arXiv subjects

M. Cristina Marchetti

Publications and source records attributed to M. Cristina Marchetti.

At least 37 records · Page 2Linked to original sources

arXiv2023

Patterning of morphogenetic anisotropy fields

Orientational order, encoded in anisotropic fields, plays an important role during the development of an organism. A striking example of this is the freshwater polyp 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 in Hydra, and stabilize aster/vortex-like defects, as observed at a Hydra's mouth. On curved surfaces mimicking the morphologies of Hydra 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 lays the foundations for future modeling efforts that will include the tissue mechanics that drive shape deformations.

physics.bio-ph↗

arXiv2023

Finite Elasticity of the Vertex Model and its Role in Rigidity of Curved Cellular Tissues

Using a mean field approach and simulation, we study the non-linear mechanical response of the vertex model (VM) of biological tissue under compression and dilation. The VM is known to exhibit a transition between rigid and fluid-like, or floppy, states driven by geometric incompatibility. Target perimeter and area set a target shape which may not be geometrically achievable, thereby engendering frustration. Previously, an asymmetry in the linear elastic response was identified at the rigidity transition between compression and dilation. Here we show and characterize how the asymmetry extends away from the transition point for finite strains. Under finite compression, an initially solid VM can totally relax perimeter tension, and thereby have reduced bulk and shear modulus. Conversely, an initially floppy VM under dilation can rigidify and have a higher bulk and shear modulus. These observations imply that re-scaling of cell area shifts the transition between rigid and floppy states. Based on this insight, we calculate the re-scaling of cell area engendered by intrinsic curvature and write a prediction for the rigidity transition in the presence of curvature. The shift of the rigidity transition in the presence of curvature for the VM provides a new metric for predicting tissue rigidity from image data for curved tissues in a manner analogous to the flat case.

cond-mat.soft↗

arXiv2022

Activity-suppressed phase separation

We use a continuum model to examine the effect of activity on a phase separating mixture of an extensile active nematic and a passive fluid. We highlight the distinct role of previously considered interfacial active stresses and bulk active stresses that couple to liquid crystalline degrees of freedom. Interfacial active stresses can arrest phase separation, as previously demonstrated. Bulk extensile active stresses can additionally strongly suppress phase separation by sustained self-stirring of the fluid, substantially reducing the size of the coexistence region in the temperature/concentration plane relative to that of the passive system. The phase separated state is a dynamical emulsion-like steady state of continuously splitting and merging droplets, as suggested by recent experiments. Using scaling analysis and simulations, we identify various regimes for the dependence of droplet size on activity. These results can provide a criterion for identifying the mechanisms responsible for arresting phase separation in experiments.

cond-mat.soft↗

arXiv2022

Shear-driven solidification and nonlinear elasticity in epithelial tissues

Biological processes, from morphogenesis to tumor invasion, spontaneously generate shear stresses inside living tissue. The mechanisms that govern the transmission of mechanical forces in epithelia and the collective response of the tissue to bulk shear deformations remain, however, poorly understood. Using a minimal cell-based computational model, we investigate the constitutive relation of confluent tissues under simple shear deformation. We show that an initially undeformed fluidlike tissue acquires finite rigidity above a critical applied strain. This is akin to the shear-driven rigidity observed in other soft matter systems. Interestingly, shear-driven rigidity can be understood by a critical scaling analysis in the vicinity of the second order critical point that governs the liquid-solid transition of the undeformed system. We further show that a solidlike tissue responds linearly only to small strains and but then switches to a nonlinear response at larger stains, with substantial stiffening. Finally, we propose a mean-field formulation for cells under shear that offers a simple physical explanation of shear-driven rigidity and nonlinear response in a tissue.

cond-mat.soft↗

arXiv2022

Active nematic defects in compressible and incompressible flows

We study the dynamics of active nematic films on a substrate driven by active flows with or without the incompressible constraint.Through simulations and theoretical analysis, we show that arch patterns are stable in the compressible case, whilst they become unstable under the incompressibility constraint. For compressible flows at high enough activity, stable arches organize themselves into a smectic-like pattern, which induce an associated global polar ordering of $+1/2$ nematic defects. By contrast, divergence-free flows give rise to a local nematic order of the $+1/2$ defects, consisting of anti-aligned pairs of neighboring defects, as established in previous studies.

cond-mat.soft↗

arXiv2022

Molecular-scale substrate anisotropy and crowding drive long-range nematic order of cell monolayers

The ability of cells to reorganize in response to external stimuli is important in areas ranging from morphogenesis to tissue engineering. Elongated cells can co-align due to steric effects, forming states with local order. We show that molecular-scale substrate anisotropy can direct cell organization, resulting in the emergence of nematic order on tissue scales. To quantitatively examine the disorder-order transition, we developed a high-throughput imaging platform to analyze velocity and orientational correlations for several thousand cells over days. The establishment of global, seemingly long-ranged order is facilitated by enhanced cell division along the substrate's nematic axis, and associated extensile stresses that restructure the cells' actomyosin networks. Our work, which connects to a class of systems known as active dry nematics, provides a new understanding of the dynamics of cellular remodeling and organization in weakly interacting cell collectives. This enables data-driven discovery of cell-cell interactions and points to strategies for tissue engineering.

physics.bio-ph↗

arXiv2022

Defect self-propulsion in active nematic films with spatially-varying activity

We study the dynamics of topological defects in active nematic films with spatially-varying activity and consider two setups: i) a constant activity gradient, and ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like $+1/2$ defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the $+1/2$ defect and has no effect on the $-1/2$ that remains a non-motile particle. A sharp jump in activity acts like a wall that traps the defects, affecting the translational and rotational motion of both charges. The $+1/2$ defect slows down as it approaches the interface and the net vorticity tends to reorient the defect polarization so that it becomes perpendicular to the interface. The $-1/2$ defect acquires a self-propulsion towards the activity interface, while the vorticity-induced active torque tends to align the defect to a preferred orientation. This effective attraction of the negative defects to the wall is consistent with the observation of an accumulation of negative topological charge at both active/passive interfaces and physical boundaries.

cond-mat.soft↗

arXiv2022

Controlling liquid-liquid phase behavior with an active fluid

Demixing of binary liquids is a ubiquitous transition, which is explained using a well-established thermodynamic formalism that requires equality of intensive thermodynamics parameters across the phase boundaries. Demixing transitions also occur when binary fluid mixtures are driven away from equilibrium, for example, by external shear flow. Predicting demixing transition under non-equilibrium non-potential conditions remains, however, a challenge. We drive liquid-liquid phase separation (LLPS) of attractive DNA nanostar molecules away from equilibrium using an internally driven microtubule-based active fluid. Activity lowers the critical temperature and narrows the coexistence concentrations, but only when there are mechanical bonds between the liquid droplets and the reconfiguring active fluid. Similar behaviors are observed in numerical simulations, suggesting that activity suppression of liquid-liquid phase separation is a generic feature of active LLPS. Our work describes a platform for building soft active materials with feedback control while also providing insight into cell biology, where phase separation emerged as a ubiquitous self-organizational principle.

cond-mat.soft↗

arXiv2022

Dynamics of active liquid interfaces

Controlling interfaces of phase separating fluid mixtures is key to creating diverse functional soft materials. Traditionally, this is accomplished with surface-modifying chemical agents. Using experiment and theory, we study how mechanical activity shapes soft interfaces that separate an active and a passive fluid. Chaotic flows in the active fluid give rise to giant interfacial fluctuations and non-inertial propagating active waves. At high activities, stresses disrupt interface continuity and drive droplet generation, producing an emulsion-like active state comprised of finite-sized droplets. When in contact with a solid boundary, active interfaces exhibit non-equilibrium wetting transitions, wherein the fluid climbs the wall against gravity. These results demonstrate the promise of mechanically driven interfaces for creating a new class of soft active matter.

cond-mat.soft↗

arXiv2022

Boundaries control active channel flows

Boundary conditions dictate how fluids, including liquid crystals, flow when pumped through a channel. Can boundary conditions also be used to control internally driven active fluids that generate flows spontaneously? By using numerical simulations and stability analysis we explore how surface anchoring of active agents at the boundaries and substrate drag can be used to rectify coherent flow of an active polar fluid in a 2D channel. Upon increasing activity, a succession of dynamical states is obtained, from laminar flow to vortex arrays to eventual turbulence, that are controlled by the interplay between the hydrodynamic screening length and the extrapolation length quantifying the anchoring strength of the orientational order parameter. We highlight the key role of symmetry in both flow and order and show that coherent laminar flow with net throughput is only possible for weak anchoring and intermediate activity. Our work demonstrates the possibility of controlling the nature and properties of active flows in a channel simply by patterning the confining boundaries.

cond-mat.soft↗

arXiv2022

Anomalous elasticity of cellular tissue vertex model

Vertex Models, as used to describe cellular tissue, have an energy controlled by deviations of each cell area and perimeter from target values. The constrained nonlinear relation between area and perimeter leads to new mechanical response. Here we provide a mean-field treatment of a highly simplified model: a uniform network of regular polygons with no topological rearrangements. Since all polygons deform in the same way, we only need to analyze the ground states and the response to deformations of a single polygon (cell). The model exhibits the known transition between a fluid/compatible state, where the cell can accommodate both target area and perimeter, and a rigid/incompatible state. %The rigid solid-like state has a single gapped ground state. We calculate and measure the mechanical resistance to various deformation protocols and discover that at the onset of rigidity, where a single zero-energy ground-state exists, %We show that in the incompatible state, where a single frustrated ground-state exists, linear elasticity fails to describe the mechanical response to even infinitesimal deformations. In particular we identify a breakdown of reciprocity expressed via different moduli for compressive and tensile loads, implying non-analyticity of the energy functional. We give a pictorial representation in configuration space that reveals that the complex elastic response of the Vertex Model arises from the presence of two distinct sets of reference states (associated with target area and target perimeter).

cond-mat.soft↗

arXiv2022

Yield Stress and Compliance in Active Cell Monolayers

The rheology of biological tissue plays an important role in many processes, from organ formation to cancer invasion. Here, we use a multi-phase field model of motile cells to simulate active microrheology within a tissue monolayer. When unperturbed, the tissue exhibits a transition between a solid-like state and a fluid-like state tuned by cell motility and deformability - the ratio of the energetic costs of steric cell-cell repulsion and cell surface tension. When perturbed, solid tissues exhibit yield-stress behavior, with a threshold force for the onset of motion of a probe particle that vanishes upon approaching the solid-to-liquid transition. This onset of motion is qualitatively different in the low and high deformability regimes. At high deformability, the tissue is amorphous when solid, it responds compliantly to deformations, and the probe transition to motion is smooth. At low deformability, the monolayer is more ordered translationally and stiffer, and the onset of motion appears discontinuous. Our results suggest that cellular or nanoparticle transport in different types of tissues can be fundamentally different, and point to ways in which it can be controlled.

cond-mat.soft↗

arXiv2022

Flow around topological defects in active nematic films

We study the active flow around isolated defects and the self-propulsion velocity of $+1/2$ defects in an active nematic film with both viscous dissipation (with viscosity $η$) and frictional damping $Γ$ with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length $\ell_d=\sqrt{η/Γ}$ that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the vortical flows around the defect is controlled by the system size $R$. In the presence of friction that leads to a finite value of $\ell_d$, the vorticity field decays to zero on the lengthscales larger than $\ell_d$. We show that the self-propulsion velocity of $+1/2$ defects grows with $R$ in small systems where $R<\ell_d$, while in the infinite system limit or when $R\gg \ell_d$, it approaches a constant value determined by $\ell_d$.

cond-mat.soft↗

arXiv2021

Symmetry, Thermodynamics and Topology in Active Matter

This article summarizes some of the open questions in the field of active matter that have emerged during Active20, a nine-week program held at the Kavli Institute for Theoretical Physics (KITP) in Spring 2020. The article does not provide a review of the field, but rather a personal view of the authors, informed by contributions of all participants, on new directions in active matter research. The topics highlighted include: the ubiquitous occurrence of spontaneous flows and active turbulence and the theoretical and experimental challenges associated with controlling and harnessing such flows; the role of motile topological defects in ordered states of active matter and their possible biological relevance; the emergence of non-reciprocal effective interactions and the role of chirality in active systems and their intriguing connections to non-Hermitian quantum mechanics; the progress towards a formulation of the thermodynamics of active systems thanks to the feedback between theory and experiments; the impact of the active matter framework on our understanding of the emergent mechanics of biological tissue. These seemingly diverse phenomena all stem from the defining property of active matter - assemblies of self-driven entities that individually break time-reversal symmetry and collectively organize in a rich variety of nonequilibrium states.

cond-mat.soft↗

arXiv2021

Topological active matter

Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in active matter through experimentally relevant examples. Here, the focus lies on topological defects and topologically protected edge modes with an emphasis on the distinctive properties they acquire in active media. These paradigmatic examples represent two physically distinct classes of phenomena whose robustness can be traced to a common mathematical origin: the presence of topological invariants. These invariants are typically integer numbers that cannot be changed by continuous deformations of the relevant order parameters or physical parameters of the underlying medium. We first explain the mechanisms whereby topological defects self propel and proliferate in active nematics, leading to collective states which can be manipulated by geometry and patterning. Possible implications for active microfluidics and biological tissues are presented. We then illustrate how the propagation of waves in active fluids and solids is affected by the presence of topological invariants characterizing their dispersion relations. We discuss the relevance of these ideas for the design of robotic metamaterials and the properties of active granular and colloidal systems. Open theoretical and experimental challenges are presented as future research prospects.

cond-mat.soft↗

arXiv2021

Fluctuations can induce local nematic order and extensile stress in monolayers of motile cells

Recent experiments in various cell types have shown that two-dimensional tissues often display local nematic order, with evidence of extensile stresses manifest in the dynamics of topological defects. Using a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, we show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key element of the model is the assumption that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resulting in anisotropy of fluctuations. Our work shows that activity can drive either extensile or contractile stresses in tissue, depending on the relative strength of the contractility of the cortical cytoskeleton and tractions by cells on the extracellular matrix.

cond-mat.soft↗

arXiv2020

The role of fluid flow in the dynamics of active nematic defects

We adapt the Halperin-Mazenko formalism to analyze two-dimensional active nematics coupled to a generic fluid flow. The governing hydrodynamic equations lead to evolution laws for nematic topological defects and their corresponding density fields. We find that $\pm 1/2$ defects are propelled by the local fluid flow and by the nematic orientation coupled with the flow shear rate. In the overdamped and compressible limit, we recover the previously obtained active self-propulsion of the +1/2 defects. Non-local hydrodynamic effects are primarily significant for incompressible flows, for which it is not possible to eliminate the fluid velocity in favor of the local defect polarization alone. For the case of two defects with opposite charge, the non-local hydrodynamic interaction is mediated by non-reciprocal pressure-gradient forces. Finally, we derive continuum equations for a defect gas coupled to an arbitrary (compressible or incompressible) fluid flow.

cond-mat.soft↗

arXiv2020

Poisson-bracket formulation of the dynamics of fluids of deformable particles

Using the Poisson bracket method, we derive continuum equations for a fluid of deformable particles in two dimensions. Particle shape is quantified in terms of two continuum fields: an anisotropy density field that captures the deformations of individual particles from regular shapes and a shape tensor density field that quantifies both particle elongation and nematic alignment of elongated shapes. We explicitly consider the example of a dense biological tissue as described by the Vertex model energy, where cell shape has been proposed as a structural order parameter for a liquid-solid transition. The hydrodynamic model of biological tissue proposed here captures the coupling of cell shape to flow, and provides a starting point for modeling the rheology of dense tissue.

cond-mat.soft↗