2005/08/31 by Rhonald C. Lua, Alexander Y. Grosberg · 1 citation
Biochemistry, Genetics and Molecular Biology · Chemistry · Engineering · Mathematics · Physics and Astronomy · #Anomalous diffusion #Asymmetry #Brownian motion #Context (archaeology) #Diffusion #Diffusion and Search Dynamics #Electrostatics and Colloid Interactions #First-hitting-time model #Geometry #Mathematical physics #Mathematics #Mean squared displacement #Molecular dynamics #Nanopore and Nanochannel Transport Studies #Physics #Quantum mechanics #Sawtooth wave #Square (algebra) #Statistical physics #cond-mat.soft #physics.bio-ph #q-bio.BM #q-bio.SC
paper · pdf · doi:10.1103/physreve.72.061918
published as Physical Review E 72, 061918 (2005); also in January 1, 2006 issue of Virtual Journal of Biological Physics Research · 10 pages, 4 figures We incorporated reviewers' suggestions from Physical Review E. We reformulated a few paragraphs in the introduction and further clarified the issue of the (a)symmetry of passage times. In the results section, we re-expressed the results in a form that manifest the important features. We also added a few references concerning anomalous diffusion. The look (but not the content) of figure 1 was also changed
arxiv created 2005/10/25 · openalex publication_date 2005/12/23 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Motivated by experiments in which single-stranded DNA with a short hairpin loop at one end undergoes unforced diffusion through a narrow pore, we study the first passage times for a particle, executing one-dimensional Brownian motion in an asymmetric sawtooth potential, to exit one of the boundaries. We consider the first passage times for the case of classical diffusion, characterized by a mean-square displacement of the form <(Delta(x))2> approximately t, and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form <(Delta(x))2> approximately t(gamma) with 0<gamma<1. In the context of classical diffusion, we obtain an expression for the mean first passage time and show that this quantity changes when the direction of the sawtooth is reversed or, equivalently, when the reflecting and absorbing boundaries are exchanged. We discuss at which numbers of "teeth" N (or number of DNA nucleotides) and at which heights of the sawtooth potential this difference becomes significant. For large N, it is well known that the mean first passage time scales as N2. In the context of subdiffusion, the mean first passage time does not exist. Therefore, we obtain instead the distribution of first passage times in the limit of long times. We show that the prefactor in the power relation for this distribution is simply the expression for the mean first passage time in classical diffusion. We also describe a hypothetical experiment to calculate the average of the first passage times for a fraction of passage events that each end within some time t*. We show that this average first passage time scales as N2/gamma in subdiffusion.