Figure 5. Charge-changing mutations demonstrate worse complex phase sampling than neutral mutations and the slowest degrees of freedom responsible for poor sampling are highly variable depending on the mutation.

Data in this plot was generated from 50 ns/replica complex phase AREX simulations. Each row of the heatmap corresponds to a mutation and each of the first five columns corresponds to a degree of freedom category: backbone torsions, sidechain torsions, intra-interface contacts, inter-interface contacts, and neighboring waters. Each category contains a set of degrees of freedom, i.e., the backbone torsions category contains the $\varphi$ and $\psi$ angles for all interface residues, sidechain torsions contains the ${\chi }_1,{\chi }_2,{\chi }_3$, and ${\chi }_4$ angles for all interface residues (if the angle is present for the residue), intra-interface contacts contains pairs of interface residues that are within the same chain, inter-interface contacts contains pairs of interface residues that span different chains, and neighboring waters involves monitoring the number of waters within 5 Å of the mutating residue. Each heatmap value (in the first five columns) is the maximum of (the absolute value of) the Pearson correlation coefficients (PCCs) between $\partial U/\partial \lambda$ and each of the degrees of freedom in the corresponding category for the corresponding mutation. For example, the top left value of the heatmap indicates that for R83Q, the backbone torsion with maximum correlation to $\partial U/\partial \lambda$ has a PCC of 0.45. The background colors for the PCC values are different shades of gray, with darker grays indicating values closer to 1. The subscript and superscript values associated with each PCC represent the 95% confidence interval. Each heatmap value in the last column corresponds to the statistical inefficiency of $\partial U/\partial \lambda$ across all replica trajectories for the corresponding mutation. Statistical inefficiency is proportional to the correlation time, where a value of 0.1 ns indicates very thorough sampling (because the sampling interval is 0.1 ns) and large values indicate poor sampling. Statistical inefficiency values are colored different shades of purple, with darker colors indicating larger values. The rows of the heatmap are ordered from highest to lowest by the statistical inefficiency of $\partial U/\partial \lambda$ across all replicas. Blue dots indicate mutations for which the degree of freedom with the largest magnitude PCC is relatively far from the mutating residue. See Detailed Methods for more information about this analysis.