Free Energy and Kinetics of Polymer Translocating Through Nanopore: Simulation and Theory
ORAL
Abstract
A 1-dimensional Fokker-Planck formalism, along with an accurately estimated free energy landscape, can provide crucial physical insights into translocation of a linear polyelectrolyte chain through a nanopore driven by a transmembrane voltage difference. Along with the drift resulting from the local gradient of the free energy landscape with respect to the 1-dimensional translocation coordinate, the formalism introduces a “diffusivity” k along this coordinate. In the literature, k is used as a uniform fitting parameter to obtain a quantitative match between the theory and the translocation time either measured in experiments or predicted by simulations. In this work, we employ enhanced sampling and Langevin dynamics simulations to gain physical insights into this parameter.
The free energy landscape of a linear polyelectrolyte of length N translocating through a cylindrical nanopore is estimated using the enhanced sampling method, metadynamics. A comparison with the analytical free energy landscape proposed in the literature allows us to make empirical corrections to the analytical free energy. Specifically, we relax the assumption that a polyelectrolyte segment loses all its conformational degrees of freedom upon entering the nanopore. Instead, we allow for a partial loss in conformational degrees of freedom, which is estimated using our metadynamics free energy landscape. Distribution of the translocation time τ obtained from the Fokker-Planck formalism using our modified free energy landscape is in quantitative agreement with that obtained from 2000 statistically independent Langevin dynamics simulation runs. In agreement with the scaling reported in literature, we observe a scaling of τ ∼ N1.4/V, where V is the driving trans-membrane voltage. Rouse dynamics predicts that the 1-dimensional diffusivity should scale as k ∼ 1/N. We report a significant deviation from this prediction, which is attributed to the local orthogonal confinement introduced by the nanopore.
The free energy landscape of a linear polyelectrolyte of length N translocating through a cylindrical nanopore is estimated using the enhanced sampling method, metadynamics. A comparison with the analytical free energy landscape proposed in the literature allows us to make empirical corrections to the analytical free energy. Specifically, we relax the assumption that a polyelectrolyte segment loses all its conformational degrees of freedom upon entering the nanopore. Instead, we allow for a partial loss in conformational degrees of freedom, which is estimated using our metadynamics free energy landscape. Distribution of the translocation time τ obtained from the Fokker-Planck formalism using our modified free energy landscape is in quantitative agreement with that obtained from 2000 statistically independent Langevin dynamics simulation runs. In agreement with the scaling reported in literature, we observe a scaling of τ ∼ N1.4/V, where V is the driving trans-membrane voltage. Rouse dynamics predicts that the 1-dimensional diffusivity should scale as k ∼ 1/N. We report a significant deviation from this prediction, which is attributed to the local orthogonal confinement introduced by the nanopore.
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Presenters
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Bhavesh R Sarode
- Indian Institute of Technology Kanpur