Macromolecule Translocation in a Nanopore: Center of Mass Drift-Diffusion over an Entropic Barrier

Many fundamental biological processes involve moving macromolecules across membranes, through nanopores, in a process called translocation. Such motion is necessary for gene expression and regulation, tissue formation, and viral infection. Furthermore, in recent years nanopore technologies have been developed for single molecule detection of biological and synthetic macromolecules, which have been most notably employed in next generation DNA sequencing devices. Many successful theories have been established, which calculate the entropic barrier required to elongate a chain during translocation. However, these theories are at the level of the translocation coordinate (number of forward steps) and thus lack a clear connection to experiments and simulations. Furthermore, the proper diffusion coefficient for such a coordinate is unclear. In order to address these issues, we propose a center of mass (CM) theory for translocation. We start with the entropic barrier approach and show that the translocation coordinate is equivalent to the center of mass of the chain, providing a direct interpretation of previous theoretical studies. We thus recognize that the appropriate dynamics is given by CM diffusion, and calculate the appropriate diffusion constant (Rouse or Zimm) as the chain translocates. We illustrate our theoretical approach with a planar nanopore geometry and calculate some characteristic dynamical predictions. Our main result is the connection between the translocation coordinate and the chain CM, however, we also find that the translocation time is sped up by 1-2 orders of magnitude if hydrodynamic interactions are present. Our approach can be extended to include the details included in previous translocation theories. Most importantly this work provides a direct connection between theoretical approaches and experiments or simulations.\n\nSIGNIFICANCEMacromolecule motion through nanopores is critical for many biological processes, and has been recently employed for nucleic acid sequencing. Despite this, direct theoretical understandings of translocation are difficult to evaluate due to the introduction of the translocation coordinate. In this manuscript, we propose a theory for translocation written at the center of mass level of the polymer chain. This theoretical approach is more easily compared to experimental and simulation results, and additionally allows one to accurately account for hydrodynamic interactions on the macromolecule dynamics.