Eur. Phys. J. E (2011) 34: 60
https://doi.org/10.1140/epje/i2011-11060-5

Regular Article

Dynamical behavior of molecular motor assemblies in the rigid and crossbridge models

¹ Physicochimie Curie (Institut Curie/CNRS-UMR168/UPMC), Institut Curie, Centre de Recherche, 26 rue d’Ulm, 75248, Paris Cedex 05, France
² ESPCI, 10 rue Vauquelin, 75231, Paris Cedex 05, France

^* e-mail: thomas.guerin.2003@polytechnique.org

Received: 10 March 2011
Accepted: 9 May 2011
Published online: 23 June 2011

Abstract

We present a detailed analysis of the dynamical instabilities appearing in two kinetic theories for the collective behavior of molecular motors: the rigid two-state model and the two-state crossbridge (or power-stroke) model with continuous binding sites. We calculate force-velocity relations, discuss their stability, plot a diagram that summarizes the oscillation regimes, identify the location of the Hopf bifurcation with a memory effect, discuss the oscillation frequency and make a link with single-molecule experiments. We show that the instabilities present in these models naturally translate into non-linearities in force-displacement relations, and at linear order give forces that are similar to the delayed stretch activation observed in oscillating muscles. We also find that instabilities can appear for both apparent load-decelerated and load-accelerated detachment rates in a 3-state crossbridge model.