A position-specific distance-dependent statistical potential for protein structure and functional study

Abstract

Although studied extensively, designing highly accurate protein energy potential is still challenging. A lot of knowledge-based statistical potentials are derived from the inverse of the Boltzmann law and consist of two major components: observed atomic interacting probability and reference state. These potentials mainly distinguish themselves in the reference state and use a similar simple counting method to estimate the observed probability, which is usually assumed to correlate with only atom types. This article takes a rather different view on the observed probability and parameterizes it by the protein sequence profile context of the atoms and the radius of the gyration, in addition to atom types. Experiments confirm that our position-specific statistical potential outperforms currently the popular ones in several decoy discrimination tests. Our results imply that, in addition to reference state, the observed probability also makes energy potentials different and evolutionary information greatly boost performance of energy potentials.

Figure 1

Distance dependence of DOPE and our potential EPAD. (A) The solid curve shows the DOPE interaction potential for atom C_α in ALA and atom C_α in LEU. The other 3 curves show the EPAD potentials for the same atom pair in three different positions of protein 1gvp. The legend shows the native distances of this atom pair in these positions. (B) The curves show the DOPE and EPAD potential for atom N in Cys and atom O in Trp in three different proteins of 1b3a, 1bkr and 1ptq.

Figure 1

Distance dependence of DOPE and our potential EPAD. (A) The solid curve shows the DOPE interaction potential for atom C_α in ALA and atom C_α in LEU. The other 3 curves show the EPAD potentials for the same atom pair in three different positions of protein 1gvp. The legend shows the native distances of this atom pair in these positions. (B) The curves show the DOPE and EPAD potential for atom N in Cys and atom O in Trp in three different proteins of 1b3a, 1bkr and 1ptq.

Figure 2

An example probabilistic neural network, in which S_i and S_j are the sequence profile contexts centered at the i^th and j^th residues, respectively. $H_q^1$ and $H_p^2$ are the neurons in the 1^st and 2^nd hidden layers.