Diffusion approximation of the stochastic process of microtubule assembly

Bulletin of Mathematical Biology
Ivan V Maly

Abstract

Microtubules are protein polymers that guide intracellular motility. Stochastic switching of a microtubule between states of elongation, shortening, and pause is described in detail by the dynamic instability (DI) model. Recently we have described the dynamics of microtubules phenomenologically as generalized diffusion of their ends. Genesis of the diffusion dynamics and accuracy of diffusion model are studied in this work. It is shown that wandering of the end of a microtubule undergoing DI asymptotically approaches the Wiener diffusion process. Accuracy of the diffusion approximation is evaluated by comparing its predictions with results of simulation of DI. Stationary distributions of microtubule length and life-time that are predicted by both models differ qualitatively between two cell types considered. However, predictions of the diffusion model are in each case practically identical to predictions of the DI model being also consistent with experimental data. The peculiar stochastic process of microtubule assembly thus converges at cell scale to a kind of widespread-in-nature diffusion process. This result is considered an example of qualitative change in dynamical properties in transition from the molecular to cellular l...Continue Reading

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Citations

Aug 19, 2007·Cell Biochemistry and Biophysics·Philip LeDuc, Russell Schwartz
Aug 25, 2011·Journal of Physics. Condensed Matter : an Institute of Physics Journal·E M CraigA Mogilner
Mar 24, 2010·Journal of Theoretical Biology·Kouroush Sadegh Zadeh, Hubert J Montas
May 22, 2007·Biophysical Chemistry·Vladimir A BaulinFabrice Thalmann
Dec 20, 2005·Cell Motility and the Cytoskeleton·Ilya GrigorievIvan Vorobjev
Oct 18, 2011·Computational Biology and Chemistry·Márcio MourãoSidney L Shaw
Aug 31, 2006·Biophysical Journal·Khuloud JaqamanGaudenz Danuser
Jun 22, 2002·Journal of Theoretical Biology·Ivan V Maly
Oct 16, 2007·Nature Cell Biology·Ge YangTarun M Kapoor
Dec 13, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Gennady MargolinMark S Alber
Nov 30, 2018·Bulletin of Mathematical Biology·Stéphane HonoréDiana White

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