Energy Functions for Protein Structure Research

The repertoire of known three-dimensional structures of proteins contains a tremendous amount of information on the chemical function and biological role of individual proteins and on the evolutionary and functional relationships among proteins and protein families. Moreover, the structures mirror the effect of atomic interactions in the folding of protein chains to well defined three-dimensional conformations. The chief goal of this project is the development of precise and accurate energy functions for the pairwise atomic interactions in proteins and their application in protein structure refinement. To obtain these energy functions we exploit the intimate relationship between structure and energy. Detailed structural information on the various pairwise atomic interactions is encoded in the respective radial distribution functions which may be compiled from the set of known protein structures. The associated potentials of mean force (energy) are then obtained by a straightforward transformation of the radial distribution functions (structure). In the refinement of structural models derived from X-ray diffraction data precise force fields are required for the accurate geometric and energetic description of densely packed atomic configurations. At close atomic contacts, minute changes in distances produce gross changes in energy and as a consequence the functional form of pairwise interactions in the short distance range is notoriously difficult to model. Therefore, it is not surprising that the structures obtained from X-ray analysis are generally afflicted by a large number of inconsistencies, in particular, unrealistic close contacts, like charges in close proximity, and unfavorable hydrogen bond geometries. Inconsistencies in experimental protein structures are necessarily inherited by the potentials derived from such structures. We have recently demonstrated that the intimate relationship between energy and structure can be used to refine structures and energy functions in a self-consistent manner. In the present project this principle of self-consistent refinement is used to correct inconsistencies in experimental structures where the refined structures immediately yield potential functions of higher accuracy. In structural biology energy functions and scoring schemes play a fundamental role. Aside from structure refinement the energy functions derived in this project will be employed in the calculation of structures from chemical shift data obtained from NMR experiments, in the prediction and modeling of protein structures, and in the discovery and analysis of protein function.

In this project we made considerable advances in two areas of structural biology: protein structure determination on the one hand and structure matching and comparative structure analysis on the other. The first concerns the observation of invariant distributions of electrons in protein molecules and their use in the determination of protein crystal structures and protein modeling. We discovered that recurring groups of atoms are surrounded by canonical electron density distributions. Deviations from these distributions reveal unrealistic molecular geometries. We showed how canonical electron densities can be combined with classical electron densities derived from X-ray diffraction experiments to drive the real space refinement of crystal structures. The refinement process generally yields superior molecular models with reduced excess electron densities and improved stereochemistry without compromising the agreement between molecular models and experimental data. The major driving force in the refinement is the difference between the calculated density derived from the molecular model and the canonical density derived from the data base of structures. Therefore, canonical distributions of electrons can be used in the refinement of structural models obtained from NMR, cryo-EM, and other imaging techniques, as well as in structure prediction and molecular modelling. Research on the extraction of canonical densities from known protein structures required the preparation of non- redundant data sets. This in turn requires techniques for structure matching and the determination of resemblances among protein structures. In fact, protein structures are frequently related by spectacular and often surprising similarities. Structural correlations on the level of protein chains are routinely detected by various structure matching techniques but the comparison of molecular complexes is largely uncharted territory. Here we solved the structure matching problem for oligomers and large molecular aggregates including the largest molecular structures known today. On the basis of this technology we were able to develop computer programs that recognize, record, retrieve and display structural similarities among all known protein structures in a most efficient way. Most important, for a given query structure retrieval of all structural matches is immediate (i.e. the speed is on the same order as a Google search). With the massive increase in the number of solved protein structures these tools reveal how new protein folds arise from old templates. In particular we identified recurring transitions in the structures of various dehydrogenase enzymes that drive the creation of new protein folds while conserving fundamental functional traits. Among the most spectacular transitions observed are the conservation of symmetry by asymmetric sequences and the truncation of protein structures by gene elongation