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. In collaboration with the experimental group of Amit Meller (Boston University), we studied the force-induced unzipping of individual DNA hairpins inside membrane-spanning nanopores (Dudko et al., Biophys. J. 2007). This experimental method has been developed with the aim of sequencing individual DNA molecules. We developed a systematic procedure for extracting kinetic information from such force-spectroscopy experiments, considering two types of measurements are considered: unzipping at constant voltage (or force), and unzipping at constant voltage-ramp speeds (or force-ramp speeds). By performing a global maximum-likelihood analysis of the experimental data at low-to-intermediate ramp speeds, we could parametrize different theoretical models. To validate the models, we compared their predictions with two independent sets of data, collected at high ramp speeds and at constant voltage, by using a quantitative relation between the two types of measurements. Microscopic approaches based on Kramers theory of diffusive barrier crossing allowed us to estimate not only intrinsic rates and transition state locations, but also free energies of activation. Our theoretical model showed that the nanopore DNA unzipping transition can be described accurately as a two-state process. However, the quantitative analysis also showed that the interactions of the DNA with the nanopore can have a significant effects on the measured rates, an observation relevant for the development of molecular sensing devices.? ? By developing a kinetic model of the mitochondrial proton pump cytochrome c oxidase at the single-molecule level, we were able for the first time to identify the minimal requirements for the function of this key enzyme (Kim et al., Proc. Natla. Acad. Sci. USA 2007). In aerobic life, the reduction of oxygen to water drives the generation of the electrochemical gradient across the inner mitochondrial (or bacterial) membrane that powers the production of ATP. Cytochrome c oxidase (CcO), the enzyme catalyzing oxygen reduction, takes up four electrons from the outside of the membrane and four protons from the inside. In addition, roughly half of the redox energy is used for translocation of four additional protons across the membrane. Even though many models have been proposed to explain this proton pumping, the central question had remained unanswered: how redox chemistry could be harnessed to move protons against both chemical and potential gradients. To explore the fundamental mechanisms of such redox coupled proton pumps, we developed kinetic models at the single-molecule level consistent with basic physical principles. We demonstrated that pumping against an electric potential can be achieved purely through electrostatic couplings, given an asymmetric arrangement of charge centers; however, nonlinear gates are essential for highly efficient real enzymes. The fundamental requirements for proton pumping identified here highlight a possible evolutionary origin of cytochrome c oxidase pumping. The general design principles identified are relevant also for other molecular machines and suggest future applications in biology-inspired fuel cells.? ? Remarkably, the theory of single-molecule force spectroscopy is also closely related to free energy calculations using computer simulations. In a book chapter (Hummer, 2007), we establish and explore this connection. We show that recent developments in the statistical physics of nonequilibrium processes lead to a practically useful theory of single-molecule pulling experiments. In particular, one can use non-equilibrium relations derived by us (Hummer and Szabo, Proc Natl Acad Sci USA, 2001) on the basis of Jarzynski's identity to extract thermodynamic properties rigorously from nonequilibrium pulling experiments.
| 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 |
