Content area
Full Text
ABSTRACT
Using a coarse-grained elastic model, we examine the bending properties of anti-parallel β-sheets comprised of uniform amino-acid residues in vacuum as well as in explicit solvent. By comparing the conformational probability of the β-sheet from molecular dynamics simulations with the same quantities obtained from the coarse-grained model, we compute the elastic bending constant, κ. Equilibrium fluctuations of the β-sheet and its response to external forces are well reproduced by a model with a uniform isotropic bending constant. An anisotropic bending model is also investigated, although the computed anisotropy is relatively weak and most of the observed properties are well described by an isotropic model. The presence of explicit solvent also lowers the bending constant. The sequence dependence of our result and its implications in protein conformational dynamics are discussed.
INTRODUCTION
In many proteins, structural flexibility is intimately related to protein function. When a protein binds small ligands or other proteins, a conformational change can occur and the protein subsequently assumes a different role. This generic mechanism is prevalent in cellular signaling, trafficking, self-assembly, and force generation. While static structures of many proteins in various conformational states are available, quantitative energetics of conformational changes are usually lacking. The strategy of this article is to develop a coarse-grained model of protein secondary structures, and ultimately make contact with a continuum description. In particular, we examine the elastic property of several prototypical anti-parallel β-sheets. Previously, the elastic property of a β-sheet in F^sub 1^-ATPase was examined using molecular dynamics (MD) simulations (1). It was found to be flexible, and can store several k^sub B^T of energy during bending (k^sub B^ is the Boltzmann constant and T is 300 K). In the present work, we introduce a general model to describe β-sheet deformations and compute the bending constant from MD results. The methodology is related to our previous study of α-helix elasticity, which computed the helix persistence length (2). We report that the bending modulus of a β-sheet of glycines is ~5 ksT. A β-sheet of alanines is slightly stiffer, and has a bending modulus of 7 k^sub B^T.
Flexibility of β-sheets has been studied using an informatics approach (3,4) and principal component analysis (4). These authors noted that there is a difference in the apparent elasticity...