This project addresses a variety of problems related to protein structure and folding, and uses methods developed in modern statistical mechanics. O current interest is the problem of developing an objective measure of accuracy for protein structures determined by multi-dimensional NMR measurements. Successful completion of this project would yield a measure of accuracy analogous to the R factor which is commonly used for assessing the accuracy of crystallographic structure determinations. An essential part of this project involves the development and exploration of new techniques for incorporating distance constraints into the statistical mechanical theory of protein structure. In the past year we have developed a theoretical approach that replaces rigid constraints with more realistic "elastic" ones. The resulting framework for confirmational analysis is also more tractable than previous methods in that it allows man calculations to be carried out simply and exactly for the simplest protein models. We are presently extending these calculations to take into account the stiffness of the protein back bone in a more rigorous manner. These extensions require the development and clarification of techniques for calculating with stiff (also known as semi-flexible or "worm-like") polymer models, and thus will also be a major contribution to basic polymer science We also plan to use these results to extend earlier work on accuracy requirements and for potential functions to yield accurate structure determinations. We are continuing our efforts to understand the physical chemistry of protein folding. In the past year we have used simple arguments to explore the nature of protein folding pathways and have shown that a protein spends only a negligible part of its time moving along the folding pathway. We plan to investigate the kinetics of protein collapse and the effects of water on hydrogen bonding in a folding protein. This theoretical work will complement the experimental work being done on early events in protein folding in the laboratory of Dr. William A. Eaton in the NIDDK.