Statistical mechanics of biomolecular condensates via cavity methods.

Physical mechanisms of phase separation in living systems play key physiological roles and have recently been the focus of intensive studies. The strongly heterogeneous nature of such phenomena poses difficult modeling challenges that require going beyond mean-field approaches based on postulating a free energy landscape. The pathway we take here is to calculate the partition function starting from microscopic interactions by means of cavity methods, based on a tree approximation for the interaction graph. We illustrate them on the binary case and then apply them successfully to ternary systems, in which simpler one-factor approximations are proved inadequate. We demonstrate the agreement with lattice simulations and contrast our theory with coacervation experiments of associative de-mixing of nucleotides and poly-lysine. Different types of evidence are provided to support cavity methods as ideal tools for modeling biomolecular condensation, giving an optimal balance between the consideration of spatial aspects and fast computational results.

Adaptive Properties of the Genetically Encoded Amino Acid Alphabet Are Inherited from Its Subsets.

Life uses a common set of 20 coded amino acids (CAAs) to construct proteins. This set was likely canonicalized during early evolution; before this, smaller amino acid sets were gradually expanded as new synthetic, proofreading and coding mechanisms became biologically available. Many possible subsets of the modern CAAs or other presently uncoded amino acids could have comprised the earlier sets. We explore the hypothesis that the CAAs were selectively fixed due to their unique adaptive chemical properties, which facilitate folding, catalysis, and solubility of proteins, and gave adaptive value to organisms able to encode them. Specifically, we studied in silico hypothetical CAA sets of 3-19 amino acids comprised of 1913 structurally diverse α-amino acids, exploring the adaptive value of their combined physicochemical properties relative to those of the modern CAA set. We find that even hypothetical sets containing modern CAA members are especially adaptive; it is difficult to find sets even among a large choice of alternatives that cover the chemical property space more amply. These results suggest that each time a CAA was discovered and embedded during evolution, it provided an adaptive value unusual among many alternatives, and each selective step may have helped bootstrap the developing set to include still more CAAs.