  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.
