Statistical torsion angle potential energy functions for protein structure modeling: a bicubic interpolation approach

A set of grid type knowledge-based energy functions is introduced for ϕ-χ₁ , ψ-χ₁ , ϕ-ψ, and χ₁ -χ₂ torsion angle combinations. Boltzmann distribution is assumed for the torsion angle populations from protein X-ray structures, and the functions are named as statistical torsion angle potential energy functions. The grid points around periodic boundaries are duplicated to force periodicity, and the remedy relieves the derivative discontinuity problem. The devised functions rapidly improve the quality of model structures. The potential bias in the functions and the usefulness of additional secondary structure information are also investigated. The proposed guiding functions are expected to facilitate protein structure modeling, such as protein structure prediction, protein design, and structure refinement.