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.

The active site a the mammalian cAMP-dependent protein kinase catalytic subunit (C-sub-unit) has a cluster of nonconserved acidic residues-Glu127, Glul 70, Glu203, Glu230, and Asp241-that are crucial for substrate recognition and binding. Studies have shown that the Glu230 to Gln mutant (E230Q) of the enzyme has physical properties similar to the wild-type enzyme and has decreased affinity for a short peptide substrate, Kemptide. However, recent experiments intended to crystallize tertiary complex of the E230Q mutant with MgATP and protein kinase inhibitor (PKI) could only, obtain crystals of the apo-enzyme of E230Q mutant. To deduce the possible mechanism that prevented tertiary complex formation, we used the relaxed-complex method (Lin, J.-H., et al. J Am Chem Soc 2002, 24, 5632-5633) to study PKI binding to the E230Q mutant C-subunit. In the E230Q mutant, we observed local structural changes of the peptide binding site that correlated closely to the reduced PKI affinity. The structural changes occurred in the F-to-G helix loop and appeared to hinder PKI binding. Reduced electrostatic potential repulsion among Asp241 from the helix loop section and the other acidic residues in the peptide binding site appear to be responsible for the structural change. (c) 2005 Wiley Periodicals, Inc.

A rigorous approach is proposed to calculate the electrostatic forces among an arbitrary number of solvated molecules in ionic solution determined by the linearized Poisson-Boltzmann equation. The variational principle is used and implemented in the frame of a boundary element method (BEM). This approach does not require the calculation of the Maxwell stress tensor on the molecular surface, therefore it totally avoids the hypersingularity problem in the direct BEM whenever one needs to calculate the gradient of the surface potential or the stress tensor. This method provides an accurate and efficient way to calculate the full intermolecular electrostatic interaction energy and force, which could potentially be used in Brownian dynamics simulation of biomolecular association. The method has been tested on some simple cases to demonstrate its reliability and efficiency, and parts of the results are compared with analytical results and with those obtained by some known methods such as adaptive Poisson-Boltzmann solver.

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.

The gating motion of the human nicotinic acetylcholine receptor (nAChR) alpha 7 was investigated with normal mode analysis (NMA) of two homology models. The first model, referred to as model 1, was built from both the Lymnaea stagnalis acetylcholine binding protein (AChBP) and the transmembrane (TM) domain of the Torpedo marmorata nAChR. The second model, referred to as model C, was based solely on the recent electron microscopy structure of the T. marmorata nAChR. Despite structural differences, both models exhibit nearly identical patterns of flexibility and correlated motions. In addition, both models show a similar global twisting motion that may represent channel gating. The similar results obtained for the two models indicate that NMA is most sensitive to the contact topology of the structure rather than its finer detail. The major difference between the low-frequency motions sampled for the two models is that a symmetrical pore-breathing motion, favoring channel opening, is present as the second most dominant motion in model 1, whilst largely absent from model C. The absence of this mode in model C can be attributed to its less symmetrical architecture. Finally, as a further goal of the present study, an approximate open channel model, consistent with many experimental findings, has been produced. (c) 2005 Elsevier Ltd. All rights reserved.

One main issue in protein-protein docking is to filter or score the putative docked structures. Unlike many popular scoring functions that are based on geometric and energetic complementarity, we present a set of scoring functions that are based on the consideration of local balance and tightness of binding of the docked structures. These scoring functions include the force and moment acting on one component (ligand) imposed by the other (receptor) and the second order spatial derivatives of protein-protein interaction potential. The scoring functions were applied to the docked structures of 19 test targets including enzyme/inhibitor, antibody/antigen and other classes of protein complexes. The results indicate that these scoring functions are also discriminative for the near-native conformation. For some cases, such as antibody/antigen, they show more discriminative efficiency than some other scoring functions. such as desolvation free energy (DeltaG(des)) based on pail-wise atom-atom contact energy (ACE). The correlation analyses between present scoring functions and the energetic functions also show that there is no clear correlation between them; therefore, the present scoring functions are not essentially the same as energy functions.

Protein-protein interactions, particularly weak and transient ones, are often mediated by peptide recognition domains, such as Src Homology 2 and 3 (SH2 and SH3) domains, which bind to specific sequence and structural motifs. It is important but challenging to determine the binding specificity of these domains accurately and to predict their physiological interacting partners. In this study, the interactions between 35 peptide ligands (15 binders and 20 non-binders) and the Abl SH3 domain were analyzed using molecular dynamics simulation and the Molecular Mechanics/Poisson-Boltzmann Solvent Area method. The calculated binding free energies correlated well with the rank order of the binding peptides and clearly distinguished binders from non-binders. Free energy component analysis revealed that the van der Waals interactions dictate the binding strength of peptides, whereas the binding specificity is determined by the electrostatic interaction and the polar contribution of desolvation. The binding motif of the Abl SH3 domain was then determined by a virtual mutagenesis method, which mutates the residue at each position of the template peptide relative to all other 19 amino acids and calculates the binding free energy difference between the template and the mutated peptides using the Molecular Mechanics/Poisson-Boltzmann Solvent Area method. A single position mutation free energy profile was thus established and used as a scoring matrix to search peptides recognized by the Abl SH3 domain in the human genome. Our approach successfully picked ten out of 13 experimentally determined binding partners of the Abl SH3 domain among the top 600 candidates from the 218,540 decapeptides with the PXXP motif in the SWISS-PROT database. We expect that this physical-principle based method can be applied to other protein domains as well.

Poisson-Boltzmann electrostatics is a well established model in biophysics; however, its application to large-scale biomolecular processes such as protein-protein encounter is still limited by the efficiency and memory constraints of existing numerical techniques. In this article, we present an efficient and accurate scheme that incorporates recently developed numerical techniques to enhance our computational ability. In particular, a boundary integral equation approach is applied to discretize the linearized Poisson-Boltzmann equation; the resulting integral formulas are well conditioned and are extended to systems with arbitrary numbers of biomolecules. The solution process is accelerated by Krylov subspace methods and a new version of the fast multipole method. In addition to the electrostatic energy, fast calculations of the forces and torques are made possible by using an interpolation procedure. Numerical experiments show that the implemented algorithm is asymptotically optimal O(N) in both CPU time and required memory, and application to the acetylcholinesterase-fasciculin complex is illustrated.

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress tensor. Compared with the variational method (also in a BEM frame) that we proposed recently, this method provides an even more efficient way to calculate the full intermolecular electrostatic interaction force, especially for macromolecular systems. Thus, it may be more suitable for the application of Brownian dynamics methods to study the dynamics of protein/protein docking as well as the assembly of large 3D architectures involving many diffusing subunits. The method has been tested on two simple cases to demonstrate its reliability and efficiency, and also compared with our previous variational method used in BEM. (c) 2005 American Institute of Physics.