  Understanding the relationship between protein sequence, function, and
stability is a fundamental problem in biology. While high-throughput methods
have produced large numbers of sequence-function pairs, functional assays do
not distinguish whether mutations directly affect function or are destabilizing
the protein. Here, we introduce a statistical method to infer the underlying
biophysics from a high-throughput binding assay by combining information from
many mutated variants. We fit a thermodynamic model describing the bound,
unbound, and unfolded states to high quality data of protein G domain B1
binding to IgG-Fc. We infer an energy landscape with distinct folding and
binding energies for each substitution providing a detailed view of how
mutations affect binding and stability across the protein. We accurately infer
folding energy of each variant in physical units, validated by independent
data, whereas previous high-throughput methods could only measure indirect
changes in stability. While we assume an additive sequence-energy relationship,
the binding fraction is epistatic due its non-linear relation to energy.
Despite having no epistasis in energy, our model explains much of the observed
epistasis in binding fraction, with the remaining epistasis identifying
conformationally dynamic regions.
