Structural evolution of proteinlike heteropolymers

Abstract

The biological function of a protein often depends on the formation of an ordered structure in order to support a smaller, chemically active configuration of amino acids against thermal fluctuations. Here we explore the development of proteins evolving to satisfy this requirement using an off-lattice polymer model in which monomers interact as low resolution amino acids. To evolve the model, we construct a Markov process in which sequences are subjected to random replacements, insertions, and deletions and are selected to recover a predefined minimum number of solid-ordered monomers using the Lindemann melting criterion. We show that polymers generated by this process consistently fold into soluble, ordered globules of similar length and complexity to small protein motifs. To compare the evolution of the globules with proteins, we analyze the statistics of amino acid replacements, the dependence of site mutation rates on solvent exposure, and the dependence of structural distance on sequence distance for homologous alignments. Despite the simplicity of the model, the results display a surprisingly close correspondence with protein data.

Anomalous diffusion in neutral evolution of model proteins

“…The polymer model and the Markov process are described in Ref. [1] and in the Appendix to this Rapid Communication.…”

“…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.In recent work, we investigated the evolution of small protein motifs using a simplified off-lattice heteropolymer model [1]. The model is analogous to a commonly used lattice model in which individual monomers interact as lowresolution amino acids [2] and evolves according to a Markov process in which sequences are subjected to replacements, insertions, and deletions, and are selected to fold reproducibly into ordered globules capable of supporting a small binding site against thermal fluctuations.…”

“…In recent work, we investigated the evolution of small protein motifs using a simplified off-lattice heteropolymer model [1]. The model is analogous to a commonly used lattice model in which individual monomers interact as lowresolution amino acids [2] and evolves according to a Markov process in which sequences are subjected to replacements, insertions, and deletions, and are selected to fold reproducibly into ordered globules capable of supporting a small binding site against thermal fluctuations.…”

Evolution of off-lattice model proteins under ligand binding constraints

“…To compute exposed surface area, monomers are viewed as interpenetrating spheres, each coated with a large number of equally spaced points [32]. The fraction of exposed surface area, δA j /A, is measured as the fraction of points coating a monomer that are not enclosed in another sphere in the reference structure of a given sequence [12]. Transition rates, ω(δA), are measured as the number of transitions from monomers with exposure δA/A divided by the amount of time (i.e., iterations of the Markov process) that monomers with exposure δA/A are exposed to mutation.…”

“…In recent work, we began to explore the first of these problems using an off-lattice model in which polymers are evolved to maintain an ordered but otherwise un-restricted folding domain [12,13]. We found that the model could recapitulate basic properties of protein evolution, such as maintenance of amino acid sequence complexity and solubility of folded structures, linear rates of amino acid change as a function of solvent exposure, and linear divergence of folded structures with the number of accepted mutations.…”