Molecular Dynamics of Apo-Adenylate Kinase: A Distance Replica Exchange Method for the Free Energy of Conformational Fluctuations

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Abstract
A large domain motion in adenylate kinase from E. coli (AKE) is studied with molecular dynamics. AKE undergoes a large-scale rearrangement of its lid and AMP-binding domains when the open form closes over its substrates, AMP, and Mg2+-ATP, whereby the AMP-binding and lid domains come closer to the core. The third domain, the core, is relatively stable during this motion. A reaction coordinate that monitors the distance between the AMP-binding and core domains is selected to be able to compare with the results of energy transfer experiments. Sampling along this reaction coordinate is carried out by using a distance replica exchange method (DREM), where systems that differ by a restraint potential enforcing different reaction coordinate values are independently simulated with periodic attempts at exchange of these systems. Several methods are used to study the efficiency and convergence properties of the DREM simulation and compared with an analogous non-DREM simulation. The DREM greatly accelerates the rate and extent of configurational sampling and leads to equilibrium sampling as measured by monitoring collective modes obtained from a principal coordinate analysis. The potential of mean force along the reaction coordinate reveals a rather flat region for distances from the open to a relatively closed AKE conformation. The potential of mean force for smaller distances has a distinct minimum that is quite close to that found in the closed form X-ray structure. In concert with a decrease in the reaction coordinate distance (AMP-binding-to-core distance) the lid-to-core distance of AKE also decreases. Therefore, apo AKE can fluctuate from its open form to conformations that are quite similar to its closed form X-ray structure, even in the absence of its substrates.