Thermodynamic stability of folded proteins against mutations

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 ∼ (λ/σμ) 1/ζs , where λ is the dispersion in the interaction free energies and σμ their typical change. Theoretical bounds and numerical estimates (based on complete enumeration on four lattices) of the instability exponent ζs 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.