Engineering Approaches to Biomolecular Motors

18 / 79

Engineering Approaches to Biomolecular Motors: From in vitro to in vivo Wednesday Speaker Abstracts
13
Discretizing the Fokker-planck Equation for Energy Conversion in a Molecular Motor to
Predict Physical Observables
Katharine J. Challis1, Phuong Nguyen1,2 , Michael W. Jack2.
1Scion, Rotorua, Bay of Plenty, New Zealand, 2University 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.