Modeling the formation of in vitro filopodia
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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.
KeywordsNonequilibrium actin bundling Filopodia Kinetic aggregation
Mathematics Subject Classification (2000)92XX
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.
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- Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2007) Molecular biology of the cell. Taylor and Francis, New YorkGoogle Scholar
- Amman KJ, Pollard TD (2001) Direct real-time observation of actin filament branching mediated by Arp2/3 complex using total internal relfection fluorescence microscopy. Proc Natl Acad Sci USA 98: 15009-15-13Google Scholar
- Carlsson AE, Sept D (2008) Mathematical modeling of cell migration. In: Correira JJ, Detrich HW (eds) Biological tools for biologists, vol 1 in vitro techniques (Methods in cell biology, vol 84). Elsevier, New York, pp 911–937 2008Google Scholar
- Gopinathan A, Lee K-C, Schwarz JM, Liu AJ (2007) Branching, capping, and severing in dynamic actin structures. Phys Rev Lett 99:058103, pp 4Google Scholar
- Grason GM, Bruinsma RF (2007) Chirality and equilibrium biopolymer bundles. Phys Rev Lett 99:098101, pp 4Google Scholar
- Henle ML, Pincus PA (2005) Equilibrium bundle size of rodlike polyelectrolytes with counterion-induced attractive interactions. Phys Rev E 71:060801, pp 4Google Scholar
- Ideses Y, Brill-Karniely Y, Haviv L, Ben-Shaul A, Bernheim-Groswasser A (2008) Arp2/3 branched actin network mediates filopodia-like bundle formation in vitro. PloS ONE 3(9):e3297. doi: 10.1371/journal.pone.0003297
- Kang K, Redner S, Meakin P, Leyvraz F (1986) Long-time crossover phenomena in coagulation kinetics. Phys Rev E 33: 1171–1182Google Scholar
- Kraikivski P, Slepchenko BM, Novak IL (2008) Actin bundling: initiation mechanisms and kinetics. Phys Rev Lett 101:128102, pp 4Google Scholar
- Mogilner A, Edelstein-Keshet L (1999) Regulation of actin dynamics in rapidly moving cells: a quantitative analysis. Biophys J 83: 11324–11329Google Scholar
- Stewman SF, Dinner AR (2007) Lattice model for self-assembly with application to the formation of cytoskeletal-like structures. Phys Rev E 76:016103, pp 9Google Scholar
- von Smoluchowski M (1916) Drei vortrage uber diffusion Brownsche molekular bewegung und koagulation von kolliodteichen. Z Phys 17: 557Google Scholar