Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session W22: Focus Session: Microtubules and Molecular Motors |
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Sponsoring Units: DBP GSNP Chair: Beate Schmittmann, Virginia Tech Room: LACC 409B |
Thursday, March 24, 2005 2:30PM - 3:06PM |
W22.00001: Molecular Motors with Finite and Infinite Processivity on Disordered Tracks Invited Speaker: The dynamics of molecular motors moving on a heterogeneous tracks, like DNA or RNA will be discussed. Motivated by recent single molecule experiments, a molecular motor which is using chemical energy to move along the substrate while an external force opposes its motion will be considered. First, the case of infinite processivity, in which the motor is assumed to remain bound to the track, will be considered. We show that near the stall force the dynamics of the motor become anomalous due to the heterogeneous track. Then the effect of finite processivity, where motors occasionally detach from the track will be discussed. Here we show that motors that remain on the track for long times can become localized at preferred positions. The conditions under which localization occurs will be discussed. [Preview Abstract] |
Thursday, March 24, 2005 3:06PM - 3:18PM |
W22.00002: Single Actin Filaments Pushing Loads: Growth Kinetics and Fluctuations Ben O'Shaughnessy, Dimitrios Vavylonis Many types of cellular motions are driven by the polymerization and depolymerization of actin filaments growing or shrinking against cellular loads. Actin growth involves polymerization of ATP-actin monomers followed by fast ATP hydrolysis and slow phosphate release generating unstable ADP-actin. We present Monte Carlo simulations and analytical theory describing growth kinetics of single filaments pushing against external loads. Our work is related to earlier work by Mogilner and Oster ({\it Biophys.J.} {\bf 71}, 3030, 1996). We find the behavior near stall is influenced by (1) hydrolysis and phosphate release and (2) fluctuations in growth rates. Fluctuations become important near stall conditions, where growth rate vanishes. We find that under zero external load actin filaments have a long fluctuation-stabilized ATP/ADP-Pi cap at the critical concentration (the corresponding stall situation) whose origin is the slow rate of Pi release. As a result, filament growth rate exhibits a smoothed slope discontinuity. Fluctuations, described by the length diffusivity, exhibit a pronounced smoothed discontinuity in magnitude whose origin is uncapping events exposing rapidly depolymerizing ADP-actin. The presence of external loads perturbs the polymerization rate constants, leading to modified kinetics which depend on filament length and imposed force-distance profile. [Preview Abstract] |
Thursday, March 24, 2005 3:18PM - 3:30PM |
W22.00003: Filament depolymerisation by motor proteins Gernot Klein, Karsten Kruse, Frank Juelicher Many active processes in cells are driven by highly specialized motor proteins, which interact with filaments of the cytoskeleton. Members of the Kin-13 kinesin subfamily are able to interact specifically with filament ends and induce depolymerisation of the filaments ends. Recent in vitro assays and single molecule studies have shown, that MCAK accumulates at both ends of stabilized microtubules and induces depolymerisation while at the same time MCAK molecules do not generate directed motion along the microtubules [1]. We analyse both, a stochastic model and a generic mean-field description of this process. We discuss conditions under which motors dynamically accumulate at the filament end. Such a dynamic accumulation occurs for processive cutting, which implies, that the motor can remain attached to the shrinking edge after subunit removal. For processive cutting, the depolymerisation speed as a function of the bulk motor concentration can exhibit a maximum for intermediate motor concentration. For high motor processivity a dynamic instability can occur. We discuss our results in relation to recent experiments on Kin-13 motor proteins [2]. [1] A.W. Hunter, et al., Mol. Cell \textbf{11, }445 (2003) [2] G.Klein, et al., submitted [Preview Abstract] |
Thursday, March 24, 2005 3:30PM - 3:42PM |
W22.00004: Self-assembly of microtubules and motors Igor Aranson, Lev Tsimring We derive a model describing spatio-temporal assembly of an array of microtubules interacting via molecular motors. Starting from a stochastic model of inelastic polar rods with a generic anisotropic interaction kernel we obtain a set of equations for the local rods concentration and orientation. At large enough mean density of rods and concentration of motors, the model describes orientational instability. We demonstrate that the orientational instability leads to the formation of vortices and (for large density and/or kernel anisotropy) asters seen in recent experiments. [Preview Abstract] |
Thursday, March 24, 2005 3:42PM - 3:54PM |
W22.00005: Stochastic Dynamical Modeling of Single-Molecular Properties of Actomyosins Hyung-June Woo A minimal stochastic dynamical model of the free energy transduction and force generation in non-processive motor protein complexes such as actomyosins will be discussed. The overall operation of a motor is described as diffusive motions of the system on two conformational free energy curves coupled to each other by ATP hydrolysis and phosphate release reactions. The key structural features of the myosin head protein responsible for the work production is thus explicitly incorporated into the two free energy profiles. Simple analytical solutions of the stationary states yield characteristic nonequilibrium distributions of forces on the nanoscale, which agree well with results of recent single-molecular experiments. [Preview Abstract] |
Thursday, March 24, 2005 3:54PM - 4:06PM |
W22.00006: Noninvasive probes of mitochondrial molecular motors Dharmakeerthna Nawarathna, David Warmflash, John Miller, James Claycomb We report on a noninvasive method of probing mitochondrial molecular motors using nonlinear dielectric spectroscopy. It has been found previously that enzymes in the plasma membrane, particularly H+ ATPase, result in a strong low frequency (less than 100 Hz) nonlinear harmonic response. In this study, we find evidence that molecular motors located in the inner membranes of mitochondria cause the generation of harmonics at relatively high frequencies (1 - 30 kHz). In particular, we find that potassium cyanide (KCN), a respiratory inhibitor that binds to cytochrome c oxidase and thus prevents transport of protons across the mitochondrial inner membrane, suppresses the harmonic response. We observe this behavior in yeast (S. cerevisiae), a eucaryote that typically contains about 300 mitochondria, and B. indicas, a procaryote believed to be related to the ancient ancestor of mitochondria. Our current modeling efforts are focusing on a Brownian ratchet model of the F0 unit of ATP synthase, a remarkable molecular turbine driven by the proton gradient across the mitochondrial inner membrane. [Preview Abstract] |
Thursday, March 24, 2005 4:06PM - 4:18PM |
W22.00007: A Monte Carlo study of some non-equilibrium driven models and their contribution to the understanding of molecular motors Irina Mazilu, Mark Allen, Christopher Gaiteri From the point of view of a physicist, a bio-molecular motor represents an interesting non-equilibrium system and it is directly amenable to an analysis using standard methods of non-equilibrium statistical physics. We conduct a rigorous Monte Carlo study of three different driven lattice gas models that retain the basic behavior of three types of cytoskeletal molecular motors. Our models incorporate novel features such as realistic dynamics rules and complex motor-motor interactions. We are interested in gaining a deeper understanding of how various parameters influence the macroscopic behavior of these systems. We answer the following questions: Does the system undergo a phase transition? If so, what are the parameters that determine this phase transition? What is the density profile of the system and what are the particle currents in the system? What is their dependence on various types of rates? How is the system behavior influenced by boundary conditions? [Preview Abstract] |
Thursday, March 24, 2005 4:18PM - 4:30PM |
W22.00008: Stochastic Mechanochemistry for Processive Motor Proteins: Kinesin Crouches before Sprinting. Young C. Kim, Michael E. Fisher Experiments by Block and coworkers (2003) applied assisting, resisting, and sideways loads {\boldmath $F$}$=(F_{x},F_{y},F_ {z})$ to single-molecules of kinesin as they moved along a microtubule (MT) taking steps of size $d\simeq 8.2$ nm. The velocity, $V_{x}$, and the randomness were observed as functions of {\boldmath $F$} and [ATP]. To uncover substeps and intermediate motions from such data, we have extended a discrete-state stochastic model, previously applied to kinesin$^ {1}$ and myosin V,$^{2}$ to allow for the {\em vectorial} loading of processive motors by invoking a {\em three}- dimensional ``energy landscape'' with a potential $\Phi(\mbox {\boldmath $F$})$.$^{3}$ The size of the attached bead and the resulting angle of the motor's tether relative to the track play a crucial role. The analysis for kinesin then indicates that on binding ATP (and, possibly, catalysing hydrolysis, etc.) the motor `crouches,' i.e., the point of attachment of the tether moves {\em downwards} (toward the MT) by 0.5-0.8 nm but {\em forwards} by only 0.1-0.2 nm, before completing a rapid swing of close to 8 nm. Unlike the scalar, $F_{x}$-only, analysis,$^{1}$ this is consistent with the observations of Higuchi and coworkers. Furthermore, assisting ({\em i.e.}, forward) loads are opposed since the `upwards' component, $F_{z} $, is enhanced by $\sim$2 pN which {\em reduces} the velocity.\\ 1. M.\ E.\ Fisher and A.\ B.\ Kolomeisky, PNAS USA {\bf 98}, 7748 (2001).\\ 2. A.\ B.\ Kolomeisky and M.\ E.\ Fisher, Biophys.\ J.\ {\bf 84}, 1642 (2003).\\ 3. M.\ E.\ Fisher and Y.\ C.\ Kim, Biophys.\ J.\ {\bf 86}, 527a, 2738-Plat.\ (2004). [Preview Abstract] |
Thursday, March 24, 2005 4:30PM - 4:42PM |
W22.00009: Hybrid molecular motors - Brownian and power stroke models Brian Geislinger, Ryoichi Kawai Whether the actin-myosin motor protein system in muscle utilizes Brownian ratchet effects to create directed motion or a more traditional power stroke event has been a matter of debate. We investigate a two dimensional ratchet designed specifically with this system in mind. We specifically look at two state (Brownian) and three state (hybrid Brownian and power stroke) variants using numerical simulations and analytical calculations. We also examine the collective effects these motors would experience in an arrangement comparable to that which would occur in real muscle tissue. [Preview Abstract] |
Thursday, March 24, 2005 4:42PM - 4:54PM |
W22.00010: Modeling studies of induced internal transmembrane potentials and molecular motors in live cells Vijayanand Vajrala, James Claycomb, John Miller Many cellular functions, including motility and receptor regulation, can be affected by applied electric fields, which perturb the transmembrane potentials across the plasma, mitochondrial, and nuclear membranes. We use the finite element method (FEM) to model the electromagnetic responses of the cell, cytoplasm, and intracellular membranes. In addition, we utilize Brownian ratchet models of molecular motors, notably the F0 subunit of ATP synthase, in order to interpret recently observed nonlinear response data. This remarkable molecular turbine is driven by the potential across the mitochondrial inner membrane. Induced changes in potentials across the plasma and mitochondrial membranes, exposed to various applied field amplitudes and frequencies, are studied in detail. The spatial variations of the transmembrane potentials are modeled for spheroidal, weakly conducting membrane shells enclosing a conductive cytoplasm with internal organelles. The modeling studies discussed here are compared to nonlinear harmonic response measurements of live cells. [Preview Abstract] |
Thursday, March 24, 2005 4:54PM - 5:06PM |
W22.00011: Building a Theoretical Model of Bidirectional Transport. Dmitri Petrov, Clare Yu, Steven Gross Intracellular transport system plays a role in many vital functions of a living cell. Most of the long range transport occurs on the microtubule based network. Cargos are propelled by two families of molecular motors of opposite polarity. Often both types of motors are present on a cargo and the transport is achieved by moving the cargo bidirectionally with net displacement in the desired direction. This implies a high degree of coordination inside the motor complex. Our goal is to gain an understanding of the mechanisms that are responsible for controlling and coordinating the activity of molecular motors. We attempt to achieve this goal by studying the tracking data of lipid droplets in a Drosophila embryo at different stages of development. We have developed a tool that interprets the tracking data as a series of regions of constant linear velocity. We believe that these regions correspond to different states of the motor complex and that a theoretical model of bidirectional transport can be developed by applying statistical methods to study these states and transitions between them. [Preview Abstract] |
Thursday, March 24, 2005 5:06PM - 5:18PM |
W22.00012: Hinge-Bending Transitions during F1 ATPase Function: Ligand-Rocked Brownian Motion? Caroline Ritz-Gold The $\beta $-subunit hinge of the F1-ATPase enzyme is a type of allosteric protein, with alternative (T-open) and [R-closed] states. In the absence of an inducing ligand, such as [ATP], the hinge is on a ground-state energy surface, whose minimum dictates the (open) state. In the presence of [ATP], it is on an excited-state surface, whose minimum now dictates the [closed] state. Thus, during the F1 ATPase catalytic cycle, the hinge undergoes two opposite bending transitions. First, it is driven by [ATP] into the excited-state force-balanced [closed] state. After loss of [$\gamma $-Pi], it relaxes back to the (open) state. We study these transitions by regarding the $\beta $-subunit hinge as a type of Brownian particle moving in a double-well potential energy function. We find that [ATP] binding rocks (tilts) this energy function ``forward,'' biasing diffusion of the particle towards the [closed] state. Likewise, loss of [$\gamma $-phosphate] rocks it ``back,'' biasing diffusion toward the (open) state. We conclude that regarding the $\beta $-subunit hinge as a ligand-rocked Brownian particle may yield physical insight into operation of this molecular motor. [Preview Abstract] |
Thursday, March 24, 2005 5:18PM - 5:30PM |
W22.00013: Behavior of T-Tubulin-Interactions at Low Concentrations of Colchicine in the Microtubule Steady State Mitra Shojania Feizabadi, William B. Spillman Microtubules are the target for a large number of anti-mitotic agents including colchicine. Colchicine is a well studied inhibitor that is believed to act by disrupting the microtubule requirements for chromosome movement during mitosis. The mechanism of action of colchicine in vitro and at low concentration is due to kinetic stabilization of spindle microtubule dynamics. In this study we investigate the behavior of free T-tubulin concentration in the microtubule steady state and in the presence colchicine. We assume that there is an excess of GTP (guanosine tri-phosphate) available in the solution, and that the D-tubulin in the solution will exchange its unit of GDP (guanosine di-phosphate) with a unit of GTP. By numerical analysis, the concentration of T-tubulin in the steady state as a function of regeneration rate was investigated in the presence and absence of colchicine. Our results show that low concentration of colchicine in the steady state does not significantly alter the amount of free total T-tubulin concentration or the polymer mass, in good agreement with experimental observations. [Preview Abstract] |
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