Journal of Mathematical Biology

, Volume 63, Issue 2, pp 229–261 | Cite as

Modeling the formation of in vitro filopodia

Open Access
Article

Abstract

Filopodia are bundles of actin filaments that extend out ahead of the leading edge of a crawling cell to probe its upcoming environment. In vitro experiments (Vignjevic et al. in J Cell Biol 160:951–962, 2003) have determined the minimal ingredients required for the formation of filopodia from the dendritic-like morphology of the leading edge. We model these experiments using kinetic aggregation equations for the density of growing bundle tips. In mean field, we determine the bundle size distribution to be broad for bundle sizes smaller than a characteristic bundle size above which the distribution decays exponentially. Two-dimensional simulations incorporating both bundling and cross-linking measure a bundle size distribution that agrees qualitatively with mean field. The simulations also demonstrate a nonmonotonicity in the radial extent of the dendritic region as a function of capping protein concentration, as was observed in experiments, due to the interplay between percolation and the ratcheting of growing filaments off a spherical obstacle.

Keywords

Nonequilibrium actin bundling Filopodia Kinetic aggregation 

Mathematics Subject Classification (2000)

92XX 

Notes

Acknowledgments

The authors would like to acknowledge helpful conversations with Andrea Liu, Ron Maimon, and Tatyana Svitkina during the early stages of this work. The authors gratefully acknowledge Louise Yang, an undergraduate summer intern who helped conduct some of the preliminary simulations in this work. The authors would also like to acknowledge the hospitality of the Aspen Center for Physics where some of this work was completed. Finally, AG acknowledges support from the James S. McDonnell Foundation and JMS acknowledges support from NSF-DMR-0645373.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California-DavisDavisUSA
  2. 2.Department of Neurobiology, Physiology and BehaviorUniversity of California-DavisDavisUSA
  3. 3.School of Natural SciencesUniversity of California-MercedMercedUSA
  4. 4.Physics DepartmentSyracuse UniversitySyracuseUSA

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