Fig. 4. Combinatorial ddPCA shows that abundant multi-mutants are binding-competent (have a conserved fold).

a, 3D structure of GRB2-SH3 (PDB: 2VWF) indicating 15 combinatorially mutated residues in library 3 (orange) and GAB2 ligand (blue). b, Overview of BindingPCA of GRB2-SH3 binding to GAB2 (ref. ²³). no, yeast growth defect; DHF, dihydrofolate; THF, tetrahydrofolate. c, Scatter plots showing the reproducibility of fitness estimates from triplicate BindingPCA experiments. Pearson’s r indicated in red. Rep., biological replicate. d, 2D density plots comparing abundance and binding fitness of third-order (left), sixth-order (middle) and ninth-order mutants (right). See Extended Data Fig. 6g for similar plots at all mutant orders. e, Three-state equilibrium and corresponding thermodynamic model. ΔG_f, Gibbs free energy of folding; ΔG_b, Gibbs free energy of binding; K_f, folding equilibrium constant; K_b, binding equilibrium constant; c, ligand concentration; p_f, fraction folded; p_fb, fraction folded and bound; R, gas constant; T, temperature in kelvin. f, Neural network architecture used to fit thermodynamic model to ddPCA data (bottom, target and output data), thereby inferring the causal changes in free energy of folding and binding associated with single aa substitutions (first-order terms) and pairwise (second-order) interaction terms (top, input values). Variables as per panel e and: g_f, nonlinear function of ΔG_f; g_fb, nonlinear function of ΔG_f and ΔG_b. g, Nonlinear relationships between observed AbundancePCA fitness and changes in free energy of folding (top) or BindingPCA fitness and free energies of both binding and folding (bottom). Thermodynamic model fit is shown in red. h, Performance of models fit to ddPCA data. R², proportion of explained variance. i, Comparisons of the model-inferred single aa substitution free energy changes to previously reported estimates using GRB2-SH3 ddPCA data²³. Pearson’s r is shown.