Institute of Fundamental Technological Research

Much research has been done on the dynamics of the peptide chain. The amount of experimental, theoretical and numerical work on structure, stability and folding is staggering. However, there is no widely known analytical model derived from first principles. In this paper we derive equations for the dynamics of a peptide chain in a “quadrilateral chip” model, passing to the continuum from the discrete chain structure and assuming various local interactions. Ours is therefore a kinematic chain [1, 2]appearing in many mechanical structures. However, we include the appropriate constraints peculiar to peptides. Dihedral interactions are included and, when strong, are seen to ensure stability. Thus, they have the same effect as the non-local hydrogen bonds. The celebrated helices are exact particular solutions of our general equations. In order to obtain eigenfrequencies, a simplified model is introduced and peptide oscillations with frequencies of the order of 1013s−1 are obtained, in agreement with observations. Solitons are found in very restricted cases, thus far. External forces, such as those due to the solvent, are included in the model (Section 8).

A simple dipole chain is the main building block of many physical models in solid state physics. Here, just such a chain of essentially identical dipoles is investigated by considering nearest-neighbor interactions of the individual charges in the dipoles. A three-dimensional model is found. In a restricted, two-dimensional picture, a nonlinear, second-order partial differential equation, more general than sine-Gordon, results. Soliton-kink solutions are found.