Volume 107, Number 1, July 2014
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||07 July 2014|
Subharmonic oscillations of collective molecular motors
1 Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona Avinguda Diagonal 647, E-08028 Barcelona, Spain
2 Department of Applied Mathematics and Theoretical Physics, University of Cambridge - Cambridge CB3 0WA, UK
3 Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford - Oxford OX2 6GG, UK
Received: 7 May 2014
Accepted: 13 June 2014
We study a generic two-state model for an assembly of molecular motors which is described by means of a pair of integro-partial differential equations and leads to oscillatory motion in the presence of an elastic coupling to its environment. We discuss a reduction of the system to a minimal set of three ordinary differential equations that successfully capture the complex nonlinear dynamics of the full system. In the limit of high mobility and large elastic modulus, we report on the emergence of subharmonics in the power spectrum of the oscillations. This provides a rationale for the unexplained observation of secondary peaks in a minimal actomyosin system in vitro (Plaçais P.-Y. et al., Phys. Rev. Lett. 103, (2009) 158102), showing that the phenomenon is robust and genuine.
PACS: 87.16.Nn – Motor proteins (myosin, kinesin dynein) / 82.40.Bj – Oscillations, chaos, and bifurcations / 87.10.-e – General theory and mathematical aspects
© EPLA, 2014
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