Gating mechanisms of mechanosensitive channels of large conductance, I: a continuum mechanics-based hierarchical framework

Abstract

A hierarchical simulation framework that integrates information from molecular dynamics (MD) simulations into a continuum model is established to study the mechanical response of mechanosensitive channel of large-conductance (MscL) using the finite element method (FEM). The proposed MD-decorated FEM (MDeFEM) approach is used to explore the detailed gating mechanisms of the MscL in Escherichia coli embedded in a palmitoyloleoylphosphatidylethanolamine lipid bilayer. In Part I of this study, the framework of MDeFEM is established. The transmembrane and cytoplasmic helices are taken to be elastic rods, the loops are modeled as springs, and the lipid bilayer is approximated by a three-layer sheet. The mechanical properties of the continuum components, as well as their interactions, are derived from molecular simulations based on atomic force fields. In addition, analytical closed-form continuum model and elastic network model are established to complement the MDeFEM approach and to capture the most essential features of gating. In Part II of this study, the detailed gating mechanisms of E. coli-MscL under various types of loading are presented and compared with experiments, structural model, and all-atom simulations, as well as the analytical models established in Part I. 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.

FIGURE 1

Tb-MscL: (a) top view and (b) side view of the closed crystal structure (15). (c) Top view and (d) side view of the continuum model used in the preliminary study (36) where only the transmembrane helices are taken into account.

FIGURE 2

E. coli-MscL: (a) top view and (b) side view of the closed structure of the homology model (16). (c) Top view and (d) side view of the full protein model in the refined MDeFEM approach in this article, where the cytoplasmic helices and loops are taken into account; the continuum model is developed based on the closed structure of the homology model (23).

FIGURE 3

Six basic deformation modes of a membrane (a) biaxial tension, (b) in-plane shear, (c) out of plane twisting, (d) bending, (e) torsion, and (f) membrane shear.

FIGURE 4

Assembled protein/lipid system. (a) The “cartoon” representation of E. coli-MscL and all-atom representation of the lipid. (b) The preliminary “minimalist” model for Tb-MscL (36) where the simulation is divided into two stages. (c) The refined MDeFEM approach and continuum model for E. coli-MscL where concurrent coupling is realized between lipid and protein.

FIGURE 5

Examples of several lowest eigenmodes and frequencies of helices and loops: comparisons between molecular mechanics and finite element simulations. Here the TM1 helix only corresponds to the segment below Pro43.

FIGURE 6

POPE lipid membrane (44): (a) the atomistic structure, (b) the density map of a monolayer, and (c) the lateral pressure profiles of a monolayer for undeformed and deformed lipid.

FIGURE 7

Example of fitting of the total nonbonded interaction energy (per area) between continuum components of E. coli-MscL. The x axis is the normalized separation between the center-of-masses (with 1.0 being the equilibrium spacing). (a) Comparison between FEM and molecular mechanics calculations for helical pairs in the closed structural model. (b) The fitted set of parameters is fairly transferable to other structural states (expanded/intermediate and opened). In b, the scale for the interaction between lipid and S1 helices is given on the right of the figure, whereas the scale for interaction between helices is given on the left.

FIGURE 8

(a) Schematic of a continuum three-layer sandwich lipid membrane containing a circular hole. (b) The normalized stress concentration factor as a function of the normalized separation between two circular cavities (46,58,59) for a plane stress problem.

FIGURE 9

Schematic of the linear effective continuum medium model (ECMM).

FIGURE 10

ENM of E. coli-MscL: (a) Protocol 1, where only the protein is modeled. (b) Protocols 2 and 3, where the lipid is also taken into account.