A drift-diffusion model for molecular motor transport in anisotropic filament bundles

Dietmar  Oelz; Alex  Mogilner

doi:10.3934/dcds.2016.36.4553

Article Contents

2016, Volume 36, Issue 8: 4553-4567. Doi: 10.3934/dcds.2016.36.4553

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A drift-diffusion model for molecular motor transport in anisotropic filament bundles

Dietmar Oelz^1, and
Alex Mogilner^2,

1.
Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York, NY 10012
2.
Courant Institute of Mathematical Sciences and Department of Biology, New York University, 251 Mercer St, New York, NY 10012

Received: May 2015

Revised: October 2015

Published: May 2017

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Abstract

In this study we consider the density of motor proteins in filament bundles with polarity graded in space. We start with a microscopic model that includes information on motor binding site positions along specific filaments and on their polarities. We assume that filament length is small compared to the characteristic length scale of the bundle polarity pattern. This leads to a separation of scales between molecular motor movement within the bundle and along single fibers which we exploit to derive a drift-diffusion equation as a first order perturbation equation. The resulting drift-diffusion model reveals that drift dominates in unidirectional bundles while diffusion dominates in isotropic bundles. In general, however, those two modes of transport are balanced according to the polarity and thickness of the filament bundle. The model makes testable predictions on the dependence of the molecular motor density on filament density and polarity.

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Mathematics Subject Classification: Primary: 92C37; Secondary: 35B40, 35Q92.

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