Single Stranded DNA Translocation Through a Fluctuating Nanopore
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SINGLE STRANDED DNA TRANSLOCATION THROUGH A FLUCTUATING NANOPORE
O. Flomenbom and J. Klafter School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel ABSTRACT We investigate the translocation of a single stranded DNA (ssDNA) through a pore, which fluctuates between two conformations, by using coupled master equations (ME). The probability density function (PDF) of the first passage times (FPT) of the translocation process is calculated, displaying a triple, double or mono-peaked behavior, depending on the system parameters. An analytical expression for the mean first passage time (MFPT) of the translocation process is derived, and provides an extensive characterization of the translocation process. INTRODUCTION Translocation of biopolymers through a membrane pore occurs in a variety of biological processes, such as gene expression in eucaryotic cells [1], conjugation between procaryotic cells, and virus infection [2]. The importance of translocation in biological systems and its possible applications have been the motivation for recent theoretical and experimental work on this topic. In experiments one usually measures the time it takes a single voltage-driven ssDNA to translocate through an α − hemolysin channel of a known structure [3]; see Fig. 1 for an illustration of the process. Since ssDNA is negatively charged (each monomer of length b has an effective charge of zq, where q is the electron charge, and z (0d) represents an effective directionality to the cis-side, which originates from the entropic factors and the average attractive interaction energy between the ssDNA and the pore. From the expressions for β ∆E j and p j , j −1 it follows that the ratio V / VC ≡ βz | q | V (1 + 1 / d ) determines the directionality of the translocation, and in particular for V / VC > 1 there is a bias towards the trans-side of the membrane. A more realistic description of the translocation can be obtained by taking into consideration fluctuations in the structure of the pore. Although it is known that α − hemolysin has a solid structure that allows its crystallization [3], during the translocation of a long polymer through the pore changes in the TPP structure can take place. Accordingly, we introduce an additional pore conformation, which is represented by the propagation matrix B . The changes in the pore conformation between A and B are controlled by the interconversion rates, ω A and ω B . ω A ( ω B ) is the rate of the change from the A (B) to the B (A) pore conformation. The physical picture of the process is that when the pore conformation changes, a different environment is created for the ssDNA occupying the TPP. This implies a change in ξ p and µ . For a large polymer N>d, we take B ≈ λA , where λ is a (dimensionless) parameter that represents the effect of the conformational change on ξ p and µ . The parameter λ may be interpreted as a measure of an effective available volume in the TPP, when the amino acids residues protruding the TPP change th
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