Colloquium: Proteins: The physics of amorphous evolving matter

Protein is matter of dual nature. As a physical object, a protein molecule is a folded chain of amino acids with diverse biochemistry. But it is also a point along an evolutionary trajectory determined by the function performed by the protein within a hierarchy of interwoven interaction networks of the cell, the organism, and the population. A physical theory of proteins therefore needs to unify both aspects, the biophysical and the evolutionary. Specifically, it should provide a model of how the DNA gene is mapped into the functional phenotype of the protein. Several physical approaches to the protein problem are reviewed, focusing on a mechanical framework which treats proteins as evolvable condensed matter: Mutations introduce localized perturbations in the gene, which are translated to localized perturbations in the protein matter. A natural tool to examine how mutations shape the phenotype are Green's functions. They map the evolutionary linkage among mutations in the gene (termed epistasis) to cooperative physical interactions among the amino acids in the protein. The mechanistic view can be applied to examine basic questions of protein evolution and design.