Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abraham, V.C., Krishnamurthi, V., Taylor, D.L., Lanni, F.: The actin-based nanomachine at the leading edge of migrating cells. Biophys. J. 77, 1721–1732 (1999)

    Google Scholar 

  2. Adelman, S.A., Doll, J.D.: Generalized Langevin equation approach for atom-solid-surface scattering—general formulation for classical scattering off harmonic solids. J. Chem. Phys. 64, 2375–2388 (1976)

    Article  ADS  Google Scholar 

  3. Alberts, J.B., Odell, G.M.: In silico reconstitution of Listeria propulsion exhibits nano-saltation. Plos Biol. 2, 2054–2066 (2004)

    Article  Google Scholar 

  4. Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Clarendon, Oxford (1987)

    MATH  Google Scholar 

  5. Atilgan, E., Wirtz, D., Sun, S.X.: Mechanics and dynamics of actin-driven thin membrane protrusions. Biophys. J. 90, 65–76 (2006)

    Article  ADS  Google Scholar 

  6. Bernheim-Groswasser, A., Wiesner, S., Golsteyn, R.M., Carlier, M.F., Sykes, C.: The dynamics of actin-based motility depend on surface parameters. Nature 417, 308–311 (2002)

    Article  ADS  Google Scholar 

  7. Betz, T., Lim, D., Kas, J.A.: Neuronal growth: A bistable stochastic process. Phys. Rev. Lett. 96, 098103 (2006)

    Article  ADS  Google Scholar 

  8. Bird, R.B., Curtiss, C.F., Armstrong, R.C., Hassager, O.: Dynamics of Polymeric Liquids: Kinetic Theory, 2nd edn. Wiley, New York (1987)

    Google Scholar 

  9. Bray, D.: Cell Movement. Garland, New York (1992)

    Google Scholar 

  10. Briels, W.J.: Theory of polymer dynamics. http://cbp.tnw.utwente.nl/PolymeerDictaat/polymerdynamics.pdf (1998)

  11. Bryce, N.S., Clark, E.S., Leysath, J.L., Currie, J.D., Webb, D.J., Weaver, A.M.: Cortactin promotes cell motility by enhancing lamellipodial persistence. Curr. Biol. 15, 1276–1285 (2005)

    Article  Google Scholar 

  12. Cascone, I., Audero, E., Giraudo, E., Napione, L., Maniero, F., Philips, M.R., Collard, J.G., Serini, G., Bussolino, F.: Tie-2-dependent activation of RhoA and Rac1 participates in endothelial cell motility triggered by angiopoietin-1. Blood 102, 2482–2490 (2003)

    Article  Google Scholar 

  13. Claessens, M., Bathe, M., Frey, E., Bausch, A.R.: Actin-binding proteins sensitively mediate F-actin bundle stiffness. Nat. Mater. 5, 748–753 (2006)

    Article  ADS  Google Scholar 

  14. Czirok, A., Schlett, K., Madarasz, E., Vicsek, T.: Exponential distribution of locomotion activity in cell cultures. Phys. Rev. Lett. 81, 3038–3041 (1998)

    Article  ADS  Google Scholar 

  15. Dickinson, R.B., Purich, D.L.: Clamped-filament elongation model for actin-based motors. Biophys. J. 82, 605–617 (2002)

    Google Scholar 

  16. Dickinson, R.B., Tranquillo, R.T.: A stochastic-model for adhesion-mediated cell random motility and haptotaxis. J. Math. Biol. 31, 563–600 (1993)

    Article  MATH  Google Scholar 

  17. Dimilla, P.A., Barbee, K., Lauffenburger, D.A.: Mathematical-model for the effects of adhesion and mechanics on cell-migration speed. Biophys. J. 60, 15–37 (1991)

    Article  Google Scholar 

  18. Doi, M., Edwards, S.F.: The Theory of Polymer Dynamics. Oxford University Press, New York (1986)

    Google Scholar 

  19. Footer, M.J., Kerssemakers, J.W.J., Theriot, J.A., Dogterom, M.: Direct measurement of force generation by actin filament polymerization using an optical trap. Proc. Natl. Acad. Sci. USA 104, 2181–2186 (2007)

    Article  ADS  Google Scholar 

  20. Frenkel, D., Smit, B.: Understanding Molecular Simulations: From Algorithms to Applications. Academic Press, New York (2002)

    Google Scholar 

  21. Gerbal, F., Chaikin, P., Rabin, Y., Prost, J.: An elastic analysis of Listeria monocytogenes propulsion. Biophys. J. 79, 2259–2275 (2000)

    Google Scholar 

  22. Gerbal, F., Laurent, V., Ott, A., Carlier, M.F., Chaikin, P., Prost, J.: Measurement of the elasticity of the actin tail of Listeria monocytogenes. Eur. Biophys. J. Biophys. 29, 134–140 (2000)

    Article  Google Scholar 

  23. Giannone, G., Dubin-Thaler, B.J., Dobereiner, H.G., Kieffer, N., Bresnick, A.R., Sheetz, M.P.: Periodic lamellipodial contractions correlate with rearward actin waves. Cell 116, 431–443 (2004)

    Article  Google Scholar 

  24. Gracheva, M.E., Othmer, H.G.: A continuum model of motility in ameboid cells. Bull. Math. Biol. 66, 167–193 (2004)

    Article  MathSciNet  Google Scholar 

  25. Herrmann, K.H., Satyanarayana, S.V.M., Sridhar, V., Murthy, K.P.N.: Monte Carlo simulation of actin filament based cell motility. Int. J. Mod. Phys. B 17, 5597–5611 (2003)

    Article  ADS  Google Scholar 

  26. Isambert, H., Venier, P., Maggs, A.C., Fattoum, A., Kassab, R., Pantaloni, D., Carlier, M.F.: Flexibility of actin-filaments derived from thermal fluctuations—effect of bound nucleotide, phalloidin, and muscle regulatory proteins. J. Biol. Chem. 270, 11437–11444 (1995)

    Article  Google Scholar 

  27. Jeon, J., Dobrynin, A.V.: Polymer confinement and bacterial gliding motility. Eur. Phys. J. E 17, 361–372 (2005)

    Article  Google Scholar 

  28. Kuo, S.C., McGrath, J.L.: Steps and fluctuations of Listeria monocytogenes during actin-based motility. Nature 407, 1026–1029 (2000)

    Article  ADS  Google Scholar 

  29. Mahadevan, L., Matsudaira, P.: Motility powered by supramolecular springs and ratchets. Science 288, 95–99 (2000)

    Article  ADS  Google Scholar 

  30. Marcy, Y., Prost, J., Carlier, M.F., Sykes, C.: Forces generated during actin-based propulsion: A direct measurement by micromanipulation. Proc. Natl. Acad. Sci. USA 101, 5992–5997 (2004)

    Article  ADS  Google Scholar 

  31. McBride, M.J.: Bacterial gliding motility: Multiple mechanisms for cell movement over surfaces. Annu. Rev. Microbiol. 55, 49–75 (2001)

    Article  Google Scholar 

  32. Mogilner, A., Edelstein-Keshet, L.: Regulation of actin dynamics in rapidly moving cells: A quantitative analysis. Biophys. J. 83, 1237–1258 (2002)

    Google Scholar 

  33. Mogilner, A., Oster, G.: Force generation by actin polymerization II: The elastic ratchet and tethered filaments. Biophys. J. 84, 1591–1605 (2003)

    ADS  Google Scholar 

  34. Mombach, J.C.M., Glazier, J.A.: Single cell motion in aggregates of embryonic cells. Phys. Rev. Lett. 76, 3032–3035 (1996)

    Article  ADS  Google Scholar 

  35. Moreno, J., Vargas, M.A., Madiedo, J.M., Munoz, J., Rivas, J., Guerrero, M.G.: Chemical and rheological properties of an extracellular polysaccharide produced by the cyanobacterium Anabaena sp ATCC 33047. Biotechnol. Bioeng. 67, 283–290 (2000)

    Article  Google Scholar 

  36. Parekh, S.H., Chaudhuri, O., Theriot, J.A., Fletcher, D.A.: Loading history determines the velocity of actin-network growth. Nat. Cell Biol. 7, 1219–1223 (2005)

    Article  Google Scholar 

  37. Peskin, C.S., Odell, G.M., Oster, G.F.: Cellular motions and thermal fluctuations—the Brownian ratchet. Biophys. J. 65, 316–324 (1993)

    ADS  Google Scholar 

  38. Pollard, T.D., Blanchoin, L., Mullins, R.D.: Molecular mechanisms controlling actin filament dynamics in nonmuscle cells. Annu. Rev. Biophys. Biomol. 29, 545–576 (2000)

    Article  Google Scholar 

  39. Prass, M., Jacobson, K., Mogilner, A., Radmacher, M.: Direct measurement of the lamellipodial protrusive force in a migrating cell. J. Cell Biol. 174, 767–772 (2006)

    Article  Google Scholar 

  40. Rubinstein, B., Jacobson, K., Mogilner, A.: Multiscale two-dimensional modeling of a motile simple-shaped cell. Multiscale Model. Simul. 3, 413–439 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  41. Satyanarayana, S.V.M., Baumgaertner, A.: Shape and motility of a model cell: A computational study. J. Chem. Phys. 121, 4255–4265 (2004)

    Article  ADS  Google Scholar 

  42. Schaus, T.E., Taylor, E.W., Borisy, G.G.: Self-organization of actin filament orientation in the dendritic-nucleation/array-treadmilling model. Proc. Natl. Acad. Sci. USA 104, 7086–7091 (2007)

    Article  ADS  Google Scholar 

  43. Stevens, M.J.: Simple simulations of DNA condensation. Biophys. J. 80, 130–139 (2001)

    ADS  Google Scholar 

  44. Theriot, J.A.: The polymerization motor. Traffic 1, 19–28 (2000)

    Article  Google Scholar 

  45. Theriot, J.A., Mitchison, T.J., Tilney, L.G., Portnoy, D.A.: The rate of actin-based motility of intracellular listeria-monocytogenes equals the rate of actin polymerization. Nature 357, 257–260 (1992)

    Article  ADS  Google Scholar 

  46. Zaman, M.H., Kamm, R.D., Matsudaira, P., Lauffenburger, D.A.: Computational model for cell migration in three-dimensional matrices. Biophys. J. 89, 1389–1397 (2005)

    Article  Google Scholar 

  47. Zamir, E., Geiger, B.: Components of cell-matrix adhesions. J. Cell Sci. 114, 3577–3579 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Vanderbilt University, Nashville, TN, 37235, USA

    Junhwan Jeon & Peter T. Cummings

  2. Vanderbilt Integrative Cancer Biology Center, Nashville, TN, 37232, USA

    Junhwan Jeon, Nelson R. Alexander, Alissa M. Weaver & Peter T. Cummings

  3. Department of Cancer Biology, Vanderbilt University Medical Center, Nashville, TN, 37232, USA

    Nelson R. Alexander & Alissa M. Weaver

  4. Nanomaterials Theory Institute, Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    Peter T. Cummings

Authors
  1. Junhwan Jeon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nelson R. Alexander
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alissa M. Weaver
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peter T. Cummings
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junhwan Jeon.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jeon, J., Alexander, N.R., Weaver, A.M. et al. Protrusion of a Virtual Model Lamellipodium by Actin Polymerization: A Coarse-Grained Langevin Dynamics Model. J Stat Phys 133, 79–100 (2008). https://doi.org/10.1007/s10955-008-9600-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-008-9600-5

Keywords

Search

Navigation