By balancing the average energy gap with its typical change due to mutations
for protein-like heteropolymers with M residues, we show that native states are
unstable to mutations on a scale M* ~ (lambda/sigma_mu)^(1/zeta_s), where
lambda is the dispersion in the interaction free energies and sigma_mu their
typical change. Theoretical bounds and numerical estimates (based on complete
enumeration on four lattices) of the instability exponent zeta_s are given. Our
analysis suggests that a limiting size of single-domain proteins should exist,
and leads to the prediction that small proteins are insensitive to random
mutations.Comment: 5 pages, 3 figures, to be published in Physical Review Letter
