A Monte Carlo algorithm to study polymer translocation through nanopores. II. Scaling laws

Area of Science:

• Computational physics
• Polymer physics
• Statistical mechanics

Background:

• Flexible chains translocating through nanopores are crucial in biological and technological applications.
• Previous work established a 1D Monte Carlo method and numerical scheme for analyzing translocation dynamics.

Purpose of the Study:

• To investigate the fundamental scaling behaviors of polymer translocation using a developed Monte Carlo approach.
• To analyze how translocation time and diffusion coefficients change with polymer length and external bias.

Main Methods:

• One-dimensional Monte Carlo simulations.
• Numerical schemes for calculating exact escape times and probabilities.
• Analysis of scaling laws for translocation time (τ) as a function of polymer length (N).

Main Results:

• Observed a change in the scaling exponent (β) for translocation time (τ) with polymer length (N) under an external bias (E).
• The exponent shifts from β=1 to β=1+ν (Rouse dynamics) or β=2ν (Zimm dynamics) for very long chains.
• An increased effective diffusion coefficient was noted for unbiased polymer chains due to entropic pulling.

Conclusions:

• The Monte Carlo method accurately predicts scaling behaviors in polymer translocation.
• External bias significantly alters the scaling law of translocation time, with distinct behaviors for different polymer dynamics.
• Entropic forces play a key role in enhancing diffusion during unbiased polymer translocation.