Force-velocity relation for actin-polymerization-driven motility from Brownian dynamics simulations.

We report numerical simulation results for the force-velocity relation for actin-polymerization-driven motility. We use Brownian dynamics to solve a physically consistent formulation of the dendritic nucleation model with semiflexible filaments that self-assemble and push a disk. We find that at small loads, the disk speed is independent of load, whereas at high loads, the speed decreases and vanishes at a characteristic stall pressure. Our results demonstrate that at small loads, the velocity is controlled by the reaction rates, whereas at high loads the stall pressure is determined by the mechanical properties of the branched actin network. The behavior is consistent with experiments and with our recently proposed self-diffusiophoretic mechanism for actin-polymerization-driven motility. New in vitro experiments to measure the force-velocity relation are proposed.

[1]  Alexander van Oudenaarden,et al.  Probing polymerization forces by using actin-propelled lipid vesicles , 2003, Proceedings of the National Academy of Sciences of the United States of America.

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

[3]  T. Steck,et al.  Length distribution of F-actin in Dictyostelium discoideum. , 1990, The Journal of biological chemistry.

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

[5]  J. Prost,et al.  Mechanism of actin-based motility: a dynamic state diagram. , 2005, Biophysical journal.

[6]  Frederick S. Soo,et al.  Adhesion controls bacterial actin polymerization-based movement. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[7]  E. Sackmann,et al.  Dynamic Light Scattering from Semidilute Actin Solutions: A Study of Hydrodynamic Screening, Filament Bending Stiffness, and the Effect of Tropomyosin/Troponin-Binding , 1996 .

[8]  Andrea J. Liu,et al.  New proposed mechanism of actin-polymerization-driven motility. , 2008, Biophysical journal.

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

[10]  T. Pollard,et al.  Interactions of ADF/cofilin, Arp2/3 complex, capping protein and profilin in remodeling of branched actin filament networks , 2000, Current Biology.

[11]  F. Lafuma,et al.  A biomimetic motility assay provides insight into the mechanism of actin-based motility , 2003, The Journal of cell biology.

[12]  J. Käs,et al.  Direct Measurement of the Wave-Vector-Dependent Bending Stiffness of Freely Flickering Actin Filaments , 1993 .

[13]  D. Weitz,et al.  Elastic Behavior of Cross-Linked and Bundled Actin Networks , 2004, Science.

[14]  Structure of autocatalytically branched actin solutions. , 2004, Physical review letters.

[15]  Joshua W Shaevitz,et al.  Load fluctuations drive actin network growth , 2007, Proceedings of the National Academy of Sciences.

[16]  G. Oster,et al.  Cell motility driven by actin polymerization. , 1996, Biophysical journal.

[17]  J A Theriot,et al.  Motility of ActA protein-coated microspheres driven by actin polymerization. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[18]  M. Footer,et al.  Biophysical parameters influence actin-based movement, trajectory, and initiation in a cell-free system. , 2004, Molecular biology of the cell.

[19]  Erwin Frey,et al.  Physics of Solutions and Networks of Semiflexible Macromolecules and the Control of Cell Function , 1998, cond-mat/9808022.

[20]  J. Taunton,et al.  Mechanism of Actin Network Attachment to Moving Membranes: Barbed End Capture by N-WASP WH2 Domains , 2007, Cell.

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

[22]  R Ezzell,et al.  F-actin, a model polymer for semiflexible chains in dilute, semidilute, and liquid crystalline solutions. , 1996, Biophysical journal.

[23]  D. Purich,et al.  Force generation by cytoskeletal filament end-tracking proteins. , 2004, Biophysical journal.

[24]  John L. Anderson,et al.  Colloid Transport by Interfacial Forces , 1989 .

[25]  D. Fletcher,et al.  Compression forces generated by actin comet tails on lipid vesicles , 2003, Proceedings of the National Academy of Sciences of the United States of America.

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

[27]  A. Carlsson.  Growth velocities of branched actin networks. , 2003, Biophysical journal.

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

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

[30]  J. Cooper,et al.  End versus side branching by Arp2/3 complex. , 2004, Biophysical journal.

[31]  Lakshminarayanan Mahadevan,et al.  The Force-Velocity Relationship for the Actin-Based Motility of Listeria monocytogenes , 2003, Current Biology.

[32]  J. Joanny,et al.  Deformations in actin comets from rocketing beads. , 2006, Biophysical journal.

[33]  Marie-France Carlier,et al.  Reconstitution of actin-based motility of Listeria and Shigella using pure proteins , 1999, Nature.

[34]  Ramin Golestanian,et al.  Propulsion of a molecular machine by asymmetric distribution of reaction products. , 2005, Physical review letters.

[35]  J. Howard,et al.  Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape , 1993, The Journal of cell biology.

[36]  Amanda Y. Chan,et al.  Relationship between Arp2/3 Complex and the Barbed Ends of Actin Filaments at the Leading Edge of Carcinoma Cells after Epidermal Growth Factor Stimulation , 1999, The Journal of cell biology.

[37]  J. Cooper,et al.  Control of actin assembly and disassembly at filament ends. , 2000, Current opinion in cell biology.

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

[39]  Jacques Prost,et al.  Soft Listeria: actin-based propulsion of liquid drops. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Alex Mogilner,et al.  On the edge: modeling protrusion. , 2006, Current opinion in cell biology.

[41]  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.

[42]  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.

[43]  I. M. Schwartz,et al.  The Role of Substrate Curvature in Actin-Based Pushing Forces , 2004, Current Biology.

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

[45]  R. Mullins,et al.  Capping Protein Increases the Rate of Actin-Based Motility by Promoting Filament Nucleation by the Arp2/3 Complex , 2008, Cell.

[46]  Andrea J. Liu,et al.  Branching, capping, and severing in dynamic actin structures. , 2007, Physical review letters.

[47]  T. Pollard,et al.  Cellular Motility Driven by Assembly and Disassembly of Actin Filaments , 2003, Cell.

[48]  A. Carlsson,et al.  Growth of branched actin networks against obstacles. , 2001, Biophysical journal.

[49]  V. Noireaux,et al.  Growing an actin gel on spherical surfaces. , 2000, Biophysical journal.