  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.
