Cho and Murakami defined the potential function for a link [Formula: see text] in whose critical point, slightly different from usual sense, corresponds to boundary-parabolic representation text]. They also showed that volume Chern–Simons invariant of can be computed with its partial derivatives. In this paper, we extend is not necessarily boundary-parabolic. We show under mild assumption it le...

Developing an accurate scoring function is essential for successfully predicting protein structures. In this study, we developed a statistical potential function, called OPUS-Beta, for energetically evaluating β-sheet contact pattern (the entire residue-residue β-contacts of a protein) independent of the atomic coordinate information. The OPUS-Beta potential contains five terms, i.e., a self-pa...