A finite element framework for studying the mechanical response of macromolecules: Application to the gating of the mechanosensitive channel MscL

¹ Columbia University
² University of Wisconsin-Madison

^* To whom correspondence should be addressed. E-mail: cui{at}chem.wisc.edu.

Submitted on March 28, 2006
Revised on April 26, 2006
Accepted on 17 May 2006

	Abstract

The gating pathways of mechanosensitive channels of large conductance (MscL) in two bacteria (Mycobacterium tuberculosis and Escherichia coli) are studied using finite element method (FEM). The phenomenological model treats transmembrane helices as elastic rods and the lipid membrane as an elastic sheet of finite thickness; the model is inspired by the crystal structure of MscL. The interactions between various continuum components are derived from molecular mechanics energy calculations using the CHARMM all-atom force field. Both bacterial MscLs open fully upon in-plane tension in the membrane and the variation of pore diameter with membrane tension is found to be essentially linear. The estimated gating tension is close to the experimental value. The structural variations along the gating pathway are consistent with previous analyses based on structural models with experimental constraints and biased atomistic molecular dynamics simulations. Upon membrane bending, neither MscL opens substantially although there is notable and non-monotonic variation in the pore radius. This emphasizes that the gating behavior of MscL depends critically on the form of the mechanical perturbation and reinforces the idea that the crucial gating parameter is lateral tension in the membrane rather than the curvature of the membrane. Compared to popular all-atom based techniques such as targeted or steered MD simulations, the FEM based continuum mechanics framework offers a unique alternative to bridge detailed intermolecular interactions and biological processes occurring at large spatial scale and long time scale. It is envisioned that such a hierarchical multiscale framework will find great value in the study of a variety of biological processes involving complex mechanical deformations such as muscle contraction and mechanotransduction.

Key Words: continuum mechanics, finite element analysis, gating, mechanosensitive channel, membrane bending, membrane tension

This article has been cited by other articles:

				X. Chen, Q. Cui, Y. Tang, J. Yoo, and A. Yethiraj Gating Mechanisms of Mechanosensitive Channels of Large Conductance, I: A Continuum Mechanics-Based Hierarchical Framework Biophys. J., July 15, 2008; 95(2): 563 - 580. [Abstract] [Full Text] [PDF]

				Y. Tang, J. Yoo, A. Yethiraj, Q. Cui, and X. Chen Gating Mechanisms of Mechanosensitive Channels of Large Conductance, II: Systematic Study of Conformational Transitions Biophys. J., July 15, 2008; 95(2): 581 - 596. [Abstract] [Full Text] [PDF]

				S. Choe, K. A. Hecht, and M. Grabe A Continuum Method for Determining Membrane Protein Insertion Energies and the Problem of Charged Residues J. Gen. Physiol., June 1, 2008; 131(6): 563 - 573. [Abstract] [Full Text] [PDF]

				J. Jeon and G. A. Voth Gating of the Mechanosensitive Channel Protein MscL: The Interplay of Membrane and Protein Biophys. J., May 1, 2008; 94(9): 3497 - 3511. [Abstract] [Full Text] [PDF]

				S. Yefimov, E. van der Giessen, P. R. Onck, and S. J. Marrink Mechanosensitive Membrane Channels in Action Biophys. J., April 15, 2008; 94(8): 2994 - 3002. [Abstract] [Full Text] [PDF]