Universality in the dynamics of vesicle translocation through a hole

TL;DR

This paper uncovers universal scaling laws governing vesicle translocation through a hole, showing critical pressure dependence and divergence of translocation time near the threshold, independent of membrane elasticity details.

Contribution

It reveals universal characteristics and scaling relations in vesicle translocation dynamics that are independent of membrane elasticity.

Findings

Critical pressure for translocation scales as (R0 - a)^{3/2}.

Translocation time diverges as (ΔP - ΔP_c)^{-1/2}.

No translocation occurs below the critical pressure ΔP_c.

Abstract

We analyze the translocation process of a spherical vesicle, made of membrane and incompressible fluid, through a hole smaller than the vesicle size, driven by pressure difference $\Delta P$. We show that such a vesicle shows certain universal characteristics which is independent of the details of the membrane elasticity; (i) there is a critical pressure $\Delta P_{\rm c}$ below which no translocation occurs, (ii) $\Delta P_{\rm c}$ decreases to zero as the vesicle radius $R_0$ approaches the hole radius $a$, satisfying the scaling relation $\Delta P_{\rm c} \sim (R_0 - a)^{3/2}$, and (iii) the translocation time $\tau$ diverges as $\Delta P$ decreases to $\Delta P_{\rm c}$, satisfying the scaling relation $\tau \sim (\Delta P -\Delta P_{\rm c})^{-1/2}$.