Bravi et al. apply Direct Coupling Analysis to an evolved allosteric elastic-network ensemble cast as a synthetic protein alignment

Bravi, Ravasio, Brito, and Wyart (arXiv:1811.10480; PLoS Comput. Biol. 16(3):e1007630, 2020) construct a literal methodological bridge between the mechanical-network modeling of allostery and the sequence-based inference of protein coevolution. They evolve elastic spring networks (L = 12, 2D, periodic boundaries) by Metropolis–Monte-Carlo selection for cooperative binding between an "allosteric" site and a distant "active" site — the same evolved-elastic-network lineage the vault already holds through Rocks et al. (claim-removing-one-percent-of-bonds-makes-a-random-network-allosteric, cited here as reference [27]). Each evolved network is a binary string over its links (a spring is present, σi = 1, or absent, σi = 0), so a population of them becomes a synthetic sequence alignment.

The analogy is stated outright: "Our set of sequences is analogous to a protein MSA – importantly, in this analogy the role of an amino-acid is played by a link, which can be stiff (σi = 1) or not (σi = 0, no springs)." Onto this synthetic Multiple Sequence Alignment of M = 135,000 networks the authors run entity-direct-coupling-analysis — the standard bioinformatics tool for inferring coevolving residue pairs from real protein families — using both Adaptive Cluster Expansion with maximum-likelihood refinement and mean-field DCA. The stated purpose is to "benchmark DCA in models of protein allostery where a material evolves in silico to achieve an 'allosteric' task."

This is the sequence-side complement to the vault's existing mechanics-side physics↔biology bridge, which runs through cheap-to-engineer allostery (claim-removing-one-percent-of-bonds-makes-a-random-network-allosteric), soft-mode structure–function (claim-physical-networks-become-what-they-learn-soft-modes), and local physical training (claim-coupled-learning-elastic-networks-compute-without-a-processor). What DCA finds when it reads these networks, and its scope limits, are developed in claim-dca-predicts-mutation-costs-but-poor-generative-model-of-allostery, claim-dca-underestimates-long-range-epistasis-in-allosteric-materials, and the real-protein test claim-pdz-dca-couplings-track-short-range-epistasis-more-than-long-range. The specific character of these networks — evolved, not coupled-learning-trained — is the scope caveat in claim-bravi-allosteric-networks-are-evolved-not-coupled-learning.