Effects of constraints in general branched molecules: A quantitative ab initio study in HCO-L-Ala-NH2

A general approach to the design of accurate classical potentials for protein folding is described. It includes the introduction of a meaningful statistical measure of the differences between approximations of the same potential energy, the definition of a set of Systematic and Approximately Separable and Modular Internal Coordinates (SASMIC), much convenient for the simulation of general branched molecules, and the imposition of constraints on the most rapidly oscillating degrees of freedom. All these tools are used to study the effects of constraints in the Conformational Equilibrium Distribution (CED) of the model dipeptide HCO-L-Ala-NH2. We use ab initio Quantum Mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of the correcting terms to the naive CED based in the Potential Energy Surface (PES) without any simplifying assumption. These terms are related to mass-metric tensors determinants and also occur in the Fixman’s compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function.