Abstract Graph Neural Networks (GNNs) are promising tools for predicting tissue dynamics, but choosing the right architecture remains difficult because experimental datasets are limited, noisy, and system-specific. We introduce a controlled in silico benchmark for comparing GNN architectures on a vertex-model task: predicting relaxed cell–cell interface lengths after a cell neighbor exchange. Because simulated data provide known ground truth, we can vary tissue geometry, mechanics, perturbation complexity, dataset size, and input features independently. Provably Powerful Graph Networks (PPGN) and Principal Neighborhood Aggregation (PNA) were most sample-efficient when pre-event edge lengths were provided, whereas performance dropped sharply with topology alone. We also revealed a predict-or-copy strategy, whereby predictions far from the exchange copied pre-event lengths instead of predicting long-range changes. Prediction was harder in disordered tissues, suggesting hexagonality as a simple indicator of difficulty. These results provide a reproducible testbed for diagnosing feature dependence, copying behavior, and geometric consistency in tissue-remodeling prediction.

Graph Neural Networks (GNNs) are increasingly applied to model collective cell behaviors during development, yet choosing an appropriate architecture remains difficult. We present an in silico benchmark of 1,615 tissue graphs, each undergoing a single T1 transition (cell-neighbor exchange), and evaluate five architectures for predicting post-T1 cell–cell interface (edge) lengths. The Provably Powerful Graph Network (PPGN) outperformed all others, achieving high accuracy with only 41 training graphs. PPGN learned a bimodal prediction strategy: near the T1 event, where deformations are large and localized, it predicts edge-length changes accurately, but several hops away it reverts to copying pre-T1 lengths, safeguarding accuracy yet risking cumulative bias. Additionally, prediction error increased almost linearly with tissue disorder but decreased with larger datasets, identifying disorder as a practical proxy for reliability. Our benchmark provides a controlled platform for evaluating GNNs in tissue-dynamics during development and offers actionable guidelines for model and dataset design.

We find a reentrant columnar-to-squamous rigidity transition in three-dimensional (3D) epithelia, governed by volume and area elasticity. Our model maps to the classic 2D area- and perimeter-elasticity model but, unlike its 2D counterpart, shows compression-induced softening or stiffening, depending on the initial state. The phase diagram reveals floppy states with vanishing shear and in-plane bulk moduli, alongside a lateral-tension-driven discontinuous columnar-to-squamous transition. The critical behavior underlying the emergence of the reentrant transition belongs to the mean-field universality class.

During the life of animals, epithelial tissues undergo extensive deformations-first to form organs during embryogensis and later to preserve integrity and function in adulthood. To what extent these deformations resemble that of non-living elastic materials is not well understood. We derive an elasticity theory of epithelia, supported by a thin layer of extracellular material and the stroma, in which the mechanics of individual cells are dominated by differential interfacial tensions stemming from cell cortical tension and adhesion. Upon coarse-graining a discrete cell-level mechanics model, we obtain a harmonic deformation energy and derive the critical conditions for the elastic instability, where an initially flat tissue either buckles out of plane or forms wrinkles. Due to the distinct origin of elasticity, the scaling of the critical buckling load and the wrinkling wavelength with layer's thickness is fundamentally different than in solid plates. The theory also naturally describes reversal of the groove-to-crest thickness-modulation phase-a recently observed epithelial shape feature which cannot be explained by the classical elasticity theory. Our work provides a guideline for understanding the relative role of cell surface tensions and the interaction of tissues with substrates during epithelial morphogenesis.

Animal tissue morphology is determined by the shape, position, and proliferative capacity of individual epithelial cells. Nevertheless, it remains incompletely understood how the dynamic shape transformations implicit in mitotic proliferation influence tissue packing, particularly at the level of basal cell contacts. Here, we use an in silico vertex model to show that epithelial mitotic rounding necessitates a sequence of dynamic basal contact rearrangements, including basal diminution of the mitotic cell volume, transient multicellular rosette assembly, basal reinsertion of daughter cells, and neighbor reorganization. We then leverage a mammalian intestinal organoid model to confirm nearly identical basal cell-contact dynamics as those predicted in silico. Pharmacological inhibition of mitotic progression reveals that two events-basal diminution of the cell body and daughter cell reinsertion-independently drive distinct contact rearrangements. Together, our results uncover a previously underappreciated topological role for basal mitotic cell dynamics in shaping epithelial packing and morphogenesis.

The mechanics of epithelial tissues, which is governed by forces generated in various cell regions, is often investigated using two-dimensional models that account for the apically positioned actomyosin structures but neglect basolateral mechanics. We employ a more detailed three-dimensional model to study how lateral surface tensions affect the structure and rigidity of such tissues. We find that cells are apicobasally asymmetric, with one side appearing more ordered than the other depending on target cell apical perimeter. In contrast to the 2D model, which predicts a rigidity transition at large target perimeters, tissues in the 3D model remain solidlike across all parameter space.

Epithelial furrowing is a fundamental morphogenetic process during gastrulation, neurulation, and body shaping. A furrow often results from a fold that propagates along a line. How fold formation and propagation are controlled and driven is poorly understood. To shed light on this, we study the formation of the cephalic furrow, a fold that runs along the embryo dorsal-ventral axis during Drosophila gastrulation and the developmental role of which is still unknown. We provide evidence of its function and show that epithelial furrowing is initiated by a group of cells. This cellular cluster works as a pacemaker, triggering a bidirectional morphogenetic wave powered by actomyosin contractions and sustained by de novo medial apex-to-apex cell adhesion. The pacemaker's Cartesian position is under the crossed control of the anterior-posterior and dorsal-ventral gene patterning systems. Thus, furrow formation is driven by a mechanical trigger wave that travels under the control of a multidimensional genetic guide.

One of the hallmarks of pre-migratory tumors is the progressive loss of compact morphology. To investigate how tumors may intrinsically regulate their shape during growth, we employ a three-dimensional (3D) vertex model of multicellular aggregates that incorporates key structural features of tumor spheroids, including its surface, a proliferative rim, and a necrotic core. Focusing exclusively on tumor-intrinsic mechanical interactions, we examine how their collective effects guide morphological evolution en route to metastasis. We show that spheroids acquire lobulated morphologies through an interplay between differential tensions at the spheroid surface and the living-necrotic interface (LNI), together with differential growth within the proliferative rim. In addition, spheroid shapes can be substantially modulated by tissue rheological properties emerging from active, cell-scale forces. Our cell- and tissue-scale simulations of tumor morphologies are enabled by a computational framework that overcomes a major limitation of 3D vertex models - the lack of cell-division - by introducing a graph-based polyhedral-division algorithm within the Graph Vertex Model (GVM).

The ability of biological systems to withstand and recover from various disruptions, such as spontaneous genetic mutations and environmental damage, largely relies on intricate feedback mechanisms. We theoretically study the mechanical response of an epithelial tissue facing damage in the form of a circular wound. Our model describes a feedback loop between the generation of active forces in the actomyosin and tissue mechanics, described by the vertex model. While the exact dynamics of wound closure may be influenced by several biophysical mechanisms that interplay in a nontrivial way, our findings suggest that the closure may initiate as an active instability, triggered by a reduced myosin turnover rate at the wound's perimeter. We explore the interplay between myosin dynamics and the elastic properties of the tissue, elucidating their collective role in determining a wound's loss of stability, leading to the initiation of the closure process.

Cell rearrangements are fundamental mechanisms driving large-scale deformations of living tissues. In three-dimensional (3D) space-filling cell aggregates, cells rearrange through local topological transitions of the network of cell-cell interfaces, which is most conveniently described by the vertex model. Since these transitions are not yet mathematically properly formulated, the 3D vertex model is generally difficult to implement. The few existing implementations rely on highly customized and complex software-engineering solutions, which cannot be transparently delineated and are thus mostly non-reproducible. To solve this outstanding problem, we propose a reformulation of the vertex model. Our approach, called Graph Vertex Model (GVM), is based on storing the topology of the cell network into a knowledge graph with a particular data structure that allows performing cell-rearrangement events by simple graph transformations. Importantly, when these same transformations are applied to a two-dimensional (2D) polygonal cell aggregate, they reduce to a well-known T1 transition, thereby generalizing cell-rearrangements in 2D and 3D space-filling packings. This result suggests that the GVM's graph data structure may be the most natural representation of cell aggregates and tissues. We also develop a Python package that implements GVM, relying on a graph-database-management framework Neo4j. We use this package to characterize an order-disorder transition in 3D cell aggregates, driven by active noise and we find aggregates undergoing efficient ordering close to the transition point. In all, our work showcases knowledge graphs as particularly suitable data models for structured storage, analysis, and manipulation of tissue data.

We investigate the elasticity of an unsupported epithelial monolayer and we discover that unlike a thin solid plate, which wrinkles if geometrically incompatible with the underlying substrate, the epithelium may do so even in the absence of the substrate. From a cell-based model, we derive an exact elasticity theory and discover wrinkling driven by the differential apico-basal surface tension. Our theory is mapped onto that for supported plates by introducing a phantom substrate whose stiffness is finite beyond a critical differential tension. This suggests a new mechanism for an autonomous control of tissues over the length scale of their surface patterns.

Active cell-junction remodeling is important for tissue morphogenesis, yet its underlying physics is not understood. We study a mechanical model that describes junctions as dynamic active force dipoles. Their instability can trigger cell intercalations by a critical collapse. Nonlinearities in tissue's elastic response can stabilize the collapse either by a limit cycle or condensation of junction lengths at cusps of the energy landscape. Furthermore, active junction networks undergo collective instability to drive active in-plane ordering or develop a limit cycle of collective oscillations, which extends over regions of the energy landscape corresponding to distinct network topologies.

Active cell-junction remodeling is important for tissue morphogenesis, yet its underlying physics is not understood. We study a mechanical model that describes junctions as dynamic active force dipoles. Their instability can trigger cell intercalations by a critical collapse. Nonlinearities in tissue's elastic response can stabilize the collapse either by a limit cycle or condensation of junction lengths at cusps of the energy landscape. Furthermore, active junction networks can undergo collective instability to drive active in-plane ordering or develop a limit cycle of collective oscillations, which extends over regions of the energy landscape corresponding to distinct network topologies.

Using a three-dimensional active vertex model, we numerically study the shapes of strained unsupported epithelial monolayers subject to active junctional noise due to stochastic binding and unbinding of myosin. We find that while uniaxial, biaxial, and isotropic in-plane compressive strains do lead to the formation of longitudinal, herringbone pattern, and labyrinthine folds, respectively, the villus morphology characteristic of, e.g., the small intestine appears only if junctional tension fluctuations are strong enough to fluidize the tissue. Moreover, the fluidized epithelium features villi even in the absence of compressive strain provided that the apico-basal differential surface tension is large enough. We analyze several details of the different epithelial forms including the role of strain rate and the modulation of tissue thickness across folds. Our results show that even unsupported, non-patterned epithelia can form nontrivial morphologies.

Adhesion-mediated cell sorting has long been considered an organizing principle in developmental biology. While most computational models have emphasized the dynamics of segregation to fully sorted structures, cell sorting can also generate a plethora of transient, incompletely sorted states. The timescale of such states in experimental systems is unclear: if they are long-lived, they can be harnessed by development or engineered in synthetic tissues. Here, we use experiments and computational modeling to demonstrate how such structures can be systematically designed by quantitative control of cell composition. By varying the number of highly adhesive and less adhesive cells in multicellular aggregates, we find the cell-type ratio and total cell count control pattern formation, with resulting structures maintained for several days. Our work takes a step toward mapping the design space of self-assembling structures in development and provides guidance to the emerging field of shape engineering with synthetic biology.

Macroscopic properties and shapes of biological tissues depend on the remodeling of cell-cell junctions at the microscopic scale. We propose a theoretical framework that couples a vertex model of solid confluent tissues with the dynamics describing generation of local force dipoles in the junctional actomyosin. Depending on the myosin turnover rate, junctions either preserve stable length or collapse to initiate cell rearrangements. We find that noise can amplify and sustain transient oscillations to the fixed point, giving rise to quasiperiodic junctional dynamics. We also discover that junctional stability is affected by cell arrangements and junctional rest tensions, which may explain junctional collapse during convergence and extension in embryos.

The study of organoids, artificially grown cell aggregates with the functionality and small-scale anatomy of real organs, is one of the most active areas of research in biology and biophysics, yet the basic physical origins of their different morphologies remain poorly understood. Here, we propose a mechanistic theory of epithelial shells which resemble small-organoid morphologies. Using a 3D surface tension-based vertex model, we reproduce the characteristic shapes from branched and budded to invaginated structures. We find that the formation of branched morphologies relies strongly on junctional activity, enabling temporary aggregations of topological defects in cell packing. To elucidate our numerical results, we develop an effective elasticity theory, which allows one to estimate the apico-basal polarity from the tissue-scale modulation of cell height. Our work provides a generic interpretation of the observed epithelial shell morphologies, highlighting the role of physical factors such as differential surface tension, cell rearrangements, and tissue growth.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Tissues transition between solid-like and fluid-like behavior, which has major implications for morphogenesis and disease. These transitions can occur due to changes in the intrinsic shape of constituent cells and cell motility. We consider an alternative mechanism by studying tissues that explore the energy landscape through stochastic dynamics, driven by turnover of junctional molecular motors. To identify the solid-fluid transition, we start with single-component tissues and show that the mean cell-shape index uniquely describes the effective diffusion coefficient of cell movements, which becomes finite at the transition. We generalize our approach to two-component tissues, and explore cell-sorting dynamics both due to differential adhesion and due to differential degree of junctional fluctuations. We recover some known characteristic scaling relations describing the sorting kinetics, and discover some discrepancies from these relations in the case of differential-fluctuations-driven sorting. Finally, we show that differential fluctuations efficiently sort two solid-like tissues with a fluid intercompartmental boundary.

Deneke et al. (2019) discover that dynamic interactions of cell cycle and actomyosin contractility systems synchronize nuclear cleavages, generating a cytoplasmic flow that results in a spatially uniform distribution of zygotic nuclei in the early Drosophila embryo. This work underscores the importance of self-organizing mechanisms before the onset of zygotic transcription.