Protein structures in 3D are large. elegant, complex, and subtle enough that their prediction and understanding still largely eludes us. In contrast, their local building blocks are quite simple: to a good approximation their connectivity is a tree graph of backbone and sidechains, and the atoms are connected with specific, near-invariant covalent bond-length and bond-angle geometry. However, the connections are mostly tetrahedral, with essentially no right angles and thus no independent, orthogonal degrees of freedom. Also, the non-local interactions such as van der Waals, hydrophobicity, and hydrogen bonds are very much weaker than the covalent bonds and produce the compact, semi-rigid "native" structure only collectively by their great numbers. These two factors are major causes of the cooperativity of protein folding, allostery, and function, and help guide the evolution of a protein sequence to achieve just one or a few equilibrium 3D structures. We will explore several ways in which geometrical analysis - or sometimes even a geometrical metaphor - has illuminated some facet of protein folding, conformation, or mobility. A final message is that the currently most successful algorithms in structure prediction and design attack the complexity by global energetics evaluated using unabashed brute-force computation. There may yet be opportunity for developing more efficient solutions by hierarchical buildup of cleaner and more intuitive geometrical understanding.

Amino acid substitutions in protein structures often require subtle backbone adjustments that are difficult to model in atomic detail. An improved ability to predict realistic backbone changes in response to engineered mutations would be of great utility for the blossoming field of rational protein design. One model that has recently grown in acceptance is the backrub motion, a low-energy dipeptide rotation with single-peptide counter-rotations, that is coupled to dynamic two-state sidechain rotamer jumps, as evidenced by alternate conformations in very high-resolution crystal structures. It has been speculated that backrubs may facilitate sequence changes equally well as rotamer changes. However, backrub-induced shifts and experimental uncertainty are of similar magnitude for backbone atoms in even high-resolution structures, so comparison of wildtype-vs.-mutant crystal structure pairs is not sufficient to directly link backrubs to mutations. In this study, we use two alternative approaches that bypass this limitation. First, we use a quality-filtered structure database to aggregate many examples for precisely defined motifs with single amino acid differences, and find that the effectively amplified backbone differences closely resemble backrubs. Second, we directly apply a provably-accurate, backrub-enabled protein design algorithm to idealized versions of these motifs, and discover that the lowest-energy computed models match the average-coordinate experimental structures. These results support the hypothesis that backrubs participate in natural protein evolution and validate their continued use for design of synthetic proteins.

MOTIVATION: The Backrub is a small but kinematically efficient side-chain-coupled local backbone motion frequently observed in atomic-resolution crystal structures of proteins. A backrub shifts the C(alpha)-C(beta) orientation of a given side-chain by rigid-body dipeptide rotation plus smaller individual rotations of the two peptides, with virtually no change in the rest of the protein. Backrubs can therefore provide a biophysically realistic model of local backbone flexibility for structure-based protein design. Previously, however, backrub motions were applied via manual interactive model-building, so their incorporation into a protein design algorithm (a simultaneous search over mutation and backbone/side-chain conformation space) was infeasible. RESULTS: We present a combinatorial search algorithm for protein design that incorporates an automated procedure for local backbone flexibility via backrub motions. We further derive a dead-end elimination (DEE)-based criterion for pruning candidate rotamers that, in contrast to previous DEE algorithms, is provably accurate with backrub motions. Our backrub-based algorithm successfully predicts alternate side-chain conformations from < or = 0.9 A resolution structures, confirming the suitability of the automated backrub procedure. Finally, the application of our algorithm to redesign two different proteins is shown to identify a large number of lower-energy conformations and mutation sequences that would have been ignored by a rigid-backbone model. AVAILABILITY: Contact authors for source code.

A parallel, analytic approach for defining and computing the inter and intra molecular interfaces in three dimensions is described. The molecular interface surfaces are derived from approximations to the power diagrams over the participating molecular units. For a given molecular interface our approach can generate a family of interface surfaces parametrized by /spl alpha/ and /spl beta/, where /spl alpha/ is the radius of the solvent molecule (also known as the probe radius) and /spl beta/ is the interface radius that defines the size of the molecular interface. Molecular interface surfaces provide biochemists with a powerful tool to study surface complementarity and to efficiently characterize the interactions during a protein substrate docking. The complexity of our algorithm for molecular environments is O(nk log/sup 2/ k), where n is the number of atoms in the participating molecular units and k is the average number of neighboring atoms-a constant, given /spl alpha/ and /spl beta/.

Article Free Access Share on VIEW: an exploratory molecular visualization system with user-definable interaction sequences Authors: Lawrence D. Bergman View Profile , Jane S. Richardson View Profile , David C. Richardson View Profile , Frederick P. Brooks View Profile Authors Info & Claims SIGGRAPH '93: Proceedings of the 20th annual conference on Computer graphics and interactive techniquesSeptember 1993 Pages 117–126https://doi.org/10.1145/166117.166132Published:01 September 1993Publication History 14citation526DownloadsMetricsTotal Citations14Total Downloads526Last 12 Months17Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF