Abstract
We present an analysis of the planar motion of single semiflexible filaments subject to viscous drag or point forcing. These are the relevant forces in dynamic experiments designed to measure biopolymer bending moduli. By analogy with the "Stokes problems" in hydrodynamics (motion of a viscous fluid induced by that of a wall bounding the fluid), we consider the motion of a polymer, one end of which is moved in an impulsive or oscillatory way. Analytical solutions for the time-dependent shapes of such moving polymers are obtained within an analysis applicable to small-amplitude deformations. In the case of oscillatory driving, particular attention is paid to a characteristic length determined by the frequency of oscillation, the polymer persistence length, and the viscous drag coefficient. Experiments on actin filaments manipulated with optical traps confirm the scaling law predicted by the analysis and provide a new technique for measuring the elastic bending modulus. Exploiting this model, we also present a reanalysis of several published experiments on microtubules.
Full Text
The Full Text of this article is available as a PDF (197.9 KB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Amblard F, Maggs AC, Yurke B, Pargellis A, Leibler S. Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks. Phys Rev Lett. 1996 Nov 18;77(21):4470–4473. doi: 10.1103/PhysRevLett.77.4470. [DOI] [PubMed] [Google Scholar]
- Cluzel P., Lebrun A., Heller C., Lavery R., Viovy J. L., Chatenay D., Caron F. DNA: an extensible molecule. Science. 1996 Feb 9;271(5250):792–794. doi: 10.1126/science.271.5250.792. [DOI] [PubMed] [Google Scholar]
- Felgner H., Frank R., Schliwa M. Flexural rigidity of microtubules measured with the use of optical tweezers. J Cell Sci. 1996 Feb;109(Pt 2):509–516. doi: 10.1242/jcs.109.2.509. [DOI] [PubMed] [Google Scholar]
- Gittes F., Mickey B., Nettleton J., Howard J. Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape. J Cell Biol. 1993 Feb;120(4):923–934. doi: 10.1083/jcb.120.4.923. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Goldstein RE, Langer SA. Nonlinear dynamics of stiff polymers. Phys Rev Lett. 1995 Aug 7;75(6):1094–1097. doi: 10.1103/PhysRevLett.75.1094. [DOI] [PubMed] [Google Scholar]
- Kurachi M., Hoshi M., Tashiro H. Buckling of a single microtubule by optical trapping forces: direct measurement of microtubule rigidity. Cell Motil Cytoskeleton. 1995;30(3):221–228. doi: 10.1002/cm.970300306. [DOI] [PubMed] [Google Scholar]
- Mendelson N. H. Bacterial macrofibres: the morphogenesis of complex multicellular bacterial forms. Sci Prog. 1990;74(296 Pt 4):425–441. [PubMed] [Google Scholar]
- Shapere A, Wilczek F. Self-propulsion at low Reynolds number. Phys Rev Lett. 1987 May 18;58(20):2051–2054. doi: 10.1103/PhysRevLett.58.2051. [DOI] [PubMed] [Google Scholar]
- Smith S. B., Cui Y., Bustamante C. Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules. Science. 1996 Feb 9;271(5250):795–799. doi: 10.1126/science.271.5250.795. [DOI] [PubMed] [Google Scholar]
- Venier P., Maggs A. C., Carlier M. F., Pantaloni D. Analysis of microtubule rigidity using hydrodynamic flow and thermal fluctuations. J Biol Chem. 1994 May 6;269(18):13353–13360. [PubMed] [Google Scholar]
- Yin H., Wang M. D., Svoboda K., Landick R., Block S. M., Gelles J. Transcription against an applied force. Science. 1995 Dec 8;270(5242):1653–1657. doi: 10.1126/science.270.5242.1653. [DOI] [PubMed] [Google Scholar]