2012/08/25 by Aleksandr Kivenson, Michael F. Hagan, Kivenson, Aleksandr +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Biomolecules (q-bio.BM) #DNA and Nucleic Acid Chemistry #Diffusion and Search Dynamics #FOS: Biological sciences #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Stochastic processes and statistical mechanics #cond-mat.soft #q-bio.BM
paper · pdf · doi:10.48550/arxiv.1208.5156
6 pages, 4 figures, submitted to Phys. Rev. E
arxiv created 2012/08/25 · openalex publication_date 2012/08/25 · arxiv updated 2015/03/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider a single-species diffusion-limited annihilation reaction with reactants confined to a two-dimensional surface with one arbitrarily large dimension and the other comparable in size to interparticle distances. This situation could describe reactants which undergo both longitudinal and transverse diffusion on long filamentous molecules (such as microtubules), or molecules that undergo truly one-dimensional translational diffusion (e.g. a transcription factor on DNA) but simultaneously exhibit diffusive behavior in a second dimension corresponding to a rotational or conformational degree of freedom. We combine simple analytical arguments and Monte Carlo simulations to show that the reaction rate law exhibits a crossover from one-dimensional to two-dimensional diffusion as a function of particle concentration and the size of the smaller dimension. In the case of a reversible binding reaction, the diffusion-limited reaction rate is given by the Smoluchowski expression, but the crossover is revealed in the statistics of particle collision histories. The results can also be applied to a particle-antiparticle annihilation reaction.