Nonlinear elasticity of an α-helical polypeptide

We study a minimal extension of the wormlike chain model to describe polypeptides having a-helical secondary structure. In this model the presence or absence of secondary structure enters as a scalar variable that controls the local chain bending modulus. Using this model we compute the extensional compliance of an a-helix under tensile stress, the bending compliance of the molecule under externally imposed torques, and the nonlinear interaction of such torques and forces on the molecule. We find that, due to coupling of the "internal" secondary structure variables to the conformational degrees of freedom of the polymer, the molecule has a highly nonlinear response to applied stress and force couples. In particular we demonstrate a sharp lengthening transition under applied force and a buckling transition under applied torque. Finally, we speculate that the inherent bistability of the molecule may underlie protein conformational change in vivo. interpretation of these protein manipulation experiments it appears to be useful to first understand in more detail the mechanical properties of simpler polypeptide-based struc- tures. A natural candidate for such a simpler structure is a protein subdomain of one secondary structure. Here too there is experimental input: single-molecule force spectroscopy via atomic force microscopy sAFMd has been used to di- rectly probe a-helical polypeptides f22g as well as synthetic polymer chains with a local helical structure such as PEG f23g. In order to understand the mechanical properties of pro- teins in general and a-helical polypeptides in particular it is necessary to develop a minimalistic model that incorporates both the conformational fluctuations of the polymer back- bone and localized structural transitions of the constituent monomers. In other words it is necessary to augment simple models of the statistical mechanics of the peptide backbone with terms to account for the presence of secondary structure along the chain. Furthermore, we must allow for the interac- tion between the degree of local secondary structure and the conformational degrees of freedom of the polypetide back- bone. In this paper we examine the predicted mechanical prop- erties of such a minimalistic model of an a-helical polypep- tide in which we allow the interaction of the local secondary structure of the chain with its conformational degrees of free- dom. We treat the local presence or absence of secondary structure as a two-state sIsing-liked variable along the chain backbone, which is itself described by a set of local tangent vectors to the chain. In order to make this simplification, we coarse-grain the polymer so that each independent monomer can be unambiguously assigned a state of secondary struc- ture. This requires us to consider a model comprised of coarse-grained chain segments si.e., monomersd, each con- sisting of about three amino acids. The interaction between the internal, secondary structure variables and the conforma- tion of the polymer chain as described by the set of backbone tangent vectors is effected by the presence of a bending modulus of the backbone whose value depends on the local state of secondary structure. When these three amino acids making up one model monomer adopt a local configuration