Demonstrated convergence of the equilibrium ensemble for a fast united-residue protein model

Because of the time-scale limitations of all-atom simulation of proteins, there has been substantial interest in coarse-grained approaches. Some methods, like "resolution exchange" (Lyman, E.; Ytreberg, F. M.; Zuckerman, D. M. Phys. Rev. Lett. 2006, 96, 028105-1-4), can accelerate canonical all-atom sampling but require properly distributed coarse ensembles. We therefore demonstrate that full sampling can indeed be achieved in a sufficiently simplified protein model, as verified by a recently developed convergence analysis. The model accounts for protein backbone geometry, in that rigid peptide planes rotate according to atomistically defined dihedral angles, but there are only two degrees of freedom (φ and ψ dihedrals) per residue. Our convergence analysis indicates that small proteins (up to 89 residues in our tests) can be simulated for more than 50 "structural decorrelation times" in less than a week on a single processor. We show that the fluctuation behavior is reasonable, and we discuss applications, limitations, and extensions of the model.