A general methodology for calculating the equilibrium binding constant of a flexible ligand to a protein receptor is formulated on the basis of potentials of mean force. The overall process is decomposed into several stages that can be computed separately: the free ligand in the bulk is first restrained into the conformation it adopts in the bound state, position, and orientation by applying biasing potentials, then it is translated into the binding site, where it is released completely. The conformational restraining potential is based on the root-mean-square deviation of the peptide coordinates relative to its average conformation in the bound complex. Free energy contributions from each stage are calculated by means of free energy perturbation potential of mean force techniques by using appropriate order parameters. The present approach avoids the need to decouple the ligand from its surrounding (bulk solvent and receptor protein) as is traditionally performed in the doubledecoupling scheme. It is believed that the present formulation will be particularly useful when the solvation free energy of the ligand is very large. As an application, the equilibrium binding constant of the phosphotyrosine peptide pYEEI to the Src homology 2 domain of human Lck has been calculated. The results are in good agreement with experimental values. Approaches at different levels of complexity and sophistication have been used to calculate binding free energies in complex biomolecular systems. Screening of large molecular databases of compounds to identify potential lead drug molecules typically relies on very simplified scoring schemes to achieve the needed efficiency (6). The binding free energy may be estimated on the basis of a continuum solvent approximation assuming quadratic fluctuations around a unique configuration (7,8). The Molecular Mechanics͞ Poisson-Boltzmann (PB) and Surface Area (MM͞PB-SA) method is a popular approach that relies on a mixed scheme combining configurations sampled from molecular dynamics (MD) simulations with explicit solvent, together with free energy estimators based on an implicit continuum solvent model (9). MM͞PB-SA shares some similarities with the linear interaction energy method, which also uses averages calculated from explicit solvent simulations within a linear response framework (10). Despite their usefulness, such approximate schemes can be limited, and how to improve the results is unclear because they do not offer a rigorous route to compute the equilibrium binding constant.In principle, treatments based on MD free energy perturbation (FEP) simulations with explicit solvent molecules offer the most powerful and promising approach to estimate the binding free energies of ligands to macromolecules (11). Nonetheless, although previous studies have provided many of the fundamental elements necessary for the calculation of binding free energy by means of MD (12-17), the computations so far have been limited mostly to fairly small and rigid ligands [e.g., rare gas atom (12, 15), water (14)...

In recent years, considerable progress has been made in the development of novel porous materials with controlled architectures and pore sizes in the mesoporous range. An important feature of these materials is the phenomenon of adsorption hysteresis: for certain ranges of applied pressure, the amount of a molecular species adsorbed by the mesoporous host is higher on desorption than on adsorption, indicating a failure of the system to equilibrate. Although this phenomenon has been known for over a century, the underlying internal dynamics responsible for the hysteresis remain poorly understood. Here we present a combined experimental and theoretical study in which microscopic and macroscopic aspects of the relaxation dynamics associated with hysteresis are quantified by direct measurement and computer simulations of molecular models. Using nuclear magnetic resonance techniques and Vycor porous glass as a model mesoporous system, we have explored the relationship between molecular self-diffusion and global uptake dynamics. For states outside the hysteresis region, the relaxation process is found to be essentially diffusive in character; within the hysteresis region, the dynamics slow down dramatically and, at long times, are dominated by activated rearrangement of the adsorbate density within the host material.

The grand canonical simulation algorithm is considered as a general methodology to sample the configuration of water molecules confined within protein environments. First, the probability distribution of the number of water molecules and their configuration in a region of interest for biochemical simulations, such as the active site of a protein, is derived by considering a finite subvolume in open equilibrium with a large system serving as a bulk reservoir. It is shown that the influence of the bulk reservoir can be represented as a many-body potential of mean force acting on the atoms located inside the subvolume. The grand canonical Monte Carlo (GCMC) algorithm, augmented by a number of technical advances to increase the acceptance of insertion attempts, is implemented, and tested for simple systems. In particular, the method is illustrated in the case of a pure water box with periodic boundary conditions. In addition, finite spherical systems of pure water and containing a dialanine peptide, are simulated with GCMC while the influence of the surrounding infinite bulk is incorporated using the generalized solvent boundary potential [W. Im, S. Berneche, and B. Roux, J. Chem. Phys. 114, 2924 (2001)]. As a last illustration of water confined in the interior of a protein, the hydration of the central cavity of the KcsA potassium channel is simulated.

Equilibrium and dynamical relaxation behavior of fluids confined in disordered mesoporous glasses such as Vycor are studied based on a lattice model using mean field theory and Monte Carlo simulations. Preferential attractive interactions between the solid surfaces and the fluid suppresses macroscopic phase separation, while making the relaxation rate increasingly slow. The free energy landscape characterized by the presence of the many metastable minima separated by finite barriers dominates both the static and dynamic behavior of fluids at low temperature. Our results provide additional insight into the nature of hysteresis in adsorption measurements of gases in porous glasses.

A realistic and computationally efficient method to model fluid adsorption in disordered mesoporous glasses is described. Local mean-field theory of a lattice model of adsorption is combined with the representations of the disordered matrix configurations generated by Gaussian random fields. The experimental structure factor and porosity of the glass serve as input. The method allows for an efficient route to perform disorder averages for large systems. The adsorption and hysteresis behaviors obtained agree closely with those observed experimentally.