Constructing smooth potential functions for protein folding

Toward correct protein folding potentials

Empirical protein folding potentialfunctions should have a global minimum nearthe native conformationof globular proteins that fold stably, andthey should give the correct free energy offolding. We demonstrate that otherwise verysuccessful potentials fail to have even alocal minimumanywhere near the native conformation, anda seemingly well validated method ofestimatingthe thermodynamic stability of the nativestate is extremely sensitive to smallperturbations inatomic coordinates. These are bothindicative of fitting a great deal ofirrelevant detail. Here weshow how to devise a robust potentialfunction that succeeds very well at bothtasks, at least for alimited set of proteins, and this involvesdeveloping a novel representation of thedenatured state.Predicted free energies of unfolding for 25mutants of barnase are in close agreementwith theexperimental values, while for 17 mutantsthere are substantial discrepancies.

Recognizing protein folds by cluster distance geometry

Cluster distance geometry is a recent generalization of distance geometry whereby protein structures can be described at even lower levels of detail than one point per residue. With improvements in the clustering technique, protein conformations can be summarized in terms of alternative contact patterns between clusters, where each cluster contains four sequentially adjacent amino acid residues. A very simple potential function involving 210 adjustable parameters can be determined that favors the native contacts of 31 small, monomeric proteins over their respective sets of nonnative contacts. This potential then favors the native contacts for 174 small, monomeric proteins that have low sequence identity with any of the training set. A broader search finds 698 small protein chains from the Protein Data Bank where the native contacts are preferred over all alternatives, even though they have low sequence identity with the training set. This amounts to a highly predictive method for ab initio protein folding at low spatial resolution.

A protein folding potential that places the native states of a large number of proteins near a local minimum

BACKGROUND

We present a simple method to train a potential function for the protein folding problem which, even though trained using a small number of proteins, is able to place a significantly large number of native conformations near a local minimum. The training relies on generating decoys by energy minimization of the native conformations using the current potential and using a physically meaningful objective function (derivative of energy with respect to torsion angles at the native conformation) during the quadratic programming to place the native conformation near a local minimum.

RESULTS

We also compare the performance of three different types of energy functions and find that while the pairwise energy function is trainable, a solvation energy function by itself is untrainable if decoys are generated by minimizing the current potential starting at the native conformation. The best results are obtained when a pairwise interaction energy function is used with solvation energy function.

CONCLUSIONS

We are able to train a potential function using six proteins which places a total of 42 native conformations within approximately 4 A rmsd and 71 native conformations within approximately 6 A rmsd of a local minimum out of a total of 91 proteins. Furthermore, the threading test using the same 91 proteins ranks 89 native conformations to be first and the other two as second.