Microtubule catastrophe under force : Mathematical and computational results from a Brownian ratchet model.

Abstract:

:In the intracellular environment, the intrinsic dynamics of microtubule filaments is often hindered by the presence of barriers of various kind, such as kinetochore complexes and cell cortex, which impact their polymerisation force and dynamical properties such as catastrophe rate. We present a theoretical study of the effect of a forced barrier, also subjected to thermal noise, on the statistics of catastrophe events in a single microtubule as well as a "bundle" of two parallel microtubules. For microtubule dynamics, which includes growth, hydrolysis and the consequent dynamic instability, we employ a one-dimensional discrete stochastic model. The dynamics of the barrier is captured by over-damped Langevin equation, while its interaction with a growing filament is assumed to be hard-core repulsion. A unified treatment of the continuum dynamics of the barrier and the discrete dynamics of the filament is realised using a hybrid Fokker-Planck equation. An explicit mathematical formula for the force-dependent catastrophe rate of a single microtubule is obtained by solving the above equation, with minimal assumptions. The prediction agrees well with results of numerical simulations. To investigate the extent of "load-sharing" in a microtubule bundle, and its impact on the frequency of catastrophes, a two-filament model is studied. While equations for the two-filament model predicts equal sharing of load between the filaments, under a mean-field assumption, numerical simulations indicate the existence of a range of load-sharing behaviours, which is characterised using a dimensionless parameter.

journal_name

Phys Biol

journal_title

Physical biology

authors

Yadav V,Srinivas B,Gopalakrishnan M

doi

10.1088/1478-3975/abc057

subject

Has Abstract

pub_date

2020-10-12 00:00:00

eissn

1478-3967

issn

1478-3975

pub_type

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