The Michaelis Complex of Arginine Kinase Samples the Transition State at a Frequency That Matches the Catalytic Rate

Arginine kinase (AK), which is a member of the phosphagen kinase family, serves as a model system for studying the structural and dynamic determinants of biomolecular enzyme catalysis of all major states involved of the enzymatic cycle. These states are the apo state (substrate free), the Michaelis complex analogue AK:Arg:Mg·AMPPNP (MCA), a product complex analogue AK:pAIE:Mg·ADP (PCA), and the transition state analogue AK:Arg:Mg·ADP:NO₃^- (TSA). The conformational dynamics of these states have been studied by NMR relaxation dispersion measurements of the methyl groups of the Ile, Leu, and Val residues at two static magnetic fields. Although all states undergo significant amounts of μs-ms time scale dynamics, only the MCA samples a dominant excited state that resembles the TSA, as evidenced by the strong correlation between the relaxation dispersion derived chemical shift differences Δω and the equilibrium chemical shift differences Δδ of these states. The average lifetime of the MCA is 36 ms and the free energy difference to the TSA-like form is 8.5 kJ/mol. It is shown that the conformational energy landscape of the Michaelis complex analogue is shaped in a way that at room temperature it channels passage to the transition state, thereby determining the rate-limiting step of the phosphorylation reaction of arginine. Conversely, relaxation dispersion experiments of the TSA reveal that it samples the structures of the Michaelis complex analogue or the apo state as its dominant excited state. This reciprocal behavior shows that the free energy of the TSA, with all ligands bound, is lower by only about 8.9 kJ/mol than that of the Michaelis or apo complex conformations with the TSA ligands present.