Protein stability is determined by single-site bias rather than pairwise covariance

The biases revealed in protein sequence alignments have been shown to provide information related to protein structure, stability, and function. For example, sequence biases at individual positions can be used to design consensus proteins that are often more stable than naturally occurring counterparts. Likewise, correlations between pairs of residue can be used to predict protein structures. Recent work using Potts models show that together, single-site biases and pair correlations lead to improved predictions of protein fitness, activity, and stability. Here we use a Potts model to design groups of protein sequences with different amounts of single-site biases and pair correlations, and determine the thermodynamic stabilities of a representative set of sequences from each group. Surprisingly, sequences excluding pair correlations maximize stability, whereas sequences that maximize pair correlations are less stable, suggesting that pair correlations contribute to another aspect of protein fitness. Consistent with this interpretation, we find that for adenylate kinase, enzyme activity is greatly increased by maximizing pair correlations. The finding that elimination of covariant residue pairs increases protein stability suggests a route to enhance stability of designed proteins; indeed, this strategy produces hyperstable homeodomain and adenylate kinase proteins that retain significant activity.