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), we have developed and analyzed formalisms to extract thermodynamic and kinetic information from single-molecule force spectroscopy experiments. In a book chapter (Hummer and Szabo, 2008),we establish the connection between recent developments in the statistical physics of nonequilibrium processes and single-molecule pulling experiments. We then show how these connections lead to novel, practically useful methods of extracting thermodynamic information from the experiments, including binding and unfolding free energies. In the same book chapter, we also showed how kinetic information, including protein and nucleic acids unfolding rates, can be extracted from single-molecule pulling experiments.? ? Protein folding under force: In collaboration with Dr. Robert Best (University of Cambdrige, UK), we have studied the folding of proteins under mechanical tension. Despite a large number of studies on the mechanical unfolding of proteins, there are still relatively few successful attempts to refold proteins in the presence of a stretching force. We explored the protein refolding kinetics under force by using simulations of a coarse-grained model of ubiquitin. The effects of force on the folding kinetics could be fitted by a one-dimensional Kramers theory of diffusive barrier crossing, resulting in physically meaningful parameters for both the height and the location of the folding activation barrier. By comparing parameters obtained from pulling in different directions, we found that the unfolded state plays a dominant role in the refolding kinetics. Our findings explain why refolding becomes very slow at even moderate pulling forces and suggest how it could be practically observed in experiments at higher forces.? ? Force-induced protein unfolding: In collaboration with Dr. Dudko (UCSD) and Dr. Best (Cambridge), we explored the validity of a theoretical approach (developed in collaboration with by Drs. Dudko and Szabo; see also above) describing molecular rupture in the presence of force. We performed extensive simulations of the unfolding kinetics in coarse-grained protein models. Unfolding rates calculated from simulations over a broad range of stretching forces, and for different pulling directions, reveal a turnover from a force-independent process at low force to a force dependent process at high force, akin to the roll-over in unfolding rates sometimes seen in studies using chemical denaturant. While such a turnover in rates is unexpected in one dimension, we demonstrated that it could occur for dynamics in just two dimensions. Our results were found to be in accord with protein engineering experiments and simulations which indicate that the unfolding mechanism at high force can differ from the intrinsic mechanism. The apparent similarity between extrapolated and intrinsic rates in experiments, unexpected for different unfolding barriers, can be explained if the turnover occurs at low forces.
| Berezhkovskii, Alexander; Hummer, Gerhard; Szabo, Attila (2009) Reactive flux and folding pathways in network models of coarse-grained protein dynamics. J Chem Phys 130:205102 |
| Best, Robert B; Hummer, Gerhard (2008) Protein folding kinetics under force from molecular simulation. J Am Chem Soc 130:3706-7 |
| Best, Robert B; Paci, Emanuele; Hummer, Gerhard et al. (2008) Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules. J Phys Chem B 112:5968-76 |
| Tuukkanen, Anne; Kaila, Ville R I; Laakkonen, Liisa et al. (2007) Dynamics of the glutamic acid 242 side chain in cytochrome c oxidase. Biochim Biophys Acta 1767:1102-6 |
| Kim, Young C; Wikstrom, Marten; Hummer, Gerhard (2007) Kinetic models of redox-coupled proton pumping. Proc Natl Acad Sci U S A 104:2169-74 |
| Dudko, Olga K; Mathe, Jerome; Szabo, Attila et al. (2007) Extracting kinetics from single-molecule force spectroscopy: nanopore unzipping of DNA hairpins. Biophys J 92:4188-95 |
