Integer defects, flow localization, and bistability on curved active surfaces

TL;DR

This study explores how integer topological defects behave on curved biological surfaces, revealing that curvature induces defect localization and flow bistability, especially in contractile active fluids, advancing understanding of morphogenetic processes.

Contribution

It uncovers the influence of deviatoric curvature on defect dynamics and flow localization in curved active surfaces, a novel insight into morphogenetic defect behavior.

Findings

Deviatoric curvature induces defect localization and flow patterns.

Contractile systems exhibit hysteresis and bistability between flow states.

Curvature effects differ between cylindrical and bump geometries.

Abstract

Biological surfaces, such as developing epithelial tissues, exhibit in-plane polar or nematic order and can be strongly curved. Recently, integer (+1) topological defects have been identified as morphogenetic hotspots in living systems. Yet, while +1 defects in active matter on flat surfaces are well-understood, the general principles governing curved active defects remain unknown. Here, we study the dynamics of integer defects in an extensile or contractile polar fluid on two types of morphogenetically-relevant substrates : (1) a cylinder terminated by a spherical cap, and (2) a bump on an otherwise flat surface. Because the Frank elastic energy on a curved surface generically induces a coupling to $\textit{deviatoric}$ curvature, $\mathcal{D}$ (difference between squared principal curvatures), a +1 defect is induced on both surface types. We find that $\mathcal{D}$ leads to surprising effects including localization of orientation gradients and active flows, and particularly for contractility, to hysteresis and bistability between quiescent and flowing defect states.