From Physics 111-Lab Wiki

Contents 1 Optical Trap (Optical Tweezer) Description 2 Optical Trapping (Tweezers) Pictures 3 Before The Lab 4 Introduction 4.1 What is an Optical Trap? 4.2 The Physics Behind Trapping 4.3 Experiment Timeline 5 Apparatus 5.1 Lasers 5.1.1 Trapping Laser 5.1.2 Fluorescence Laser 5.2 Safety Measures 5.3 Optical Paths 5.4 Stage 5.5 Quadrant Photo-Diode (QPD) 6 Operating Procedures 6.1 The Optical Trapping Program 6.2 How to pipette 6.3 Preparing a Slide 6.4 Microscope Operation 6.5 Trapping Laser operation 6.6 QPD Centering 6.7 Trapping Procedure 7 Part I. Calibration of the Optical Trap 7.1 Microscope and Stage Calibration 7.2 Position and Stiffness Calibration of the QPD 7.2.1 Stuck Bead Scanning Method (Position Calibration) 7.2.2 Power Spectrum Method (Position and Stiffness) 7.2.3 Equipartition Method (for Stiffness) 8 Part II. Investigating Flagellar Locomotion in E. Coli 8.1 Planning Your Investigation 8.2 Methods 8.2.1 Preparing Cultured E. coli 8.2.2 Handling cultures 8.2.3 Trapping Bacteria 8.2.4 Using Matlab 9 Part III. Investigating Internal Transport in Onion Cells 9.1 Mechanisms of Internal Transport 9.2 Methods 9.2.1 Making an onion slide 9.2.2 Observing cells and trapping vesicles 9.3 Your Investigation 10 References

Optical Trap (Optical Tweezer) Description

1. Note that there is NO eating or drinking in the 111-Lab anywhere, except in room 282 LeConte on the bench with the BLUE tape around it. Thank You the Staff.

An optical trap is a device used to apply piconewton sized forces and make precise measurements on a scale of roughly one micron. It can be created by applying a precisely focused laser onto a dielectric material. It allows scientists to make very detailed manipulations and measurements on very small objects, and thus is a very important tool in biophysics. They are used in biological experiments ranging from cell sorting to the unzipping of DNA and also in physical applications such as atom cooling. A little history of optical traps: Arthur Ashkin discovered the method of optical trapping in 1970. He calculated that the momentum from a high power laser, focused entirely onto a micron bead would propel the bead forward with 100,000 g's of acceleration. Taken by curiosity he performed this experiment and found that not only was the intended bead pushed downstream by the laser but also that other beads in his solution were highly attracted to the beam-path and flew in laterally from other parts of his slide. He then created the first working trap by using two opposing laser beams. At one point a bacterium that had contaminated a sample flew into the trap and was trapped, thus instigating the trap's revolutionary use in cell biology. Today optical traps are used extensively in both atom-trapping experiments and in biophysics labs worldwide. Local UCB uses include Steven Chu's Nobel Prize winning work as well as the Liphardt and Bustamente labs.

1. Pre-requisites: None
2. Days Alloted for the Experiment: 8
3. Extra Study: 6/10
4. Difficulty of Lab Work: 7/10
5. Analysis: 6/10
6. Combined Overall: 6/10

• Other reprints and materials can be found on the Physics 111 Library Site

This lab will be graded 20% on theory, 40% on technique, and 40% on analysis. For more information, see the Advanced Lab Syllabus.

Comments: E-mail Don Orlando

Optical Trapping (Tweezers) Pictures

Optical Trap Setup Click here to see larger picture

Electronic Controls Click here to see larger picture

Laser Controller Click here to see larger picture

Sample Prep Table Click here to see larger picture

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Before The Lab

Complete the following before your experiment's scheduled start date:

1. Complete the training in the safe use of lasers detailed on the Laser Safety Training page. This includes readings, watching a video, taking a quiz, and filling out a form.
2. Watch the introductory Optical Tweezer video by Professor Jan Liphardt.
3. Complete the OTZ Pre Lab and Evaluation sheets. Print and fill it out. The Pre-Lab must be printed separately. Discuss the experiment and pre-lab questions with any faculty member or GSI and get it signed off by that faculty member or GSI. Turn in the signed pre-lab sheet with your lab report.
4. Read this lab writeup through the end of Part I. Calibration of the Optical Trap

Suggested Reading:

1. Read K. C. Neuman and S. M. Block, "Optical Trapping," Rev. Sci. Instrum. 75(9), 2787-2809 (2004) . Pay particular attention to the overview and theory of of optical trapping and the sections on calibration techniques. You may also refer to the Wikipedia article Optical Tweezers.
2. Carefully examine the optical trapping apparatus and trace the paths of the trapping and fluorescence laser beams and the illuminator light. Make sure you understand what each component does and what you may and may not adjust yourself. Ask an instructor if you have any questions about this.

• References

You should keep a laboratory notebook. The notebook should contain a detailed record of everything that was done and how/why it was done, as well as all of the data and analysis, also with plenty of how/why entries. This will aid you when you write your report.

Introduction

What is an Optical Trap?

An optical trap, or laser tweezers, is a device used to apply piconewton sized forces and make precise measurements on a scale of roughly one micron. The trap is created by focusing a laser onto a dielectric material such as a silica bead or small living cell. The size and force scales make optical traps particularly useful in studying biological systems. Cells and organelles within cells can be manipulated and sorted. The forces and step-sizes of individual motor molecules such as kinesin and myosin can be measured by using beads as convenient handles to tug on and follow motors moving along cytoskeletal proteins. Optical traps are also used to study structural properties of cells, membranes, viruses, and DNA.

Arthur Ashkin discovered the method of optical trapping in 1970^{[1] [2]}. He calculated that the momentum from a high power laser, focused entirely onto a micron bead would propel the bead forward with 100,000 g's of acceleration. Taken by curiosity he performed this experiment and found that not only was the intended bead pushed downstream by the laser but also that other beads in his solution were highly attracted to the beam-path and flew in laterally from other parts of his slide. He then created the first working trap by using two opposing laser beams. At one point a bacterium that had contaminated a sample flew into the trap and was trapped, thus instigating the trap's revolutionary use in cell biology. Today optical traps are used extensively in both atom-trapping experiments and in biophysics labs worldwide. Faculty in Berkeley's Physics Department who use optical traps (and sometimes have research openings for undergrads) include Professors Jan Liphardt, Carlos Bustamente, and Ahmet Yildiz.

The Physics Behind Trapping

A ray diagram showing how the gradient force stabilizes the trap laterally

The most straightforward mechanism to understand the physics of trapping is to consider the change in momentum of light that is scattered by and refracted by the dialectic material, in our case a silica glass bead. Any change in the direction of light imparts momentum to the bead. This mechanism holds for objects much larger in diameter than the wavelength of the laser. A ray-tracing argument holds that the scattered light creates a scattering force in the direction of light propagation, while the refracted light creates an opposing gradient force. When the bead is in the center of the trap, these forces cancel. When a bead moves slightly away from the center, a net force is applied towards the center, making this a stable equilibrium.

In order to understand how the equilibrium is stable, it will help to consider how the gradient force responds to displacement of a bead from the center. In the figure to the right, the red region represents the "waist" of the laser at its focus point, with the laser passing upward through the sample chamber. The blue ball is the bead, and the black arrows (1) and (2) represent light rays whose thicknesses correspond to their intensities (note that the beam is brightest at its center). In case (a), with the particle slightly to the left of center, the two rays refract through the particle and bend inwards. The reactionary force vectors, F1 and F2, of each ray on the bead are shown. Because ray (2) is more intense (and thus carries more momentum) than ray 1, the net force on the bead is to the right. Thus, a perturbation to the left causes a rightward-directed force back towards the trap's center.

In case (b) the particle is centered laterally in the beam and will not be pushed left or right. The net gradient force is downward, which is balanced by an upward scattering force (not shown) due to reflection of some of the light.

To better understand how the scattering and gradient forces and the trap's stability vary with bead displacement both vertically and horizontally, try this Java applet from the Di Leonardo lab^[3] in Italy. The model used for this applet shows the importance of a high numerical aperture lens, as the extremal rays illustrated contribute disproportionately to the change in gradient force vertically. (Note that you must adjust the numerical aperture at the bottom of the applet in order to obtain a stable trap.) By moving the bead around and looking at the net force vector, you can get a pretty good feel for how the restoring force varies as a bead is displaced horizontally or vertically from the trap's center. Note particularly how the trap is less stiff as the bead is displaced above the trap's center. Remember this when you trap your first bead and try moving the bead with the stage and focus controls.

The ray optics approach described above holds for trapped objects whose diameter is much larger than the wavelength of the laser. For objects much smaller than this wavelength, ray optics are not valid. In this case, conditions for Raleigh scattering are satisfied and the object can be treated as a point dipole. The scattering force then is due to absorption and reradiation of light by the dipole, and the gradient force arises from the interaction of the induced dipole with an inhomogeneous electromagnetic field. This mechanism is detailed in the Neuman and Block review^[4] and the Wikipedia article on optical trapping. Since the 1 micrometer diameter beads we use in this lab essentially match the 845 nm wavelength of our laser, neither of these mechanisms is quite right. More complicated electromagnetic theories have been invoked to account for the observed forces^{[4][5] [6]}. However, these theories are not particularly useful in calculating forces from first principles; the ray optics approach is useful for guiding trap design and beam alignment, while calibration is based on direct measurements of bead motion.

Experiment Timeline

Days 1 and 2

• Learn to trap beads and collect data for calibrations
• Tell Tom Colton or Don Orlando what day you want to start working with E. coli so that cultures can be started the day before (so not available on Mondays).

Day 3

• Analyze calibration data enough to show that you have good data and understand how to analyze.
• Read the E. coli references and consider what kind of investigation you want to do.

Days 4-5

• Investigation of E. coli locomotion.

Days 6-7

• Investigation of internal transport in onion cells (bring your own onion). You can do this investigation before the E. coli investigation if you prefer.

Apparatus

The key to a successful optical trap is to create a well-collimated beam that slightly overfills the aperture of the microscope's objective lens and is aligned perfectly with the optical axis of the objective lens. The numerous mirrors and lenses that steer and shape the beam to this end require delicate alignment by a trained staff member with safety goggles, an IR viewer, and special tools. Do not tamper with anything in the laser beam path unless specifically instructed! Even a slight nudge of a mirror or lens can result in an asymmetric or off-center beam that will ruin the function of the trap and require hours of realignment. (If you're curious about the process, see the laser alignment and collimation procedure, but don't do any of this yourself!) If there is any problem with the function of the trap itself, notify the staff and do NOT try to fix it.

Lasers

Trapping Laser

The Lumics LU0845 M200 diode laser ^[7] has a maximum power output of 200 mW, though a fraction is lost traveling through all the optics. The 845nm wavelength is far enough from the resonant frequency of water to prevent much heating of live cells and is less likely to affect the behavior of cells than visible wavelengths. The diode laser is coupled to an optical fiber. If this fiber is broken or kinked it could cause backwards reflections of the beam, destroying the laser. The laser diode is mounted in a standard butterfly mount that acts as a heat sink and cooling device. Two cables connect it to a laser diode controller (LDC)^[8] and thermoelectric temperature controller (TEC)^[9] located on a shelf above the optical table. Avoid touching the laser or its butterfly mount because static discharge can destroy the laser.

Fluorescence Laser

The smaller laser is an over-the-counter, <5mW, 532nm diode laser. It is just as dangerous as the average green laser pointer, so as long as you don't look into the beam you will remain sighted.

Safety Measures

The trapping laser has a power output of up to 200 mW and a wavelength of 845nm, which is in the near infrared. Even a brief exposure to the focused beam at this power can cause permanent damage to the retina of your eye. Because the beam is invisible, you could be exposed without even realizing it. For this reason, the beam path is shielded. Still, the laser safety training and measures below are essential for your protection.

1. Do not operate the laser unless you have completed the laser safety training and submitted the signed laser safety form and quiz to the course staff.
2. Never bypass any safety devices, e.g. NEVER REMOVE A LENS TUBE.
3. Check for stray beams: Every day, the first time you turn on the trapping laser you should perform a survey of the beam around the objective to check if there are any stray beams (diffuse or specular) coming from any part of the laser or optics, and then document this in the Laser Log Book in wall pocket.
4. The survey is done by using the IR Viewer, if it is not in the room find a staff member to locate it. The IR viewer is blue and you use it with your goggles on. The laser beam is invisible and very powerful; the IR viewer allows you to see it, but even if you can't see it you can still be blinded.

Optical Paths

The microscope has a dual function. One is to allow us to see our specimen at high magnification by sending visible light through the specimen to a video camera. The other function is to focus the laser beam to create the optical trap and collect the laser light to focus it on a quadrant photodiode (QPD) that tells us how close the trapped object is to the trap's center. Keep in mind that there are three light sources, and though their paths coincide through much of the microscope they are still distinct, with distinct focal and afocal points. A useful concept for understanding microscopy optics is that of conjugate planes, which groups all the optics into two complementary sets: imaging and illumination.

Trapping Laser

The trapping beam exits the diode and travels through a fiber optic cable to a cable termination fitting, then through a collimating lens. It then passes through two steering mirrors and a beam expander that expands the diameter 2.5x to match the 6 mm aperture of the microscope objective. It joins the microscope at a dichroic mirror, which reflects IR light but allows visible wavelengths to pass through. A mirror at the bottom front of the microscope reflects the beam up through the objective lens, which focuses the beam down to a tiny waist just above the lens, creating the trap. Above this waist, the beam diverges and is recollimated by a condenser lens. Above the condenser the beam is reflected off another dichroic mirror and focused by a lens onto the quadrant photodiode (QPD) for position detection.

Illumination

The trap has two illumination systems: the green laser and the red LED. You will only need the LED, but a single-molecule experiment requiring fluorescence microscopy is under development. It is to your advantage to understand all parts of the apparatus, as it will only deepen your understanding.

LED Illuminator

This is an inverted compound microscope, so it may be backwards from what you have used before. At the top is the illuminator, a red LED. The light passes straight through a dichroic mirror and is focused on the condenser, which collimates it, giving even illumination of the sample. As it then passes through the objective lens the image is magnified by 100x. The mirror below the objective reflects the light to the dichroic mirrors (and emission filter if it's in), which allow red light through. The light is focused by a 200mm lens (the "eyepiece" of the microscope), and bounced off a mirror onto the CCD camera.

Fluorescence Laser

The fluorescence laser's alignment is less critical than the trapping laser's, since at the sample it provides broad illumination rather than a tight focus. This is why we can get away with mounting it on a post rarther than the cage system. The beam exits the laser unit collimated and goes through 8x expansion (a 2x unit and a 4x pair of lenses). It bounces off one steering mirror and through a lens, which (after it reflects off a dichroic mirror) focuses it on the back focal plane of the objective, which collimates it to provide the nice, even illumination we want. The condenser refocuses it, and then it passes through the QPD's dichroic mirror. The illuminator acts as a beam stop.

Fluorescent dye emission

The dye fluoresces in every direction, but the part we are interested in goes through the objective (where it is magnified), off a mirror and through both dichroics and a lens for focusing. It then passes through the emission filter, which is a very tight bandpass to block everything except the dye's emission (which peaks at 570 nm) and the LED. Finally its journey is over when it reaches the CCD focused.

Stage

The microscope stage holds the specimen slide and allows fine control over horizontal positioning. It is useful for finding beads or cells to trap and moving them once trapped. Two piezo electric picomotors drive the stage in the X and Y directions. The knurled knob on each picomotor allows for manual positioning. The motors can be controlled by a joystick or by software. The joystick is best for hunting for specimens to trap and moving the trapped specimens around. The software control is useful for calibration procedures when you want to move the slide at a constant speed. The specimen is held on the stage between a microscope slide and a thin glass coverslip suspended beneath.

Vertical positioning (Z axis) is accomplished by moving the objective lens with the positioning knob; 1μm/gradation. This has the effect of moving both the plane of focus of the microscope and the center of the optical trap. So, for instance, if you focus on a bead resting on the coverslip, turn on the laser to trap it; you can then move the objective lens up to raise the bead off the coverslip.

The gap between the coverslip and objective lens is filled with immersion oil which, by virtue of its high(er than air's) refractive index, improves both the resolution and the numerical aperture of the lens.

Quadrant Photo-Diode (QPD)

The quadrant photodiode (QPD) is our principal way of collecting data on the position of the trapped particle relative to the center of the trap. This distance also tells us the force the trap exerts on the particle since force increases linearly with distance from the trap's center. Some simpler optical traps use the video camera image to provide position information, but a photodiode allows finer spatial resolution and much higher frequencies (we'll be collecting data at 12 kHz for power spectrum analysis -- compared with 30-500 Hz for video cameras).

The QPD consists of 4 photodiodes in a quadrant formation to allow X and Y position calculation. Within a certain range of light intensities, the output voltage of a photodiode scales linearly with the intensity of light incident upon the diode. The light incident upon each quadrant in the QPD generates a voltage. The analog circuitry then outputs a voltage Vx and Vy which are proportional to the actual X and Y position of the incident beam. As the light scatters in a predictable way off of the spherical beads, this information can be used to recover actual bead position within a narrow range around the center of the trap. Further information can be found in reference: Gittes and Schmidt.

With nothing in the trap (or a trapped bead exactly centered in the trap), the laser beam is tightly focused on the center of the QPD, giving Vx and Vy signals of zero. When a trapped bead moves slightly away from the center of the trap, the laser spot moves on the QPD, causing Vx and Vy to vary accordingly.

Operating Procedures

The Optical Trapping Program

We use a program written in C# to control the camera and motorized stage and to record and process data from the QPD and camera. To open the program, go to the folder: C:\Optical Trapping Code\BrownianApplication\bin\Release Double click BrownianApplication.exe. (Not BrownianApplication.vshost.exe) DO NOT EDIT THE PROGRAM! Ignore the red exclamation points on the folders.

5 windows will open:

• Stage Control Window controls the X and Y picomotors. The motors can be controlled with this software or with the joystick, or the stage can be moved manually by turning the X and Y knobs on the picomotors.
  • To use the joystick, press the first button on the joystick labeled "Set Axis/Enable" once, then the third button labeled "Motor" once, and then "Set Axis/Enable" again. This sets the X and Y axes appropriately. To switch between step mode and joystick mode, use the control window. Be aware that in switching back to "joystick mode" from "Step Mode" you must also press the "JON" button to activate the joystick. The joystick should vary the frequency of the picomotor steps depending on how far you push it to one side. It will not go diagonally, i.e. only one motor will operate at a time.
  • Note that if the joystick stops to function you may have to re-start the computer 2 or 3 times depending. There seems to be a bug in the program that is just annoying.
  • To use software control, select the "steps mode", set the frequency and number of steps (by typing into the text boxes and then hitting the "set" button). Now when you press Up, Down, Left and Right on the stage control the stage will be moved at this preset direction. You can hit "stop" to abort the current movement.
  • If the stage control or joystick ever malfunction, the program may need to be restarted. Sometimes the power to the joystick may also need to be cycled. Turn off the laser first, if it is already on, then flip the power switch on the box marked "QPD and Joystick Box" to the off position. Please wait 15 seconds or more before turning it back on, as cycling power too quickly will cause the joystick not to work.
• Control Window controls the camera and provides for data analysis from the video images. The "Camera Go" button will bring up the camera image in the Pass Through Window (see below). The rest of the controls in this window handle the particle tracking feature, which is used extensively in the Brownian Motion in Cells experiment but is not necessarily needed in this lab. If you want to try tracking particles, consult the software page for that lab to learn how.
• Pass Through Window displays the live images from the camera. The red-bordered selection box is used to select the region for particle tracking analysis, which you may not need. However, it is useful to position this box (by clicking with the mouse) so that one corner is located exactly where the trap is focused to use as a marker for the trap location.
• Images Window is used for the particle tracking feature to show the image of the area within the selection box before and after processing. Unless you are using this feature, just minimize this window.
• QPD Readout Window is responsible for displaying voltage signals from the QPD and saving data to file. With this window you can view the average position of the particle, X and Y positional data, and a power spectrum of the data in real time. You can also record at different frequencies and for different periods of time. Here is more detail about the controls in this window:
  • Under 'Real Time Readout', two buttons allow a choice of time for the chunk of data displayed on the graphs and other buttons start and stop the display.
  • Under 'Write Data', you choose what types and durations of data to save and specify the directory and filename to save data. Create a new folder in the "C:\OTZ Student Data" directory, and save all your data to that folder. One button collects data for 8 seconds at lower frequencies, which is useful for certain calibrations and for recording from biologically interesting specimens. Two other buttons collect data at high frequency and calculate the power spectral density. The 'PSD 4/3s@12kHz' button has the added feature of repeating the data collection multiple times (set in 'Num Averages') and averaging the PSD to reduce variance. This is very useful for doing stiffness calibrations on beads. (The 'PSD 1/6s@12 kHz' button just collects one run.)

How to pipette

Pipettors are a standard tool in most biology, biophysics, and chemistry labs, but you may not have encountered them in physics courses. We have three models, each with a different range of volumes it can dispense, 1-10 μL, 10-100 μL, and 100-1000 μL. Disposable plastic tips are sized for each pipettor (labelled small, medium, large, respectively). The volume dispensed is adjusted with a thumbwheel and displayed in a window on the side of the pipettor.

1. Mount the appropriate plastic tip on the end of the pipettor
2. Dial in the volume you want to dispense.
3. Depress the push button to the first stop.
4. Dip the tip under the surface of the liquid and slowly release the push button. Withdraw the tip from the liquid touching it against the edge of the reservoir to remove excess liquid.
5. Deliver the liquid by gently depressing the push button to the first stop. After a delay of about one second, continue to depress the push button all the way to the second stop. This action will empty the tip.
6. Release the push button to the ready position.
7. When finished pipetting a particular solution, dispose of the tip in the trash and replace it with a fresh tip before moving on to another solution.

Never allow liquid to enter the body of the micropipette

Preparing a Slide

For the calibration section of the lab, you'll be trapping synthetic silica microspheres, or beads, available as stock solutions in the refrigerator. Be careful not to contaminate or spill the stock solutions, as they cost more than $100 each. Whether using beads or bacteria, it is generally necessary to dilute the stock considerably to reduce the concentration of particles. You want particles to be somewhat scarce on the slide so that when you do trap one, you don't have other nearby particles being sucked into the trap and ruining your measurements.

Starting with the 1 micron silica bead stock, make a 1:5000 dilution with distilled water in a small plastic vial. (Note: A 1:5000 dilution of 1 micron beads is 1 part concentrated bead solution out of 5000 parts by volume of final bead water solution. Hint: the vial will hold 5 mL of solution). Be sure to shake the stock solution vigorously right before pipetting, as the beads are all in that thin white layer on the bottom of the vial. You can store your diluted sample in the refrigerator for several days if needed.

Slide Assembly

1. Place a Kimwipe on the table to the left of the trap to create a clean place to set the slide. Any dirt or oil from your finger can obscure the light and/or scatter the laser beam, polluting the results of your measurement. Hence, keeping the center of the slide clean and the cover slip clean are important. Take out a microscope slide and place it on the clean surface.
2. Create a "channel" about half as wide as a coverslip by placing two thin pieces of double-sided tape on the slide as shown in the diagram. Do not make the tape slices too wide or the slide will rest unevenly in the slots on the microscope stage.
3. Place a coverslip directly over the gap between the two double sided tape strips without applying any of the sample. The tape should hold the coverslip firmly in place. If you run into trouble with the sample leaking under the tape, try rolling a pencil eraser over it to attach it more firmly.
4. After shaking your sample solution in the vial, deposit ~10-15 μL into the channel by using the pipette just outside of the coverslip. The channel will suck the fluid under the slide and fill the gap. You could, of course, put the sample in first but if you put too much, the coverslip will force some of it on top of the tape and weaken the bond. The former method prevents the coverslip from sliding around when it is in place over the objective.

Microscope Operation

Illuminator

Turn on the red LED by turning on the power supply on the shelf over the optical table. You should see an eerie red glow emitted from above the stage. Adjust the voltage slightly to make the image brighter or darker, you do not need to adjust the current.

Joystick

Turn on the power switch on the controller for picomotors and the QPD located on the shelf above the optical table. To use the joystick, you need to select which motor drives which axis by pressing the "set axis" and "motor" buttons on the joystick. To set motor A to drive the x-axis and motor B to drive the y-axis, use the following button sequence:

1. set axis
2. motor
3. set axis

Slide Loading

1. Lower the objective lens using the micrometer adjustment knob (turn it counterclockwise as viewed from below) so that the lens will not be scratched (or even touched) by the microscope slide as it is being loaded.
2. Place a tiny drop of the immersion oil on the lens using the dip stick in the bottle of oil. Let the oil run off of the dip stick back into the bottle for 10 sec before proceeding. Avoid touching the dip stick to the glass in the center of the objective. Oil only needs to be added to the objective about every other slide. (Note: if immersion oil doesn't fill the gap between objective and coverslip, air bubbles will prevent stable trapping or deflect the beam off the center of the QPD.)
3. Place the slide into the slot on the stage with the cover slip down. This is an inverted microscope, after all!
4. Raise the objective until you see the oil make contact with the cover slip. Make sure there are no air bubbles in the immersion oil or in the chamber where the light passes through. You'll continue to adjust the objective height to focus on the specimen, below.

Viewing the specimen

1. Start the optical trapping program and use the Control Window to turn on the camera. The live video image should be visible in the Pass Through Window.
2. Move the objective up and down to find beads or other objects to focus on. Keep track of the position of the objective relative to the coverslip. The lens should never be so low that immersion oil fails to fill the gap, nor so high that it pushes the slide up off the stage. If beads are scarce, you may need to move the stage horizontally with the joystick to find some.
3. Adjust the LED voltage as needed to get a good image.

After you are finished

When you are done trapping and collecting data (see below) power down everything and remove the slide from the stage. Dispose of slides in the glass disposal box out in the lab. Dispose of pipette tips and kimwipes in the regular trash.

Trapping Laser operation

Temperature Control The two controllers for the trapping laser are stacked on the shelf above the table. The top one is the Temperature Controller (TEC). Turn the power on and press the 'enable' button to engage it before turning on the laser controller. The TEC has a preset current limit, I_LIM, of 1.4 A and the resistance, T_ACT, should be around 10.0 kΩ, and always within the range 9.5 to 10.5 kΩ. This should already be set, but it is important to make sure it is not changed. To change the resistance, 'enable' the TEC, go to the T_SET mode in the display section, and turn the knob to just below 10 kΩ. The TEC, when set properly and 'enabled', will control the temperature of the laser diode , which prevents temperature-related power fluctuations. It should not need to be adjusted.

Powering the Laser Control of the laser diode power is via the Laser Diode Controller (LDC). Once the TEC has been set and 'enabled' the LDC can be used.

1. Turn on the power.
2. Before 'enabling' the LDC, turn the gray control knob counterclockwise until the stop point.
3. Under the display menu, scroll down to the P_LD to set the LDC in the power (P) mode. The current limit I_LIM has been set to 285 mA which is 95% of the maximum current the laser can handle.
4. Press the 'enable' button to turn on the laser; then turn the control knob to set the desired power. The display indicates the power delivered to the laser and varies from zero to a little over 1.0, so can be thought of as the proportion of full power. The actual power delivered to the focus of the trap is well below the power emitted by the diode, but is proportional to the power setting on the LDC. If the max current, I_LIM, is reached, a 'beep' will sound, a red indicator is lit, and the current will not increase anymore. This should occur around the 1.08 power level. The laser should be operated slightly below the limit.
5. You can control the laser by setting the desired power level, then toggling on and off with the 'enable' button, or just adjust the control knob as needed.
6. When finished, always toggle off the 'enable' button before turning off the power.

QPD Centering

Before taking data from the QPD, the QPD should be aligned so that the laser hits it in the center, resulting in voltages Vx and Vy being zero. Once you have opened the program, have turned on the LED and QPD, and are running the laser in an area of a slide free of beads, you can zero the QPD signal in the QPD readout window.

The QPD signal is indicated by the yellow circle on the Vy vs. Vx graph. If this is not centered at the origin, adjust the knurled adjusting screws on the top and front of the QPD mount to bring the yellow circle to the origin. It will be easiest to do this if the real time readout is set for 1/6 sec at 12 kHz, as the response to your actions will show up faster.

If you are unable to zero the signal, first check to see if something like a bead or debris has entered the trap (e.g. disable the laser and move the slide to a new spot to be sure). If you still can't zero it, return the adjusting screws to a middle setting and use the adjusting screws for centering the condenser. This functions as a "coarse" adjustment for the QPD signal, which can be followed by fine adjustment again at the QPD.

The QPD zero signal will vary somewhat with the power level of the laser. Hint: If you are doing calibrations with beads at multiple power levels, you can zero the QPD signal at the highest power level, then trap the bead and switch to lower and lower power levels without too much problem. If you precisely zero it at a low power level, you will find more drift in Vx and Vy as you move to higher power levels.

Trapping Procedure

1. To get familiar with the location of the laser trap vertically with respect to the slide and coverslip and horizontally with respect to the camera's field of view, find a place on the slide with no beads or cells nearby and turn on the laser at a medium power level. As you move the objective up and down, you will see a faint reflection of the laser off the coverslip and off the slide when each is in focus. You may find it useful to relocate the red selection box (click with the mouse in the pass through window) so that one corner marks the position of the trap. Then when you are not focused on the slide or coverslip, you'll still know where the trap is within the camera's field of view.
2. Make sure that the QPD is centered (Vx and Vy are zero).
3. To trap a bead, you can search with the laser on or turned down or disabled until you find one to trap. Silica beads tend to sink rapidly to the bottom of the chamber formed by the slide and coverslip, meaning that they will be sitting on the coverslip. If beads are dense, then look for one that is isolated from others before turning the laser power up.
4. Once a bead is trapped, it will appear slightly unfocused because the equilibrium position of the trapped bead is generally slightly above the optical focus of the lens. You should be able to move the slide with the joystick, and the bead will remain fixed by the trap while the other contents of the slide move by.
5. To take QPD data from a free bead or other trapped object, move the bead away from the coverslip and slide so that its motion will not be influenced by the wall effect. You'll notice that the trap is less stiff in the Z direction than in X or Y, so moving the bead up off the coverslip may require a delicate touch.
6. As you collect data, keep an eye on the trapped object in the pass through window to make sure that another object does not get sucked into the trap. This is a problem especially with dense suspensions and higher power levels. When you finish with a bead, it is wise to release it and check the image to see if another bead was hiding below it in the trap.

• Experiment with trapping multiple beads at once to see if you can tell from the camera what is going on. How many can you trap at once?

• How low can you turn the laser power before a bead escapes the trap? How does the behavior of the bead change at lower power?

Part I. Calibration of the Optical Trap

Observing specimens and trapping small objects is straightforward with the procedures described above. But to tap the full potential of the laser tweezers to precisely quantify size, position, and forces at nanometer and piconewton scales requires careful calibration. To save time, we are providing you with calibrations of the microscope image scale and the step-size of stage movements by the picomotors. We leave to you the more interesting calibrations, including translating the voltage measurements from the QPD into the position of the trapped particle relative to the center of the trap (QPD position calibration) and the force exerted by the trap on the particle (trap stiffness calibration). There are multiple techniques used to calibrate traps, and we'll let you try a few of them and compare their results and appropriateness.

Microscope and Stage Calibration

Results of these calibrations are provided below for your use. If you would like to perform them as part of your lab exercise, that is an option you may choose and we might substitute your results in the future.

Pixel to meter conversion of the microscope image

A micrometer slide with markings at 10 micron increments was used to measure the pixels/micron of the video image. The result: . If you want to use images captured from the video camera to analyze movements or sizes of structures, this information may come in handy.

Stage picomotor step size

The nominal step size given in the specs of these picomotors is 30nm and ideally would not vary with motors or between directions for one motor. However, the motors have to work against various springs in the X- and Y- stages, so the resistance to motion left and right (X) varies, as does resistance forwards and backwards (Y). In addition, the first few steps may vary in size as the stage starts up.

To find the average step size of motorized stage movements in +Y,-Y,+X,-X directions, beads were caused to stick to a microscope slide (see technique under position calibration below) and the slide was moved in each direction at a controlled rate with the picomotors. The particle tracking feature of the optical trapping software was used to record trajectories of several beads as they were moved by the stage with the laser off. The position of a bead was plotted vs. step number for 3 different frequencies of motor operation, as shown in the accompanying graphs. Step size was found to be pretty consistent for one direction after the first few steps, and step frequency did not seem to matter from 100 to 225 Hz. This calibration was last performed by Shawn Tang in November, 2011.

The average step sizes were:

left: 39.13 nm/step

right: 29.21 nm/step

up: 38.22 nm/step

down: 26.81 nm/step

Note: The directions above (left, right, up, down) refer to the apparent movements of the stage according to the camera image, e.g. when a stuck bead appears to be moving to the right in the video, we call that "right." One complication introduced by the fact that the camera looks at the slide from underneath is that left and right are reversed from our perspective looking down at the slide. Up and down are not reversed, meaning that up indicates movement of the slide away from you and down is towards you. To avoid confusion, we use the directions apparent from the camera image.

Position and Stiffness Calibration of the QPD

Calibration of the QPD's response to movements of the trapped objects typically use microspheres because of their symmetry and standardized characteristics, such as refractive index, size, shape, etc. In some cases, calibration is performed with a bead that is similar in size and shape to the biological specimen of interest. In others, the bead itself is used in an experiment to apply forces to the biological specimen. For example, a bead can be attached to one end of a macromolecule such as DNA as a handle to pull on. If the other end of the molecule is stuck to a coverslip or a pipette, the bead can be moved by the trap to apply precise forces to the molecule or other structure. In this lab you can do your calibration with Silica beads of 1 or 2 micron diameter, and should plan to use the same bead size for all of your calibration techniques.

What is Position Calibration? Within a narrow range around the trap (about 100-200 nm), the voltages Vx and Vy from the QPD are linearly related^[10] to the distance of the bead from the center of the trap along each axis. The position calibration, also called sensitivity, allows us to translate our raw Vx and Vy data into distance data. Sensitivity, ρ, is usually given in units of Volts/μ. Of course, the power setting of the laser will affect the light intensity incident on the QPD, and thus the voltage responses, so rather than a single conversion we really want the relationship between sensitivity and laser power. This normally is fairly linear, so measuring sensitivity at 4 power levels is plenty to characterize the relationship.

We have two independent methods for performing position calibrations. The first, called the stuck bead scanning method, is to move a bead stuck to a slide through the center of the trap at a controlled speed with the motorized stage and record the Vx or Vy. In the linear region near the center of the trap, the slope of Vx vs. distance is the inverse of sensitivity. The second method, less direct, is to apply our understanding of the physics of Brownian motion of a bead of known size in a medium (water) of known viscosity. By trapping a free bead and recording Vx and Vy at high frequency, a Power Spectrum Density (PSD) can be calculated to give an estimate of sensitivity. We'll call this the PSD method. Try both of these methods as detailed below and see how comparable are the results.

What is Stiffness Calibration?Forces in optical traps generally cannot be measured directly. Rather, the force on a trapped particle is calculated by multiplying the displacement of the particle from the trap's center by the stiffness of the trap. That is, the trap obeys Hooke's law, F = -kx, where 'k' is the stiffness of the trap.

Method/how to sample	Position	Stiffness
1. Stuck Bead: sample 8s@1 kHz	X
2. PSD (with free bead): sample 4/3 s@12kHz	X	X
3. Equipartition (with free bead): sample 8s@1kHz, down-sample to 30 Hz		X

A variety of methods can be used to calculate trap stiffness, each with advantages and drawbacks. We'll use two in this lab, both exploiting the effect that the trap has on inhibiting Brownian motion of a trapped particle. The Power Spectrum Method uses the same data as for the position calibration method of that name. The second, called the Equipartition Method, analyzes the variance in position of the particle over a longer time period at much lower frequency. Compare the results of these two methods and consider which might be preferable in different applications.

To summarize, you will use three techniques for position and stiffness calibration, resulting in two position calibrations and two stiffness calibrations, as depicted in the accompanying table.

Stuck Bead Scanning Method (Position Calibration)

We recommend scanning a stuck bead along each orthogonal axis through the center of the trap, considering Vx and Vy independently of one another. A more complete calibration would require raster scanning back and forth in a grid to cover the entire active 2D region of sensor, but this is problematic due to some hysteresis and imprecision in our motorized stage so we'll stick to measurements along the axes.

Stuck Bead Sample Preparation Exposing the beads to a salt solution causes them to stick to glass by hydrophobic interactions. A 1 M NaCl solution is provided for this purpose. You could combine this with a bead sample directly on a slide rather than making a separate vial. To do this, try adding 5 microliters of a 1:5000 dilution of a bead stock in water to 30 microliters of 1 M NaCl on a slide. After adding a coverslip, invert the slide. It may take up to 30 min to get good adhesion, and some beads will stick better than others. You may need to adjust these amounts to get a reasonable density of beads on your slide.

Scanning Procedure

1. Center the QPD signal without a bead near the trap and with the laser at the highest power you will be using.
2. Locate a bead that is firmly stuck, that is, it does not seem to "wobble" as it is dragged through the center of the trap.
3. Focus the microscope so that the bead is at the same height that it would be if it were freely suspended but trapped. It should be a little out of focus. (Use your prior experience trapping beads to judge this.)
4. Center the stuck bead in the laser trap, using the joystick. The QPD signal should read approximately Vx=0,Vy=0 and small motions along the X or Y axis should cause large changes in Vx or Vy, respectively).
5. Once the bead is centered, switch to software control of the stage and set the step number (preferably at least 100) and frequency (50-150 Hz) how you want.
6. Move the bead away from the trap center in the -X direction (direction is arbitrary) by the set number of steps and stop the QPD readout.
7. Set the stage control window to move the bead in the +X direction twice as far as you moved the bead in the -X direction.
8. Click the Write 8s at 1kHz button and immediately start scanning the bead across the trap (in +X direction) using the preset frequency.

This will take 8 seconds of QPD voltage data sampled at 1kHz and saved as a text file with name and location you specified. A graph of the QPD readout will be shown after the 8s period on the Vx and Vy versus time graphs on the QPD Readout Window. The graphs should both read roughly 0 at the very beginning and end of the run and you should see a signal like that of the one pictured above in the direction in which you are scanning the bead. The perpendicular direction (in our case, Y) should show very little change and be roughly symmetric around the center of the trap, as determined from the Vx plot. If Vy varies a lot, you might recenter the bead and try again. Keep in mind that there is some hysteresis in the motors/stage and sometimes the coverslip may be dragged a little by the viscosity of the immersion oil. Reducing the number of steps you go away from the center of the trap may help.

Repeat this measurement for the Y axis and then repeat both X and Y for each power level you choose for calibration.

Plot both Vx and Vy vs. time and zoom in to note the time points that bound the linear region that lies in the center of the trap. Perform a linear regression on this time range of data only and use the appropriate step size and frequency to calculate the sensitivity for this axis and power level.

Using Matlab

The functions Vvarplot.m and Vregression.m are designed to help you carry out the analysis of a stuck bead. Right click and download the following functions:

Media:Vvarplot.m Use this function to make quick plots of Vx vs Time and Vy vs Time to select the linear region of each graph (the beginning and ending time of the region you need to perform a regression on).

Media:Vregression.m Use this function to perform linear regressions on the range of values determined above. These slopes, when converted to units of Volts/μ, are your sensitivities.

The first line of the function Vvarplot.m is shown below.

function [ ] = Vvarplot(axis,graph,varargin)

The first input to this function is to specify the axis we are looking at, either X or Y. If you want to analyze Vx vs time data, type in 'x' for the axis input. For now, type in 'diff' into the graph input (you can read more about this in the comments for this function). Lastly, type in the name of your data variable (that you imported into your Matlab workspace from the collected text file) followed by the power at which the data was collected. In this function, there is no output (there is no value placed in the brackets on the left hand side). Note: the varargin input can take a variable number of inputs which means you can input more data at different power levels to generate multiple graphs in one run.

Sample input: Looking at Vx vs time, data0.4 is the matrix that contains all our data (the matrix imported from the .txt file), and 0.4 is the power of the laser when the data was collected.

Vvarplot('x','diff',data0.4,0.4)

This command should pop up a window that plots Vx vs time, which you can now inspect to pick out the linear region of interest. A regression on this region can then be performed using the Vregression function (look at the comments to see how to format the inputs).

Once you have calculated the sensitivities for all four power levels in X and Y, plot them versus laser power in Matlab.

• How does sensitivity vary with power level?

Power Spectrum Method (Position and Stiffness)

The thermal motion of a spherical bead of known size suspended in water is well characterized. As the laser power is turned up on a trapped bead, the Brownian motion of the bead is constrained more and more by the increasing trap force restoring the bead to the center of the trap. A statistical analysis of this motion allows us to estimate both the sensitivity of the trap and its stiffness.

Procedure

1. Starting with a slide loaded with a sparse suspension of beads in water, trap a bead and move it well away from the coverslip, slide, and other beads.
2. Specify the filename and directory to save your data. (Subsequent data filenames will be incremented numerically so it is not necessary to change the filename manually for each run.)
3. Record QPD data using the 'PSD 4/3s@12kHz' button with 'Num Averages' set to 10. This will collect 4/3 sec of data ten times and compute the average power spectral density (PSD) function over those ten trials, which greatly reduces the variance.
4. Repeat data collection at each of the laser power settings you have chosen for your calibration. (If you have centered the QPD at the highest power setting, you don't have to release the bead and recenter between power settings.)
5. Collect data on at least two beads.

The PSD Method stiffness measurement requires knowledge of the hydrodynamic drag on the particle. For a sphere, the Stoke's drag relation is well known, and requires knowing the diameter of the bead and viscosity of the fluid. The Stoke's relationship is not valid close to a wall, so a particle must not be near the surface of a slide or coverslip.

The Power Spectral Density (PSD)^[11] of a trapped bead has a Lorentzian profile described by:

in Volts² / Hertz. Where β = 3πηd is the drag, η is the fluid viscosity of water, d is the diameter of the bead, ρ is the sensitivity of the trap, and f is the frequency of bead vibrations. If the fluid is water then we can take: η = 8.90 * 10 ^{- 4}Pa * s. Using this, a curve can be fit to the log of the data sets giving the rolloff frequency f_o. In addition the rolloff frequency relates to the relaxation time: .

• It should be noted that the notepad file with the PSD data in it gives the PSD data for X and Y directions at the n^th reading. As the n^th reading is NOT the frequency, it should be transformed into the frequency: .
• Because the PSD is a result of a Discrete Fourier Transform, the data is symmetric and hence the upper half of the data were discarded before the program did the averaging.

Using Matlab

Several Matlab programs are provided, including:

Media:FitlogcurvevarX.m

Media:FitlogcurvevarY.m

Media:SensVSpower.m

Media:StiffnessVSpower.m

One useful analytic method for this part of the lab minimizes the least-squares distance of every point from the predicted curve, giving two parameters of the equation, alpha and f_o. The Lorentzian can be recast as the equation: .

To use Matlab, you will have to import your data from the text files into the workspace. The functions fitlogcurvevarX and fitlogcurvevarY allow you to input as many data sets at once as you wish. They use a non-linear fitting procedure to fit the theoretical curve to log transformed data, returning alpha (a_x or a_y) and rolloff frequencies (fo_x or fo_y). The plot(s) from the functions relate log(PSD) vs. log(freq), and should look like the Power Spectrum Density as it appears in the QPD readout window.

[a_x fo_x] = fitlogcurvevarX( data1, pwr1, data2, pwr2, ... )

Using properties of logarithms and the two Lorentzian equations above, it should be possible to solve for sensitivity. The program SensVSpower.m allows you to input your alpha values at their corresponding power levels to find sensitivity measurements.

The rolloff frequency parameters found from fitlogcurvevarX and fitlogcurvevarY give the trap stiffnesses from the following relation:

k = 2πf_oβ again where β = 3πηd is the drag, η = 8.90 * 10 ^{- 4}Pa * s is the viscosity of water, and d is the diameter of the bead (in meters).

The function StiffnessVSpower allows you to input the alpha and rolloff frequency vectors, along with bead diameter (in METERS), and will output trap stiffnesses.

Equipartition Method (for Stiffness)

This method is based on the equipartition theorem, which states that each degree of freedom in a harmonic potential has of energy. Using this theory, we can relate the thermal energy of a system to the instantaneous displacement of small particles via the statistical mechanical idea of heat as: , where < x > denotes the average over x, the position of the particle along the x direction. Since < (x - < x > )² > is the variance of x, stiffness can simply be calculated from the variance of the bead position at each power level.

This method has a few requirements you should be aware of.

1. The variance used must be of particle position (distance from the center of the trap in x or y), not of the voltage from the QPD. So you need to use the position calibration (sensitivity) to convert Vx to x before taking the variance. You can try using sensitivities from the Stuck Bead and PSD methods, and you may find that this choice has a big effect on the stiffness values you obtain.
2. The observations used in this analysis are assumed to be independent of one another. Hence, the particle positions must be taken at intervals greater than the relaxation time, > > τ_o, which can be derived from the rolloff frequency, of the trap. As the relaxation time of the trap is be around 10ms, the data points should be taken at around 30Hz to to avoid any correlation between successive data points. Since the slowest sampling rate available is 1kHz, the data must be down sampled, which has been done automatically by the program. two of the columns in the 8 second: 1kHz notepad file are downsampled to approximately 30Hz, giving around 240 independent data points.

The procedure for this calibration is the same as for the PSD method with one exception: use the "8 sec@1kHz" button to collect data from the QPD. You can in fact collect these data on the same beads used for the PSD method to save time.

Using Matlab

Here we will use the program Media:Equipartition.m. After inputting the values for sensitivity at each power in both the x and y-directions, as well as the data sets with their corresponding power levels, it will graph and calculate stiffnesses in both X and Y and perform a linear fit. A quick glance at the program in the Matlab editor should be sufficient to understand how it operates.

[Kx,Ky] = equipartition(x_sensvspwr, y_sensvspwr, data1, pwr1, data2, pwr2, ...)

• Why might there be a difference in ?
• How do the assumptions of the PSD method and Equipartition method for measuring stiffness differ?
• Why must the successive data points be independent?
• How does this idea of autocorrelation between successive values of the position, x, relate to the Power Spectrum Density?
• BONUS: How can this independence be tested? i.e. How can the correlation be measured?
  • To understand how to test this it may help to consult Reif and look into the ideas of covariance and autocorrelation. If time permits and you are interested in this idea, by taking several data sets (maybe 100 of 1 second each), each giving a value: k_i, you should see some variance in k. You can measure the mean and standard deviation in k using 2 different sampling rates (one above and one below the correlation time of the trap) and then measure the autocorrelation.

Part II. Investigating Flagellar Locomotion in E. Coli

Escherichia coli (abbreviated E. coli) is a rod-shaped bacterium about 1 μ in diameter by 2-4 μ long. It normally occurs in the intestines of humans and all warm-blooded animals. Most strains, including the one we will study, are harmless to humans. E. coli has a bad reputation due to some pathogenic strains that produce dangerous toxins causing diarrhea and some other diseases.

E. coli is propelled in liquids by a set of four or more helical flagellar filaments that arise from separate positions on the cell surface but intertwine to appear as a single flagellum in forward movement. A cell may lose its flagella under some conditions, and regenerate them under others. Although motile cells on a crowded slide may appear to be moving pretty randomly, a cell actually can modulate its swimmming to follow gradients of chemicals, temperature, or light. It accomplishes this by varying the ratio of two swimming behaviors. The first, called a "run", is swimming forward in a steady, mostly straight path. The second behavior, called a "tumble", is an erratic motion that causes the next run to be in a new direction, pretty much at random. If the cell senses that the environmental gradient is getting worse as it swims, then a tumbles are more frequent; if it is getting better, tumbles are less frequent. So motility of the cell is facultative and under at least crude directional control.

The running and tumbling behaviors are caused by a simple switching of direction of motors. Each flagellar filament is driven by a rotary motor at its base that turns counterclockwise (CCW) in forward swimming, as all the filaments intertwine together. During running, the cell swims steadily forward in a direction parallel to the long axis of the cell with the flagellum pushing. Tumbling occurs when one or more of the flagellar filaments turns clockwise (CW), causing the flagellar filaments to separate and beat erratically. You can see the run and tumble pattern of behavior in this movie of fluorescently labelled E. coli.

With the optical trap, you can trap individual cells, characterize the running and tumbling motions from the QPD signal, and investigate some aspects of the motion.

Planning Your Investigation

Begin by reading carefully the following two papers on using optical traps to study swimming in E. coli,

• S. Chattopadhyay, R. Moldovan, C. Yeung, X. L. Wu, Swimming efficiency of bacterium Escherichia coli. Proc. Natl. Acad. Sci. 103(37): 13712-13717 (2006). Uses optical trap similar to ours; good intro to E. coli locomotion and ideas for experiments.
• T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, Y. R. Chemla, High-resolution, long-term characterization of bacterial motility using optical tweezers, Nature Methods 6, 831-835 (2009) . Note that following the reference section of the paper there is a supplemental online methods section, which contains links to a separate pdf of supplemental figures. This studey features excellent experimental work on E. coli swimming using a setup that generates two traps with a single laser beam, allowing better control over the orientation of the cell.

Consider what kinds of patterns you might expect in your data on trapped cells and what questions you might be able to investigate.

Some suggestions you might try:

1. How fast do cells rotate during a run? Is it consistent for one cell? Does it vary with the power of the laser?
2. What is the pattern of running and tumbling? How frequently is a run interrupted by a tumble?
3. Does reversal of the cell direction ever occur while the cell is trapped? (Reversal would occur by the flagella reorienting to the other end of the cell rather than the cell turning abound.)
4. What is the distribution of cell swimming speeds? (You can use the particle tracker feature on the video camera images to measure this without using the trapping laser.)
5. What is the propulsive force required to offset hydrodynamic drag? The Stoke's Drag for laminar flow past a spherical bead of diameter d is: F = βv, where β = 3πηd, v is the velocity of the water flow past the object, and where η is the fluid viscosity, which we may take to be water: η = 8.90 * 10 ^{- 4}Pa * s.
6. Is swimming velocity or cell rotation related to cell size?

Choose one or two questions to focus on and collect sufficient data to be able to quantify your results and provide error bars and/or statistical tests for your hypotheses.

Methods

Preparing Cultured E. coli

We are using a wild-type strain of E. coli known as RP437. This is a naturally occurring strain that has not been genetically modified or made resistant to antibiotics. It is not considered pathogenic, nor would its release into the environment cause spread of antibiotic resistance. Nevertheless, you should practice good hygiene and observe the restriction that no food or drink is allowed in the room. Since you will be reusing cultures and innoculating new ones for another day, you should practice some aseptic technique as described below.

The bacteria cultures are maintained for us by the Bio 1A course staff in the Molecular and Cell Biology Department. They are grown in liquid LB media at 30 degrees C. in a shaking incubator before we bring them to the lab to grow overnight at room temperature without shaking. You will be provided with a tube containing this culture, another tube of sterile medium to use for diluting samples, and some small (1.5 mL) tubes of sterile medium to innoculate each day for use the following day. The cultures grow fine at room temperature and seem to show higher motility than if grown on a shaker.

Handling cultures

1. Wash your hands. Disinfect the work surface by spraying 70% ethanol on it and wiping with a paper towel.
2. Prepare a dilution of the cells in sterile medium in a separate tube. 1:500 may be about right, but will depend on how long and fast the culture has grown. When transferring cultures or sterile medium, uncover the tube only long enough to withdraw the sample and avoid touching the inside of the cap or the top of the tube. Use a fresh pipette tip to avoid contamination.
3. Use the current culture to innoculate a small tube of sterile medium to use the next day. Label the tube with the strain and date innoculated.
4. Dispose of used pipette tips in the regular trash and slides in the glass disposal box.
5. To dispose of old cultures/diluted samples, add 70% ethanol, shake, and pour down the sink. Tubes then go in the regular trash.
6. When finished, wash hands and wipe down the work surface with 70% ethanol.

Trapping Bacteria

1. Dilute your culture with culture medium to obtain a reasonable density (this obviously requires some trial and error depending on the growth of the culture since innoculation).
2. Prepare a slide as for the silica beads.
3. Some cells may not be motile and some may move just a little. To look at cell rotation frequency, seek out very active cells, using the joystick and focus knob to pursue them (video game experience may actually be useful here!).
4. Note the orientation of the cell once trapped. Experiment with varying the laser power to see what level is required to retain the cell and how it affects the cell motion and rotation.
5. Collect QPD data with the 8 sec@1kHz button.

Using Matlab

The text files from the QPD (8sec@1kHz) can be used to generate plots of Vx and Vy vs. time in Matlab.

Sometimes it is interesting to plot Vx vs. Vy to see the shape of the motion. The functions MovingAve.m smooths the data and plots Vx vs. Vy. The AnimatedPlot.m function creates an animation of the trajectory shown in MovingAve.m. To use AnimatedPlot without saving the animation as a AVI file, type in the following in the command window

AnimatedPlot(Xdata,Ydata,'off','')

Xdata and Ydata represent the variables for the voltage data in the X and Y directions respectively

Media:MovingAve.m

Media:AnimatedPlot.m

It may also be useful to perform a FFT on the Vx or Vy data to look for patterns in the frequency.

Part III. Investigating Internal Transport in Onion Cells

To begin, you must first have an onion you provide and a bag to hold it after you cut it open in the lab. First, read through the "Analyzing Intracellular Movement in Onion Cells" under the Brownian Motion in Cells page. Our goal in this section is to analyze the force exerted by Myosin to move the granules in the onion cell. These small granules (or vesicles) are about 1 micron in diameter.

• NOTE: The saline solution may be in the cupboard above the BMC lab area.

Mechanisms of Internal Transport

The eukaryotic cytoskeleton. Actin filaments are shown in red, microtubules in green, and the nuclei are in blue.

In this part of the experiment, you will observe the motion of particles inside a living cell. Cells transport food, waste, information, etc. in membrane-bound vesicles, which are visible under a light microscope. An old-fashioned view of a cell was that it is a "bag of water" containing various enzymes in which matter is transported passively by diffusion. Though diffusion is an important mechanism, it is too slow and random for long distance transport and directing materials where they are most needed, especially in larger cells. It is now understood that cells have highly developed and intricate mechanisms for directed transport of materials.

Most motions within and of cells involve two components, a cytoskeletal fiber that serves as a track, and a motor protein that does the work. The motor molecule uses energy from the hydrolysis of one ATP molecule to bind to the fiber, bend to pull itself along the fiber, and release, all of which constitutes one "step". For an animation of this stepping process, see this movie animation from the Vale lab web site at UC San Francisco. One can divide cellular motility mechanisms into two classes based on the cytoskeletal fibers involved. (1) Microtubule-based mechanisms involve dynein or kinesin motors pulling on microtubules made of the protein tubulin. (2) Actin-based mechanisms involve myosin motors pulling on actin fibers, also called microfibers.

Cartoon of myosin motors pulling organelles along an actin filament.

Binding of kinesin motor to microtubule.

Virtually all cell types exhibit directed intracellular transport, but some cell types are particularly suitable for transport studies. Fish-scale pigment cells work well, since a large fraction of the cargoes that are transported are pigmented and thus easy to observe – the disadvantage is that you would need to bring a living fish into lab as a source of these cells. For convenience, we will use epidermal cells from onion bulbs that you can easily acquire in a grocery store. With some care, a single layer of cells can be peeled off an inner section of the onion bulb and mounted flat on a slide.

Onion cells in bright-field illumination. Round object in each cell is the nucleus.

Vesicles in the cytoplasm of a plant cell, as seen in dark-field.

In this experiment, we will be viewing the movement of vesicles within the cytoplasm of onion epidermal cells, shown above as they appear in bright-field and dark-field microscopy. The layers you see in an onion bulb develop into leaves when it sprouts. Both sides of the leaf are covered with an epidermis consisting of brick-shaped cells, each with a cell wall and cell membrane on the outside. Most of the interior of the cell is filled with a clear vacuole that functions in storage and in maintenance of hydrostatic pressure essential to the stiffness of the plant (the difference between crisp lettuce and wilted lettuce). The cytoplasm, containing all of the other cell contents, occurs in a thin layer between the cell membrane and the vacuole, and in thin extensions through the vacuole called transvacuolar strands. It is within the cytoplasm that you will be observing directed transport of vesicles by an actin-based mechanism. These vesicles are spherical or rod-shaped organelles such as mitochondria, spherosomes, and peroxisomes ranging in size from 0.5 to 3 microns. The diagram of an onion cell below shows the location of the cell wall, cytoplasm and vesicles in a typical cell; you will not be able to see much of the endoplasmic reticulum or the vacuole depicted because of their transparency. Under the microscope, you will notice the vesicles are located just along the edges of the cell, or near the top and bottom surface if you focus up and down. When you see a narrow band of moving vesicles in the center of the cell, it is located in a transvacuolar strand, which may be a handy place to study motion.

In plant cells, vesicles are transported along actin fibers by myosin motor molecules. An actin filament is composed of two intertwined actin chains, about 7 nm in diameter. An actin fiber is considered structurally polar, having a (+) end and a (-) end, and most myosin motors move only towards the (+) end of the actin fiber. In order to reverse the direction of a vesicle's motion, the vesicle must grab on to another actin fiber oriented in the opposite direction. There are at least eighteen described classes of myosin, of which three, myosin VIII, XI, and XII are found in plant cells. Some myosin motors are processive, meaning that they remain bound to an actin fiber as they move step-by-step along it (analagous to this movie animation of kinesin. Other myosins are non-processive, releasing from the actin fiber after each step. Myosin II found in muscle cells is non-processive, as illustrated in this video animation. In the muscle functional unit, there are many myosin motors acting together, so there are always some attached to the actin fiber. The myosin XI responsible for transport of plant cell vesicles is the fastest myosin known and is processive. It is not certain how many myosin molecules are attached to the surface of a vesicle or how many of those are active at one time in pulling the vesicle along an actin fiber.

In some plant cells and algal cells, a large-scale streaming motion of the cytoplasm is observed, logically called cytoplasmic streaming. This bulk flow is believed to be caused by myosin motors pulling the extensive endoplasmic reticulum along actin fibers lining the cell membrane. Many other vesicles are then dragged along with the endoplasmic reticulum. Lodish and Berk, et al. provide a detailed explanation of this process and a video of cytoplasmic streaming in the pond weed Elodea can be viewed here.

In your observations of vesicles in onion epidermal cells, you should distinguish between the random Brownian motion of vesicles that are unattached (or at least not actively moving along) actin filaments, the directed transport of vesicles by attached myosin motors, and possibly (though we are not sure this really happens in onions) bulk flow of vesicles in cytoplasmic streaming.

Methods

Making an onion slide

• Before coming to lab obtain an onion from your favorite produce store. If you have forgotten one you can try the Seven Palms deli located conveniently at Euclid and Ridge, perhaps a five minute walk from LeConte.
• Use a knife, box-cutter, razorblade or whatever other cutting tool is provided to cut out a half-inch cube from the onion.
• Take one of the lower layers (activity depends somewhat on depth) and remove the lower membrane using the forceps, this is similar to pulling off a sticker. The easier it peels off, the less damage to the cells, so try several.
• The membrane is a single layer of cells which makes it particularly clean when viewing through a microscope. It should appear translucent and should be relatively strong.
• Make a slide using this membrane
  • Place a drop of saline solution (contact lens solution works well) onto a clean slide (don't use water)
  • Place the membrane onto the drop of saline on the slide
  • Drop another drop onto the onion and cover with a cover slip
  • Blot excess liquid using a paper towel
• Mount onto microscope
• Keep in mind that the lifetime of an onion slide is about 30-60 minutes before it dries out.
• Put the remainder part of the onion into a plastic baggy and put it into the refrigerator.
• For the benefit of all future users of the refrigerator, please remove your onion when you have finished the lab. Do not leave it for the next group.

Observing cells and trapping vesicles

Scan the slide to find regions where cells aren't covered by air bubbles or badly damaged. Look for cells with an intact nucleus and some non-random motions of small vesicles. Occasionally a preparation will not show good motion and you should try another slide.

Examine patterns of motion within a cell. Some regions will show little activity, others will have large numbers of vesicles in motion. To study internal transport along actin filaments it will be helpful to find relatively isolated tracks along which small numbers of vesicles travel. Try trapping vesicles and see what happens to the movement of other vesicles along the same track. How does the vesicle behave when it is released? With a vesicle trapped, you can try moving it through the cytoplasm by moving the stage.

Your Investigation

Here are some ideas you could try:

1. How do vesicles in active transport respond to manipulation by the trap? Does stopping and releasing a vesicle result in resumed motion, motion in the opposite direction, or ceasing of motion? What effect does trapping a vesicle have on other vesicles travelling the same route?
2. Calibrate the trap stiffness using a vesicle. Many of the vesicles are similar in size to the beads you've used for calibration, but the vesicle's optical properties and the viscosity of the cytoplasm differ from the beads in water you used. By trapping a vesicle that is showing Brownian motion (not active transport), you could use the PSD method to estimate sensitivity and stiffness. (You will have to find a value from the literature for the viscosity of the cytoplasm to do your sensitivity calibration.) Or use the Equipartition method for stiffness and assume the same sensitivity you obtained with a bead. How does this compare with values obtained with beads in water?
3. Measure the velocity of vesicles in active transport. If you set the laser power low enough that it doesn't appreciably slow down motion of vesicles in internal transport and position the trap so that a vesicle passes through the center (preferably in the X or Y direction), then you can use the QPD vs. time plot to estimate the speed of the vesicle. You can use the particle tracker software to make independent measurements of velocities (see the Brownian Motion in Cells lab for more details on this).
4. Measure forces involved in active transport of vesicles. If the laser power is high enough to retard motion of the vesicle but not stop it, you might be able to use the QPD output vs. time to calculate the force that the trap is exerting on the vesicle. Or you might stop a vesicle and then reduce laser power until the vesicle can break free and look at the QPD reading at this power. This may be tricky to do. How do these measurements compare with the Stokes drag force calculated using vesicle size, velocity, and cytoplasm viscosity?

References

1. ↑ Arthur Ashkin, "Acceleration and trapping of particles by radiation pressure", Physical Rev. Let. 24(4), 156-159 (1970). This is the original paper debuting the practice of optical trapping using two opposing lasers.
2. ↑ Arthur Ashkin, Optical trapping and manipulation of neutral particles using lasers, Proc. Natl. Acad. Sci. 94,4853-4860 (1997).Ashkin describes his discovery of optical trapping and how it developed into tools of atom trapping and optical tweezers widely used in physics and biology.
3. ↑ [1] Trap forces applet by Roberto Di Leonardo, CNR-IPCF Dipartimento di Fiscica, Universita di Roma Sapienza
4. ↑ ^{4.0 4.1} K. C. Neuman and S. M. Block, "Optical Trapping," Rev. Sci. Instrum. 75(9), 2787-2809 (2004)
5. ↑ J. Bechhoefer, S. Wilson, "Faster, cheaper, safer optical tweezers for the undergraduate laboratory", Am. J. Phys., 70(4), 393-400 (2002). Concise summary of optical trapping theory. Explores trapped particle theory using Equipartition method in considerable detail.
6. ↑ J. W. Shaevitz, A practical guide to optical trapping, A concise guide to physics of trapping, principles of trap building, and theory and practical issues of trap calibration. Written while Shaevitz was a Miller Postdoc Fellow at Berkeley - he is now a professor at Princeton.
7. ↑ This data sheet for the 150mW model is the closest we could find to the 200mW model we have.
8. ↑ Manual for Thorlabs LDC 2000
9. ↑ Manual for Thorlabs TEC 2000
10. ↑ F. Gittes and C. F. Schmidt, Interference model for back-focal-plane displacement detection in optical tweezers. Optics Letters, 23(1), 7-9 (1998) Derivation of theory explaining the response of the quadrant photodiode to displacements of the trapped object.
11. ↑ F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw Hill, New York, 1965. A useful reference, available in the physics library, for understanding the autocorrelation function and Power Spectrum Density: Chap. 15, especially Secs. 6 and 10.

Other References

1. Laser trapping of microscopic particles for undergraduate experiments ;Robert Pastel,a) Allan Struthers;Am. J. Phys. 68 ~11!, November 2000;
2. Faster, cheaper, safer optical tweezers for the undergraduate laboratory ; Am. J. Phys. 70 ~4!, April 2002; John Bechhoefera) and Scott Wilson;
3. Other reprints and materials can be found on the Physics 111 Library Site