Probing the dark energy in the functional protein universe.

We show how to localize and quantify the functional evolutionary constraints on natural proteins. Protein folding has been one of the strongest constraints in sequence evolution. The method we propose compares the perturbations caused by local sequence variants to the energetics of the protein folding process and to the corresponding change to the apparent selection landscape of sequences over the evolutionary time scale. The difference between the physical folding free energies and the evolutionary free energies can be called a "dark energy." We analyze various protein sets and thereby show that dark energy is largely localized at functional sites, which are also often energetically frustrated from the point of view of folding. Overall, we find that about 25% of the positions of the folded globular proteins display some significant dark energy. When a function relies on a free energy that can be thermodynamically quantified, such as the binding energy to a partner, the relationship of this physical free energy with dark energy can be used to define a functional selection temperature, just as there is a selection temperature for folding. We show that selection for folding and binding functions bear similar weights in specific protein-protein interactions.