Theoretical Studies On The Dynamic Aspects Of Macromolecular Function

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To understand how polypeptide chains can fold into well-defined three-dimensional structures, one must be able to characterize the nature of the transition state ensemble of this unimolecular reaction.. Theoretically, this ensemble is defined as the set of conformations with pfold equal to a half. The pfold of a conformation is the probability that starting from this conformation the protein folds before it unfolds. Experimentally, this ensemble is probed by phi-value analysis. The measured phi value is the ratio of the changes in the logarithms of the folding rate and the equilibrium constant when the system is perturbed by an amino-acid mutation. Phi-value analysis is the most important way the mechanism of protein folding is studied experimentally. We have recently discovered an unexpected quantative relation between these quantaties. In addition to laying the theoretical foundation of phi-value analysis, our results should prove usefull in performing such analyses within the framework of microscopic models with a large number of conformational states. Dramatic advances have been made recently in our ability to study the behavior of single macromolecules. These new experiments require sopisticated cutting-edge technologies and the development of new theoretical approaches to interpret them. As reported last year, we have developped a novel theory to extract kinetic information ( specifically the intrinsic rates and free energies of activation) from single molecule pulling experiments performed using optical tweezers and atomic force microscopes. This year, in collaboration with the experimental group of Amit Meller, we published, what we believe will become an influential article, that applies this theory to the nanopore unzipping of individual DNA hairpins. In these experiments, a single DNA molecule is denatured by threading it through a nanopore which is formed by reconstituting a channel protein in a lipid bilayer. Two types of measurements were analyzed: unzipping at constant voltage and unzipping at constant voltage ramp speeds. A theoretical expression that relates these two different kinds of experiments was tested and found to be remarkably accurate. This established, in a model-free way, the fact that these two protocals yield the same information about the nature of the rupture process. Microscopic approaches based on the Kramers theory of diffusive barrier crosssing allowed us to obtain not only the intrinsic rates and transition state locations but also the free energies of activation. This represents a significant advance over the commonly used phenomenological approach. Consequently we believe that our procedure will become the de facto standard way of interpreting experimental data in this rapidly emerging area.