Li-Zhen Sun

Monte Carlo simulation on polymer translocation in crowded environment.

The effect of crowded environment with static obstacles on the translocation of a three-dimensional self-avoiding polymer through a small pore is studied using dynamic Monte Carlo simulation. The translocation time τ is dependent on polymer-obstacle interaction and obstacle concentration. The influence of obstacles on the polymer translocation is explained qualitatively by the free energy landscape. There exists a special polymer-obstacle interaction at which the translocation time is roughly independent of the obstacle concentration at low obstacle concentration, and the strength of the special interaction is roughly independent of chain length N. Scaling relation τ ~ N(1.25) is observed for strong driving translocations. The diffusion property of polymer chain is also influenced by obstacles. Normal diffusion is only observed in dilute solution without obstacles or in a crowded environment with weak polymer-obstacle attraction. Otherwise, subdiffusion behavior of polymer is observed.

Free energy landscape for the translocation of polymer through an interacting pore.

Free energy landscapes for polymer chain translocating through an interacting pore are calculated by using exact enumeration method. A potential barrier exists at weak attractive or repulsive polymer-pore interaction and it changes to a potential well with the increase in the attraction. The result reveals that there is a free translocation point where polymer is free of energy barrier. Using the free energy landscape, the translocation time tau for polymer worming through the pore and the migration time tau(m) for polymer migrating from cis side to trans side are calculated with the Fokker-Plank equation. It shows that a moderate attractive polymer-pore interaction accelerates the migration of polymer from cis side to trans side.

Polymer translocation through a gradient channel

The translocation of polymer through a channel with a gradient interaction between the polymer and the channel is studied. The interaction is expressed by E = E0 + kx, where E0 is the initial potential energy at the entrance, x is the position of the monomer inside the channel, and k is the energy gradient. The mean first passage time τ is calculated by using Fokker-Planck equation for two cases (1) N > L and (2) N < L under the assumption that the diffusion rate D is a constant, here N is the polymer length and L is the length of channel. Results show that there is a minimum of τ at k = k(c) for both cases, and the value kc is dependent on E0 and driving force f. At large f, the scaling relation τ ∼ N is observed for long polymer chains. But the scaling relation is dependent on the energy gradient k for an unforced driving translocation.

Langevin dynamics simulation on the translocation of polymer through α-hemolysin pore.

The forced translocation of a polymer through an α-hemolysin pore under an electrical field is studied using a Langevin dynamics simulation. The α-hemolysin pore is modelled as a connection of a spherical vestibule and a cylindrical β-barrel and polymer-pore attraction is taken into account. The results show that polymer-pore attraction can help the polymer enter the vestibule and the β-barrel as well; however, a strong attraction will slow down the translocation of the polymer through the β-barrel. The mean translocation time for the polymer to thread through the β-barrel increases linearly with the polymer length. By comparing our results with that of a simple pore without a vestibule, we find that the vestibule helps the polymer enter and thread through the β-barrel. Moreover, we find that it is easier for the polymer to thread through the β-barrel if the polymer is located closer to the surface of the vestibule. Some simulation results are explained qualitatively by theoretically analyzing the free-energy landscape of polymer translocation.

Simulation study on the translocation of a partially charged polymer through a nanopore

The translocation of a partially charged polymer through a neutral nanopore under external electrical field is studied by using dynamic Monte Carlo method on a simple cubic lattice. One monomer in the polymer is charged and it suffers a driving force when it locates inside the pore. Two time scales, mean first passage time τ(FP) with the first monomer restricted to never draw back into cis side and translocation time τ for polymer continuously threading through nanopore, are calculated. The first passage time τ(FP) decreases with the increase in the driving force f, and the dependence of τ(FP) on the position of charged monomer M is in agreement with the theoretical results using Fokker-Planck equation [A. Mohan, A. B. Kolomeisky, and M. Pasquali, J. Chem. Phys. 128, 125104 (2008)]. But the dependence of τ on M shows a different behavior: It increases with f for M < N/2 with N the polymer length. The novel behavior of τ is explained qualitatively from dynamics of polymer during the translocation process and from the free energy landscape.

Simulation on the translocation of polymer through compound channels

The translocation of a polymer through compound channels under external electrical field was investigated by Monte Carlo simulation on a three-dimensional simple cubic lattice. The compound channel is composed of two parts: part α with length L(pα) and part β with length L(pβ). The two parts have different polymer-channel interactions: a strong attractive interaction with strength ε(α) for part α and a variable interaction with strength ε(β) for part β. Results show that the translocation process is remarkably affected by both ε(β) and L(pα), and the fastest translocation can be achieved with a proper choice of ε(β) and L(pα). When ε(β) is large, the translocation is dominated by the last escaping process as it is difficult for the polymer chain to leave the channel. Whereas when L(pα) is small and ε(β) ≪ ε(α), the translocation is determined by the initial filling process. For this case, there is a free-energy well at the interface between the part α and the part β, which not only influences the filling dynamics but also affects the translocation probability.

DYNAMICAL MODES OF POLYMER TRANSLOCATING THROUGH INTERACTING PORE UNDER CHEMICAL POTENTIAL DIFFERENCE

The translocation of polymer chain through an interacting pore under chemical potential difference Δμ is simulated using Monte Carlo technique. Three translocation modes, dependent on the polymer–pore interaction e and Δμ, are discovered. The translocation process is found to be an nonequilibrium process, which influences the dependence of translocation time τ on e and Δμ. It is found that τ decreases in a power law relation with the increase of Δμ, and the exponent is dependent on the interaction.