7 M ay 2 00 9 epl draft Dynamics of forced biopolymer translocation

  • V . V . L EHTOLA, Rudoy Inna, K . K ASKI
  • Published 2009

Abstract

We present results from our simulations of biopolymer translocation in a solvent which explain the main experimental findings. The forced translocation can be described by simple force balance arguments for the relevant range of pore potentials in experiments and biological systems. Scaling of translocation time with polymer length varies with pore force and friction. Hydrodynamics affects this scaling and significantly reduces translocation times. The transport of biopolymers through a nano-scale pore in a membrane is a ubiquitous process in biology. For example, in protein import into mitochondria, chloroplasts, and peroxisomes the translocation occurs with the aid of a membrane potential [1]. Experimental work on forced (or biased) translocation is largely motivated by finding methods for reading the DNA and RNA sequences. These nanopores are typically either fabricated solid-state [2, 3] or α-hemolysin (α−HL) pores in lipid bi-layer membranes [4, 5]. Foundation for the theoretical work was laid in the classic treatment by Sung and Park [6], which was based on the assumption that the polymer segments on the two sides of the membrane reside close to separate thermal equilibria. However, the validity of this approach was questioned already in [7, 8], where the authors noted that the pore force regime in which the polymer’s relaxation time towards equilibrium is smaller than the characteristic translocation time is marginal and that the approach would be invalid even in the unforced translocation for sufficiently long polymers. Theoretical work, inconsistent with experiments, has since evolved in different directions. The role of computer simulations has been largely to support the theoretical work which neglects hydrodynamics. Hence, results from simulations where hydrodynamic interactions are included are few and, due to their being computationally demanding, often fairly qualitative [9, 10]. In addition, the generally used Monte Carlo method gives unphysical behaviour for larger pore force values relevant for experiments and biological systems [2, 4, 5], as we have shown [11]. Very recently multiscale simulations on biopolymer translocation in a solvent were reported to give results in accordance with experiments [12,13]. Our motivation for the present study is two-fold. First, by using realistic dynamics we want to find explanation for the dynamics of the experimentally observed translocation processes. Secondly, we want to determine the effect of hydrodynamics on forced polymer translocation, previously studied only in the unforced case [9, 10]. We use a hybrid multi-scale method, where the polymer follows detailed molecular dynamics and the coarse-grained solvent stochastic rotation dynamics (SRD). The solvent is divided into cells, within which fictitious solvent particles perform simplified dynamics where collisions among them and with the polymer beads are taken effectively into account by performing random rotations of the random part of their velocities, vi(t+∆tSRD) = R[vi(t)− vcm(t)]+ vcm(t), where vi are the particle velocities inside a cell, ∆tSRD is the time step for solvent dynamics, R is the rotation matrix, and vcm is the centre-of-mass velocity of the particles within the cell. Hydrodynamic modes are supported over the cells. Optionally, they can be switched off by not adding back vcm after the random rotation, which is particularly feasible for pinning down the effect of hydrodynamics. The abovedescribed collision step is followed by the free-streaming step ri(t+∆tSRD) = ri(t) + vi(t)∆tSRD . Thermostating is done by rescaling all solvent particle velocities so that equipartition theorem is fulfilled at all times. More detailed descriptions of the method can be found e.g. in [14–16]. In this paper we study the forced translocation where the two sides separated by walls are not hydrodynamically coupled. To achieve this we use a non-aqueous pore, i.e. there are no solvent particles inside the pore. This corresponds closely to the experiments we aim to model and also addresses the theoreti-

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Cite this paper

@inproceedings{EHTOLA20097MA, title={7 M ay 2 00 9 epl draft Dynamics of forced biopolymer translocation}, author={V . V . L EHTOLA and Rudoy Inna and K . K ASKI}, year={2009} }