dorsal/arxiv
View SchemaFirst passage times and asymmetry of DNA translocation
| Authors | Rhonald C. Lua, Alexander Y. Grosberg |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0508010 |
| URL | https://arxiv.org/abs/q-bio/0508010 |
| DOI | 10.1103/PhysRevE.72.061918 |
| Journal | Physical Review E 72, 061918 (2005); also in January 1, 2006 issue of Virtual Journal of Biological Physics Research |
Abstract
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 $< (\Delta x)^2> \sim t$, and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form $< (\Delta x)^2> \sim t^{\gamma}$ 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 $N^2$. 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 $N^{2/\gamma}$ in subdiffusion.
{
"annotation_id": "04430074-0b2f-46f7-a6d3-87661a0f2c10",
"date_created": "2026-03-02T18:01:31.356000Z",
"date_modified": "2026-03-02T18:01:31.356000Z",
"file_hash": "932a8d4df464803d2d446ece9c8f5e18d565a44f771f5f8d1abf7e861c30062b",
"private": false,
"record": {
"abstract": "Motivated by experiments in which single-stranded DNA with a short hairpin\nloop at one end undergoes unforced diffusion through a narrow pore, we study\nthe first passage times for a particle, executing one-dimensional brownian\nmotion in an asymmetric sawtooth potential, to exit one of the boundaries. We\nconsider the first passage times for the case of classical diffusion,\ncharacterized by a mean-square displacement of the form $\u003c (\\Delta x)^2\u003e \\sim\nt$, and for the case of anomalous diffusion or subdiffusion, characterized by a\nmean-square displacement of the form $\u003c (\\Delta x)^2\u003e \\sim t^{\\gamma}$ with\n$0\u003c\\gamma\u003c1$. In the context of classical diffusion, we obtain an expression\nfor the mean first passage time and show that this quantity changes when the\ndirection of the sawtooth is reversed or, equivalently, when the reflecting and\nabsorbing boundaries are exchanged. We discuss at which numbers of `teeth\u0027 $N$\n(or number of DNA nucleotides) and at which heights of the sawtooth potential\nthis difference becomes significant. For large $N$, it is well known that the\nmean first passage time scales as $N^2$. In the context of subdiffusion, the\nmean first passage time does not exist. Therefore we obtain instead the\ndistribution of first passage times in the limit of long times. We show that\nthe prefactor in the power relation for this distribution is simply the\nexpression for the mean first passage time in classical diffusion. We also\ndescribe a hypothetical experiment to calculate the average of the first\npassage times for a fraction of passage events that each end within some time\n$t^*$. We show that this average first passage time scales as $N^{2/\\gamma}$ in\nsubdiffusion.",
"arxiv_id": "q-bio/0508010",
"authors": [
"Rhonald C. Lua",
"Alexander Y. Grosberg"
],
"categories": [
"q-bio.BM",
"cond-mat.soft",
"physics.bio-ph",
"q-bio.SC"
],
"doi": "10.1103/PhysRevE.72.061918",
"journal_ref": "Physical Review E 72, 061918 (2005); also in January 1, 2006 issue\n of Virtual Journal of Biological Physics Research",
"title": "First passage times and asymmetry of DNA translocation",
"url": "https://arxiv.org/abs/q-bio/0508010"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "4e78295f-490a-4c60-a6b7-3f470520d9de",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}