Theoretical Studies On The Dynamic Aspects Of Macromolecular Function

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Membrane channels that allow metabolites to exchange between cells or different cellular compartments are protein structures with water-filled pores. Traditionally such channels were thought to be molecular sieves which discriminate between different solutes based only on size. In other words, they were regarded as low-selectivity structures that allow passage of the solute without any significant interaction with the channel pore. We have shown how nature can in principle exploit and tune the solute-pore interaction in such a way to maximize the solute flux(i.e., the number of molecules translocated per second) and therefore increase the efficiency of the channel. The basic idea is that when only one solute can be in the channel, the flux must have a maximum as a function of the solute-channel interaction. Physically the reason is the following.If the interaction is too attractive, the solute will never leave the channel thus blocking it for the passage of other molecules. If it is too repulsive, the solute molecule will never enter the channel. Since the flux vanishes in both these limits, there must exist an optimum interaction for which the transport is the fastest. We have constructed a quantitative mathematical model for this process and using the calculus of variations determined the optimal intrachannel interaction potential that maximizes the flux. This optimum potential turns out to be tilted towards the side with lower concentration. This makes the counterintuitive prediction that it is better for the solute to "bind" more strongly near the "exit" of the channels rather than near the "entrance". In addtion we found that the value of the optimum interaction potential depends on the concentration od solute outside the channel. This suggests that in a given organism, channel proteins designed to transport the same molecule may have different amino acid sequences. One gene might code for a channel protein that functions at high solute concentrations, while another for one that works at low concentrations. Dramatic advances have been made recently in our ability to study the behavior of single macromolecules. The controlled application of mechanical forces on single molecules has provided a powerful tool to study their structure, function and dynamics. These new experiments require sopisticated cutting-edge technologies and the development of new theoretical approaches to interpret them. Dynamic force spectroscopy probes both kinetics and thermodynamics and a long term interest of this laboratory has been the development of the theory required to analyze such experiments. In order to make the advances we made over the years accessible to a wide audience of potential users, we have written a chapter entitled "Thermodynamics and Kinetics from Single-Molecule Force Spectroscopy" in a book published this year that contains contributions from all the leading research groups throuhout the world. The major contribution we made this year was the development of a novel and simple procedure 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. The cornerstone of our method is a transformation ot the rupture-force histograms obtained at different force-loading rates into the force dependent lifetimes measurable in contant-force experiments. To interpret these force dependent lifetimes we derived a generalization ot the widely-used Bell's formula that is exact within the framework of Kramers theory of diffusive barrier crossing. We have illustrated our procedure by analyzing the nanopore unzipping of DNA hairpins and the unfolding of a protein attached by flexible linkers to an atomic force miscroscope. We have shown that our approach remains valid even when the molecular extension is a poor reaction coordinate and higher dimensional free energy surfaces must be considered. We believe that our procedure will become the de facto standard way of interpreting experimental data in this rapidly emerging area.