Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session L16: Focus Session: Brownian Motors |
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Sponsoring Units: DBP Chair: Martin Bier, East Carolina University Room: Morial Convention Center 208 |
Tuesday, March 11, 2008 2:30PM - 3:06PM |
L16.00001: Stochastic path integrals and geometric theory of mesoscopic stochastic pumps and reversible ratchets. Invited Speaker: A variety of stochastic systems, from enzyme kinetics to epidemiology, exhibit pump-like behaviors, where adiabatic changes of parameters result in a nonzero directed current through the system. Using the stochastic path integral technique from mesoscopic physics, we have been able to relate these and similar phenomena to geometric effects in mesoscopic stochastic kinetics and construct their unifying theory. In the talk, this methodology will be demonstrated on three examples: (1) an adiabatic pump effect in the evolution of a Michaelis-Menten enzyme, treated as a classical two-state stochastic system; (2) a reversible ratchet; and (3) a related novel phenomenon in a previously unexplored domain, namely the SIS epidemiological model. In all of these examples, pump-like currents follow from very similar geometric phase contributions to the effective action in the stochastic path integral representation of the moment generating functional, and our construction provides the universal technique for identification, prediction, and calculation of these currents in an arbitrary mesoscopic stochastic framework. [Preview Abstract] |
Tuesday, March 11, 2008 3:06PM - 3:18PM |
L16.00002: ABSTRACTS WITHDRAWN |
Tuesday, March 11, 2008 3:18PM - 3:30PM |
L16.00003: Failure of Overdamped Models for Buttiker-Landauer Heat Engine: Molecular Dynamics Simulation Ronald Benjamin, Ryoichi Kawai A spatially inhomogeneous temperature profile in presence of a periodic potential leads to directed current of Brownian particles, commonly known as B{\"u}ttiker-Landauer ratchet. Under a small external load the system can do work as a heat engine. Overdamped models, neglecting inertial effect ($m=0$), predict that the engine can reach Carnot efficiency. On the other hand, the overdamped limit ($m\rightarrow 0$) predicts the opposite due to the kinetic energy contribution to the heat transfer, suggesting that $m=0$ is mathematically a singular point. A phenomenological argument predicts that the heat from the hot to the cold reservoir diverges as $1/\sqrt{m}$ [1,2]. We confirmed this singular behavior by Molecular Dynamics (MD) simulation and also by numerically solving the corresponding inertial Langevin equation. We obtain good agreement between the MD simulation and the inertial Langevin equation whereas the solution of the overdamped Langevin equation qualitatively disagrees with them. We also confirmed, from the numerical simulation, that the efficiency of the engine does not reach the Carnot limit. \newline [1] I. Derenyi and R. D. Astumian, Phys. Rev.E {\bf 59}, R6219 (1999). \newline [2] T. Hondou and K. Sekimoto, Phys. Rev. E {\bf 62}, 6021 (2000). [Preview Abstract] |
Tuesday, March 11, 2008 3:30PM - 3:42PM |
L16.00004: Modeling an efficient Brownian heat engine Mesfin Asfaw Taye We investigate the effect of subdividing the ratchet potential on the performance of a tiny Brownian heat engine that modeled as a Brownian particle hopping in a viscous medium in a sawtooth potential (with or without load) assisted by $\it {alternately}$ placed hot and cold heat baths along its path. We obtain analytic expression for the steady state current. The expressions for velocity, efficiency and coefficient of performance of refrigerator are reported for different number of barrier subdivisions. We find that the velocity, the efficiency and the coefficient of performance of the refrigerator maximize as the number of barrier subdivisions increase. [Preview Abstract] |
Tuesday, March 11, 2008 3:42PM - 4:18PM |
L16.00005: Trajectories of a Brownian Motor Invited Speaker: Many bio-molecular motors are dimers that move by a ``hand-over-hand'' mechanism along polar bio-polymeric tracks. Examples include kinesin, that ``walks" on microtubule and myosin V that ``walks" on actin. These molecular motors share two important symmetries. Typically the motor dimers have approximate mirror symmetry, and their tracks have translational, but not mirror, symmetry. Here we use a trajectory approach to analyze a minimal model for a generic dimeric motor that moves on a polymer track incorporating these two symmetry features. The analysis focuses of the relative probabilities of forward, reverse, backward, backward reverse trajectories and provides an experimentally accessible measure of the relative importance of a ``Brownian motor'' vs. ``Power stroke'' mechanism. Reciprocal relations, similar to those derived for the linear regime by Onsager for the fluxes (generalized velocities), hold for arbitrary magnitude forces (i.e.,far from the linear regime) for the net probabilities for stepping and for chemical reaction. [Preview Abstract] |
Tuesday, March 11, 2008 4:18PM - 4:30PM |
L16.00006: ABSTRACT WITHDRAWN |
Tuesday, March 11, 2008 4:30PM - 4:42PM |
L16.00007: Nonequilibrium Fluctuations and Mechanochemical Couplings of a Molecular Motor Andy Lau, David Lacoste, Kirone Mallick We investigate theoretically the non-equilibrium features of a single processive motor operating far from equilibrium using an externsion of the two-state model introduced by Kafri {\em et al} [Biophys.\ J.\ {\bf 86}, 3373 (2004)]. By including an important variable, namely, the number of ATP consumed, we construct a thermodynamic framework, which allows us to characterize the ATP consumption rate of a motor, its run length, and its thermodynamic efficiency. Additionally, with the aid of the Fluctuation Theorem, we analyze the violations of Einstein and Onsager relations as functions of generalized forces. Our main results are (i) one of the Einstein relations holds near stalling, (ii) the degree by which the Onsager symmetry is broken is largely determined by the underlying asymmetry of the substrate, (iii) kinesin's maximum efficiency and its maximum violation of Onsager symmetry occur roughly at the same energy scale, corresponding to that of an ATP hydrolysis ($\sim 20\,k_B T$). [Preview Abstract] |
Tuesday, March 11, 2008 4:42PM - 4:54PM |
L16.00008: Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability Bo Sun, Yohai Roichman, Allan Stolarski, David G. Grier We demonstrate both experimentally and theoretically that a colloidal sphere trapped in an optical tweezer does not come to equilibrium, but rather reaches a steady state in which its probability flux traces out a toroidal vortex. This non-equilibrium behavior can be ascribed to non-conservative optical forces and constitutes a particularly simple thermal ratchet. We briefly discuss ramifications of this effect for previous experiments in which optical tweezers have been treated as conservative potential energy wells. [Preview Abstract] |
Tuesday, March 11, 2008 4:54PM - 5:06PM |
L16.00009: Anomalous single-particle diffusion in a tilted washboard potential Ke Xiao, Yael Roichman, Sanghyuk Lee, David Grier A corrugated optical vortex acts as a tilted washboard potential for micrometer-scale colloidal particles. A single particle circulating around a corrugated optical vortex undergoes normal diffusion in the limit of strong driving and high temperatures. In the opposite limit, a particle becomes localized. When the effective barrier height is comparable to the thermal energy scale, the particle switches intermittently between stationary and running states. This intermittent switching results in a giant enhancement of the particle's effective self-diffusion coefficient, which has been predicted theoretically and demonstrated experimentally. The observed enhancement is at least one order of magnitude larger than predicted. Simulations of this system reveal that, contrary to predictions, the single particle undergoes anomalous diffusion, and that this explains the unexpectedly large enhancement of the thermally driven fluctuations. In particular, we show that giant diffusivity arises from the competition between sticking and running states, and can be related to the anomalous diffusion characteristics. We show that the system crosses over from superdiffusive behavior to subdiffusion as the driving increases relative to the barrier height, in agreement with experiments. [Preview Abstract] |
Tuesday, March 11, 2008 5:06PM - 5:18PM |
L16.00010: New Proposed Mechanism for Actin-Polymerization-Mediated Propulsion Kun-Chun Lee, Andrea Liu An important component of the cellular cytoskeleton is F-actin, a biopolymer whose non-equilibrium self-assembly is key to the process of cell crawling. We have reported previously how the polymerization and branching of F-actin near the cell membrane drives cell crawling using a physically-consistent Brownian Dynamics model. Here we show that the creation of new polymerizing filaments by the branching process leads to a steady-state concentration profile of actin away from the moving surface. This non-equilibrium concentration profile is associated with an osmotic pressure profile. The gradient of the osmotic pressure, evaluated at the surface, is the force density on the actin. This force pushes actin backwards, away from the surface. By Newton's third law, this force has a reaction force on the disk; this is the force pushing the disk forwards. [Preview Abstract] |
Tuesday, March 11, 2008 5:18PM - 5:30PM |
L16.00011: Stochastic Regulation of Actin Bundles Growth Dynamics Pavel Zhuravlev, Yueheng Lan, Garegin Papoian Actin polymerization in living cells exemplifies biological dynamical processes where mechanics is intrinsically coupled to chemistry. Modeling the dynamics of biochemical reaction networks may by itself be challenging, because ordinary chemical kinetics is often inapplicable when a small copy number of individual proteins are involved. Instead, to treat large fluctuations, the reaction dynamics should be computed with stochastic methods. We have developed an extensible mechano-chemical model describing the dynamics of actin bundle growth and retraction, where all reaction and diffusion processes are treated stochastically. We have applied our computational algorithm to study the dynamics of filopodia, where polymerization rate at the tip is coupled to the membrane force and fluctuations. Our approach allows to investigate how a particular regulatory protein, participating in the relevant signaling network, influences the distribution of filaments in the bundle, growth and retraction rates and other dynamical characteristics. Among these proteins, the most interesting are capping proteins (that block polymerization), formins (that promote polymerization), fascins (that connect the filaments in the bundle together) and myosins (molecular motors that have been observed in filopodia and may participate in active transport to the tip). [Preview Abstract] |
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