Stochastic resonance during a polymer translocation process

Abstract

We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly. C 2016 AIP Publishing LLC. [http://dx

Frequency-control of protein translocation across an oscillating nanopore

“…Our study differs from previous ones [10][11][12][13][14][15][16] that focused on bead-spring polymers, for it investigates the translocation of a protein-like chain. The translocation of proteins is known to strongly deviates from that of polymers as their compactness presents much more resistance to the passage through narrow paths.…”

“…However, it is important to warn that formula (16) constitutes only a reasonable approximation of the true solution, indeed as it discussed by Molini et al [60] and in Appendix B, the image method to work, when applied to Smoluchowski equations with time dependent coefficients, requires a rigorous proportionality between drift and diffusion; a condition which is not verified in Eq. (14). In addition, we assumed the further simplification of strong enough drift that soon pushes the trajectories away from the Q = 0-boundary, so that the no-flux condition is automatically implemented.…”

Nucleotide Dynamics During Flossing of Polycation-DNA-Polycation through a Nanopore using Molecular Dynamics

“…The average residence time of a nucleotide within the nanopore was too small to be of any practical use (6-30 ns) and the stochastic nature of the polymer dynamics made it difficult to monitor the position of the nucleotides within the nanopore, precisely. As proposed by Mondal and Muthukumar, 31 alternating eternal force may allow for precise monitoring of the nucleotides due to stochastic resonance, hence we used square wave type alternating voltage for precise control of nucleotide dynamics. Using alternating voltage, we increased the average residence time of nucleotides by an order of magnitude but the individual trajectories were stochastic.…”

“…Moreover, the average residence time was also too small to be of practical use (τ ≤ 0.01 µs). As proposed by Mondal and Muthukumar, 31 the signal to noise ratio can be improved by applying alternating external force, we performed simulation with alternating voltage and applied similar analysis. Figure 4: (a) Mean probability distribution (p i ) of finding a nucleotide i within ∆z (-1.5 Å-1.5Å along the z-axis) for N A = 10 and V = 0.18 volts; all simulations were initiated by tethering i =1 at z =3 Å.…”

“…Along those lines, using alternating external force, stochastic resonance has been reported during the translocation of a polyelectrolyte through a nanopore. 31 Using Fokker-Planck formalism, Mondal and Muthukumar 31 derived an analytical expression for determining the signal to noise ratio as a function of the system parameters. For example, knowing the pore length, polymer length, and the pore-polymer interaction strength, the frequency and magnitude of the external force to detect highest signal to noise ratio can be predicted.…”