  How DNA is mapped to functional proteins is a basic question of living
matter. We introduce and study a physical model of protein evolution which
suggests a mechanical basis for this map. Many proteins rely on large-scale
motion to function. We therefore treat protein as learning amorphous matter
that evolves towards such a mechanical function: Genes are binary sequences
that encode the connectivity of the amino acid network that makes a protein.
The gene is evolved until the network forms a shear band across the protein,
which allows for long-range, soft modes required for protein function. The
evolution reduces the high-dimensional sequence space to a low-dimensional
space of mechanical modes, in accord with the observed dimensional reduction
between genotype and phenotype of proteins. Spectral analysis of the space of
$10^6$ solutions shows a strong correspondence between localization around the
shear band of both mechanical modes and the sequence structure. Specifically,
our model shows how mutations of the gene and their correlations occur at amino
acids whose interactions determine the functional mode.
