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The entropic cost due to the loss of translational and rotational (T-R) degree of freedom upon binding has been well recognized for several decades. Tightly bound ligands have higher entropic costs than loosely bound ligands. Quantifying the ligand's residual T-R motions after binding, however, is not an easy task. We describe an approach that uses a reduced Hessian matrix to estimate the contributions due to translational and rotational degrees of freedom to entropy change upon molecular binding. The calculations use a harmonic model for the bound state but only include the T-R degrees of freedom. This approximation significantly speeds up entropy calculations because only 6 x 6 matt-ices need to be treated, which makes it easier to be used in computer-aided drug design for studying many ligands. The methodological connection with other methods is discussed as well. We tested this approximation by applying it to study the binding of ATP, peptide inhibitor (PKI), and several bound water molecules to protein kinase A (PKA). These ligands span a wide range in size. The model gave reasonable estimates of the residual T-R entropy of bound ligands or water molecules. The residual T-R entropy demonstrated a wide range of values, e.g., 4 to 16 cal/K(.)mol for the bound water molecules of PKA. (c) 2005 Wiley Periodicals, Inc.

Substrate phosphorylation by cAMP-dependent-protein kinase A (protein kinase A. PKA) has been studied extensively. Phosphoryl transfer was found to be fast, whereas ADP release was found to be the Slow. rate-limiting step. There is also evidence that ADP release may be preceded by a partially rate-limiting conformational change. However, the atomic details of the conformational change and the mode of ADP release are difficult to obtain experimentally. In this work, we studied ADP release from PKA by carrying out molecular dynamics simulations with different pulling forces applied to the ligand. The. detailed ADP release pathway and the associated conformational changes were analyzed. The ADP release process was found to involve a swinging motion with the phosphate of ADP anchored to the Gly-rich loop, so that the more buried adenine base and ribose ring came out before the phosphate. In contrast to the common belief that a hinge-bending motion was responsible for the opening of the ligand-binding cleft, our simulations showed that the small lobe exhibited a large amplitude "rocking" motion when the ligand came out. The largest conformational change of the protein was observed at about the first quarter time point along the release pathway. Two prominent intermediate states were observed in the release process.