# Uniform description of polymer ejection dynamics from capsid with and without hydrodynamics

## TL;DR

This study investigates polymer ejection from a capsid using stochastic rotation dynamics, revealing how hydrodynamics influence ejection speed, polymer expansion, and the universal scaling of waiting times, with implications for understanding ejection times.

## Contribution

It introduces a universal scaling function for polymer ejection dynamics and compares hydrodynamic effects using SRD and Langevin simulations, providing new insights into ejection time scaling.

## Key findings

- Hydrodynamics speed up ejection and allow closer to equilibrium expansion.
- Waiting times grow with ejected monomers as a sum of two exponents.
- Ejection time scales linearly with polymer length for long polymers.

## Abstract

We use stochastic rotation dynamics to examine the dynamics of the ejection of an initially strongly confined flexible polymer from a spherical capsid with and without hydrodynamics. The results obtained using SRD are compared to similar Langevin simulations. Inclusion of hydrodynamic modes speeds up the ejection but also allows the part of the polymer outside the capsid to expand closer to equilibrium. This shows as higher values of radius of gyration when hydrodynamics are enabled. By examining the waiting times of individual polymer beads we find that the waiting time $t_w$ grows with the number of ejected monomers $s$ as a sum of two exponents. When $\approx 63 \%$ of the polymer has ejected the ejection enters the regime of slower dynamics. The functional form of $t_w$ vs $s$ is universal for all ejection processes starting from the same initial monomer densities. Inclusion of hydrodynamics only reduces its magnitude. Consequently, we define a universal scaling function $h$ such that the cumulative waiting time $t = N_0 h(s/N_0)$ for large $N_0$. Our unprecedently precise measurements of force indicate that this form for $t_w(s)$ originates from the corresponding force towards the pore decreasing super exponentially at the end of the ejection. Our measured $t_w(s)$ explains the apparent superlinear scaling of the ejection time with the polymer length for short polymers. However, for asymptotically long polymers $t_w(s)$ predicts linear scaling.