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Dynamic coupling between the LID and NMP domain motions in the catalytic conversion of ATP and AMP to ADP by adenylate kinase

The catalytic conversion of ATP and AMP to ADP by adenylate kinase (ADK) involves large amplitude, ligand induced domain motions, involving the opening and the closing of LID and NMP domains, during the repeated catalytic cycle. We discover and analyze an interesting dynamical coupling between the motions of the two domains during the opening, using large scale atomistic molecular dynamics trajectory analysis, covariance analysis and multi-dimensional free energy calculations with explicit water. Initially, the LID domain must open by a certain amount before the NMP domain can begin to open. Dynamical correlation map shows interesting cross-peak between LID and NMP domain which suggests the presence of correlated motion between them. This is also reflected in our calculated two dimensional free energy surface contour diagram which has an interesting elliptic shape, revealing a strong correlation between the opening of the LID domain and that of the NMP domain. Our free energy surface of the LID domain motion is rugged due to interaction with water and the signature of ruggedness is evident in the observed RMSD variation and its fluctuation time correlation functions. We develop a correlated dynamical disorder type theoretical model to explain the observed dynamic coupling between the motions of the two domains in ADK. Our model correctly reproduces several features of the cross-correlation observed in simulations.