"Multiplex" rheostat positions cluster around allosterically critical regions of the lactose repressor protein

Amino acid variation at "rheostat" positions provides opportunity to modulate various aspects of protein function - such as binding affinity or allosteric coupling - across a wide range. Previously a subclass of "multiplex" rheostat positions was identified at which substitutions simultaneously modulated more than one functional parameter. Using the Miller laboratorys dataset of [~]4000 variants of lactose repressor protein (LacI), we compared the structural properties of multiplex rheostat positions with (i) "single" rheostat positions that modulate only one functional parameter, (ii) "toggle" positions that follow textbook substitution rules, and (iii) "neutral" positions that tolerate any substitution without changing function. The combined rheostat classes comprised >40% of LacI positions, more than either toggle or neutral positions. Single rheostat positions were broadly distributed over the structure. Multiplex rheostat positions structurally overlapped with positions involved in allosteric regulation. When their phenotypic outcomes were interpreted within a thermodynamic framework, functional changes at multiplex positions were uncorrelated. This suggests that substitutions lead to complex changes in the underlying molecular biophysics. Bivariable and multivariable analyses of evolutionary signals within multiple sequence alignments could not differentiate single and multiplex rheostat positions. Phylogenetic analyses - such as ConSurf - could distinguish rheostats from toggle and neutral positions. Multivariable analyses could also identify a subset of neutral positions with high probability. Taken together, these results suggest that detailed understanding of the underlying molecular biophysics, likely including protein dynamics, will be required to discriminate single and multiplex rheostat positions from each other and to predict substitution outcomes at these sites.