Entropy tree networks of residue dynamics encode protein allostery

Abstract

To respond to environmental cues, proteins must amplify angstrom-scale signals across nanometers in the presence of thermal fluctuations. A prevailing view is that thermal fluctuations attenuate (1-7) signal-bearing coherent motions (8-11), yet numerous experiments correlate signaling state with fluctuations themselves (12-36). Here, we show that residue-level fluctuations encode "geometric bits" that are communicated within a sparse 3D network of shared entropy. We demonstrate this by developing an open-source framework that discovers shared entropy networks by inferring discrete residue conformations from molecular dynamics simulations of protein structure and finding maximum-likelihood tree distributions with minimal assumptions, enabling multiscale conformational entropy calculation without exhaustive enumeration. We validate our approach against an array of experimental data modalities probing sequence and ligand-dependent functions of PDZ and estrogen receptor ligand-binding domains, accurately predicting allosteric hotspots in saturation mutagenesis with residue-scale resolution, local entropies correlated with NMR and HDX dynamics, and global entropies in agreement with calorimetry without fitting. Comparing networks of the six human steroid receptors recovers phylogenetic history, providing evidence that evolution achieves functional diversity by reprogramming entropy within a fixed protein fold. The ability to transmit signals by harnessing thermal fluctuations categorically distinguishes proteins from human-designed communication channels, for which fluctuations are noise to be minimized.