Protein Structure and Energy Landscape Dependence on Sequence Using a Continuous Energy Function

We have recently described a new conformational search strategy for protein folding algorithms called the CGU (convex global underestimator) method. Here we use a simplified protein chain representation and a differentiable form of the Sun/Thomas/Dill energy function to test the CGU method. Standard search methods, such as Monte Carlo and molecular dynamics are slowed by kinetic traps. That is, the computer time depends more strongly on the shape of the energy landscape (dictated by the amino acid sequence) than on the number of degrees of freedom (dictated by the chain length). The CGU method is not subject to this limitation, since it explores the underside of the energy landscape, not the top. We find that the CGU computer time is largely independent of the monomer sequence for different chain folds and scales as O(n4) with chain length. By using different starting points, we show that the method appears to find global minima. Since we can currently find stable states of 36-residue chains in 2.4 hours, the method may be practical for small proteins.