A statistical mechanical method to optimize energy functions for protein folding

Abstract

We present a method for deriving energy functions for protein folding by maximizing the thermodynamic average of the overlap with the native state. The method has been tested by using the pairwise contact approximation of the energy function and generating alternative structures by threading sequences over a database of 1, 169 structures. With the derived energy function, most native structures: (i) have minimal energy and (ii) are thermodynamically rather stable, and (iii) the corresponding energy landscapes are smooth. Precisely, 92% of the 1,013 x-ray structures are stabilized. Most failures can be attributed to the neglect of interactions between chains forming polychain proteins and of interactions with cofactors. When these are considered, only nine cases remain unexplained. In contrast, 38% of NMR structures are not assigned properly.

Figure 1

Fraction of intrachain contacts as a function of the number of residues to the power −1/3. Filled symbols are protein chains whose ground state does not coincide with the native structure.

Figure 2

Normalized energy gap vs. the overlap q for six protein chains.

Figure 3

Distribution of the normalized stability parameter α(S)/, where N is the number of residues and only chains with q_o = 1 are included.

Figure 4

Histograms of the overlap q₁ between the best prediction and the native structure and of the maximal overlap q_max for single chains. (Inset) Average value of q₁/q_max as a function of q_max.