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Spatiotemporal patterns in multicellular systems are important to understanding tissue dynamics, for instance, during embryonic development and disease. Here, we use a multiphase field model to study numerically the behavior of a near-confluent monolayer of deformable cells with intercellular friction. Varying friction and cell motility drives a solid–liquid transition, and near the transition boundary, we find the emergence of local nematic order of cell deformation driven by shear-aligning cellular flows. Intercellular friction contributes to the monolayer’s viscosity, which significantly increases the spatial correlation in the flow and, concomitantly, the extent of nematic order. We also show that local hexatic and nematic order are tightly coupled and propose a mechanical-geometric model for the colocalization of
nematic defects and 5–7 disclination pairs, which are the structural defects in the hexatic phase. Such topological defects coincide with regions of high cell–cell overlap, suggesting that they may mediate cellular extrusion from the monolayer, as found experimentally. Our results delineate a mechanical basis for the recent observation of nematic and hexatic order in multicellular collectives in experiments and simulations and pinpoint a generic pathway to couple topological and physical effects in these systems. Free, publicly-accessible full text available October 1, 2025 -
Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living tissue, the theoretical underpinnings have not been fully explored. We show that a two-dimensional version of the model, which is commonly employed to study tissue monolayers, can be derived from a three-dimensional version in the presence of a substrate. We also show how viscous forces, which arise from friction between different cells, can be included in the model. Finally, we numerically simulate a tissue monolayer and find that intercellular friction tends to solidify the tissue.
Published by the American Physical Society 2024 Free, publicly-accessible full text available October 1, 2025 -
Topological defects play a central role in the physics of many materials, including magnets, superconductors, and liquid crystals. In active fluids, defects become autonomous particles that spontaneously propel from internal active stresses and drive chaotic flows stirring the fluid. The intimate connection between defect textures and active flow suggests that properties of active materials can be engineered by controlling defects, but design principles for their spatiotemporal control remain elusive. Here, we propose a symmetry-based additive strategy for using elementary activity patterns, as active topological tweezers, to create, move, and braid such defects. By combining theory and simulations, we demonstrate how, at the collective level, spatial activity gradients act like electric fields which, when strong enough, induce an inverted topological polarization of defects, akin to a negative susceptibility dielectric. We harness this feature in a dynamic setting to collectively pattern and transport interacting active defects. Our work establishes an additive framework to sculpt flows and manipulate active defects in both space and time, paving the way to design programmable active and living materials for transport, memory, and logic.
Free, publicly-accessible full text available May 21, 2025 -
In recent years, non-reciprocally coupled systems have received growing attention. Previous work has shown that the interplay of non-reciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We show that these phenomena are generically found in a broad class of pattern-forming systems, including mass-conserving reaction--diffusion systems and viscoelastic active gels. All these systems share a characteristic dispersion relation that acquires a non-zero imaginary part at the edge of the band of unstable modes and exhibit a regime of propagating structures (traveling wave bands or droplets). We show that models for these systems can be mapped to a common ``normal form'' that can be seen as a spatially extended generalization of the FitzHugh--Nagumo model, providing a unifying dynamical-systems perspective. We show that the minimal non-reciprocal Cahn--Hilliard (NRCH) equations exhibit a surprisingly rich set of behaviors, including interrupted coarsening of traveling waves without selection of a preferred wavelength and transversal undulations of wave fronts in two dimensions. We show that the emergence of traveling waves and their speed are precisely predicted from the local dispersion relation at interfaces far away from the homogeneous steady state. The traveling waves are therefore a consequence of spatially localized coalescence of hydrodynamic modes arising from mass conservation and translational invariance of displacement fields. Our work thus generalizes previously studied non-reciprocal phase transitions and identifies generic mechanisms for the emergence of dynamical patterns of conserved fields.
Free, publicly-accessible full text available April 1, 2025 -
Orientational order, encoded in anisotropic fields, plays an important role during the development of an organism. A striking example of this is the freshwater polypmore » « less
Hydra , where topological defects in the muscle fiber orientation have been shown to localize to key features of the body plan. This body plan is organized by morphogen concentration gradients, raising the question how muscle fiber orientation, morphogen gradients and body shape interact. Here, we introduce a minimal model that couples nematic orientational order to the gradient of a morphogen field. We show that on a planar surface, alignment to a radial concentration gradient can induce unbinding of topological defects, as observed during budding and tentacle formation inHydra , and stabilize aster/vortex-like defects, as observed at aHydra ’s mouth. On curved surfaces mimicking the morphologies ofHydra in various stages of development—from spheroid to adult—our model reproduces the experimentally observed reorganization of orientational order. Our results suggest how gradient alignment and curvature effects may work together to control orientational order during development and lay the foundations for future modeling efforts that will include the tissue mechanics that drive shape deformations.