Self-Consistent Framework Connecting Experimental Proxies of Protein Dynamics with Configurational Entropy

The recently developed NMR techniques enable estimation of protein configurational entropy change from the change in the average methyl order parameters. This experimental observable, however, does not directly measure the contribution of intramolecular couplings, protein main-chain motions, or angular dynamics. Here, we carry out a self-consistent computational analysis of the impact of these missing contributions on an extensive set of molecular dynamics simulations of different proteins undergoing binding. Specifically, we compare the configurational entropy change in protein complex formation as obtained by the maximum information spanning tree approximation (MIST), which treats the above entropy contributions directly, and the change in the average NMR methyl and NH order parameters. Our parallel implementation of MIST allows us to treat hard angular degrees of freedom as well as couplings up to full pairwise order explicitly, while still involving a high degree of sampling and tackling molecules of biologically relevant sizes. First, we demonstrate a remarkably strong linear relationship between the total configurational entropy change and the average change in both methyl and backbone-NH order parameters. Second, in contrast to canonical assumptions, we show that the main-chain and angular terms contribute significantly to the overall configurational entropy change and also scale linearly with it. Consequently, linear models starting from the average methyl order parameters are able to capture the contribution of main-chain and angular terms well. After applying the quantum-mechanical harmonic oscillator entropy formalism, we establish a similarly strong linear relationship for X-ray crystallographic B-factors. Finally, we demonstrate that the observed linear relationships remain robust against drastic undersampling and argue that they reflect an intrinsic property of compact proteins. Despite their remarkable strength, however, the above linear relationships yield estimates of configurational entropy change whose accuracy appears to be sufficient for qualitative applications only.