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Correlated random walks inside a cell: actin branching and microtubule dynamics

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Abstract

Correlated random walks (CRW) have been explored in many settings, most notably in the motion of individuals in a swarm or flock. But some subcellular systems such as growth or disassembly of bio-polymers can also be described with similar models and understood using related mathematical methods. Here we consider two examples of growing cytoskeletal elements, actin and microtubules. We use CRW or generalized CRW-like PDEs to model their spatial distributions. In each case, the linear models can be reduced to a Telegrapher’s equation. A combination of explicit solutions (in one case) and numerical solutions (in the other) demonstrates that the approach to steady state can be accompanied by (decaying) waves.

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Acknowledgements

AB is supported by an NSERC post-doctoral fellowship; LEK is supported by an NSERC Discovery grant; We are grateful to the Pacific Institute for Mathematical Sciences for providing space and resources for AB’s postdoctoral research.

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  1. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Andreas Buttenschön & Leah Edelstein-Keshet

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  1. Andreas Buttenschön
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  2. Leah Edelstein-Keshet
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Correspondence to Andreas Buttenschön.

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Buttenschön, A., Edelstein-Keshet, L. Correlated random walks inside a cell: actin branching and microtubule dynamics. J. Math. Biol. 79, 1953–1972 (2019). https://doi.org/10.1007/s00285-019-01416-6

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  • DOI: https://doi.org/10.1007/s00285-019-01416-6

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