Protrusion of a Virtual Model Lamellipodium by Actin Polymerization: A Coarse-Grained Langevin Dynamics Model

We report the development of a coarse-grained Langevin dynamics model of a lamellipodium featuring growing F-actin filaments in order to study the effect of stiffness of the F-actin filament, the G-actin monomer concentration, and the number of polymerization sites on lamellipodium protrusion. The virtual lamellipodium is modeled as a low-aspect-ratio doubly capped cylinder formed by triangulated particles on its surface. It is assumed that F-actin filaments are firmly attached to a lamellipodium surface where polymerization sites are located, and actin polymerization takes place by connecting a G-actin particle to a polymerization site and to the first particle of a growing F-actin filament. It is found that there is an optimal number of polymerization sites for rapid lamellipodium protrusion. The maximum speed of lamellipodium protrusion is related to competition between the number of polymerization sites and the number of available G-actin particles, and the degree of pulling and holding of the lamellipodium surface by non-polymerizing actin filaments. The lamellipodium protrusion by actin polymerization displays saltatory motion exhibiting pseudo-thermal equilibrium: the lamellipodium speed distribution is Maxwellian in two dimensions but the lamellipodium motion is biased so that the lamellipodium speed in the direction of the lamellipodium motion is much larger than that normal to the lamellipodium motion.

[1]  L. Mahadevan,et al.  Motility powered by supramolecular springs and ratchets. , 2000, Science.

[2]  José C. M. Mombach,et al.  Single cell motion in aggregates of embryonic cells. , 1996, Physical review letters.

[3]  Berend Smit,et al.  Understanding molecular simulation: from algorithms to applications , 1996 .

[4]  E. Zamir,et al.  Components of cell-matrix adhesions. , 2001, Journal of cell science.

[5]  R. Tranquillo,et al.  A stochastic model for adhesion-mediated cell random motility and haptotaxis , 1993, Journal of mathematical biology.

[6]  George Oster,et al.  Force generation by actin polymerization II: the elastic ratchet and tethered filaments. , 2003, Biophysical journal.

[7]  J A Theriot,et al.  The Polymerization Motor , 2000, Traffic.

[8]  M. Sheetz,et al.  Periodic Lamellipodial Contractions Correlate with Rearward Actin Waves , 2004, Cell.

[9]  Thomas E. Schaus,et al.  Self-organization of actin filament orientation in the dendritic-nucleation/array-treadmilling model , 2007, Proceedings of the National Academy of Sciences.

[10]  M. McBride.  Bacterial gliding motility: multiple mechanisms for cell movement over surfaces. , 2001, Annual review of microbiology.

[11]  D. Purich,et al.  Clamped-filament elongation model for actin-based motors. , 2002, Biophysical journal.

[12]  Nicole S. Bryce,et al.  Cortactin Promotes Cell Motility by Enhancing Lamellipodial Persistence , 2005, Current Biology.

[13]  Jt Johan Padding,et al.  Theory of polymer dynamics , 2007 .

[14]  Marie-France Carlier,et al.  Forces generated during actin-based propulsion: a direct measurement by micromanipulation. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[15]  D A Lauffenburger,et al.  Mathematical model for the effects of adhesion and mechanics on cell migration speed. , 1991, Biophysical journal.

[16]  Jonathan B. Alberts,et al.  In Silico Reconstitution of Listeria Propulsion Exhibits Nano-Saltation , 2004, PLoS biology.

[17]  C S Peskin,et al.  Cellular motions and thermal fluctuations: the Brownian ratchet. , 1993, Biophysical journal.

[18]  Manfred Radmacher,et al.  Direct measurement of the lamellipodial protrusive force in a migrating cell , 2006, The Journal of cell biology.

[19]  Paul Matsudaira,et al.  Computational model for cell migration in three-dimensional matrices. , 2005, Biophysical journal.

[20]  J. D. Doll,et al.  Generalized Langevin equation approach for atom/solid-surface scattering: General formulation for classical scattering off harmonic solids , 1976 .

[21]  P. Chaikin,et al.  Measurement of the elasticity of the actin tail of Listeria monocytogenes , 2000, European Biophysics Journal.

[22]  Julie A. Theriot,et al.  Loading history determines the velocity of actin-network growth , 2005, Nature Cell Biology.

[23]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[24]  Leah Edelstein-Keshet,et al.  Regulation of actin dynamics in rapidly moving cells: a quantitative analysis. , 2002, Biophysical journal.

[25]  J. Jeon,et al.  Polymer confinement and bacterial gliding motility , 2005, The European physical journal. E, Soft matter.

[26]  Robert C. Armstrong,et al.  Dynamics of polymeric liquids: Kinetic theory , 1987 .

[27]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[28]  Erwin Frey,et al.  Actin-binding proteins sensitively mediate F-actin bundle stiffness , 2006 .

[29]  K. Herrmann,et al.  MONTE CARLO SIMULATION OF ACTIN FILAMENT BASED CELL MOTILITY , 2003 .

[30]  M. Stevens.  Simple simulations of DNA condensation. , 2001, Biophysical journal.

[31]  J. Rivas,et al.  Chemical and rheological properties of an extracellular polysaccharide produced by the cyanobacterium Anabaena sp. ATCC 33047. , 2000, Biotechnology and bioengineering.

[32]  Alex Mogilner,et al.  Multiscale Two-Dimensional Modeling of a Motile Simple-Shaped Cell , 2005, Multiscale Model. Simul..

[33]  Hans G. Othmer,et al.  A continuum model of motility in ameboid cells , 2004, Bulletin of mathematical biology.

[34]  J. Käs,et al.  Neuronal growth: a bistable stochastic process. , 2006, Physical review letters.

[35]  James L. McGrath,et al.  Steps and fluctuations of Listeria monocytogenes during actin-based motility , 2000, Nature.

[36]  Julie A. Theriot,et al.  The rate of actin-based motility of intracellular Listeria monocytogenes equals the rate of actin polymerization , 1992, Nature.

[37]  Denis Wirtz,et al.  Mechanics and dynamics of actin-driven thin membrane protrusions. , 2006, Biophysical journal.

[38]  P. Chaikin,et al.  An elastic analysis of Listeria monocytogenes propulsion. , 2000, Biophysical journal.

[39]  Marileen Dogterom,et al.  Direct measurement of force generation by actin filament polymerization using an optical trap , 2007, Proceedings of the National Academy of Sciences.

[40]  A. Czirók,et al.  Exponential Distribution of Locomotion Activity in Cell Cultures , 1998, physics/9902022.

[41]  D. L. Taylor,et al.  The actin-based nanomachine at the leading edge of migrating cells. , 1999, Biophysical journal.

[42]  T D Pollard,et al.  Molecular mechanisms controlling actin filament dynamics in nonmuscle cells. , 2000, Annual review of biophysics and biomolecular structure.

[43]  S. Satyanarayana,et al.  Shape and motility of a model cell: a computational study. , 2004, The Journal of chemical physics.

[44]  H. Isambert,et al.  Flexibility of actin filaments derived from thermal fluctuations. Effect of bound nucleotide, phalloidin, and muscle regulatory proteins , 1995, The Journal of Biological Chemistry.

[45]  Marie-France Carlier,et al.  The dynamics of actin-based motility depend on surface parameters , 2002, Nature.

[46]  John G. Collard,et al.  Tie-2-dependent activation of RhoA and Rac1 participates in endothelial cell motility triggered by angiopoietin-1. , 2003, Blood.