Research

The main research topic in our group Self-Organization of Multicellular Systems is the biophysics of cells and tissues (nomen est omen), but we have wider research interests in mathematical biology and soft matter physics.

Our main research focus is the mechanics of cells and tissues. In particular, we want to understand how the mechanical behaviour of tissues emerges from the mechanics at the cell scale, and how robust development is compatible with mechanical constraints and biological variability. We therefore derive novel continuum theories for biological tissues and apply them to experimental data of the rich mechanical behaviour of tissues during development. Although our research is theoretical, we work in close collaboration with experimental groups at the MPI-CBG and beyond.

The cell cortex and cell adhesion contribute to the mechanics of epithelial cells and hence tissues. Vertex models of epithelia represent the cell cortex and cell adhesion, but these models mostly ignore the other subcellular structures that compose the cytoplasm surrounded by the cortex. Here, we reveal the mechanical consequences of these structures in a minimal vertex model of an epithelial monolayer, in which the single-cell energy includes a cytoplasmic contribution that represents, e.g., the cost of confinement of cytosolic polymers. Strikingly, our simulations show that the buckling transition of the monolayer under compression becomes discontinuous in an intermediate range of values of the associated cytoplasmic modulus. By asymptotic solution of this buckling problem in the continuum limit of the model, we explain this reentrant behaviour in terms of the tricritical points of a sixth-order Landau theory. Our results thus underline how cell-scale mechanics beyond the cortex and cell adhesion can change emergent, tissue-scale behaviour even qualitatively. [Text and figure from Guha Ray & Haas, arXiv (2026)]

The nonconservative elastic responses of active solids have driven a recent explosion of interest in two-dimensional "odd" elasticity: small, linear deformations of these Cauchy elastic solids enable new behaviour absent from classical, passive elasticity. Here, we establish the description of large, nonlinear deformations of isotropic two-dimensional Cauchy elastic solids. We apply our framework to the Rivlin problem, perhaps the simplest problem of elasticity lacking a linear analogue: a square deforms under dead load tractions. Surprisingly, we find that oddness suppresses the bifurcations of a passive Rivlin square. By contrast, we discover that the bifurcations of a three-dimensional Rivlin cube survive oddness even though there is no isotropic, odd linear elasticity in three dimensions. Our results thus form the basis for describing large deformations of active, biological solids while revealing their unexpected nonlinear behaviour that arises even in minimal problems. [Text and figure from Zhao & Haas, arXiv (2026)]

The processes of morphogenesis that give rise to the shapes of organs and organisms during development are often driven by mechanical instabilities. Can such mechanical bifurcations also drive or constrain the evolution of these processes in the first place? We discover an instance of these constraints in the green algae of the family Volvocaceae. During their development, their bowl-shaped embryonic cell sheet turns itself inside out. This inversion is driven by a simple wave of cell wedging in the genus Pleodorina (16-128 cells) and more complex programmes of cell shape changes in Volvox (~400-50000 cells). However, no species with intermediate cell numbers (256 cells) have been described. Here, we relate this gap to a mechanical bifurcation: Focusing on the inversion of Pleodorina californica (64 cells), we develop a continuum model, in which the cell shape changes driving inversion appear as changes of the intrinsic curvature of an elastic surface. A mechanical bifurcation in this model predicts that inversion is only possible in a subset of its parameter space. Strikingly, parameters estimated for P. californica fall into this possible subset, but those that we extrapolate to 256 or more cells using allometric observations and a model of cell cleavage in Volvocaceae do not. Our work thus suggests that the more complex inversion strategies of Volvox are an evolutionary necessity to obviate this bifurcation and indicates more broadly how mechanical bifurcations can drive the evolution of morphogenesis. [Text and figure from Tribet & Haas, arXiv (2026)]

Across development, the morphology of fluid-filled lumina enclosed by epithelial tissues arises from an interplay of lumen pressure, mechanics of the cell cortex, and cell-cell adhesion. Here, we explore the mechanical basis for the control of this interplay using the shape space of MDCK cysts and the instability of their apical surfaces under tight junction perturbations. We discover that the cysts respond to these perturbations by significantly modulating their lateral and basal tensions, in addition to the known modulations of pressure and apical belt tension. We develop a mean-field three-dimensional vertex model of these cysts that reproduces the experimental shape instability quantitatively. This reveals that the observed increase of lateral contractility is a cellular response that counters the instability. Our work thus shows how regulation of the mechanics of all cell surfaces conspires to control lumen morphology. [Text and figure from Guha Ray, Mukenhirn, et al., PRX Life 4, 013037 (2026)]

Euler buckling epitomises mechanical instabilities: An inextensible straight elastic line buckles under compression when the compressive force reaches a critical value F*> 0. Here, we extend this classical, planar instability to the buckling under compression of an inextensible relaxed elastic line on a curved surface. By weakly nonlinear analysis of an asymptotically short elastic line, we reveal that the buckling bifurcation changes fundamentally: The critical force for the lowest buckling mode is F* = 0 and higher buckling modes disconnect from the undeformed branch to connect in pairs. Solving the buckling problem numerically, we additionally find a new post-buckling instability: A long elastic line on a curved surface snaps through under sufficient compression. Our results thus set the foundations for understanding the buckling instabilities on curved surfaces that pervade the emergence of shape in biology. [Text and figure from Zhao & Haas, Phys. Rev. Lett. 135, 247201 (2025)]

When cell sheets fold during development, their apical or basal surfaces constrict and cell shapes approach the geometric singularity in which these surfaces vanish. Here, we reveal the mechanical consequences of this geometric singularity for tissue folding in a minimal vertex model of an epithelial monolayer. In simulations of the buckling of the epithelium under compression and numerical solutions of the corresponding continuum model, we discover an "unbuckling" bifurcation: At large compression, the buckling amplitude can decrease with increasing compression. By asymptotic solution of the continuum equations, we reveal that this bifurcation comes with a large stiffening of the epithelium. Our results thus provide the mechanical basis for absorption of compressive stresses by tissue folds such as the cephalic furrow during germband extension in Drosophila. [Text and figure from Guha Ray & Haas, Phys. Rev. Lett. 134, 118402 (2024)]

Buckling instabilities driven by tissue growth underpin key developmental events such as the folding of the brain. Tissue growth is disordered due to cell-to-cell variability, but the effects of this variability on buckling are unknown. Here, we analyse what is perhaps the simplest setup of this problem: the buckling of an elastic rod with fixed ends driven by spatially varying growth. Combining analytical calculations for simple growth fields and numerical sampling of random growth fields, we show that variability can increase as well as decrease the growth threshold for buckling, even when growth variability does not cause any residual stresses. For random growth, we find that the shift of the buckling threshold correlates with spatial moments of the growth field. Our results imply that biological systems can either trigger or avoid buckling by exploiting the spatial arrangement of growth variability. [Text and figure from Ramachandran et al., Phys. Rev. E 110, 054405 (2024)]

Hepatocytes have a unique multiaxial polarity with several apical and basal surfaces. The prevailing model for the emergence of this multipolarity and the coordination of lumen formation between adjacent hepatocytes is based on asymmetric cell division. Here, investigating polarity generation in liver cell progenitors, the hepatoblasts, during liver development in vivo and in vitro, we found that this model cannot explain the observed dynamics of apical lumen formation in the embryonic liver. Instead, we identified a new mechanism of multi-axial polarization: We found that polarization can be initiated in a cell-autonomous manner by re-positioning apical recycling endosomes (AREs) to the cell cortex via fibronectin sensing through Integrin αV. Using live cell imaging we showed that this process repeats, leading to multiaxial polarity independently of cell division. We found that the establishment of oriented trafficking leads to the secretion of the metalloprotease MMP13, allowing neighboring hepatoblasts to synchronize their polarization by sensing extracellular matrix (ECM) distribution and enabling lumen opening. Finally, active remodeling of ECM in the proximity of nascent apical surfaces closes a positive feedback loop of polarization, whereas disruption of this loop by either blocking MMP13 or downregulating Integrin αV prevents the formation of the bile canaliculi network. Integration of this feedback loop into a simple mathematical model reproduces the observed dynamics of bile canaliculi network formation during liver development quantitatively. Our combined findings thus suggest a new mechanism of polarization coupling to self-organization at the tissue scale. [Text and figure from Delpierre et al., biorXiv (2024)]

The formation of complex tissues during embryonic development requires an intricate spatiotemporal coordination of local mechanical processes regulating global tissue morphogenesis. Here, we uncover a novel mechanism that mechanically regulates the shape of the anterior neural plate (ANP), a vital forebrain precursor, during zebrafish gastrulation. Combining in vivo and in silico approaches we reveal that the ANP is shaped by global tissue flows regulated by distinct force generating processes. We show that mesendoderm migration and E-cadherin-dependent differential tissue interactions control distinct flow regimes in the neuroectoderm. Initial opposing flows lead to progressive tissue folding and neuroectoderm internalisation which in turn provide forces driving ANP tissue reshaping. We find that convergent extension is dispensable for internalisation but required for ANP tissue extension. Our results highlight how spatiotemporal regulation and coupling of different mechanical processes between tissues in the embryo controls the first folding event in the developing brain. [Text and figure from Inman et al., Nat. Commun. 16, 6187 (2025)]

Deformations of cell sheets during morphogenesis are driven by developmental processes such as cell division and cell shape changes. In morphoelastic shell theories of development, these processes appear as variations of the intrinsic geometry of a thin elastic shell. However, morphogenesis often involves large bending deformations that are outside the formal range of validity of these shell theories. By asymptotic expansion of three-dimensional incompressible morphoelasticity in the limit of a thin shell, we have derived a shell theory for large intrinsic bending deformations and emphasize the resulting geometric material anisotropy and the elastic role of cell constriction. Taking the invagination of the green alga Volvox as a model developmental event, we have shown how results for this theory differ from those for a classical shell theory that is not formally valid for these large bending deformations and reveal how these geometric effects stabilize invagination. [Text and figure from Haas & Goldstein, Phys. Rev. E 103, 022411 (2021).]

The embryos of the green alga Volvox carteri are spherical sheets of cells that turn themselves inside out at the close of their development through a program of cell shape changes. This process of inversion is a model for morphogenetic cell sheet deformations; it starts with four lips opening up at the anterior pole of the cell sheet, flipping over, and peeling back to invert the embryo. Experimental studies have revealed that inversion is arrested if some of these cell shape changes are inhibited, but the mechanical basis for these observations has remained unclear. We have analyzed the mechanics of this inversion by deriving an averaged elastic theory for these lips and we have interpreted the experimental observations in terms of the mechanics and evolution of inversion. [Text and figure from Haas & Goldstein, Phys. Rev. E 98, 052415 (2018).]

Deformations of cell sheets are ubiquitous in early animal development, often arising from a complex and poorly understood interplay of cell shape changes, division, and migration. We have explored perhaps the simplest example of cell sheet folding: the “inversion” process of the algal genus Volvox, during which spherical embryos turn themselves inside out through a process hypothesized to arise from cell shape changes alone. We have used light sheet microscopy to obtain the first three-dimensional visualizations of inversion in vivo, and have developed the first theory of this process, in which cell shape changes appear as local variations of intrinsic curvature, contraction and stretching of an elastic shell. Our results support a scenario in which these active processes function in a defined spatiotemporal manner to enable inversion.

We study the Lotka–Volterra system from the perspective of computational algebraic geometry, focusing on equilibria that are both feasible and stable. These conditions stratify the parameter space with the feasible-stable semialgebraic sets. We encode them on the real Grassmannian via a parameter matrix representation, and use oriented matroid theory to develop an algorithm, combining Grassmann–Plücker relations with branching under feasibility and stability constraints. This symbolic approach determines whether a given sign pattern in the parameter space admits a consistent extension to Plücker coordinates. As an application, we establish that certain interaction networks are impossible ecologies in which stable and feasible coexistence is nontrivially impossible because the corresponding sign patterns admit no such extension satisfying the feasibility and stability conditions and we discover a combinatorial obstruction to stable and feasible coexistence in symmetric interaction networks. Finally, we show how to decompose the parameter space using numerical nonlinear algebra to detect rare feasible-stable sign patterns. [Text and figure from Özlüm Çelik, Haas, Scholten, Wang, Zucal, arXiv (2025).]

Clonal microbes can switch between different phenotypes and recent theoretical work has shown that stochastic switching between these subpopulations can stabilize microbial communities. This phenotypic switching need not be stochastic, however, but can also be in response to environmental factors, both biotic and abiotic. Motivated by the bacterial persistence phenotype, we have explored the ecological effects of such responsive switching by analyzing phenotypic switching in response to competing species. We have shown how the stability of microbial communities with responsive switching differs generically from that of communities with stochastic switching only. To understand this effect, we have gone on to analyse simple two-species models. Combining exact results and numerical simulations, we have extended the classical stability results for models of two competing species without phenotypic variation to the case where one of the two species switches, stochastically and responsively, between two phenotypes. In particular, we have shown that responsive switching can stabilize coexistence even when stochastic switching on its own does not affect the stability of the community.  [Text and figure from Haas et al., Phys. Rev. Research 4, 033224 (2022).]

In microbial communities, each species often has multiple, distinct phenotypes, but studies of ecological stability have largely ignored this subpopulation structure. We have shown that such implicit averaging over phenotypes leads to incorrect linear stability results. We have gone on to analyze the effect of phenotypic switching in detail in an asymptotic limit and have partly overturned classical stability paradigms: Abundant phenotypic variation is linearly destabilizing but, surprisingly, a rare phenotype such as bacterial persisters has a stabilizing effect. We have extended these results by showing how phenotypic variation modifies the stability of the system to large perturbations such as antibiotic treatments. [Text and figure from Haas et al., Phys. Rev. Research 2, 022036(R) (2020).]

In later work, combining experiment and theory, we have analyzed the initial stages of the evolution of these “shape-shifting” droplets, during which a polyhedral droplet flattens into a polygonal platelet under cooling and gravity. Using reflected-light microscopy, we have revealed how icosahedral droplets evolve through an intermediate octahedral stage to flatten into hexagonal platelets. This behavior is reproduced by a theoretical model of the phase transition mechanism, but the buckling mechanism can only reproduce the flattening if the deformations are driven by buoyancy. This requires surface tension to decrease by several orders of magnitude during cooling and yields bending modulus estimates orders of magnitude below experimental values.

Others have since shown that the observed phenomena are also consistent with an "augmented" elastic mechanism based on the intrinsic curvature of the droplet surface, but we have commented that this interplay between surface tension and intrinsic curvature is in fact mathematically equivalent to the physically very different phase-transition mechanism. The mathematical models cannot therefore distinguish between the two mechanisms, and we have argued that differences in experimental suggest that the observed phenomena are therefore physically very different realizations of a general "shape-shifting" mechanism based on the inter-play of positive surface tension and negative edge tension in faceted droplets. [Text and figures from Haas et al., Phys. Rev. Lett. 118, 088001 (2017), iid., Phys. Rev. Research 1, 023017 (2019), and iid., Phys. Rev. Lett. 126, 259801 (2021).]