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 $M^{\star }\sim (\lambda /{\sigma }_{\mu }{)}^{1/\zeta s}$, where $\lambda$ is the dispersion in the interaction free energies and ${\sigma }_{\mu }$ is 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.