendorf micro tube labeled "bead first dilution".

• Using the 1-20 µl pipette, put 3 µl of the bead first dilution into a new Eppendorf tube. Make sure that every time you use the pipette you put on a new tip!

• Using the 20-200 µl pipette, add 27 µl of buffer solution to the 3 µl of bead first dilution to get 30 µl of bead second dilution. This procedure will result in a further 10 fold dilution so that the beads are now 100 x less concentrated than when the arrived from the factory. Label it. This should be adequate for viewing.

4.2 Viewing Chamber Construction Make a chamber using two cover slips and double sided tape. Wear gloves while you do this and take care. If your chamber is poorly constructed the fluid can leak out causing a drift as well as drying out

Condenser lens adjust

lamp

Eyepieces

stage

objectives

Coarse focus

Fine focus

x-y stage control

Output selector

Viewing Chamber

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your sample. Air bubbles inside may act like springs causing other fluctuations.

• Take a square microscope cover slip and apply the two strips of tape to it leave a narrow gap (approximately 1 mm) between the two strips of tape. Cut your tap a little long so that a couple millimeters hang over to help it stick to the stage.

• Place the round cover slip on top of the gap and make sure that the slip is firmly stuck by rubbing it with a pen cap. Be careful not to create small cracks in the slide.

• Pipette 5 µl of bead suspension and place a drop at the edge of the gap between the pieces of tape. Bead suspension will move in by capillary action. If you are careful you will pipette just enough to fill the chamber without excess or big air bubbles.

• Seal the ends with nail polish and then leave to dry. Take care if you pick up the slide early as the acetone in the nail polish can soften the tape and cause the top slide to slip when touched.

4.3 Using the Water Objective The microscope you are using has several objective lenses to choose from. The two you will be using are the oil 100x and water 60x objectives. There are also three air objectives. The water objective has a smaller numerical aperture (NA). You will however be able to see deeper into the sample than you could with the oil objective and have a wider field of view. Make sure that you do not get oil on the water objective! Keep in mind that any slide used previously on the oil objective has oil on it and you cannot clean it well enough to reuse.

• Make a viewing chamber with the 2 µm beads that you mixed previously. Ensure that the beads are well dispersed in the buffer before you pipette them into the slide by vortexing the vial or flicking it with a finger.

• Remove any previous slide. Label it and place on the tissue work space in case you wish to work with it later.

• Lower the microscope objective lenses with the focus knob. Rotate the 60x water objective into place.

• Pipette 40 µl of water onto the water objective. • Carefully place the sample on the stage and then raise the objective until the water

touches the glass. 4.4 Using HOTGui with the Water Objective HOTGui is a computer program designed for use with the Arryx Holographic Optical Trap kit.

• Open HOTgui.exe on the desktop • Switch the output selector on the microscope to use the camera.

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• After 10 seconds the Laser Warning window will pop up. Click on don’t warn me again and then OK.

• Click on File>Options… and then in the window select the objective lens that you are using, in this case the 60x Water Objective.

• Create a folder with your name in E:\Experiments\2008_Winter • Go to File>Video Settings and click on the record tab. Enter

E:\Experiments\2008_Winter\YourName\capture0001.avi in the Output Filename box. Video files you record will be entered sequentially into this file. Make sure you annotate each file and what you recorded in your lab notebook.

• Switch on the power to the laser and then turn the key to the laser to the on position. There is a slide cover on the front of the laser to cut the beam. You can check the beam with the IR viewing card or the IR viewing scope.

• Adjust the focus and illumination until you find the beads. • Make sure the blue dichroic is selected so that you can find the laser’s reflection on the

glass. Find the bottom and top of the glass by adjusting the focus control until you see the reflection of the laser. Make a note of the depth of the glass according the focus knob.

• To create a trap click on the icon and then click on the screen where you want the trap. There will be a residual trap in the center where the laser was and every time you make a new trap the trapping potential will be spread out between them.

• Try to trap beads at various levels and record your observations, especially close to the top of the glass. Do you have a stable 3D trap at the top of the slide or are you getting help?

• Measure the beads and the screen size with the ruler control. Make a note! • Move the focus to the middle depth of the viewing chamber and cut off the laser. Record

a ten second video of beads in Brownian motion. Make sure to record the filename and screen width in µm’s.

• If you can get a good trap with the water objective record it. 4.5 Use Microscope Oil Objective It is important to only put the supplied oil on the oil objective and pure water on the water objectives. Keep in mind that once a slide is used on the oil objective you cannot place it on the water objective. You shouldn’t be putting anything on the air objectives.

• Lower the objective lens with the focus knob. • Before you do anything else ensure that you have the oil objective under the stage.

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• Remove any previous slide. Label it and place on the tissue work space in case you wish to work with it later.

• Open the immersion oil which should be on the table next to the microscope. Allow the excess to drip off of the dropper and then allow one drop to fall on the center of the objective without touching it.

• Carefully place your slide on the microscope stage. And then raise the oil objective until you see the oil contact the slide.

• Turn on the microscope illumination and then make sure that the output selector is switched to the eyepiece.

At this point you should be able to look through the eyepiece and adjust the focus and

illumination until the beads are in view. Move the stage with the x-y stage control arm to move the beads over the center of the objective. 4.3 Using HOTGui with the Oil Objective

• If it is not open already open HOTgui.exe on the desktop • Switch the output selector on the microscope to use the camera. • After 10 seconds the Laser Warning window will pop up. Click on don’t warn me again

and then OK.

• Click on File>Options… and then in the window select the objective lens that you are using, in this case the 100x Oil 1.45 NA.

• Any files you record should go to the same folder you created for the water objective. • Switch on the power to the laser and then turn the key to the laser to the on position.

There is a slide cover on the front of the laser to cut the beam. You can check the beam with the IR viewing card or the IR viewing scope.

• To create a trap click on the icon and then click on the screen where you want the trap. There will be a residual trap in the center where the laser was and every time you make a new trap the trapping potential will be spread out between them.

• Click on the icon to select traps. You can now click on a trap and drag it. • Adjust the depth of the focus and see how this affects your ability to trap. Using the blue

dichroic see if you can find the microscope glass by adjusting the focus until you see glare from the laser on the glass. Be careful that you don’t adjust the focus so far that it raises the slide.

• Measure and record the size of the screen and the beads themselves using the ruler

function which has been calibrated for you. The icon is the compass and you should see the distance that you measure at the bottom of the screen.

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• Now use the path function to create a path that you want to move the bead on and then activate it with the () icon.

• Select a trap and raise and lower the trap location with the scroll bar. This may be tricky and the bead may fall out of the trap depending on how good the trap is.

• Use the record icon to record short clips of traps you make. Press to stop recording. The files are avi files and are very large so don’t just record the whole time you are using the trapping. A good idea is to rename each clip for something you will remember and then record what you filmed in your notebook.

• Take 10 second clips of a single trap then of two traps and then three traps. It doesn’t matter if other beads are in the screen, you can take them out when you extract the data later so long as there is only one bead in each trap. Make sure that you write down the file names that you give them with the screen width µm’s. It will also help to have the frames per second.

5. Data Extraction First you will extract the data for Boltzmann’s Constant from your clip of Brownian motion taken with the water objective using 5.1-5.4. Then calculate the x and y trap stiffness for one of the trap videos that you made using 5.1-5.3 and 5.5. If you have time then calculate the trap stiffness from the multiple trap videos to see how they compare. 5.1 Changing Your Video into TIFF Stacks To analyze your video you must break it down into individual pictures. To do this you will use a program called VideoMach. It will allow you to save your video as sequentially labeled images.

• Double click the icon on the desktop to open VideoMach. • Click on File>Open and select the clip from your water objective. • Click on File>Save As • Select Video Format – TIFF • Create a new folder inside your video folder and select the file to write to as

E:\Experiments\2008_Winter\YourName\Objectivetype\image001 • Click on the video tab and deselect the color setting then select Grayscale to change the

video to black and white. • Click Save and VideoMach will save your frames as image001.tif… • Close VideoMach • Open the first TIFF image in ImageJ to measure the diameter of the beads in pixels. This

will help you later to track the beads. • Close ImageJ

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5.2 Tracking Your Beads with Rytrack Rytrack is an easy to use GUI based particle tracking interface written by Ryan Smith of Gabe Spalding's lab of Illinois Wesleyan University. It uses some routines from a set of very comprehensive particle tracking routines written for IDL by John Crocker, Eric Weeks and David Grier. The program is compiled to work with the freeware version of IDL. You will be using the full version to extract the data you need from the position and velocity data you get from Rytrack.

To use Rytrack to accurately and effectively track your beads you will need to understand the various filters that it applies to your images. The filters are controlled by slider bars and you can observe the effects of the changes you make on frames from the stack of frames before you run the tracking routine. The following are the important filters and how to calculate the values you need for them.

• Image directory: This is where you enter in the location of the stack of images that you made earlier. It should be in the form E:\Experiments\2008_Winter\YourName\ObjectiveType\*.tif

• Bandpass 1: The bandpass filter smoothes the image and removes the background. Bandpass 1 is the low end and is the length scale in pixels of noise in the image. You should set this to 1.

• Bandpass 2: This is the high end and should be set to slightly larger than the diameter of each of your beads in pixel. It should also be an odd number.

• Sobel Smooth: An edge enhancing function. You can leave this as is or see how adjusting it affects your image.

• Threshold: Discards pixels that don’t meet a level you set. • Invert Image: Your beads must be white on a black background to track, if they are not

select this to invert the image. • Particle Radius: Approximate size of your beads in pixels. It works better if you use the

diameter, not the radius. • Particle Spacing: Defines how far apart two particles should be. Set it to your particle

diameter in pixels plus 1. • Mass Cut: This is one you can play with. Usually you will set it around a few thousand.

Find a threshold that cuts out all the extra stuff and keeps your particles. • Eccentricity: This is how round or not round your particles are. It is best left alone, but

the program will tell you if you have set it too something that won’t work. • Tracking Parameters: The following parameter will give the rules for which particles to

keep once it has begun tracking. • Maximum Displacement: Maximum number of pixels a particle can jump and still be

the same particle. Generally you can just leave this one alone. • Good Enough: This is important. It sets the number of frames that a particle must be in

to be kept as a particle. Set it to the number of frames you have. If you set it too low then you will have to spend a lot of time scrubbing your data to make sure you have an x and y position for each particle for each frame. If it eliminates all your particles then the other parameters weren’t set well enough for accurate tracking anyway.

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• Steps Memory: Number of frames a particle can be missing from and still be the same particle. Keep it low but it shouldn’t matter if you are filtering out any particles that aren’t there the whole time.

• Overlay Original: This will overlay the upper, original image with markers to show you what is being tracked. You can activate it and then observe how your changes affect the tracking.

• Overlay Filtered: Same as above, but it puts the markers on the filtered images. Generally it is best just to overlay the original as you might be missing something in the filtered image.

• Start: Click on this after you enter your filename into the image directory to bring up your images and start finding particles.

• ID and Track: Starts tracking particles once you are satisfied with your parameters. • Just Track: Same as above if you have already run ID and track and just want to track. • Close: What it says.

When you are correctly tracking beads you will see in the bottom right of the screen

something like the following lines. If it gets hung up somewhere you may have to close the program and do it again. Make sure you record what parameters you used so that you can debug which one messed things up, they will be in params.txt if you got that far.

Feature and Track has started E:\Experiments\2008_Winter\YourName\ObjectiveType\001.tif 32 features identified [These two lines will repeat for each frame] Combining and sending to track 30trackoutput.gdf has been written trackoutput.dat has been written params.txt has been written Tracking Complete. If you are finished, press Close 32 elements found 32 elements retained

If you look in the folder with the images you should now see a .gdf file for each image and then six new files. The two important ones are trackoutput.gdf and trackplusvels.gdf. They contain your position as well as other data of interest. You will only analyze the data from trackoutput.gdf. Trackplusvels.gdf is essentially the same, but includes the x and y velocities and the number of frames jumped.

5.3 Converting GDF Files in IDL To see your data you will use the full version of IDL and a routine written for the purpose of converting .gdf files into .txt files. To open the project go to the Physics 372 Lab folder on the desktop and open the project file “Convert GDF to txt.prj” in IDL 6.3. You will see a window like the one below.

In the project window you will see the routine written for reading .gdf files, appropriately called “read_gdf.pro” and also a file that contains the command lines that you need. Instructions and notes are in green. Double click on read_gdf.pro and then go to Run>Compile read_gdf.pro

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in the Menu Bar. Now double click on Read GDF commands.pro and follow the instructions. Make sure you analyze the correct trackoutput.gdf file.

Now you must put the text file into a format that can be read back into IDL for the routine that will make your data easy to analyze. Open the text file that you created in Excel.

• Select the first column and then go to Data>Text to Columns and then just click finish. • If you did it right every other line should have jumped left. • Now Select all your data and click on Data>Sort and then click ok which should sort the

data by column A. • If you did evertything write your data should now be in seven colums. • Column 1 is the id number of the particle. • Column 2 is the x coordinate in pixels. • Column 3 is the y coordinate in pixels. • Column 4 is the integrated intensity. • Column 5 is the square of the radius of gyration. • Column 6 is the eccentricity. • Column 7 is the frame number. Make sure that for each particle you have all the frames.

If not delete all the data for that particle or average the x and y coordinates for the previous and next positions from the one that is missing.

5.4 Extracting Your Brownian Motion Data with IDL To calculate Boltzmann’s constant, the diffusion and Avogadro’s number from the data you must transfer it into a more usable form. First you will subtract any drift from the data. This may come from a leak in your slide. To do this you will double click on Diffusion.prj which will open in IDL. Double click on Instructions for Center of Mass in the project window. Follow the instructions and you will get a set of x and y coordinates for the center of mass of the system for each frame. You can graph them with excel individually vs time or together to see how much drift you had.

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Now you will run a routine which will give you <r2> for each frame. Keep in mind that you have pixels2 per frame not m2/s. Go back into IDL in the Diffusion Project. Double click on the Instructions for Diffusion in the project window and follow the instructions there. 5.5 Extracting Your Trap Strength Data with IDL Extracting the data from your trap video will be similar to what you did to get your Brownian motion data to determine Boltzmann’s constant. You will run through the same particle tracking routine. The only difference will be that you will have to find the location in pixels of your trap so that you can pull that set of data.

• Change your video into a tiff stack as in 4.7. Keep in mind you will want a new folder for your trap data.

• Track the particles with RyTrack as in 4.8 • Convert the .gdf file in IDL as in 4.9 • Open one of the TIFF images in ImageJ, which is on the desktop. Use the cursor to

identify the pixel location of your trap. With this you can isolate your trap data from the other beads into its own text file.

• Open the Trap Strength project in IDL. • Double Click on the Instructions for Trap Strength program in the project window.

Follow the instructions and you will come out with the statistical variance (<(x-x0)2>) of the particles x position and y position independently.

5.6 Analyze Your Data This part you will have to figure out for yourself. Use the theory given to you and the data extracted for you and it shouldn’t be too difficult. 6. References Overview of optical trapping: K.C. Neuman and S.M. Block, Rev. Sci. Instrum., Vol. 75, No. 9, (2004). Optical trapping and sorting: Graham Milne, “Optical Sorting and Manipulation of Microscopic Particles”, PhD Thesis University of St Andrews (2007). Instrumental limitations in calibrating trap: Wesley P.Wong and Ken Halvorsen, Optics Express, Vol. 14 No. 25 (2006) Browian motion lab: P. Nakroshis, M. Amoroso, J. Legere, and C. Smith, Am. J. Phys., Vol. 71, No. 6, (2003) Useful Paper on optical trapping: K. Svoboda & S. M. Block, Ann. Rev. Biophys. Biomol. Struct., 23:247-285, 1994

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Appendix C

9 Appendix C: Protocol for labeling lambda DNA 1.1 Outline: 1) Heat DNA to 65°C and then cool quickly in ice/water bath to loosen sticky ends 2) λ DNA in a test tube with dATP, dGTP, bio-dUTP +Klenow-exo 3) Stop reaction 4) Filter out all excess nucleotides 5) Add dATP, dGTP, Dig-dUTP + dCTP +Klenow-exo 6) Stop reaction 7) Filter out all excess nucleotides 1.2 Materials needed: λ DNA, N3011S New England Biolabs http://www.neb.com (NEB), 250ug at 500ug/ml 31.5x106 gram/mole = 500ul @ 16 nM dNTPs, N0446S NEB each at 25ul @ 100mM Biotin-16-dUTP, Roche Applied Science 50ul @ 1 mM Dig-dUTP, Roche Applied Science 125ul @ 125 nM Mix1 : 5uM each, of Bioin-dUTP, dGTP, dATP ( NO dCTP) Mix2 : 5uM each of Dig-dUTP, dGTP, dATP and dCTP Klenow-exo, M0212S, NEB, 5000U/ml (40 ul @ Reaction buffers 10 X

38

Appendix C

1.3 Protocol: Tris: 2 ml Tris @ 1 M 38 ml H2O Result 40 ml @ 50 mM dNTP: 2 µl dNTP 198 µl Tris @ 50 mM Result 200 µl dNTP @ 1 mM dNTP, dUTP-Biotin, dUTP-Dig: 1 µl dNTP 19 µl Tris Result 20 µl dNTP @ 50 µM, repeat for dUTP-Biotin and dUTP-Dig Mix I: 35 µl Tris 5 µl dATP @ 50 µM 5 µl dGTP @ 50 µM 5 µl dUTP-Biotin @ 50 µM Result 50 µl @ 5 µM each and 50 mM Tris Mix II: 30 µl Tris 5 µl dATP @ 50 µM 5 µl dGTP @ 50 µM 5 µl dCTP @ 50 µM 5 µl dUTP-Dig @ 50 µM Result 50 µl @ 5 µM each and 50 mM Tris

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Appendix C

1.4 Reaction 1:

Add: 6.5 pure water 2.5 ul 10x reaction buffer ( NEBuffer) 10 ul of DNA ( @16nM) 5 ul of Mix I ( 5uM each BiotinU, G, A) 1ul of Klenow ( @ 5U/ul) Keep at room temperature for 1 hour Add: 125 ul PB buffer from Qiagen (This is from 5X the amount to be filtered) Put in filter Centrifuge 1 minute at 13000 rpm then discard fluid from tube Add: 0.75ml PE Centrifuge for 30 sec @ 13000 Discard PE and continue to spin for 1 minute Put new vial on filter tube and add 50 µl EB elution buffer Let stand 1 minute Centrifuge 1 minute

1.5 Reaction 2:

Add: 4 ul 10x reaction buffer ( NEBuffer) ~40 ul of DNA (everything from spin vial) 5 ul of Mix II ( 5uM each DigU, G, A,C) 1ul of Klenow (@ 5U/ul)

Keep at room temperature for 1 hour Add: 125 ul PB buffer from Qiagen (This is from 5X the amount to be filtered) Put in filter Centrifuge 1 minute at 13000 rpm then discard fluid from tube

40

Appendix C

Add: 0.75ml PE Centrifuge for 30 sec @ 13000 Discard PE and continue to spin for 1 minute Put new vial on filter tube and add 50 µl EB elution buffer Let stand 1 minute Centrifuge 1 minute

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