Solving the low dimensional Smoluchowski equation with a singular value basis set.
Reaction kinetics on free energy surfaces with small activation barriers can be computed directly with the Smoluchowski equation. The procedure is computationally expensive even in a few dimensions. We present a propagation method that considerably reduces computational time for a particular class of problems: when the free energy surface suddenly switches by a small amount, and the probability distribution relaxes to a new equilibrium value. This case describes relaxation experiments. To achieve efficient solution, we expand the density matrix in a basis set obtained by singular value decomposition of equilibrium density matrices. Grid size during propagation is reduced from (100-1000)(N) to (2-4)(N) in N dimensions. Although the scaling with N is not improved, the smaller basis set nonetheless yields a significant speed up for low-dimensional calculations. To demonstrate the practicality of our method, we couple Smoluchowsi dynamics with a genetic algorithm to search for free energy surfaces compatible with the multiprobe thermodynamics and temperature jump experiment reported for the protein alpha(3)D.
Scott
Gregory
G
Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA.
Gruebele
Martin
M
D000465:Algorithms; D003198:Computer Simulation; D007700:Kinetics; D013696:Temperature; D013816:Thermodynamics