Engineering Approaches to Biomolecular Motors

Engineering Approaches to Biomolecular Motors: From in vitro to in vivo Wednesday Speaker Abstracts

Discretizing the Fokker-planck Equation for Energy Conversion in a Molecular Motor to Predict Physical Observables Katharine J. Challis 1 , Phuong Nguyen 1,2 , Michael W. Jack 2 . 1 Scion, Rotorua, Bay of Plenty, New Zealand, 2 University of Otago, Dunedin, Otago, New Zealand. Energy conversion in a molecular motor has been described in terms of Brownian motion on a free-energy surface. Free-energy surfaces for molecular motors such as F1-ATPase are emerging from single-molecule experiments and molecular dynamics simulations. Brownian motion on a free-energy surface is governed by a multidimensional Fokker-Planck equation that predicts physical observables. We have developed a suite of theoretical methods for systematically transforming the Fokker-Planck equation to simpler tractable discrete master equations. Our approach is to expand the Fokker-Planck equation in a localized basis of discrete states tailored to the free-energy potential surface. For periodic potentials with a single minimum and maximum per period we use a Wannier basis originally developed for quantum systems. For bichromatic potentials with multiple minima per period we generalize the Wannier basis to potentials with spatially fast- and slow-varying components. For more sophisticated potentials we expand in the lowest eigenstates of metastable approximations to the free-energy surface. The main benefits of our methods are that they take into account local details of the potential and make clear the validity regime of the discretization. We apply our methods to derive discrete master equations for a range of potential surfaces. This yields analytic expressions for the rate of thermal hopping between localized meta-stable states. We relate characteristics of the free- energy surface to physical observables including the drift and diffusion, the rate and efficiency of energy transfer, and single trajectories and hopping statistics.

Artificial Molecular Switches and Motors by Synthetic Design Amar Flood . University of Indiana, Bloomington, IN, USA.

Nature’s biological motors and the engineered machines in our everyday world serve as inspirations for the creation of small-molecule systems that undergo controllable motion. That motion has historically relied upon the creation of molecules with simple moving parts, like, rings, rods, and rotors. The resulting synthetic systems have led to a plethora of molecular switches. These same switches now serve as the testing ground to consider more complex and synchronized motions needed for performing work. Yet, they must also reflect the operating principles seen in biology. To these ends, this talk will present the development of a class of voltage-driven molecular switches and outline a roadmap for its transformation into a molecular muscle. Our progress along that path will be described. Along the way, we also address interchangeable parts and the option to access Brownian ratchet motions.

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