Statistical Formulae of the Energy Distribution among a Globular Protein Structure Ensemble

In prediction of a protein main-chain structure into which a query sequence of amino acids folds, one evaluates the relative stability of a candidate structure against reference structures. We developed a statistical theory for calculating the energy distribution over a main-chain structure ensemble, only with an amino acid composition given as a single argument. Then, we obtained a statistical formulae of the ensemble mean 〈E〉 and ensemble variance V[E] of the reference structural energies, as explicit functions of the amino acid composition. The mean 〈E〉 and the variance V[E] calculated from the formulae were well or roughly consistent with those resulting from a gapless threading simulation. We can use the formulae not only to perform the high-through-put screening of sequences in the inverse folding problem, but also to handle the problem analytically.