Investigation of Molecular Level Stress-Strain Relationships in Systems of Entangled F-actin by Combined Force-Measuring Optical Tweezers and Fluorescence Microscope

Kent Lee, Janet Chao, & Rae M. Robertson-Anderson University of San Diego

Abstract Actin plays a major role in cell structure, cell motility, vesicle and organelle transport, and muscle contraction. Actin’s ability to play these major roles is a direct consequence of the intricate relationship between stress and strain in a variety of filamentous actin (F-actin) networks. A thorough understanding of the unique stress-strain relationships in complex F-actin networks at the molecular-level is currently lacking despite the importance of such networks to fields such as biomimetic material engineering and cell biology1,2. Here we develop novel single-molecule instrumentation that combines dual-trap force-measuring optical tweezers with fluorescence microscopy to enable simultaneous characterization of intermolecular forces and molecular dynamics within F-actin networks. This instrumentation is combined with a novel technique in which single F-actin “probes” are used to apply molecular-level strains and measure induced stress within entangled F-actin systems while the deformations and dynamics of surrounding fluorescent-labeled filaments are simultaneously imaged. Specifically, a fluorescent-labeled, microsphere-conjugated probe filament is held by its ends via dual optical traps, and the force induced on the probe is measured as it is moved through a network of selectively-labeled entangled F-actin by using a nanoprecison piezoelectric stage to move the sample chamber relative to the traps. Fluorescence microscopy is used simultaneously to image the dynamics of the moving probe as well as the surrounding labeled molecules subject to the applied strain. Specific bioconjugation of the fluorescent polystyrene microspheres to the ends of labeled F-actin is achieved by carbodiimide attachment of gelsolin to microspheres and combining gelsolin-coated microspheres with fluorescent-labeled actin. This powerful single-molecule technique allows simultaneous measurement of intermolecular forces and dynamics and deformations of single molecules, providing the much needed link between stress and strain at the molecular level in complex F-actin networks.

1. Pollard, T. D.; Cooper, J. A., Actin, a Central Player in Cell Shape and Movement. Science 2009, 326 (5957), 1208-1212. 2. Gardel, M. L.; Kasza, K. E.; Brangwynne, C. P.; Liu, J.; Weitz, D. A., Chapter 19: Mechanical response of cytoskeletal networks. Methods Cell Biol 2008, 89, 487-519 3. Ferrer, J. M.; Lee, H.; Chen, J.; Pelz, B.; et al, Measuring molecular rupture forces between single actin filaments and actin-binding proteins. PNAS 2008, 105 (27),

9221-9226. 4. Suzuki, N.; Miyata, H.; Ishiwata, S.; Kinosita Jr, K., Preparation of Bead-Tailed Actin Filaments: Estimation of the Torque Produced by the Sliding Force in an In Vitro

Motility Assay. Biophysical Journal 1996, 70, 401-408. 5. Shimozawa, T.; Ishiwata, S., Mechanical Distortion of Single Actin Filaments Induced By External Force: Detection by Fluorescence Imaging. Biophysical Journal 2009,

96 (3) 1036-1044. 6. Robertson, R.M.; Smith, D. E., Macromolecules 2007, 40 (9), 3373-3377. 7. Robertson, R.M.; Smith, D. E., Physical Review Letters 2007, 99 (12).

References

Force Detection and Calibration

Because optical traps behave similar to a spring, the force exerted on a trapped object can be described with Hooke’s Law, F = -kx, where x is the deflection of the laser forming the trap (measured using PSD). Before using a trap for force detection, it must be calibrated to find the trap stiffness k along each axis. To do this, we need to relate a known force on a trapped object to the measured laser deflection along each axis. The drag force on a microsphere in water can be accurately calculated using Stoke’s Drag Theorem, F=6prhv, where r is radius of the object, h is dynamic viscosity (10-3 Ns/m2 for water) , and v is the velocity of the object. The ratio of this calculated force versus the measured trap deflection gives us the trap stiffness (F/x = k) and thus the calibration for the trap. To use this method, we trap a microsphere (2-mm in diameter, in a water solution) and move the piezoelectric stage sinusoidally in either the x or y direction (see top figure) according to the equation s(t) = 14.85sin(5t) , where s is in mm and t is in seconds. The position of the stage, the trap deflection, and the time are recorded at a rate of 1 kHz using Labview. The stage velocity (and thus the velocity of the trapped microsphere) v(t) is calculated by differentiating the stage position (x(t) or y(t)) with respect to time. The stage velocity and measured PSD signal (laser deflection) versus time are plotted for both the x-direction (top) and y-direction (bottom). Both stage velocities are reduced by a factor of 1000 to make the scales of velocity and laser deflection comparable. The average trap constants (using 10 trials of 10 seconds each for each axis) are kx = 94 pN/V and ky = 115 pN/V for x and y respectively. The two trap constants are very similar indicating the symmetry of the trap, and values are comparable to optical traps we have used previously that lack fluorescence detection and two-axis force measurement capabilities6,7.

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F-actin Preparation and Imaging

Instrumentation

A highly modified inverted fluorescence microscope (Olympus IX71) with 1.2 NA 60X objective and 1.4 oil immersion condensor is the base for this instrument. To visualize 488-Phalloidin-labeled actin filaments, a mercury arc lamp (Nikon) is combined with a set of optical filters to specifically illuminate the sample chamber with 480 nm light for excitation and pass 535 nm fluorescence emission from the sample to a high speed CMOS camera (Hamamatsu). The digital camera and LED light source can be used for brightfield sample visualization to facilitate preparation and manipulation of experimental conditions with reduced photobleaching effects. A flipper mirror allows fast switching between brightfield and fluorescence imaging. A 1064 nm Nd:Yag DPSS laser (CrystaLaser) provides the electromagnetic gradient to trap dielectric particles. A polarization beam splitter is used to split the infrared signal to form two optical traps of equal strength. A dichroic is used to direct the focused laser onto the sample chamber and eliminate infrared backscatter/reflection. A piezoelectric tip-tilt mirror (PhysikInstrumente) allows precise steering of one optical trap. Two separate two-axis position sensing detectors (Pacific Silicon Sensors) track the laser deflection along both axes from each trap to determine the force exerted on a trapped object. A piezoelectric stage (Mad City Labs) is used to make precise movements of the sample chamber.

High Speed Prolonged Imaging

To enable visualization of F-actin dynamics, F-actin is labeled with Acti-stain-488-phalloidin at a 1:1 molar ratio. Fluorescence microscopy combined with a high speed CMOS camera (~200 ms exposure) allows for detection of fast dynamics. The combined excitation due to the focused trapping laser and fluorescence excitation light source can increase the photobleaching rate of the 488-phalloidin, which can hinder the instrumentation’s measurement ability. To counter photobleaching, oxygen scavengers (glucose, glucose oxidase, catalase, and β-mercaptoethanol) have been added to the sample chamber, resulting in reduced photobleaching rate and extended sample imaging time of up to 10 minutes of visualization before photobleaching (well within the time frame of proposed measurements).

Conjugating Microspheres to F-actin

Carboxylated microspheres (1 μm in diameter) are covalently conjugated with fluorescent BSA and gelsolin by carbodiimide activation3,4. The fluorescent BSA coats the microsphere to allow fluorescence imaging of the microsphere while gelsolin, an actin capping protein, allows the F-actin to bind to the microsphere. Because the carboxylated microspheres can be trapped by the optical tweezers, they serve as “handles” for manipulating the F-actin probe. Gelsolin is only able to cap the pointed end of F-actin, so to form a second “handle”, microspheres coated with fluorescent BSA and myosin (able to bind to either end of F-actin) are introduced into the sample chamber5. The two distinct microspheres attached to either end of an actin filament create the probe.

Experimental Schematic

The relationship between stress and strain in systems of entangled F-actin can be studied by trapping a fluorescently labeled actin filament with two optical tweezers before measurement (Figure A) and vertically translating the trapped filament during measurement (Figure B). Deformations of surrounding fluorescent-labeled filaments are visualized by fluorescence microscopy while the force responsible for the deformations is simultaneously measured by the traps. The measured force is compared with the deformation visualized to discover the unique and complex relationships between stress and strain in systems of entangled F-actin.

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Actin Polymerization & F-actin Length Distribution

Actin filaments were formed via polymerization of actin monomers (Cytoskeleton) from rabbit skeletal muscle. Polymerization was carried out by incubating actin monomers in F-buffer (5 mM Tris-HCl, 0.2 mM CaCl2. 50 mM KCl, 2 mM MgCl2, 1.2 mM ATP, 0.5 mM DTT) for 24 hours at 40

C. Following polymerization, Acti-stain-488-phalloidin (Cytoskeleton) is added with a 1:1 molar ratio to stabilize F-actin, prevent depolymerization, and enable visualization of filaments. The average length of the filaments is 7 μm with a distribution width of 4 μm. The lengths achieved are long enough to (1) be captured and manipulated with the dual traps without trap interference, and (2) form a sufficient number of entanglements at modest concentration levels. The distribution is relatively well-controlled allowing us to better relate the dynamics and forces measured to the filament length.

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