Solving the low dimensional smoluchowski equation with a singular value basis set

Gregory Scott, Martin Gruebele

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)2428-2433
Number of pages6
JournalJournal of Computational Chemistry
Issue number13
StatePublished - Oct 2010


  • Fokker-Planck equation
  • Free energy surface
  • Genetic algorithm
  • Protein folding
  • Singular value decomposition

ASJC Scopus subject areas

  • Chemistry(all)
  • Computational Mathematics


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