A computational model for controlling conformational cooperativity and function in proteins.

We present a computational model that allows for rapid prediction of correlations among a set of residue pairs when the fluctuations of another set of residues are perturbed. The simple theory presented here is based on the knowledge of the fluctuation covariance matrix only. In this sense, the theory is model independent and therefore universal. Perturbation of any set of fluctuations and the resulting response of the remaining set are calculated using conditional probabilities of a multivariate normal distribution. The model is expected to rapidly and accurately map the consequences of mutations in proteins, as well as allosteric activity and ligand binding. Knowledge of triple correlations of fluctuations of residues i, j, and k, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>〈</mml:mo> <mml:mrow><mml:mo>Δ</mml:mo> <mml:msub><mml:mi>R</mml:mi> <mml:mi>i</mml:mi></mml:msub> <mml:mo>Δ</mml:mo> <mml:msub><mml:mi>R</mml:mi> <mml:mi>j</mml:mi></mml:msub> <mml:mo>Δ</mml:mo> <mml:msub><mml:mi>R</mml:mi> <mml:mi>k</mml:mi></mml:msub> </mml:mrow> <mml:mo>〉</mml:mo></mml:mrow> </mml:math> emerges as the necessary source of information for controlling residue pairs by perturbing a distant residue. Triple correlations have not received wide attention in literature. Perturbation-response-function relations for ubiquitin (UBQ) are discussed as an example. Covariance matrix for UBQ obtained from the Gaussian Network Model combined with the present computational algorithm is able to reflect the millisecond molecular dynamics correlations and observed NMR results. © 2018 Wiley Periodicals, Inc.