The European Physical Journal E

Epithelial monolayers are the foundation of many mammalian organs and have a significant impact on numerous biological processes, including the secretion of cytokines, absorption of waste products and barrier function. During organ development epithelia are subject to many external forces due to the growth of the surrounding tissues. They exhibit complex responses to such forces, with deformation occurring on short timescales (seconds), and relaxation and remodelling occurring on longer timescales (minutes or hours). Existing mathematical and computational models do not typically account for subcellular remodelling, assuming instead that the response to an applied force or strain acts on a single timescale. In this paper we extend an off-lattice, cell-centre modelling framework to account for subcellular and tissue remodelling by introducing a Dynamic Reference Frame (DRF). The DRF provides a discrete, cell-based analogue of morpho-elasticity: it decouples the evolution of each cell's mechanical reference configuration from its instantaneous deformation, providing a phenomenological description of subcellular remodelling processes - cytoskeletal reorganisation, myosin turnover and adhesion bond remodelling - at the cellular scale. Using this extended multicellular model, we reproduce multiscale responses to external mechanical forces, including creep and stress relaxation experiments, and demonstrate that the history of applied deformation influences tissue recovery upon release. Additionally we identify and quantify where and how these multiscale responses occur. The resulting framework allows for more detailed descriptions and analyses of the development and function of biological tissues.

Healing of the gastrointestinal (GI) tract following surgical interventions is governed by coupled mechanobiological processes and may lead to severe complications such as perforation or stricture formation. A first comprehensive mechanobiological modeling framework of GI healing is herein proposed. The framework addresses two clinically relevant applications of bioprinting: endoscopic treatment of GI tissue defects and bioprinting-assisted surgical anastomosis. Tissue remodeling is based upon a hyperelastic material model with fiber dispersion coupling the spatiotemporal reaction diffusion dynamics of fibroblasts and cytokines with collagen deposition, reorientation, and plastic deformation. An active stress formulation drives fibroblasts and myofibroblast contraction while a multiplicative decomposition approach is adopted for collagen remodeling as a permanent change. The governing equations are discretised in time with an implicit Euler scheme, finite element in space and solved by a staggered algorithm implemented in the open-source platform FEniCS. Numerical simulations show that the initial collagen fibers content and orientation strongly influence fibroblast infiltration and scar contracture formation. The study quantifies the advantage of having a collagen bioprinted architecture aligned with tissue fibers, to reduce structural remodeling distortion. The model also predicts a strong correlation between collagen deposition and luminal burst pressure during the recovery of mechanical integrity in GI anastomosis.

High-speed atomic force microscopy (HS-AFM) experiments provide unique insights into nanoscale biological processes by directly visualizing the surface topography dynamics of biomolecules, such as proteins, over extended periods of time and generating large imaging data sets. However, the lack of computational methods for automated data analysis has thus far limited the full utilization of these data for the quantitative understanding of single-molecule dynamic. Here, we present the AFM Analysis Arena (A3) within BioAFMviewer as a software platform for automated, high-throughput quantitative analysis of AFM topographic imaging data within a user-friendly interactive graphical interface, implementing a convenient workflow from raw HS-AFM (AFM) imaging to statistical analysis. In several applications to HS-AFM imaging data, we demonstrate methods of automatized molecule detection and dynamic tracking to highlight the available capacities, aiming to transform HS-AFM measurements from observations towards an analytical tool in nanoscale biology.

Tumor spheroid mechanics arise from both the mechanical properties of individual cells and the adhesive interactions that organize them into tissues. The relative contribution of these two factors to the bulk mechanical behavior, however, remains difficult to disentangle experimentally. Here, we develop a computational model of micropipette aspiration to compare the mechanical response of isolated cells and multicellular spheroids within a common computational framework. By independently varying single-cell stiffness and cell-cell adhesion, we quantify their effects on aspiration dynamics, effective elastic modulus, and viscoelastic relaxation. Our results show that increasing single-cell stiffness substantially alters the mechanics of isolated cells but has limited influence on the effective elastic modulus of multicellular spheroids. In contrast, changes in cell-cell adhesion produce pronounced effects on spheroid effective elastic modulus. Nevertheless, both parameters increase the retardation time governing the transition from the initial elastic response to long-time viscous deformation. These findings suggest that multicellular elasticity is governed primarily by intercellular mechanical coupling, whereas the dynamical response to applied stress depends jointly on cell-scale mechanics and cell-cell adhesion.

Wound repair is an important mechanism to preserve tissue integrity in organisms after injury. However, why different tissues exhibit different mechanisms to repair wounds is a long-standing question that remains unanswered. In this work, we theoretically explore the role of the purse string, an actomyosin contractile cable used by tissues to close small wounds. Does the tissue 3D geometry influence the efficiency of the purse string in driving wound closure? Using a 3D biophysical model, we study in silico tissues with the same cell volumes but different aspect ratios, ranging from squamous to thick and tall tissues. The model predicts that taller cells are easily deformed by the purse string. In contrast, very squamous cells require a very strong purse string that might demand additional cellular mechanisms to close the gap. These findings establish a theoretical framework to predict the optimal biophysical mechanisms of wound healing in different tissues. Graphical abstractCells of different aspect ratios can be observed in a range of organisms with different function and mechanics. The wound healing efficiency of the purse string increases with the cell aspect ratio in our theoretical exploration. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=135 SRC="FIGDIR/small/743165v1_ufig1.gif" ALT="Figure 1"> View larger version (23K): org.highwire.dtl.DTLVardef@d44ab0org.highwire.dtl.DTLVardef@1737cbaorg.highwire.dtl.DTLVardef@101b5d4org.highwire.dtl.DTLVardef@1487f26_HPS_FORMAT_FIGEXP M_FIG C_FIG

Non-genetic adaptation enables cancer cells to alter their phenotype under stress without requiring new mutations. However, the mechanisms by which electrical, mechanical, and hypoxic cues combine to shape this process in 3D tissues remain poorly understood. This work presents an agent-based tumor model that integrates vascular oxygen supply, a globally imposed electric field, mechanically mediated crowding and compression cues, phenotype transitions, cell growth, mitosis, death, and inheritance of adaptive memory across division. The simulated tumors exhibit a three-stage trajectory consisting of necrosis onset, transient collapse of live mass, and partial regrowth accompanied by progressive accumulation of adapted cells. Continuous electrical stimulation produces a dose-dependent reduction in live mass while markedly increasing the adapted fraction, with comparatively limited changes in final necrotic burden. This response is strongly conditioned by mechanics and reshapes (and is reshaped by) adaptive capacity. Pulsed stimulation further shows that, in the model, electric field amplitude and temporal schedule jointly determine memory phenomena, phenotypic diversification, and growth recovery. These results show that coupling local oxygen availability, mechanical constraints, electrical forcing, and history-dependent phenotype transitions can generate distinct tissue-level patterns of phenotypic heterogeneity. Both stimulus magnitude and temporal protocol influenced the resulting population structure, suggesting that the history of physical stress may be an important determinant of adaptive dynamics in spatially organized tumor models.

Electrostatic actuation is an emerging technology for generating tactile sensations on capacitive touchscreens through voltage-induced attractive forces between a fingertip and the surface. However, accurate control of electrostatic attraction during natural touchscreen interactions remains challenging because the applied normal force and sliding speed continuously vary, and their effects on the fingertip-screen contact and resulting actuation strength are not fully characterized. Here, we show how normal force and sliding speed systematically alter fingertip- screen contact area and electrical impedance, and use these measured changes to estimate electrostatic attraction during sliding. Contact area, interaction forces, and electrical impedance were measured simultaneously as participants slid their fingertips across an electrostatic surface under systematically varied normal forces and sliding speeds. These measurements revealed condition-dependent changes in fingertip contact, electrical interaction impedance, effective capacitance, derived effective gap thickness, and electrostatic attraction. We then incorporated these measured contact quantities into a physics-informed, data-driven model based on parallel-plate capacitor theory, in which effective capacitance, apparent contact area, and effective voltage determine the estimated electrostatic attraction. The resulting model links force- and speed-dependent changes in these quantities to electrostatic attraction while accounting for inter-participant variability through a participant-specific scaling factor. These findings provide experimentally grounded guidance for designing electrostatic surface-haptic feedback and future adaptive control strategies under realistic touch conditions.

Cardiomyocyte contraction is essential for the pumping action of the heart and deteriorates after myocardial damage, either as a consequence of irreversible cardiomyocyte injury or stiffening of the extracellular matrix, a process described as fibrosis. Cell geometry and substrate stiffness not only influence sarcomere architecture and contractility, they also determine how much work the cardiomyocytes can transfer to their environment. Human induced pluripotent stem cell (hiPSC)-derived cardiomyocytes provide a model system to examine these effects in a controlled manner, enabling us to mimic key features of the cardiac environment in vitro. Here we show that geometric confinement and substrate stiffness influence different aspects of cardiomyocyte force generation. By combining traction force microscopy and live-cell imaging of hiPSC-derived cardiomyocytes on soft and patterned substrates, we find that geometric confinement leads to longer resting sarcomeres and more pronounced sarcomere shortening on substrates with both physiological (10 kPa) and fibrotic (30 kPa) stiffness. Interestingly, the substrate stiffness itself has little effect on resting sarcomere length, but influences the peak contractile stress. On 10 kPa substrates, confined cells generate higher peak contractile stresses than unconfined cells, whereas this difference is not observed at 30 kPa. Confinement also results in faster mechanical relaxation at 10 kPa, with no detectable difference at 30 kPa. The combination of defined cell geometry and physiological stiffness leads to longer resting sarcomere lengths, more pronounced sarcomere shortening, higher peak contractile stress, and faster relaxation, features associated with a more mature cardiomyocyte phenotype. These findings show that the mechanical consequences of cell geometry depend on substrate stiffness and, therefore, both aspects have to be considered when employing hiPSC-derived cardiomyocytes as a model system in mechanobiology research, disease modeling and drug testing.

Cellulose has long been viewed as the major load-bearing component in plant primary cell walls. Recent studies, however, suggest that pectin plays a significant role in cell wall mechanics despite a kPa-scaled modulus. Here we quantify the mechanical properties of centimeter-sized internodal cell walls of Chara corallina following treatments to remove calcium crosslinks or digest pectin. We also characterize the flow of water and gas through the cell wall as a function of pressure. We found that removal of calcium crosslinks did not affect wall strength and stress-relaxation behavior, yet it decreased the elastic modulus and increased permeability to water. In contrast, pectin removal had a dramatic impact on all measurements. Samples from which pectin had been removed exhibited lower strength and stiffness and had greater stress relaxation under constant strain. Pectin removal increased the permeability of the cell wall to water above that observed when calcium was removed and reduced the pressure at which gas "tunnels" through the cell wall ~ 2-fold. Our findings support the idea that pectin locally restricts the movement of cellulose microfibrils, with implications for understanding functional properties of primary cell walls in vascular plants and developing high-performance double-network materials.

Fingertip friction plays a central role in tactile exploration and object manipulation. During sliding, tangential force depends jointly on the real contact area and the interfacial shear stress, both of which can be influenced by sliding conditions. However, changes in fingertip friction are often interpreted primarily through changes in real contact area, whereas the accompanying changes in interfacial shear stress remain less well characterized. This gap is especially relevant for electrostatic surface haptic displays, which modulate fingertip friction by applying a voltage between the finger and the touch surface. Here, we experimentally quantify the mean interfacial shear stress of a sliding fingertip on an electrostatically actuated touchscreen using simultaneous measurements of tangential force and optically resolved real contact area. Ten participants performed sliding trials across three speeds and three normal forces with and without electrostatic actuation. Interfacial shear stress increased with speed and decreased with normal force; in both cases, these trends arose because real contact area varied more strongly than tangential force. Electrostatic actuation further reduced interfacial shear stress, as increasing voltage produced a larger increase in real contact area than in tangential force. These findings show that interfacial shear stress varies systematically with sliding conditions and electrostatic actuation, clarifying how changes in real contact area and interfacial shear stress combine to shape fingertip-surface friction.

Biofilm mechanics depend strongly on growth history, hydration, nutrient availability, and interfacial attachment, yet conventional rheology requires harvesting and transfer that can perturb the as-grown structure. Here, we introduce bioRheoFlow, a 3D-printed rheometer-mounted platform for cultivation and mechanical characterization without sample transfer. The platform combines evaporation compensation with static or axial nutrient flow, and benchmark measurements validate its rheometric performance. Applied to Pseudomonas putida and Pantoea sp., bioRheoFlow reveals that biofilms cultivated in situ under axial flow exhibit substantially higher elastic moduli than conventionally grown and scraped samples. Despite similar linear-viscoelastic stress ranges, the species show distinct nonlinear responses: P. putida exhibits a lower crossover stress and more abrupt failure, whereas Pantoea sp. sustains larger stresses and deformations. Creep suggests contributions from bulk deformation and biofilm-substrate interactions. bioRheoFlow provides a controlled framework for probing growth-conditioned mechanics in living biofilms.

Rule-based languages have proven effective for modeling systems of interacting structured entities as typically encountered in chemistry and molecular biology. We present PyKappa, a rule-based modeling package written in Python whose interpreted nature enables interactive simulation and analysis, including by agentic AI. The package seeks to broaden the base of developers by utilizing a widely known programming language and serves as an easy-to-deploy teaching tool. Using PyKappa, we conduct a case study of phase separation.

In epithelial wounds, physically enlarged cells emerge along injury edges where they interact with regular-size cells during collective migration to repair tissue continuity. Although such large cells are often interpreted as migration leaders, recent observations suggest that regular-size cells can reciprocally influence them and that mixed-size cell clusters engage in distinct rotational motion before merging into confluent sheets. How cell size, polarity and adhesive coupling jointly control distinct collective migration modes remains unclear. Because many features of collective epithelial migration, including large and regular-size cell phenotypes, are conserved between in vivo and in vitro systems, here we developed a multi-scale computational model of interacting epithelial cells in two-dimensional culture with dynamic cell-substrate adhesion, cell-cell interactions, protrusion-based polarity, and contact-induced myosin redistribution as polarity regulator. We also explicitly modeled two functionally distinct cell states, featuring regular and large sizes respectively. Simulations showed that symmetric and asymmetric myosin redistribution at cell-cell junctions can produce stable cell contacts and persistent rotational motions by cell doublets. Intriguingly, in mixed-size cell clusters, straight translation can arise both from leader-like large cell and regular-size cell-mediated motion, whereas rotation emerges when large-cell-generated torque overcomes translation while cell-cell adhesion is maintained. Thus, collective migration mode depends on the balance among myosin-driven torque, regular-size cell-mediated translation, substrate coupling, and cell-cell adhesion. These modeling results suggest that collective epithelial migration can emerge in vitro from reciprocal biomechanical interactions between distinct cell states, rather than from leader-like cell behavior alone, and that such interactions can produce a predator-prey-like pursuit-escape mode of collective migration. Our model also provides a framework for investigating the biochemical and biomechanical regulation of collective cellular migration. It can be readily extended from in vitro to in vivo context and can incorporate the effects of substrate topology and soluble signaling factor-driven chemotaxis. Author summaryWhen epithelial cells repair a wound, they move as coordinated groups rather than as isolated individuals. Cells of different sizes may contribute in distinct but connected ways. We developed a computational model to examine how a large cell and neighboring regular-size cells move together. In the model, cells attach to the underlying surface and one another, form protrusions that set their direction, and redistribute the force-generating protein myosin after contact. We found that group motion depends on a balance among surface attachment, cell-cell adhesion, movement of regular-size cells toward the large cell, and myosin-driven turning of the large cell. Depending on this balance, a mixed-size cluster can travel along a nearly straight path or rotate persistently, exhibiting pursuit-and-escape-like interactions between the large cell and surrounding regular-size cells. Rotation occurs when the large cells turning effect outweighs the translational motion driven by regular-size cells, while cell-cell adhesion keeps the cluster together. Our results show that collective migration can emerge from reciprocal mechanical interactions between cells in different states, not only from a "leader" cell acting alone. The model also provides experimentally testable predictions for how cell size, adhesion, and internal myosin distribution shape cell cluster movement.

Epithelial tissues continuously remodel their curvature during morphogenesis, homeostasis, regeneration, and disease, yet experimental access to time-varying curvature remains limited. Here, we introduce CurvoChip, a pneumatically actuated microsystem that reversibly deforms confluent epithelial monolayers cultured on a 20-m elastic membrane into concave or convex geometries. The device operates either in a standard incubator or on a microscope stage and provides programmable control over pressure amplitude, direction, and cycling. Analytical scaling, finite-element simulations, and confocal profilometry establish predictable membrane deformation across the operating range, whereas cycling between -400 and +400 mbar for 120 cycles produces stable deflection without detectable drift or residual deformation. We further implement a three-dimensional surface-reconstruction and segmentation workflow to quantify cell and nuclear morphology on curved monolayers. Acute curvature induction produces a marked polarity-dependent response: convex deformation causes greater cell spreading and epithelial thinning than concave deformation, while nuclear projected area, thickness, and volume change in a direction- and position-dependent manner. These results show that epithelial architecture is sensitive not only to curvature magnitude but also to its orientation relative to the apico-basal axis. CurvoChip therefore provides an accessible platform for dissecting how epithelial tissues integrate dynamic geometric cues.

Skin growth and remodeling underlies health, disease, and treatments such as tissue expansion (TE). The mechanotransduction pathways in dermal fibroblasts are increasingly well characterized, and tissue-level growth has been described phenomenologically, but coupling between cell-level signaling and tissue-level growth remains poorly understood. We develop a dermal fibroblast signaling network through extensive literature data curation, comprising 151 reactions among 96 nodes. The inputs are mechanical stretch and eight ligands (TGF{beta}, PDGF, FGF, IL1, IL6, TNF, AngII, ET1); outputs of interest span ECM-enzymes (proMMP1/2/9, MMP1/2/9), ECM proteins (CImRNA, collagen I, fibronectin), and fibroblast activity (SMA, proliferation). Implemented as a logic-based ODE system, the network reproduces 82% of the calibration dataset and agrees with independent validation data. Sensitivity analysis reveals a tension-dependent regulation of signaling: at baseline tension, outputs are governed by many boosters (nodes that positively influence downstream targets) and one dominant brake, LATS1/2, whereas at high tension control consolidates and new, tension-specific regulators such as integrin (ITGB1) emerge. Multiple pathway axes converge on a few central regulators, producing pronounced crosstalk, most notably between TGF{beta} and mechanical tension. Finally, linking the collagen outputs to a tissue-level growth formulation yields a bidirectional mechanical-biochemical coupling that reproduces tension-induced skin growth measured in a porcine TE model. This framework establishes a comprehensively calibrated dermal fibroblast signaling network coupled to tissue-level growth, opening opportunities for targeted TE interventions.

Known for their rapid water surface locomotion, whirligig beetles (Gyrinidae) are also fast divers. They can transition from the surface to underwater swimming in under 100 ms. Diving requires them to generate sufficient hydrodynamic torque to break the water surface and reorient the body. However, the mechanism by which whirligigs create the necessary pitch-down torque is unknown. Here, we show that their diving is achieved by bending the abdomen. The inertial hydrodynamic pressure on the flexed abdomen generates the torque necessary for surface breaking and body rotation. The torque is maximized at an abdominal angle of 45{degrees}, whereas for effective diving, whirligigs display a preferential abdominal angle of around 28{degrees}, closely aligning with the angle that maximizes the torque-to-drag ratio. This abdominal angle is optimized by balancing torque generation with the drag penalty. Our findings inspire a mechanism for surface-to-underwater transition, offering design principles for multimodal robots capable of locomotion across the air-water interface.

One goal of Scientific Machine Learning (SciML) is to advance traditional scientific computing frameworks with modern machine learning tools. This includes extending established methods, such as the finite element method, with cardiac function applications due to their complexity and need for very rapid execution times for real time clinical use. In this work, we present an advanced form of the Neural Network Finite Element (NNFE) method specialized for cardiac simulations, termed CARDIAX-NNFE. The NNFE method learns the parameter-to-displacement field map by training over the residual of the hyperelastic material PDE, using the domain represented by finite elements. The implementation is developed in Python using JAX to leverage its automatic differentiation, highly parallel GPU, and JIT-compilation capabilities. To demonstrate CARDIAX-NNFE effectiveness, we trained full cardiac pressure-volume responses using a simplified heart model, spanning the entire cardiac physiological functional range. Results indicated the ability to simulate a family of pressure-volume solutions with average nodal positional error of 0.023 mm and maximal error of 0.054 mm, with a single complete PV loop evaluated in 0.002 seconds. The CARDIAX-NNFE software platform thus provides for a robust platform for cardiac functional simulations. Moreover, it provides the structure for residual-based SciML methods, which can apply to a variety of physics-based biomedical problems that require high execution speed for clinical applications.

While geometric constraints shape tissue development, quantifying the resulting growth dynamics remains a central challenge in tissue engineering. Conventional methods often struggle to capture multi-scale kinetics without complex labeling or difficult single-cell tracking. Here, we analyze geometrically controlled growth of microtissues derived from human dermal fibroblasts using time-resolved, label-free brightfield microscopy, combined with optical flow and semi-automated deep learning mitosis detection. By extracting multi-scale flow fields and integrating them with tissue segmentation, we quantify directional tissue dynamics, separating flow into parallel and normal components relative to the local tissue contour. Applying this framework, we contrast the quiescent tissue interior with the advancing growth front where localized dynamics and cell proliferation drive expansion. Our results demonstrate that, compared to the bulk, the growth front exhibits higher fluctuations parallel to the tissue contour, positive mean normal flow, and significantly increased mitotic activity. Furthermore, evaluating flow divergence around mitotic events reveals distinct spatial behaviors: with the onset of mitosis, a contraction and subsequent expansion occurs in the vicinity of the dividing cells. Beyond the immediate cellular neighborhood, the broader regional dynamics remain consistent before and after mitosis onset, with net tissue expansion in proximity to the growth front and contraction within the tissue interior. By extracting continuous kinetic data from easily accessible, label-free brightfield imaging, this approach serves as a non-invasive, complementary tool for evaluating in vitro tissue morphogenesis and growth dynamics. This analytical framework can be expanded to study locally resolved tissue morphogenesis and growth kinetics in other microsystems, ranging from embryos to organoids. Statement of SignificanceUnderstanding how localized cellular forces drive tissue growth is critical for mechanobiology. However, mapping these dynamics traditionally requires complex, invasive fluorescent labeling. We present an accessible, label-free computational framework combining optical flow and deep learning-based mitosis detection to quantify continuous tissue kinematics directly from standard brightfield microscopy. Applying this to 3D microtissues, we reveal a distinct spatial coupling between cell division, local mechanical fluctuations, and directed tissue expansion at the active growth front. This non-invasive approach bridges the gap between single-cell mechanics and macroscopic morphogenesis, offering a versatile tool to monitor complex in vitro model systems-like organoids and bioengineered tissues-without disrupting their native state.

Mechanical properties of biological tissues, driven by passive and active forces, play a vital role in several processes ranging from development to cancer metastasis. However, the dynamical responses of cells in tissues, subject to mechanical deformations such as shear and the associated rheological properties, are not well characterized. Here, we use three-dimensional agent-based models for normal and cancer tissues to investigate their responses to simple shear as a function of cell stiffness and stochastic active forces. In the normal epithelium, with uniform strength of active force, the yield stress as a function of shear rate follows the Herschel-Bulkley form over a range of cell volume fraction. Strikingly, the shear rate dependence and the elasticity-dependent changes in the yield stress fall on master curves upon suitable scaling. To model cancer-like behavior, a certain fraction (Np) of cells was chosen to have enhanced activity and decreased stiffness. As Np increases, the extent of collective cell movement decreases, transitioning from affine (collective) to non-affine (individualistic) movement, a finding that is in accord with imaging experiments. Simulations of a model of a stiff solid tumor, with radius Rs embedded in normal tissue, show that as Rs increases, the yield stress increases. Interestingly, the cells migrate collectively as Rs increases. A Gaussian Mixture Model (GMM) and a mean field theory quantitatively account for the simulation as well as experimental results on cancerous, non-cancerous, and a mixture of these two types. The combined theoretical and experimental study establishes that heterogeneity in stiffness and activity determines non-affine movements in normal and cancer tissues.

We investigate the mechanical principles underlying fruiting body morphogenesis in Dictyostelium discoideum. Quantitative shape analysis based on the Young--Laplace law, together with AFM indentation measurements, indicate surface tension as the dominant tissue-scale force acting on the culminating fruiting body. Based on this observation, we construct a hydrodynamic phase-field model with tunable surface and interfacial tensions, and analyze its behavior numerically. Our results show that, once a stalk begins to form, the elevation of the cell mass arises naturally through a dewetting process. Through quantitative comparisons with experimental measurements, we identify the mechanical conditions required for detachment from the substrate and for establishment of the characteristic morphology of the culminating fruiting body. Together, our model analysis highlights the importance of stalk-tip elongation and tissue-scale surface and interfacial tensions in the construction of large-scale three-dimensional tissues.