Unifying polar and nematic active matter: emergence and co-existence of half-integer and full-integer topological defects

Abstract

The presence and significance of active topological defects is increasingly realised in diverse biological and biomimetic systems. We introduce a continuum model of polar active matter, based on conservation laws and symmetry arguments, that recapitulates both polar and apolar (nematic) features of topological defects in active turbulence. Using numerical simulations of the continuum model, we demonstrate the emergence of both half- and full-integer topological defects in polar active matter. Interestingly, we find that crossover from active turbulence with half- to full-integer defects can emerge with the coexistence region characterized by both defect types. These results put forward a minimal, generic framework for studying topological defect patterns in active matter which is capable of explaining the emergence of half-integer defects in polar systems such as bacteria and cell monolayers, as well as predicting the emergence of coexisting defect states in active matter.

Mechanical basis and topological routes to cell elimination

“…It is noteworthy that unlike previous studies of active nematic behavior in 2D cell layers ( Mueller et al, 2019 ; Wenzel and Voigt, 2021 ), the nematic defects here emerge in the absence of any active dipolar stress or subcellular fields as the only active driving in these simulations is the polar force that the cells generate. Therefore, although the cells are endowed with polarity in terms of their self-propulsion, the emergent symmetry in terms of their orientational alignment is nematic, which is in line with experimental observations in cell monolayers ( Saw et al, 2017 ; Blanch-Mercader et al, 2018 ), discrete models of self-propelled rods ( Bär et al, 2020 ; Meacock et al, 2021 ), and recently proposed continuum model of polar active matter ( Amiri et al, 2022 ).…”

Active morphogenesis of patterned epithelial shells

“…Such an interplay between topological defect and shape changes is a recurring theme that may play a key role in morphogenesis ( Frank and Kardar, 2008 ; Metselaar et al, 2019 ; Hoffmann et al, 2021 ; Blanch-Mercader et al, 2021a ; Blanch-Mercader et al, 2021b ). In practice +1 nematic defects are unstable to separation into two +1/2 defects; however, it is conceivable that a polar or additional weakly polar field stabilises the +1 defects ( Amiri et al, 2022 ). Extension of the present work beyond axisymmetric structures will allow to distinguish more clearly the purely nematic and polar cases.…”

Thermodynamically consistent coarse-graining of polar active fluids

“…Finally, the simulations in Section VI reveal many directions for future work. Tractable three-dimensional simulations allow for detailed numerical studies, which, for example, could be used to characterize the topology of threedimensional polar defects, their dependence on particle activity, and their interplay with nematic defects [23,26]. The model could also be used to study the multiscale statistics of polar active turbulence, which is largely unaddressed with full hydrodynamic theories in either two or three dimensions, all in a way that is statistically consistent with the kinetic theory.…”

“…In polar fluids, orientation is typically described by a signed vector quantity called the polarity vector, though the director is still defined for such systems. The introduction of a well-defined sign to the orientation means the polarity vector does not exhibit ±1/2 defects, but rather ±1 defects [24][25][26]. Polar fluids also demonstrate a range of flows which do not occur in active nematics, especially involving concentration instabilities and travelling waves driven by polar fluxes [27][28][29][30].…”