  The catalytic conversion ATP + AMP -> 2ADP by the enzyme adenylate kinase
(ADK) involves the binding of one ATP molecule to the LID domain and one AMP
molecule to the NMP domain. The latter is followed by a phosphate transfer, and
then the release of two ADP molecules. We have computed a novel two dimensional
configurational free energy surface (2DCFES), with one reaction coordinate each
for the LID and the NMP domain motions, with explicit interactions with water.
Our computed 2DCFES clearly reveals the existence of a stable
half-open-half-closed (HOHC) intermediate state of the enzyme. Cycling of the
enzyme through the HOHC state reduces the conformational free energy barrier
for the reaction by about 20 kJ/mol. We find that the stability of the
half-open-half-closed state (missed in all earlier studies with implicit
solvent model) is largely because of the increase of specific interactions of
the polar amino acid side chains with water, particularly with the arginine and
the histidine residues. Free energy surface of the LID domain is rather rugged,
which can conveniently slow down LID's conformational motion, thus facilitating
a new substrate capture after the product release in the catalytic cycle.
