Fig. 2

Fitting biophysical models to DMS data with MoCHI. a Library design and yeast growth-based functional assay used to interrogate the effects of single AA substitutions on the heterodimerization of FOS and JUN via BindingPCA (bPCA) [41]. Red cross, yeast growth defect; DHF, dihydrofolate; THF, tetrahydrofolate. b Library design and mRNA display-based in vitro assay used to interrogate the effects of all single and double AA substitutions in the IgG-binding domain of protein G (GB1) [31]. c, d Two- and three-state equilibria, thermodynamic models, neural network architectures, and corresponding MoCHI model design tables used to infer the binding and folding free energy changes (∆∆G_f, ∆∆G_b) of the mutant libraries depicted in panels a and b, respectively. ∆G_b, Gibbs free energy of binding; ∆G_f, Gibbs free energy of folding; K_b, binding equilibrium constant; K_f, folding equilibrium constant; c, standard reference concentration; p_b, fraction bound; g, nonlinear function of ∆G_b (panel c) or ∆G_f and ∆G_b (panel d); R, gas constant; T, temperature in Kelvin. e Nonlinear relationship (global epistasis) between observed BindingPCA fitness and inferred changes in free energy of binding. Thermodynamic model fit shown in red. f Performance of two-state biophysical model. R² is the proportion of variance explained. g Nonlinear relationship between observed mRNA display fitness and inferred changes in free energies of binding and folding. h Performance of three-state biophysical model. i Violin plots showing the distributions of binding free energy changes for mutations in different structural/heptad positions in the FOS-JUN heterodimer (see legend). j Comparisons of confident model-inferred free energy changes to previously reported in vitro measurements [31, 44]. Error bars indicate 95% confidence intervals from a Monte Carlo simulation approach (n = 10 experiments). Pearson’s r is shown