Summary

The ability to tolerate neutral mutations correlates with protein thermostability (1). Direct manifestations of this are uncoupling of tightly packed, stable structures such as TIM barrels and immunoglobulin folds, from the loops mediating function (in antibodies, the CDRs).

Details

An interesting counterpoint are Intrinsically disordered regions and viral proteins which are extremely unstable and evolve extremely fast; it is unclear why.

See also

1.
DePristo MA, Weinreich DM, Hartl DL. Missense meanderings in sequence space: a biophysical view of protein evolution. Nature Reviews Genetics. 2005;6(9):678–87. Available from: https://doi.org/10.1038/nrg1672