Buckling, stiffening, and negative dissipation in the dynamics of a biopolymer in an active medium

doi:10.1073/pnas.0900451106

Buckling, stiffening, and negative dissipation in the dynamics of a biopolymer in an active medium

^aCentre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560 012, India;
^bTranslational Medicine, Brigham and Women's Hospital, Harvard Medical School, One Blackfan Circle, Karp 6, Boston, MA 02115;
^cInstitute of Soft Matter Physics, Universität Leipzig, Linnéstrasse 5, 04103 Leipzig, Germany;
^dCondensed Matter Theory Unit, Jawaharlal Nehru Center for Advanced Scientific Research, Bangalore 560 064, India;
^eRaman Research Institute, C.V. Raman Avenue, Bangalore 560 080, India; and
^fNational Centre for Biological Sciences, Tata Institute of Fundamental Research, Bellary Road, Bangalore 560 065, India

Edited by Tom C. Lubensky, University of Pennsylvania, Philadelphia, PA, and approved September 23, 2009 (received for review January 14, 2009)

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 or buckle, depending on both the contractile or tensile nature of the activity and the filament-medium anchoring interaction. 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 [Martin P, Hudspeth AJ, Juelicher F (2001) Proc Natl Acad Sci USA 98:14380–14385] on auditory hair cells. Detailed tests of our predictions can be made by using a single filament in actomyosin extracts or bacterial suspensions.

Footnotes

¹To whom correspondence should be addressed. E-mail: sriram{at}physics.iisc.ernet.in
Author contributions: N.K., A.E., D.K., J.A.K., S.R., and M.R. designed research, performed research, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/cgi/content/full/0900451106/DCSupplemental.
↵* If included, these terms would lead to shifts of effective Frank constants and additional possible instabilities in the effective equation of motion Eq. 4.
↵† Passive stresses arising from the free-energy functional enter only at higher order in gradients.