Collectively migrating cells in living organisms are often guided by their local environment, including physical barriers and internal interfaces. Well-controlled in vitro experiments have shown... Show moreCollectively migrating cells in living organisms are often guided by their local environment, including physical barriers and internal interfaces. Well-controlled in vitro experiments have shown that, when confined in adhesive stripes, monolayers of moderately active spindle-shaped cells self-organize at well-defined angle to the stripes' longitudinal direction and spontaneously give rise to a simple shear flow, where the average cellular orientation smoothly varies across the system. However, the impact of physical boundaries on highly active, chaotic, multicellular systems is currently unknown, despite its potential relevance. In this work, we show that human fibrosarcoma cells (HT1080) close to an interface exhibit a spontaneous edge current with broken left-right symmetry, while in the bulk the cell flow remains chaotic. These localized edge currents result from an interplay between nematic order, microscopic chirality, and topological defects. Using a combination of in vitro experiments, numerical simulations, and theoretical work, we demonstrate the presence of a self-organized layer of thorn 1/2 defects anchored at the boundary and oriented at a well-defined angle close to, but smaller than, 90 degrees with respect to the boundary direction. These self-organized defects act as local sources of chiral active stress generating the directed edge flows. Our work therefore highlights the impact of topology on the emergence of collective cell flows at boundaries. It also demonstrates the role of chirality in the emergence of edge flows. Since chirality and boundaries are common properties of multicellular systems, this work suggests a new possible mechanism for collective cellular flows. Show less
We formulate a hydrodynamic theory of p-atic liquid crystals, namely, two-dimensional anisotropic fluids endowed with generic p-fold rotational symmetry. Our approach, based on an order parameter... Show moreWe formulate a hydrodynamic theory of p-atic liquid crystals, namely, two-dimensional anisotropic fluids endowed with generic p-fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discrete rotational symmetry of p-atic phases, allows us to unveil several unknown aspects of flowing p-atics, that previous theories, characterized by O(2) rotational symmetry, could not account for. This includes the onset of long-ranged orientational order in the presence of a simple shear flow of arbitrary shear rate, as opposed to the standard quasi-long-ranged order of two-dimensional liquid crystals, and the possibility of flow alignment at large shear rates. Show less
We formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic p-fold rotational symmetry, also known as p-atics, of which nematics (p = 2) and hexatics (p = 6)... Show moreWe formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic p-fold rotational symmetry, also known as p-atics, of which nematics (p = 2) and hexatics (p = 6) are the two best known examples. Previous hydrodynamic theories of p-atics are characterized by continuous O(2) rotational symmetry, which is higher than the discrete rotational symmetry of p-atic phases. By contrast, here we demonstrate that the discrete rotational symmetry allows the inclusion of additional terms in the hydrodynamic equations, which, in turn, lead to novel phenomena, such as the possibility of flow alignment at high shear rates, even for p > 2. Furthermore, we show that any finite imposed shear will induce long-ranged orientational order in any p-atic liquid crystal, in contrast to the quasi-long-ranged order that occurs in the absence of shear. The induced order parameter scales like a nonuniversal power of the applied shear rate at small shear rates. Show less
The variation associated with different observable characteristics-phenotypes-at the cellular scale underpins homeostasis and the fitness of living systems. However, if and how these noisy... Show moreThe variation associated with different observable characteristics-phenotypes-at the cellular scale underpins homeostasis and the fitness of living systems. However, if and how these noisy phenotypic traits shape properties at the population level remains poorly understood. Here we report that phenotypic noise self-regulates with growth and coordinates collective structural organization, the kinetics of topological defects and the emergence of active transport around confluent colonies. We do this by cataloguing key phenotypic traits in bacteria growing under diverse conditions. Our results reveal a statistically precise critical time for the transition from a monolayer biofilm to a multilayer biofilm, despite the strong noise in the cell geometry and the colony area at the onset of the transition. This reveals a mitigation mechanism between the noise in the cell geometry and the growth rate that dictates the narrow critical time window. By uncovering how rectification of phenotypic noise homogenizes correlated collective properties across colonies, our work points at an emergent strategy that confluent systems employ to tune active transport, buffering inherent heterogeneities associated with natural cellular environment settings.The first step of biofilm formation is a transition from a single layer of bacteria to multiple layers. Now, there is evidence that this transition is determined by the phenotypic noise associated with cell geometry and growth rate. Show less
Hoffmann, L A..; Carenza, L.N..; Eckert, J.; Giomi, L. 2022
Growing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon,... Show moreGrowing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon, rooted in the buckling theory of deformable active polar liquid crystals. Using a combination of linear stability analysis and computational fluid dynamics, we demonstrate that active layers, such as confined cell monolayers, are unstable to the formation of protrusions in the presence of disclinations. The instability originates from an interplay between the focusing of the elastic forces, mediated by defects, and the renormalization of the system's surface tension by the active flow. The posttransitional regime is also characterized by several complex morphodynamical processes, such as oscillatory deformations, droplet nucleation, and active turbulence. Our findings offer an explanation of recent observations on tissue morphogenesis and shed light on the dynamics of active surfaces in general. Show less
When interacting motile units self-organize into flocks, they realize one of the most robust ordered states found in nature. However, after 25 years of intense research, the very mechanism... Show moreWhen interacting motile units self-organize into flocks, they realize one of the most robust ordered states found in nature. However, after 25 years of intense research, the very mechanism controlling the ordering dynamics of both living and artificial flocks has remained unsettled. Here, combining active-colloid experiments, numerical simulations, and analytical work, we explain how flocking liquids heal their spontaneous flows initially plagued by collections of topological defects to achieve long-ranged polar order even in two dimensions. We demonstrate that the self-similar ordering of flocking matter is ruled by a living network of domain walls linking all +/- 1 vortices and guiding their annihilation dynamics. Crucially, this singular orientational structure echoes the formation of extended density patterns in the shape of interconnected bow ties. We establish that this double structure emerges from the interplay between self-advection and density gradients dressing each -1 topological charge with four orientation walls. We then explain how active Magnus forces link all topological charges with extended domain walls, while elastic interactions drive their attraction along the resulting filamentous network of polarization singularities. Taken together, our experimental, numerical, and analytical results illuminate the suppression of all flow singularities and the emergence of pristine unidirectional order in flocking matter. Show less
Recent experiments on monolayers of spindle-like cells plated on adhesive stripe-shaped domains have provided a convincing demonstration that certain types of collective phenomena in epithelia are... Show moreRecent experiments on monolayers of spindle-like cells plated on adhesive stripe-shaped domains have provided a convincing demonstration that certain types of collective phenomena in epithelia are well described by active nematic hydrodynamics. While recovering some of the hallmark predictions of this framework, however, these experiments have also revealed a number of unexpected features that could be ascribed to the existence of chirality over length scales larger than the typical size of a cell. In this article we elaborate on the microscopic origin of chiral stresses in nematic cell monolayers and investigate how chirality affects the motion of topological defects, as well as the collective motion in stripe-shaped domains. We find that chirality introduces a characteristic asymmetry in the collective cellular flow, from which the ratio between chiral and non-chiral active stresses can be inferred by particle-image-velocimetry measurements. Furthermore, we find that chirality changes the nature of the spontaneous flow transition under confinement and that, for specific anchoring conditions, the latter has the structure of an imperfect pitchfork bifurcation. Show less
You, Z.H.; Pearce, D.J.G.; Sengupta, A.; Giomi, L. 2019
The transition from monolayers to multilayered structures in bacterial colonies is a fundamental step in biofilm development. Observed across different morphotypes and species, this transition is... Show moreThe transition from monolayers to multilayered structures in bacterial colonies is a fundamental step in biofilm development. Observed across different morphotypes and species, this transition is triggered within freely growing bacterial microcolonies comprising a few hundred cells. Using a combination of numerical simulations and analytical modeling, here we demonstrate that this transition originates from the competition between growth-induced in-plane active stresses and vertical restoring forces, due to the cell-substrate interactions. Using a simple chainlike colony of laterally confined cells, we show that the transition sets when individual cells become unstable to rotations; thus it is localized and mechanically deterministic. Asynchronous cell division renders the process stochastic, so that all the critical parameters that control the onset of the transition are continuously distributed random variables. Here we demonstrate that the occurrence of the first division in the colony can be approximated as a Poisson process in the limit of large cell numbers. This allows us to approximately calculate the probability distribution function of the position and time associated with the first extrusion. The rate of such a Poisson process can be identified as the order parameter of the transition, thus highlighting its mixed deterministic-stochastic nature. Show less
Pearce, D.J.G.; Ellis, P.W.; Fernandez-Nieves, A.; Giomi, L. 2019
We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal constrained to a curved surface. Using a combination of hydrodynamic and particle-based simulations, we... Show moreWe investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal constrained to a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural features of the fluid, such as the topological charge density, the defect number density, the nematic order parameter, and defect creation and annihilation rates, are approximately linear functions of the substrate Gaussian curvature, which then acts as a control parameter for the chaotic flow. Our theoretical predictions are then compared with experiments on microtubule-kinesin suspensions confined on toroidal droplets, finding excellent qualitative agreement. Show less
We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil–water interface. Kinesin motors continuously inject mechanical... Show moreWe study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil–water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the chaotic flows are exponentially distributed, which allows us to extract the characteristic system length scale. We probe the dependence of this length scale on the ATP concentration, which is the experimental knob that tunes the magnitude of the active stress. Our data suggest a possible mapping between the ATP concentration and the active stress that is based on the Michaelis–Menten kinetics that governs the motion of individual kinesin motors. Show less
Fonda, P.; Rinaldin, M.; Kraft, D.J.; Giomi, L. 2019
