TY - JOUR

T1 - First passage times and asymmetry of DNA translocation

AU - Lua, Rhonald C.

AU - Grosberg, Alexander Y.

PY - 2005/12

Y1 - 2005/12

N2 - 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 (δ)2 t, and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form (δ)2 t with 0< Y <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 0.5 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/y in subdiffusion.

AB - 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 (δ)2 t, and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form (δ)2 t with 0< Y <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 0.5 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/y in subdiffusion.

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U2 - 10.1103/PhysRevE.72.061918

DO - 10.1103/PhysRevE.72.061918

M3 - Article

C2 - 16485985

AN - SCOPUS:33244487421

VL - 72

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 6

M1 - 061918

ER -