A key question in human genetics and evolutionary biology is how mutations in different genes combine to alter phenotypes. Efforts to systematically map genetic interactions have mostly made use of gene deletions. However, most genetic variation consists of point mutations of diverse and difficult to predict effects. Here, by developing a new sequencing-based protein interaction assay - - we quantified the effects of >120,000 pairs of point mutations on the formation of the AP-1 transcription factor complex between the products of the FOS and JUN proto-oncogenes. Genetic interactions are abundant both in (within one protein) and (between the two molecules) and consist of two classes - interactions driven by thermodynamics that can be predicted using a three-parameter global model, and structural interactions between proximally located residues. These results reveal how physical interactions generate quantitatively predictable genetic interactions.