Computational simulation of the statistical properties of unfolded proteins

A simple Monte Carlo method was used to generate ensembles of simulated polypeptide conformations that are restricted only by steric repulsion. The models used for these simulations were based on the sequences of four real proteins, ranging in size from 26 to 268 amino acid residues, and included all non-hydrogen atoms. Two sets of calculations were performed, one that included only intra-residue steric repulsion terms and those between adjacent residues, and one that included repulsion terms between all possible atom pairs, so as to explicitly account for the excluded volume effect. Excluded volume was found to increase the average radius of gyration of the chains by 20-40%, with the expansion factor increasing with chain length. Contrary to recent suggestions, however, the excluded volume effect did not greatly restrict the distribution of dihedral angles or favor native-like topologies. The average dimensions of the ensembles calculated with excluded volume were consistent with those measured experimentally for unfolded proteins of similar sizes under denaturing conditions, without introducing any adjustable scaling factor. The simulations also reproduced experimentally determined effective concentrations for the formation of disulfide bonds in reduced and unfolded proteins. The statistically generated ensembles included significant numbers of conformations that were nearly as compact as the corresponding native proteins, as well as many that were as accessible to solvent as a fully extended chain. On the other hand, conformations with as much buried surface area as the native proteins were very rare, as were highly extended conformations. These results suggest that the overall properties of unfolded proteins can be usefully described by a random coil model and that an unfolded polypeptide can undergo significant collapse while losing only a relatively small fraction of its conformational entropy.