Dynamics of Molecular Motors and Polymer Translocation with Sequence Heterogeneity

TL;DR

This paper investigates how sequence heterogeneity affects the dynamics of polymer translocation and molecular motors, revealing anomalous sublinear growth in displacement near stall forces through exact lattice model solutions.

Contribution

It provides exact solutions to lattice models of polymer translocation and molecular motors incorporating sequence heterogeneity, showing its impact on anomalous dynamics.

Findings

Sequence heterogeneity causes sublinear displacement growth near stall force.

Exact solutions reveal anomalous dynamics in polymer translocation and motor models.

Heterogeneity effects are detectable under specific experimental conditions.

Abstract

The effect of sequence heterogeneity on polynucleotide translocation across a pore and on simple models of molecular motors such as helicases, DNA polymerase/exonuclease and RNA polymerase is studied in detail. Pore translocation of RNA or DNA is biased due to the different chemical environments on the two sides of the membrane, while the molecular motor motion is biased through a coupling to chemical energy. An externally applied force can oppose these biases. For both systems we solve lattice models exactly both with and without disorder. The models incorporate explicitly the coupling to the different chemical environments for polymer translocation and the coupling to the chemical energy (as well as nucleotide pairing energies) for molecular motors. Using the exact solutions and general arguments we show that the heterogeneity leads to anomalous dynamics. Most notably, over a range of forces around the stall force (or stall tension for DNA polymerase/exonuclease systems) the displacement grows sublinearly as t^\mu with \mu<1. The range over which this behavior can be observed experimentally is estimated for several systems and argued to be detectable for appropriate forces and buffers. Similar sequence heterogeneity effects may arise in the packing of viral DNA.