JARZYNSKY EQUALITY IN THE POLYMER TRANSLOCATION PROBLEM

The process of polymer translocation occurs in many biological
and biotechnological phenomena. It has received great attention
in both experimental and theoretical studies in recent years due
to its important role in many crucial biological processes, such as
mRNA translocation across a nuclear pore complex, drug delivery,
injection of DNA from a virus head into a host cell and
gene therapy. However, due to the complexity of the interactions
involved, especially between the pore and the membrane,
computer simulations have been widely used as a fundamental research
tool. Most of the numerical studies can be classified into
the topical issues of (i) translocation driven by chemical potential
gradients, (ii) translocation driven by external forces,
and (iii) unbiased translocation.

We perform, with the help of cloud computing resources, extensive Langevin simulations, which provide
free energy estimates for unbiased three-dimensional polymer translocation. We employ the Jarzynski
equality in its rigorous setting, to compute the variation of the free energy in single monomer
translocation events. In our three-dimensional Langevin simulations, the excluded-volume and van der
Waals interactions between beads (monomers and membrane atoms) are modeled through a repulsive
Lennard-Jones (LJ) potential and consecutive monomers are subject to the Finite-Extension Nonlinear
Elastic (FENE) potential. Analysing data for polymers with different lengths, the free energy profile is
noted to have interesting finite-size scaling properties.