Theory of single-molecule biophysics

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In single-molecule experiments forces can be exerted directly on individual molecules and their response can be followed as a function of time. These experiments reveal fundamentally novel and unique information on the structure, dynamics, and interactions of individual biomolecules. Theory of single molecule force spectroscopy. In collaboration with Dr. Szabo (NIDDK, NIH) and Prof. Dudko (UC San Diego), we have continued our development of formalisms to extract accurate kinetic information from single-molecule force spectroscopy experiments (Dudko et al., Proc. Natl. Acad. Sci. USA 2008). We developed and applied a simple procedure to extract kinetic information from pulling experiments by transforming the rupture-force histograms obtained at different force-loading rates into the force-dependent lifetimes measurable in constant-force experiments. To interpret the resulting force-dependent lifetimes, we derived a generalization of Bells formula that is formally exact within the framework of Kramers theory. This result complements the analytical expression for the lifetime that we derived previously for a class of model potentials. The procedure was applied to the nanopore unzipping of DNA hairpins and the unfolding of a protein attached by flexible linkers to an atomic force microscope. We could show that our procedure to transform rupture-force histograms into the force-dependent lifetimes remains valid even when the molecular extension is a poor reaction coordinate and higher-dimensional free-energy surfaces must be considered. Protein folding under force: In collaboration with Dr. Robert Best (University of Cambdrige, UK) we have examined the coupled folding, calcium binding, and target peptide binding of calmodulin in the presence of force (Best et al. Science 2009) in a commentary on a recent experimental study by the group of Rief. Master-equation descriptions of protein dynamics. In collaboration with Drs. Berezhkovskii and Szabo (LCP, NIDDK), we described the folding dynamics of a two-state protein by a master equation, and showed that the reactive flux between folded and unfolded states can be expressed in terms of the commitment or splitting probabilities of the microstates in the bottleneck region (Berezhkovskii et al, J. Chem. Phys. 2009). This general formalism allows one to determine how much each microscopic transition through a dividing surface contributes to the overall reactive flux. Our results for the flux in a network with complex connectivity, obtained using the discrete counterpart of Kramers theory of activated rate processes, show that the number of reactive transitions is typically much smaller than the total number of transitions that cross a dividing surface at equilibrium.