Universal properties of active membranes

TL;DR

This paper develops a general field theory for active membranes with embedded activators, revealing universal scaling regimes and critical properties that describe cellular edge dynamics and distinguish from passive interface models.

Contribution

It introduces a unified theoretical framework for active membranes, analyzing their critical behavior and identifying universal scaling regimes using renormalization group methods.

Findings

Identification of crossover between acoustic and diffusive scaling regimes

Derivation of universal critical exponents for active membranes

Evidence of strong-coupling behavior distinct from passive interface models

Abstract

We put forward a general field theory for membranes with embedded activators and analyse their critical properties using renormalization group techniques. Depending on the membrane-activator coupling, we find a crossover between acoustic and diffusive scaling regimes, with mean-field dynamical critical exponents z = 1 and 2 respectively. We argue that the acoustic scaling, which is exact in all spatial dimensions, is a suitable candidate for the universal description of the spatiotemporal patterns observed at the leading edge of motile cells. Furthermore, one-loop corrections to the diffusive mean-field exponents reveal universal behaviour distinct from the Kardar-Parisi-Zhang scaling of passive interfaces and signs of strong-coupling behaviour.