Combinatorial design of protein sequences with applications to lattice and real proteins

Understanding the evolution of protein structures from specific sequences may be achieved by predicting the desired folded structure from a given sequence and by predicting compatible sequences from a known structure using principles of protein folding and design. Protein design requires the synthesis of a broad range of sequences consistent with a preassigned target conformation. However, the number of possible protein sequences for a given target structure exponentially increases with the number of residues making the explicit tabulation of all sequences intractable experimentally and computationally. For sequence libraries of arbitrary size, the results of a self-consistent mean field theory is applied to a three-dimensional cubic lattice model of proteins and real homologous protein sequences to estimate the number and probabilistic composition of sequences consistent with a generalized foldability criterion. Theoretically calculated site-specific monomer probabilities and the monomer pair probabilities at each position in a sequence are compared to those obtained from exact enumeration for cubic lattice proteins. For real proteins the theoretically predicted sequence variability are compared to that obtained from a set of homologous protein sequences. The theory results match extremely well with both the cubic lattice protein and real protein results. The theory also evaluates the mutability of specific residues and identifies the beneficial mutations. The theory may be used to quantify particular design strategies and explore site-directed mutagenesis strategies in crafting de novo proteins in context of in vitro protein evolution.