Preprint version. Published in Journal of Computational Chemistry, Volume 31, Issue 13, October 1, 2010, pages 2428-2433.
NOTE: At the time of publication, the author Gregory Scott was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1002/jcc.21535.
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 α3D.
Biochemistry | Chemistry
This is the pre-peer reviewed version of the following article: Solving the Low Dimensional Smoluchowski Equation with a Singular Value Basis Set, Gregory Scott and Martin Gruebele, Journal of Computational Chemistry, 31.