Anomalous diffusion in neutral evolution of model proteins

Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jun;91(6):060701. doi: 10.1103/PhysRevE.91.060701. Epub 2015 Jun 1.


Protein evolution is frequently explored using minimalist polymer models, however, little attention has been given to the problem of structural drift, or diffusion. Here, we study neutral evolution of small protein motifs using an off-lattice heteropolymer model in which individual monomers interact as low-resolution amino acids. In contrast to most earlier models, both the length and folded structure of the polymers are permitted to change. To describe structural change, we compute the mean-square distance (MSD) between monomers in homologous folds separated by n neutral mutations. We find that structural change is episodic, and, averaged over lineages (for example, those extending from a single sequence), exhibits a power-law dependence on n. We show that this exponent depends on the alignment method used, and we analyze the distribution of waiting times between neutral mutations. The latter are more disperse than for models required to maintain a specific fold, but exhibit a similar power-law tail.

MeSH terms

  • Diffusion
  • Evolution, Molecular*
  • Models, Molecular
  • Mutation
  • Protein Folding
  • Proteins / chemistry*
  • Proteins / genetics
  • Proteins / metabolism*


  • Proteins