Using self-consistent fields to bias Monte Carlo methods with applications to designing and sampling protein sequences

For complex multidimensional systems, Monte Carlo methods are useful for sampling probable regions of a configuration space and, in the context of annealing, for determining “low energy” or “high scoring” configurations. Such methods have been used in protein design as means to identify amino acid sequences that are energetically compatible with a particular backbone structure. As with many other applications of Monte Carlo methods, such searches can be inefficient if trial configurations (protein sequences) in the Markov chain are chosen randomly. Here a mean-field biased Monte Carlo method (MFBMC) is presented and applied to designing and sampling protein sequences. The MFBMC method uses predetermined sequence identity probabilities wi(α) to bias the sequence selection. The wi(α) are calculated using a self-consistent, mean-field theory that can estimate the number and composition of sequences having predetermined values of energetically related foldability criteria. The MFBMC method is applied to both ...

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