Minimum Free Energy Path of Ligand-Induced Transition in Adenylate Kinase

Abstract

Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.

Sampling large conformational transitions: adenylate kinase as a testing ground

“…The most commonly used pair of order parameters for plotting 2D free energy surfaces of snapshots of simulation conformers is a heuristic measure consisting of the mass-center distances between domains (center of mass distance between the LID and CORE, and the center of mass distance between NMP and CORE) [24,58,[61][62][63][64][65][66]. Several studies use a LID-CORE and NMP-CORE angle pair, as shown in Figure 1, to independently quantify LID and NMP opening motions [15,31,59,67,68].…”

“…Lou and Cukier [71], Brokaw and Chu [72], and Pontiggia et al [73] all measure NMP-CORE separation with the distance between residues 55 and 169, but each, respectively, monitor LID-CORE variation differently: LID-CORE mass-center distance [71], C α distance between residues 127 and 194 [72], and LID-CORE angle [73]. Progress along one dimension (e.g., plotting the potential of mean force) was captured using domain mass-center distances [24,58,69,74], RMSD to and/or from crystal structures [15,61,67,75], and indices or distances along a computed reaction coordinate pathway [24,47,48,66,76,77]. …”

“…Comparison of such distances with the thermodynamic free energy landscape derived from MD simulations [31] showed that the distance between residues A55-V169 (NMP-CORE, Sinev et al [37]) and A127-A194 (LID-CORE, Hanson et al [39]) track the major conformational changes in apo-AdK in an almost orthogonal manner. A 2D space spanned by these two observables can serve to study the conformational dynamics of AdK at the level of individual domain motions Collective variables/Order parameters References 1D LID/NMP-CORE MCD [24,58,61,69,74] RMSD (to an end structure) [15,61,67,75] Indices along Rxn Coordinate [24,47,48,66,76,77] 2D LID/NMP-CORE MCD [24,58,[61][62][63][64][65][66] LID/NMP-CORE angle [15,31,59,67,68] RMSD (to end structures) [23,59,62] Essential Variables [8,23,43,65,69,70] Fraction of Native Contacts [16,59] Other [71][72]…”

“…The simulation of conformational transitions can be roughly subdivided into three distinct, but interdependent objectives: (1) accurately simulate conformational transition ensembles, (2) determine underlying free energy landscapes, and (3) predict transition probabilities and rates. A wide range of computational approaches to simulate rare transition events have been proposed [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], which all, however, necessitate certain assumptions; furthermore, it is not known how accurately these different methods reproduce real transition events. Nevertheless, due to their computational efficiency in comparison to pure equilibrium MD, they remain important tools for generating transition ensembles and gaining intuition for the dynamics of macromolecular systems.…”

Multiscale enhanced path sampling based on the Onsager-Machlup action: Application to a model polymer

“…In order to apply this method to complex molecular systems, which is obviously the next step, it is indispensable to make a great use of parallel calculation techniques. For a future work, the authors are interested in studying the conformational change of adenylate kinase [39], for which the minimum free energy path was recently elucidated by the on-the-fly string method [40].…”