New statistical potential for quality assessment of protein models and a survey of energy functions

Abstract

Background: Scoring functions, such as molecular mechanic forcefields and statistical potentials are fundamentally important tools in protein structure modeling and quality assessment.

Results: The performances of a number of publicly available scoring functions are compared with a statistical rigor, with an emphasis on knowledge-based potentials. We explored the effect on accuracy of alternative choices for representing interaction center types and other features of scoring functions, such as using information on solvent accessibility, on torsion angles, accounting for secondary structure preferences and side chain orientation. Partially based on the observations made, we present a novel residue based statistical potential, which employs a shuffled reference state definition and takes into account the mutual orientation of residue side chains. Atom- and residue-level statistical potentials and Linux executables to calculate the energy of a given protein proposed in this work can be downloaded from http://www.fiserlab.org/potentials.

Conclusions: Among the most influential terms we observed a critical role of a proper reference state definition and the benefits of including information about the microenvironment of interaction centers. Molecular mechanical potentials were also tested and found to be over-sensitive to small local imperfections in a structure, requiring unfeasible long energy relaxation before energy scores started to correlate with model quality.

Figure 1

Statistical significance of rank distributions obtained with different methods. Only p-values obtained with one-tailed Wilcoxon test above 0.05 are shown. Alternative hypothesis in the test was that location of the distribution obtained with scoring function in a row is lower than the one in the column. Interaction centers are color coded in row titles as follows: black is used for residue-based potentials, blue is used for atom-based potentials, and red designates composite scoring functions. Certain interaction types are color coded in column titles, specifically, scoring functions making use of solvent accessibility (green), torsion angle dependence (blue), secondary structure dependence (red), and orientation-dependence (in italic).

Figure 2

Performance of different potentials as a function of the quality of the best available model. Average rank calculated by (A) composite functions, (B) heavy-atom based functions, and (C) residue-based potential functions for targets having best model with GDT_TS better than 95.0 (11 targets), between 87.5 and 95.0 (25 targets), between 80.0 and 87.5 (32 targets), between 72.5 and 80.0 (47 targets) and between 65.0 and 72.5 (28 targets).

Figure 3

Definition of residue orientation used to derive potentials. (A) interaction i → j is considered "parallel" if the scalar product of C_α-C_β vectors for residues i (vector a) and j (vector b) is positive; (B) interaction i → j is considered "antiparallel i facing j" if scalar product of a and b is non-positive and scalar product of vector a and vector from C_α atom of residue i to C_α atom of residue j (vector c) is positive; (C) interaction i → j is considered as "antiparallel i pointing away from j" if both a·b and a·c scalar products are non-positive.

Figure 4

Superimposition of models of different quality with the experimental solution structure. Experimental structure of the CASP8 target T0502 (violet) and its models, (A) METATASSER_TS5, GDT_TS = 80.357, (B) 3Dpro_TS4, GDT_TS = 60.204, and (C) panther_server_TS2, GDT_TS = 44.643 are shown as C_α traces. Those parts of the models, where the experimental positions are not known are colored white. Parts of models deviating from experimentally determined positions less than 4 Å are colored green, and the rest is colored bronze. C_α-C_α pseudobonds longer than 3.9 Å are shown thin. This plot has been generated using MOLSCRIPT software [63].