A major goal of structural biology is to understand how molecules recognize and interact with one another. Comprehension of details of interactions would enhance our understanding of numerous biological processes, as well as provide a sounder basis for drug design. A basic comprehension of molecular interactions has been the goal of many of our studies, particularly through the use of coarse-grained models. Extracting interaction energies from structures, together with the general form of the overall energy distributions are some of our major efforts. During this period we have investigated two different ways to extract short-range interaction energies from protein structures and have combined them with long-range potentials to improve threading. Other studies have included how composition recognizes the type of structure (helix, sheet, alpha+beta or alpha/beta), and threading with gaps and insertions. For more efficient conformation generation, we are developing a new method to enumerate or count all compact structures on a lattice using a transfer matrix formalism. The number of conformations accessible on points within predefined three-dimensional shapes is readily found with this method, yielding precise counts of conformations up to the order of 10/20. The method could therefore efficiently serve for estimating conformational entropy changes associated with changes in the shapes of compact protein structures, as well as for estimating other entropies or evaluating the feasibility of a conformation enumeration. In studies on residue packing we have investigated the distinct directional ways in which amino acids pack together. The most critical element for observing highly regular packing has been to look at residue packing in a coarse-grained way, rather than at the details of atom packing. For all interacting groups surrounding a central residue, we reorient the rigid packing unit to obtain the best overall coincidence of positions for all cases. The residue packing then becomes highly regular and leads somewhat surprisingly to discrete preferred relative positions for non-bonded residues around any interacting residue, where the geometries follow a rule of high-density sphere packing. Thus, protein residues pack closely in accord with this model in a highly regular, lattice-like way. For protein conformation simulations, this discrete view of the packing of interacting non-bonded residues reduces in significant ways, the size of the conformational space requiring either enumeration or sampling. We have begun investigating protein dynamics with a coarse-grained model having one point per residue only. This new development is based on a simple theory of fluctuations about known protein structures, the Gaussian network model. This procedure is being shown to sample satisfactorily the distribution of atomic fluctuations about the native conformation in proteins, and to yield remarkably good agreement with crystallographic temperature factors and hydrogen exchange data. Although this method is simple, results are intuitive and compelling. This approach yields a series of modes of motion, including even the slowest, most global motions, that lead to new, exciting prospects for comprehending the functional dynamics of extremely large, even supra- molecular structures. Initially we investigated the fluctuations within an entire immunoglobulin and showed directly that the hypervariable CDR loops have the highest conformational flexibilities.
