Thermodynamic Stability of Folded Proteins against Mutations

By balancing the average energy gap with its typical change due to mutations for proteinlike heteropolymers with M residues, we show that native states are unstable to mutations on a scale M^~(λ/σ_μ)^1/ζs, where λ is the dispersion in the interaction free energies and σ_μ is 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.