Simplifield Dynamics of a Continuous Peptide Chain
The chain is regarded as the continuum limit of rigid units-quadruples (their diameter tends to zero), connected at points called nods. The relative motion of the neighbouring units is described by two angles called dihedrals [l].The rigidity and planarity of the units is well established experimentally for most peptide chains. It is shown that the difficult kinematic relation (1.4) at every point of the chain is identically satisfied for the case of the travelling waves. This fact and the planarity of the units lead to a simplification of the inertia term in the equations of motion resulting in a system of nonlinear wave equations or even one equation, the nonlinearity being due now to the static term, i.e. the constitutive law for the continuous chain. In a particular periodic case the problem is governed by the pendulum equation. To examine the latter, in Sect. 2 we present a procedure applied to the discrete system of rigid units, introducing an average argument in the interaction energy. Thus, the continuum equations of motion are further simplified.
KeywordsInternal Energy Dihedral Angle Continuum Limit Peptide Chain Nonlinear Wave Equation
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