Free energies of protein decoys provide insight into determinants of protein stability

Abstract

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.

Fig. 1.

The total excess free energy as a function of the RMSD for decoys of three proteins (1ctf, 1r69, and 4pti) from the Park and Levitt decoy set (Park and Levitt 1996). The excess energy is defined relative to the native structure. The two lowest energy points, RMSD 3.2 Å (circles) and RMSD 3.6 Å (diamonds), belong to the 1ctf_a19727 and 4pti_c20227 decoys, respectively; the dashed line is the minimum discrimination line.

Fig. 2.

The total excess free energy as a function of the RMSD for models of the CASP3 targets t004 (1HKA) and t0082 (1BK7) and the Park and Levitt decoys; the dashed line is the minimum discrimination line.

Fig. 3.

The excess packing energy as a function of the RMSD for the Park and Levitt decoys.

Fig. 4.

The excess packing energy as a function of the RMSD for the CASP3 models and the Park and Levitt decoys.

Fig. 5.

The excess molecular surface area as a function of the RMSD for the Park and Levitt decoys.

Fig. 6.

The excess molecular surface area as a function of the RMSD for the CASP3 models and the Park and Levitt decoys.

Fig. 7.

The excess total electrostatic free energy as a function of the RMSD for the Park and Levitt decoys.

Fig. 8.

The excess total electrostatic free energy as a function of the RMSD for the CASP3 models and the Park and Levitt decoys.

Fig. 9.

The excess internal electrostatic energy as a function of the RMSD for the Park and Levitt decoys.

Fig. 10.

The excess internal electrostatic energy as a function of the RMSD for the CASP3 models and the Park and Levitt decoys.

Fig. 11.

The excess total energy in a vacuum as a function of the RMSD for the Park and Levitt decoys.

Fig. 12.

The excess total energy in a vacuum as a function of the RMSD for the CASP3 models and the Park and Levitt decoys.

Fig. 13.

The excess free energy of solvent polarization versus the internal electrostatic energy for the CASP3 models and the Park and Levitt decoys.

Fig. 14.

Rmsd versus simulation time in a free molecular dynamic relaxation of two low-energy decoys (4pti_c20227 and 1ctf_a19727) from the Park and Levitt decoy set.

Fig. 15.

The total free energy versus simulation time in a free molecular dynamic relaxation of two low-energy decoys (Fig. 14 ▶); the thin lines represent instantaneous values; the bold lines, averages over a 50-ps window.