Fig. 6

Biophysical models inferred from DMS and MPRA data. a Thermodynamic model for IgG binding by GB1. This model assumes that GB1 can be in one of three states (unfolded, folded-unbound, and folded-bound). The Gibbs free energies of folding (ΔG_F) and binding (ΔG_B) are computed from sequence using additive models, which in biophysical contexts like these are called energy matrices [1, 12]. The latent phenotype is given by the fraction of time GB1 is in the folded-bound state. b The ΔΔG parameters of the energy matrices for folding and binding, inferred from the data of Olson et al. [8] by fitting this thermodynamic model using GE regression. The amino acid ordering used here matches that of Otwinowski [47]. Additional file 1: Fig. S5 plots folding energy predictions against the measurements of Nisthal et al. [49]. c A four-state thermodynamic model for transcriptional activation at the E. coli lac promoter. The Gibbs free energies of RNAP-DNA binding (ΔG_R) and CRP-DNA binding (ΔG_C) are computed using energy matrices, whereas the CRP-RNAP interaction energy ΔG_I is a scalar. The latent phenotype is the fraction of time a promoter is bound by RNAP. d,e The latent phenotype model inferred from the sort-seq MPRA data of Kinney et al. [12]. This model includes both the MPA measurement process (d) and the parameters of the thermodynamic G-P map (e). Additional file 1: Fig. S4 provides detailed definitions of the thermodynamic models in panels a and c. Sequence logos in panel e were generated using Logomaker [40]. Standard errors on ΔG_I were determined using the parametric bootstrap approach described in “Methods”. DMS: deep mutational scanning; MPRA: massively parallel reporter assay; IgG: immunoglobulin G; GB1: protein G domain B1; GE: global epistasis. RNAP: σ⁷⁰ RNA polymerase; CRP: cAMP receptor protein; MPA: measurement-process agnostic. G-P: genotype-phenotype