Diffusion of small ligands in complex confining and reactive landscapes: The geometry of chemoreception
July 31-August 4, 2017
The rate constant that describes the diffusive encounter/reaction between a particle and a large sphere can be computed easily by solving the stationary diffusion (i.e. Laplace) equation for the particle density with appropriate boundary conditions imposed on the surface of the sphere. In one classic, textbook example, this calculation is used to estimate the binding rate constant of a ligand to a receptor-covered cell.
But what happens if the particles are diffusing in the presence of many reactive boundaries of different strength (intrinsic reaction rate), which compete for the same ligands and amidst a landscape of inert obstacles? In spite of the apparent overwhelming complexity, the same mathematical framework as the two-body problem can be used to solve the N-body problem exactly, by resorting to addition theorems for the appropriate fundamental solutions of the Laplace equation.
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Francesco Piazza, Duccio Fanelli, Marta Galanti, and Sergey Traytak, "Diffusion of small ligands in complex confining and reactive landscapes: The geometry of chemoreception" in "Association in Solution IV", Ulf Olsson, Lund University, Sweden Norman Wagner, University of Delaware, USA Anand Yethiraj, Memorial University of Newfoundland, Canada Eds, ECI Symposium Series, (2017). https://dc.engconfintl.org/assoc_solution_iv/34