Appleyard et al - Vanderbilt University

More documents

Recommendations

Info

$' \^' I$

We found the position calibrations to be consistent above 70 mW and recommend the power spectrum method for lower powers. Because of the lack of dependence on position calibration, we used the stiffness derived from the power spectrum for a majority of the experiments. We encourage researchers and students alike to characterize their own instrument to evaluate which method works best. IV. EXPERIMENT: ROTATING E. COLI The low force regime at which optical traps work make them optimal for investigating the mechanical output of biological molecular motors. 4,20 A supply of flagellar motors that are easy to work with can be found by using the bacterium E. coli. The bacterial populations are easy to culture and simple to visualize with a light microscope, making them optimal for this laboratory environment. The tethered bacterium or rotating bacterial cell assay uses torque from the flagellar motor to rotate the body of the cell. This robust assay has been used to study chemotaxis and the biophysics of the flagellar motor. 21,22 Additionally, the visual nature of the experiment quickly captures the students’ attention. For students this assay provides access to molecular motors, highlights scientific estimation, uses the time and frequency domain representation, and exposes them to doing collaborative studies. Probing flagellar motion can seed discussion of bacterial propulsion including random walks as well as life at low Reynolds number. 23 Two characteristics that can be quantified individually with E. coli using the optical trap are the rotation frequency and stall torque of the flagellar motor. 22 In this module a weak trap can monitor rotation and a strong trap can be used to halt rotation. The ease with which measurements can be collected supports the compilation of population data and the opportunity to explore the heterogeneity in a sample. A. E. coli: Materials and methods To easily measure rotation parameters a specific strain of E. coli that can quickly attach to the coverslip is required. The KAF95 strain is nonpathogenic, exhibits only clockwise rotation, and has sticky flagellum that can attach to glass. 24 Samples of KAF95 are available to institutions uponc request. A small sample of E. coli can be grown in culture and then either frozen for future use as an inoculation or used directly in the experiment. To grow a culture, 10 mL of a solution containing 10 mg/mL Bacto-Tryptone Becton, Dickinson and Company, 5 mg/ml NaCl Sigma, and 100 g/mL ampicilin Sigma in water is inoculated with a 5–10 L aliquot of frozen KAF95. This solution is incubated in a water bath at 37 °C for 24–36 h. We suggest that instructors culture the E. coli prior to the class; the construction of the E. coli slides is simple and can be accomplished by students if facilities are available for wetlab work using biological material. To make the slides, a 15 L aliquot of the grown culture is loaded into a flow chamber assembled as described previously and allowed to incubate for 5 min to permit bacterial attachment to the coverglass surface. The flow chamber is then flushed with 300 L of motility buffer 10 mM potassium phosphate, 0.1 mM EDTA, pH 7.4 using vacuum suction to remove unattached bacteria. A 10% bleach solution should be made available for cleanup of the biological samples. Those unfamiliar with the basics of cell Fig. 6. Power spectral density of the Y axis voltage from the quadrant photodiode for a spinning E. coli showing a peak near 7 Hz, A, and a harmonic at 14 Hz, B. Inset: Raw Y axis quadrant photodiode voltage used to generate a position sensitive device, reflecting a 7 Hz rotation speed. Cartoon: Assay geometry depicting trap position for optimized stalling and monitoring solid line and a trap position that is not optimal for stall and would give 2 actual rotation speed dashed line. The distance between the trap center and point of rotation d is indicated. culture are directed to Ref. 25 for an introduction to these techniques. The first measurement uses a very weak trap to detect rotation as the bacterium occludes the beam. The trap is set to a laser power just above the lasing threshold 7 mW so trap forces will not interfere with rotation. The focus of the optical trap is placed at the edge of the zone through which the rotating bacterium sweeps. The quadrant photodiode voltage signal is collected for both the X and Y axes Fig. 6, inset. A power spectral density of a trace of the voltage signal will show a peak identifying the rotation frequency Fig. 6, label A. A second measurement seeks the minimum laser power required to stall rotation of the flagellar motor. The laser power is increased to approximately 120 mW forming a relatively stiff 0.08 pN/nm trap and a bacterium is moved into the trap where the tip of the bacteria is trapped in three dimensions and rotation is halted. The laser power is reduced until the bacterium escapes the trap and begins rotating. The approximate trap stiffness at the final power is estimated from a linear fit of previous power calibrations Sec. III. A calculation of the stall force F requires an assumption of the displacement x out of the center of the trap. The value of x can be estimated by a knowledge of the trap potential or by experimental observation of the maximum displacement at which a bead or bacterium exposed to Stokes flow falls out of the trap. We found an estimate of 100 nm to be reasonable for the displacement in our setup. The stall torque generated by the flagellar motor can then be determined by treating the trap as a point force acting perpendicular to the direction of rotation on the outer tip of the E. coli as =Fd. This determination requires a measurement of the distance d between the rotation point and the tip of the bacteria on which the trap acts. This lever arm length is typically between 1 and 3 m and can be obtained by visual inspection of images with a calibrated field of view. A simple comparison to the size of a bead offers a quick value. As a general idea of the population characteristics, a majority of the bacteria were between 2 and 3 m in length. The measurements and estimations used in this procedure provide good discussion points and experience with error estimation, 10 Am. J. Phys., Vol. 75, No. 1, January 2007 Appleyard et al. 10
Analysis can include fitting DNA stretching curves with the wormlike chain or more advanced polymer stretching models. 29,30 Fig. 7. Population distribution of rotation frequency bottom abscissa and stall torque top abscissa for a sample of 41 bacteria. The population had an average rotation speed of 5.8 Hz and an average stall torque of 3200 pN nm. and the results provide a reasonable final value of the stall torque. B. E. coli: Experimental results A student using the optical trap to measure both rotational speed and stall torque can evaluate about ten individual E. coli in an hour. Aggregating data from multiple students can provide a good examination of population characteristics. Representative population distributions of both rotation speed and torque are displayed in Fig. 7. Despite multiple “back of the envelope” assumptions, the spin rate and estimated torque are within range of previously reported values. The fundamental rotation frequency was easy to extract from both the power spectrum Fig. 6 and from the raw voltage versus time trace Fig. 6, inset. The average rotation speed in our sample population was 5.8 Hz, which is within the 2 to 9 Hz rotation speed span noted by Silverman. 26 In some cases the position of the trap relative to the rotating point provided a detector response from both ends of the bacteria, giving a fundamental frequency twice that of the actual Fig. 6, inset. Often this situation can be diagnosed from the raw voltage signal because each end of the bacteria deflects the trap differently. Stall torque values were estimated using the calculated stiffness for a 1 m bead, a 100 nm displacement, and the comparison to bead diameter method for determining the lever arm length. We measured an average torque of 3200 pN nm, on the order of the reported value of 4000 pN nm. 22 V. EXPERIMENT: DNA TETHER EXTENSION The tethered bead assay is probably the most versatile geometry in optical trapping based single molecule biophysics experiments. This geometry has been widely used with single molecules such as DNA, kinesin, RNA polymerase, and Myosin. 3,4,27,28 The classical experiment underlying the tethered bead assay is the DNA tether stretching measurement. This measurement introduces parameters such as contour length, persistence length, and effective spring constant scaling laws for entropic and enthalpic regions of stretching curves. Here we discuss a module where we stretch a DNA tether between the coverglass surface and a bead. This experiment may be approached on several different levels providing both wet lab experience in preparing the samples and physical insight into the mechanical properties of DNA. A. DNA tether stretching: Background theory The wormlike chain model has two main parameters, the contour length c and the persistence length p , and has been used to describe the elastic behavior of DNA. 29 The contour length refers to the end-to-end length of the polymer backbone under no tension, and the persistence length is the length of a segment at which there is no longer a correlation between the direction of the beginning and end of the segment. The persistence length p can be defined as p = YI k B T , where Y is the Young’s modulus of the material and I reflects the moment of inertia of the cross-section. We use the following interpolation of the wormlike chain model 29 F = k BT p 41 1 − x −2 c − 1 4 + x c, where F is the applied force and x is the end-to-end extension distance of the DNA tether. This interpolation fits the data well for p c and F5 pN. 30 Modifications to the wormlike chain model have also been applied to DNA stretching and were reviewed in Ref. 30. A comprehensive introduction to persistence length, contour length, and filament models can be found in Refs. 31 and 32. B. DNA tether stretching: Materials and methods The assay geometry arranges a 3500 base pair double stranded DNA dsDNA tether between the coverglass surface and a bead. The tether attachment is mediated by a digoxigenin/anti-digoxigenin interaction at the coverglass surface and a biotin/avidin connection to the bead. The construction of the tether geometry is split into production of the dsDNA complexes and final assembly of the tether in the flow cell. The 3500 base pair dsDNA tether complexes are constructed using a polymerase chain reaction PCR technique to amplify a segment of the M13mp18 plasmid Bayou Biolabs making multiple copies with appropriate functional ends. PCR is a common biological technique and information on the method can be found in Ref. 33. Amplification is accomplished using Taq polymerase Invitrogen. A 5 forward primer functionalized with biotin biotin-5-AAT CCG CTT TGC TTC TGA CT-3, Integrated DNA Technologies and a 5 reverse primer with digoxigenin digoxigenin-5-TTG AAA TAC CGA CCG TGT GA-3, Integrated DNA Technologies yield a tether with a biotin moiety on one end and a digoxigenin on the other. Each PCR reaction tube contains 10 L of 10 PCR buffer Invitrogen, 3 L of 50 mM MgCl 2 Invitrogen, 10 L of 2.5 mM dNTP cocktail 6 L of 100 mM dATP, 6 L of 100 mM dCTP, 6 L of 100 mM dGTP, 6 L of 100 mM dTTP, Invitrogen, 2L of Taq polymerase, and 61 L of H 2 O. To this mixture a combination of 10 L of 5 g/mL M13mp18 in a TE buffer 1 mM Tris, Sigma, 1 mM EDTA, Acros, pH 7.5 and 2 L each of the 20 M forward and reverse primers in TE buffer is added. 6 7 11 Am. J. Phys., Vol. 75, No. 1, January 2007 Appleyard et al. 11
Page 1 and 2: Optical trapping for undergraduates
Page 3 and 4: A three-axis stage Newport 562 ULTR
Page 5: Table I. Measured trap stiffness fo
Page 9 and 10: form a construction set for student

Appleyard et al - Vanderbilt University

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?