Conceptual framework for performing simultaneous fold and sequence optimization in multi-scale protein modeling

We present a dual optimization concept of predicting optimal sequences as well as optimal folds of off-lattice protein models in the context of multi-scale modeling. We validate the utility of the recently introduced hidden-force Monte Carlo optimization algorithm by finding significantly lower energy folds for minimalist and detailed protein models than previously reported. Further, we also find the protein sequence that yields the lowest energy fold amongst all sequences for a given chain length and residue mixture. In particular, for protein models with a binary sequence, we show that the sequence-optimized folds form more compact cores than the lowest energy folds of the historically fixed, Fibonacci-series sequences of chain lengths of 13, 21, 34, 55, and 89. We then extend our search algorithm to use UNRES, one of the leading united-residue protein force fields. Our combined fold and sequence optimization on three test proteins reveal an inherent bias in UNRES favoring alpha helical structures even when secondary structure prediction clearly suggests only beta sheets besides random coil, and virtually no helices. One test in particular, a triple-stranded antiparallel beta-sheet protein domain, demonstrates that by permutations of its sequence UNRES re-folds this structure into a perfect alpha helix but, in fact, the helix is just an artefact of the force field, the structure quickly unfolds in all-atom state-of-the-art molecular dynamics simulation.