Sequence-function-stability relationships in proteins from datasets of functionally annotated variants: The case of TEM β-lactamases

► Loops are the main evolvable hotspots in TEMs and proteins in general. ► The generation of more complex functions requires more mutations to accumulate. ► Many new-function mutations are already present in the simpler enzymes. ► New-function and stability-restoring substitutions cluster to two groups of sites. ► Functional changes upon mutation can be predicted from physicochemical properties.