From the Cell Membrane to the Nucleus: Unearthing Transport Mechanisms for Dynein

Abstract

Mutations in the motor protein cytoplasmic dynein have been found to cause Charcot-MarieTooth disease in humans, spinal muscular atrophy and severe intellectual disabilities in humans.In mouse models neurodegeneration is observed. We sought to develop a novel model which could incorporate the effect of mutations on distance travelled and velocity. A mechanical model for the dynein mediated transport of endosomes is derived from first principles and solved numerically. The effects of variations in model parameter values are analysed to find those that have a significant impact on velocity and distance travelled. The model successfully describes the processivity of dynein and matches qualitatively the velocity profiles observed in experiments.

A mathematical understanding of how cytoplasmic dynein walks on microtubules

“…While these experimental studies enable detailed understanding of dynein's structure [2,4,7,18 -21,35] and transport mechanism [3,34,36,37,42,47,48,52]; to our knowledge, few models have been developed to describe such observations [53][54][55]. Our results bridge this gap, by presenting a robust integrative mechanical and stochastic model describing the stepping behaviour of cytoplasmic dynein.…”

“…Following our previous study by Crossley et al [53], we derive from first principles a system of six second-order nonlinear ordinary differential equations (ODEs) to model the transport mechanisms of a single dynein acting on a cargo. Let x C ( t ), x T ( t ), x A ( t ), x B ( t ), x D ( t ) and x E ( t ) denote the positions of the cargo, tail, AAA+ rings A and B, and the MTBDs D and E, respectively, at time t ∈ [0, T Final ] for some end time T Final > 0.…”

“…A schematic diagram of the mechanical model (adapted from [53]). The cargo is modelled as a sphere (grey) and regulators of binding to dynein are modelled as part of this cargo.…”

“…The non-dimensionalized coefficients of the acceleration terms turn out to be small and the dynamics are dominated by the viscous drag [53]. Hence, neglecting the small coefficients of the second derivatives, we obtain the following non-dimensional system: ${\alpha }_{\mathrm{C}}\frac{\mathrm{normald}{\chi }_{\mathrm{normalC}}}{\mathrm{normald}\tau }=(\frac{1}{{\rho }_1}{\chi }_{\mathrm{normalT}}-1)-\lambda -{\chi }_{\mathrm{C}},$ ${\alpha }_{\mathrm{normalT}}\frac{\mathrm{d}{\chi }_{\mathrm{T}}}{\mathrm{d}\tau }=(\frac{1}{{\rho }_2}false({\chi }_B+{\chi }_{A}false)-\cos false({\theta }_{\mathrm{normalBT}}false)+\cos false({\theta }_{\mathrm{normalAT}}false))+{\rho }_1{\kappa }_1({\chi }_{\mathrm{normalC}}+1)-(2+{\kappa }_1){\chi }_{\mathrm{normalT}},$ ${\alpha }_M\frac{\mathrm{d}{\chi }_A}{\mathrm{d}\tau }={\rho }_2{\kappa }_2({\chi }_{\mathrm{normalT}}-\cos ({\theta }_{\mathrm{AT}}))+({\chi }_D+\cos ({\theta }_{\mathrm{AD}}))-({\kappa }_{2+1}){\chi }_A,$ ${\alpha }_M\frac{\mathrm{d}{\chi }_B}{\mathrm{d}\tau }=({\chi }_E-\cos ({\theta }_{\mathrm{BE}}$…”

Simple qualitative deterministic model of dynein

“…Let us mention, e.g. pure deterministic model (Crossley et al (2012)), stochastic model (Goedecke and Elston (2005)) or the very simple model (Zhao et al (2014)) which omits e.g. the possibility of the backward stepping.…”