“…Only 0.57% (12 of 2,101) of double amino acid substitutions in the measured data have EC 50 values that differ from the log-additive effects of the single substitutions by more than 2.5-fold (Fig 4). This result, combined with the wide distribution of residues that affect EC 50 , reinforces the view that allostery is a distributed biophysical phenomenon controlled by a free energy balance with additive contributions from many residues and interactions, a mechanism proposed previously (Marzen et al, 2013;Motlagh et al, 2014) and supported by other recent studies (Leander et al, 2020), rather than a process driven by the propagation of local, contiguous structural rearrangements along a defined pathway. The log-additive EC 50 for double-substitution LacI variants (i.e., two amino acid substitutions) was calculated assuming log-additivity of the effect of each single substitution on the EC 50 relative to wild-type LacI: log(EC 50,AB / EC 50,wt ) = log(EC 50,A /EC 50,wt ) + log(EC 50,B /EC 50,wt ), where "wt" indicates the wild type, "A" and "B" indicate the single-substitution variants, and "AB" indicates the double-substitution variant.…”