Mechanical function of proteins constrains sequence space to a low dimension: a simple physical model.

DNA genes are mapped to 3D arrangements of amino acids that make functional proteins. We will discuss this back-and-forth mapping, between the many-body physics within the protein and evolutionary forces acting on the gene. To look into the geometry of the map, we introduce a simple physical model in which proteins are treated as amino acid networks that adapt their connectivity to evolve a specific mechanical mode. Such large-scale conformational changes -- where big chunks of the protein move with respect to each other -- are known to be central to the function of many proteins. We will discuss how the collective physical interaction within the proteins projects the high-dimensional sequence space onto a low-dimensional space of mechanical modes: most of the gene records random evolution, while only a small non-random fraction is constrained by the biophysical function. Spectral analysis reveals a strong signature of the protein's structure and function within correlation `ripples' that appear in the space of DNA sequences. These findings propose a testable basic principle of the protein as amorphous matter whose dynamics encode the evolutionary learning process. [1] Tlusty, Libchaber {\&} Eckmann, \textit{Physical model of the sequence-to-function map of proteins} (arXiv:1608.03145).