The interaction of protein molecules with all kinds of other molecules, substrates, effectors, inhibitors, nucleic acids, lipids and other protein molecules) is at the heart of the machinery of living systems. Better understanding of these interactions is of fundamental importance; furthermore, this is an important aspect of rational drug design. Several years ago, Hermans and Shankar showed how the affinity of xenon for the protein myoglobin could be accurately modeled with free-energy simulation methods. In the past year, this has been extended to modeling the binding of water molecules to interior sites in protein molecules. Here it was found that not only the binding free energy, but also the binding energy (which is much easier to compute) can be used as a measure of which interior cavities are occupied and which are empty. This has led to a new Technical R&D project for the development and distribution of a tool (Dowser) for water placement. More recently, the free-energy approach used for xenon and water molecules has been extended to larger poly-atomic molecules. The new approach solves the problem of accounting for the loss of translational and rotational freedom that occurs when two molecules form a complex, a term which favors the dissociated state. The importance of this result can be judged from the fact that numerous recent publications in which so-called binding free energies were reported ignore this effect, and, in fact, report false results. A. FREEZING POINT OF MODEL WATER FROM DYNAMICS SIMULATIONS WITH POSITION RESTRAINTS. (Sam Kalat and Jan Hermans) Molecular dynamics simulations have been used to calculate energy and density of liquid water and ice Ih over a temperature range from 200 to 400 K, using the Simple Point Charge (SPC) model. From simulations in which the model's intermolecular forces were gradually diminished to zero, the excess free energy of both phases was calculated. In the solid, each water molecule's oxygen atom was restrained to remain near its crystal position with a quadratic potential in order to make the transformations reversible; the calculated excess free energies were corrected for the effect of this potential. The excess free energies were extrapolated to different temperatures, and from the intersection of these two data sets a "freezing point" could be determined. Simulations were done using a cutoff on non-bonded interactions in a range from 6 to 12 , and some simulations of the liquid were done with no cutoff on electrostatic forces, using a fast-multipole algorithm. Some dependence of the results on the value of the cutoff distance, Rc was found for values of Rc between 6 and 10 , but this dependence became negligible for larger values of Rc . The experimental temperature dependence of the specific volume of the liquid, v was poorly reproduced; v did appear to tend to a maximum at temperatures well below 277 K. The specific volume of ice Ih was found to slowly increase with temperature, but a rather sudden decrease of the density indicated instability of the solid phase at some temperature dependent on system size and cutoff. The low-temperature densities of the solid phase extrapolated to 0.92 at 273 K, in good agreement with the experimental value. The freezing point of the model was determined to be between 260 and 270 K. The calculated excess free energy of ice was not sensitive, over a wide range, to the exact choice of force constant of the potential used to restrain the water molecules. (manuscript in preparation) B.i. HYDROPHILICITY OF CAVITIES IN PROTEINS. (Hermans and Zhang) Water molecules inside cavities in proteins constitute integral parts of the structure. We have sought a quantitative measure of the hydrophilicity of the cavities by calculating energies and free energies of introducing a water molecule into these cavities. A threshold value of the water-protein interaction energy at -12Ekcal/mol was found to be able to distinguish hydrated from empty cavities. It follows that buried waters have entropy comparable to that of liquid water or ice. A simple consistent picture of the energetics of the buried waters provided by this study enabled us to address the reliability of buried waters assigned in experiments. (Proteins, 24: 433-438, 1996.) B.ii. DOWSER PROJECT. (Hermans and Xia) This project is the development of a tool for general use in crystallographic refinement of protein structure and in studies of protein structure by simualtion. Given the coordinates of the protein, Dowser seeks out internal cavities, and determine the hydrophilicity of each cavity in terms of the energy of placing a water molecule in the cavity, and reports coordinates of water molecules placed in the most hydrophilic cavities. This project is an offshoot of the research described under 2B, and is being continued as a Technical R&D project. c. INCLUSION OF LOSS OF TRANSLATIONAL AND ROTATIONAL FREEDOM IN THEORETICAL ESTIMATES OF FREE ENERGIES OF BINDING. APPLICATION TO A COMPLEX OF BENZENE AND MUTANT T4-LYSOZYME. (Hermans and Wang) We present the first complete treatment for calculating theoretical estimates of free energies of formation of macromolecule-ligand complexes with of molecular dynamics simulations, in which one calculates the free energy for transforms the ligand into a non-interacting state by gradually diminishing the forces between macromolecule (plus solvent) and ligand. The calculations become possible due to the introduction of a specially designed restraint potential which restrains the spatial position and orientation of the ligand molecule, and is gradually applied as the transformation proceeds from complexed to non-interacting components. The binding of benzene to a mutant T4 lysozyme has been used as a test case. The simulations reproduce the value of the free energy of binding (-5.13 kcal/mol if the standard state of benzene is a 1 M aqueous solution) within experimental error. Another series of such simulations with a rigid protein molecule provided an estimate of the dependence of the free energy of binding on the protein conformation. The free energy of binding was found to increase in the series: energy-minimized ligand-free protein, experimental structure, energy-minimized ligand-containing protein, a series of snapshots from a protein-ligand dynamics trajectory, with a difference of 8 kcal/mol between extremes. Finally, it proved possible to roughly estimate the translational and rotational freedom of the benzene molecule in the binding pocket, at 0.4 for the positional range and 3- for the angular range. (Manuscript in preparation for J. Am. Chem. Soc.).Vaism