Dynamics of a stiff biopolymer in an actively contractile background: buckling, stiffening and negative dissipation

Abstract

We present a generic theory for the dynamics of a stiff filament under tension, in an active medium with orientational correlations, such as a microtubule in contractile actin. In sharp contrast to the case of a passive medium, we find the filament can stiffen, and possibly oscillate, \textit{or} buckle, depending on the contractile or tensile nature of the activity \textit{and} the filament-medium anchoring interaction. We present experiments on the behaviour of microtubules in the growth cone of a neuron, which provide evidence for these apparently opposing behaviours. We also demonstrate a strong violation of the fluctuation-dissipation (FD) relation in the effective dynamics of the filament, including a negative FD ratio. Our approach is also of relevance to the dynamics of axons, and our model equations bear a remarkable formal similarity to those in recent work [PNAS (2001) {\bf 98}:14380-14385] on auditory hair cells. Detailed tests of our predictions can be made using a single filament in actomyosin extracts or bacterial suspensions.