Theoretical physics of biological development

How morphological diversity arises from variations in biomechanical processes remains an open question. Although forces shape tissues, how force-generating systems differ across species to create diverse forms is unclear. Here, we combine comparative morphogenesis and active matter theory across six cnidarian species spanning 500 million years of divergence to identify the mechanical basis of larval shape diversity. We define species-specific configurations of mechanical modules-termed mechanotypes-that quantitatively predict larval shapes across taxa. We find that shape elongation is a simple trait at the mesoscale level, as its variation depends on one mechanical module, whereas shape polarity is a complex trait dependent on several modules. Perturbations mimicking interspecies regulatory differences reshape these modules, reprogramming larval morphology into forms resembling sister species. By establishing a mesoscale mechanical framework for cross-species comparison, this work reveals how variations in a limited set of tissue-scale parameters generate morphological diversity.

The range over which a morphogen gradient provides reliable positional information is limited by intrinsic noise. We identify a regulatory circuit that counteracts this constraint for Dpp, a BMP that organizes the anterior/posterior axis of Drosophila wings. The transcriptional repressor Brinker (Brk), a Dpp target, enhances positional precision by repressing Dad, an inhibitory Smad, thereby extending Dpp's effective range. Thus, Brk mediates a feedback circuit that selectively amplifies low-level Dpp signals as would a logarithmic amplifier. This circuit also achieves temporal integration, mitigating the inevitable noise penalty associated with amplification. Although a core component of BMP signaling in flies, Brk is found exclusively in insects. Phylogenetic and expression analyses in the apterygote insect Thermobia domestica suggest that Brk originated in insects and was incorporated into the BMP network in pterygotes, possibly to permit long-range signaling in wing primordia. Brk exemplifies how gene regulatory network (GRN) evolution can enhance developmental precision, thus opening the door to increased morphological complexity.

How cell fate decisions and tissue remodeling are coordinated to establish precise and robust patterns is a fundamental question in developmental biology. Here, we investigate this interplay during the refinement of Drosophila wing veins. We show by live imaging that vein refinement is driven initially by local tissue deformation, followed by cell fate adjustments orchestrated by a signaling network involving Notch, EGFR, and Dpp. Dynamic tracking of signaling reporter activity uncovers a wave of Notch signaling that converts wide crude proveins into thin stereotypical veins. Perturbing large-scale convergence and extension does not affect vein refinement, and optogenetically induced veins refine irrespective of their orientation, demonstrating that the signaling network suffices for refinement, independently of large-scale tissue flows. A minimal biophysical description recapitulates the signaling network's ability to coordinate vein refinement in various experimental situations. Our results illustrate how cell fate decisions are updated for robust patterning in a remodeling tissue.

Blood vessels expand and contract actively as they continuously experience dynamic external stresses from blood flow. The mechanical response of the vessel wall is that of a composite material: its mechanical properties depend on its cellular components, which change dynamically as the cells respond to external stress. Mapping the relationship between these underlying cellular processes and emergent tissue mechanics is an ongoing challenge, particularly in endothelial cells. Here we assess the mechanics and cellular dynamics of an endothelial tube using a microstretcher that mimics the native environment of blood vessels. The characterization of the instantaneous monolayer elasticity reveals a strain-stiffening, actin-dependent and substrate-responsive behaviour. After a physiological pressure increase, the tissue displays a fluid-like expansion, with the reorientation of cell shape and actin fibres. We introduce a mechanical model that considers the actin fibres as a network in the nematic phase and couples their dynamics with active and elastic fibre tension. The model accurately describes the response to the pressure of endothelial tubes.

Blood vessels expand and contract actively as they continuously experience dynamic external stresses from blood flow. The mechanical response of the vessel wall is that of a composite material: its mechanical properties depend on its cellular components, which change dynamically as the cells respond to external stress. Mapping the relationship between these underlying cellular processes and emergent tissue mechanics is an ongoing challenge, particularly in endothelial cells. Here we assess the mechanics and cellular dynamics of an endothelial tube using a microstretcher that mimics the native environment of blood vessels. The characterization of the instantaneous monolayer elasticity reveals a strain-stiffening, actin-dependent and substrate-responsive behaviour. After a physiological pressure increase, the tissue displays a fluid-like expansion, with the reorientation of cell shape and actin fibres. We introduce a mechanical model that considers the actin fibres as a network in the nematic phase and couples their dynamics with active and elastic fibre tension. The model accurately describes the response to the pressure of endothelial tubes.

We present a generic framework for describing interacting, spinning, active polar particles, aimed at modeling dense cell aggregates, where cells are treated as polar, rotating objects that interact mechanically with one another and their surrounding environment. Using principles from nonequilibrium thermodynamics, we derive constitutive equations for interaction forces, torques, and polarity dynamics. We subsequently use this framework to analyze the spontaneous motion of cell doublets, uncovering a rich phase diagram of collective behaviors, including steady rotation driven by flow-polarity coupling or interactions between polarity and cell position.

Mechanical interactions between cells play a fundamental role in the self-organization of organisms. How these interactions drive coordinated cell movement in three dimensions remains unclear. Here we report that cell doublets embedded in a three-dimensional extracellular matrix undergo spontaneous rotations. We investigate the rotation mechanism and find that it is driven by a polarized distribution of myosin within cell cortices. The mismatched orientation of this polarized distribution breaks the doublet mirror symmetry. In addition, cells adhere at their interface through adherens junctions and with the extracellular matrix through focal contacts near myosin clusters. We use a physical theory describing the doublet as two interacting active surfaces to show that rotation is driven by myosin-generated gradients of active tension whose profiles are dictated by interacting cell polarity axes. We also show that three-dimensional shape symmetries are related to broken symmetries of the myosin distribution in cortices. To test for the rotation mechanism, we suppress myosin clusters using laser ablation and generate new myosin clusters by optogenetics. Our work clarifies how polarity-oriented active mechanical forces drive collective cell motion in three dimensions.

The steroid hormone 20-hydroxy-ecdysone (20E) promotes proliferation in Drosophila wing precursors at low titer but triggers proliferation arrest at high doses. Remarkably, wing precursors proliferate normally in the complete absence of the 20E receptor, suggesting that low-level 20E promotes proliferation by overriding the default anti-proliferative activity of the receptor. By contrast, 20E needs its receptor to arrest proliferation. Dose-response RNA sequencing (RNA-seq) analysis of ex vivo cultured wing precursors identifies genes that are quantitatively activated by 20E across the physiological range, likely comprising positive modulators of proliferation and other genes that are only activated at high doses. We suggest that some of these "high-threshold" genes dominantly suppress the activity of the pro-proliferation genes. We then show mathematically and with synthetic reporters that combinations of basic regulatory elements can recapitulate the behavior of both types of target genes. Thus, a relatively simple genetic circuit can account for the bimodal activity of this hormone.

Segmenting cells within cellular aggregates in 3D is a growing challenge in cell biology, due to improvements in capacity and accuracy of microscopy techniques. Here we describe a pipeline to segment images of cell aggregates in 3D. The pipeline combines neural network segmentations with active meshes. We apply our segmentation method to cultured mouse mammary duct organoids imaged over 24 hours with oblique plane microscopy, a high-throughput light-sheet fluorescence microscopy technique. We show that our method can also be applied to images of mouse embryonic stem cells imaged with a spinning disc microscope. We segment individual cells based on nuclei and cell membrane fluorescent markers, and track cells over time. We describe metrics to quantify the quality of the automated segmentation. Our segmentation pipeline involves a Fiji plugin which implement active meshes deformation and allows a user to create training data, automatically obtain segmentation meshes from original image data or neural network prediction, and manually curate segmentation data to identify and correct mistakes. Our active meshes-based approach facilitates segmentation postprocessing, correction, and integration with neural network prediction.

Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the interplay of local differential tensions with tissue geometry and with external forces results in tissue-scale morphogenesis remains an open question. Here, we describe epithelial sheets as active viscoelastic surfaces and study their deformation under patterned internal tensions and bending moments. In addition to isotropic effects, we take into account nematic alignment in the plane of the tissue, which gives rise to shape-dependent, anisotropic active tensions and bending moments. We present phase diagrams of the mechanical equilibrium shapes of pre-patterned closed shells and explore their dynamical deformations. Our results show that a combination of nematic alignment and gradients in internal tensions and bending moments is sufficient to reproduce basic building blocks of epithelial morphogenesis, including fold formation, budding, neck formation, flattening, and tubulation.

We introduce a modelling and simulation framework for cell aggregates in three dimensions based on interacting active surfaces. Cell mechanics is captured by a physical description of the acto-myosin cortex that includes cortical flows, viscous forces, active tensions, and bending moments. Cells interact with each other via short-range forces capturing the effect of adhesion molecules. We discretise the model equations using a finite element method, and provide a parallel implementation in C++. We discuss examples of application of this framework to small and medium-sized aggregates: we consider the shape and dynamics of a cell doublet, a planar cell sheet, and a growing cell aggregate. This framework opens the door to the systematic exploration of the cell to tissue-scale mechanics of cell aggregates, which plays a key role in the morphogenesis of embryos and organoids.

Collective motions of epithelial cells are essential for morphogenesis. Tissues elongate, contract, flow, and oscillate, thus sculpting embryos. These tissue level dynamics are known, but the physical mechanisms at the cellular level are unclear. Here, we demonstrate that a single epithelial monolayer of MDCK cells can exhibit two types of local tissue kinematics, pulsations and long range coherent flows, characterized by using quantitative live imaging. We report that these motions can be controlled with internal and external cues such as specific inhibitors and substrate friction modulation. We demonstrate the associated mechanisms with a unified vertex model. When cell velocity alignment and random diffusion of cell polarization are comparable, a pulsatile flow emerges whereas tissue undergoes long-range flows when velocity alignment dominates which is consistent with cytoskeletal dynamics measurements. We propose that environmental friction, acto-myosin distributions, and cell polarization kinetics are important in regulating dynamics of tissue morphogenesis.

We derive a fully covariant theory of the hydrodynamics of nematic and polar active surfaces, subjected to internal and external forces and torques. We study the symmetries of polar and nematic surfaces and find that in addition to five different types of in-plane isotropic surfaces, polar and nematic surfaces can be classified into five polar, two pseudopolar, five nematic and two pseudonematic types of surfaces. We give examples of physical realisations of the different types of surfaces we have identified. We obtain expressions for the equilibrium tensions, moments, and external forces and torques acting on a passive polar or nematic surface. We calculate the entropy production rate using the framework of thermodynamics close to equilibrium and find constitutive equations for polar and nematic active surfaces with different symmetries. We study the instabilities of a confined flat planar-chiral polar active layer and of a confined deformable polar active surface with broken up-down symmetry.

Proper orientation of the mitotic spindle plays a crucial role in embryos, during tissue development, and in adults, where it functions to dissipate mechanical stress to maintain tissue integrity and homeostasis. While mitotic spindles have been shown to reorient in response to external mechanical stresses, the subcellular cues that mediate spindle reorientation remain unclear. Here, we used a combination of optogenetics and computational modeling to investigate how mitotic spindles respond to inhomogeneous tension within the actomyosin cortex. Strikingly, we found that the optogenetic activation of RhoA only influences spindle orientation when it is induced at both poles of the cell. Under these conditions, the sudden local increase in cortical tension induced by RhoA activation reduces pulling forces exerted by cortical regulators on astral microtubules. This leads to a perturbation of the balance of torques exerted on the spindle, which causes it to rotate. Thus, spindle rotation in response to mechanical stress is an emergent phenomenon arising from the interaction between the spindle positioning machinery and the cell cortex.

Entropy production plays a fundamental role in the study of nonequilibrium systems by offering a quantitative handle on the degree of time-reversal symmetry breaking. It depends crucially on the degree of freedom considered as well as on the scale of description. How the entropy production at one resolution of the degrees of freedom is related to the entropy production at another resolution is a fundamental question which has recently attracted interest. This relationship is of particular relevance to coarse-grained and continuum descriptions of a given phenomenon. In this work, we derive the scaling of the entropy production under iterative coarse graining on the basis of the correlations of the underlying microscopic transition rates for noninteracting particles in active disordered media. Our approach unveils a natural criterion to distinguish equilibrium-like and genuinely nonequilibrium macroscopic phenomena based on the sign of the scaling exponent of the entropy production per mesostate.

As organs and tissues approach their normal size during development or regeneration, growth slows down, and cell proliferation progressively comes to a halt. Among the various processes suggested to contribute to growth termination, mechanical feedback, perhaps via adherens junctions, has been suggested to play a role. However, since adherens junctions are only present in a narrow plane of the subapical region, other structures are likely needed to sense mechanical stresses along the apical-basal (A-B) axis, especially in a thick pseudostratified epithelium. This could be achieved by nuclei, which have been implicated in mechanotransduction in tissue culture. In addition, mechanical constraints imposed by nuclear crowding and spatial confinement could affect interkinetic nuclear migration (IKNM), which allows G2 nuclei to reach the apical surface, where they normally undergo mitosis. To explore how mechanical constraints affect IKNM, we devised an individual-based model that treats nuclei as deformable objects constrained by the cell cortex and the presence of other nuclei. The model predicts changes in the proportion of cell-cycle phases during growth, which we validate with the cell-cycle phase reporter FUCCI (Fluorescent Ubiquitination-based Cell Cycle Indicator). However, this model does not preclude indefinite growth, leading us to postulate that nuclei must migrate basally to access a putative basal signal required for S phase entry. With this refinement, our updated model accounts for the observed progressive slowing down of growth and explains how pseudostratified epithelia reach a stereotypical thickness upon completion of growth.

During development, multicellular organisms undergo stereotypical patterns of tissue growth in space and time. How developmental growth is orchestrated remains unclear, largely due to the difficulty of observing and quantitating this process in a living organism. Drosophila histoblast nests are small clusters of progenitor epithelial cells that undergo extensive growth to give rise to the adult abdominal epidermis and are amenable to live imaging. Our quantitative analysis of histoblast proliferation and tissue mechanics reveals that tissue growth is driven by cell divisions initiated through basal extracellular matrix degradation by matrix metalloproteases secreted by the neighboring larval epidermal cells. Laser ablations and computational simulations show that tissue mechanical tension does not decrease as the histoblasts fill the abdominal epidermal surface. During tissue growth, the histoblasts display oscillatory cell division rates until growth termination occurs through the rapid emergence of G0/G1 arrested cells, rather than a gradual increase in cell-cycle time as observed in other systems such as the Drosophila wing and mouse postnatal epidermis. Different developing tissues can therefore achieve their final size using distinct growth termination strategies. Thus, adult abdominal epidermal development is characterized by changes in the tissue microenvironment and a rapid exit from the cell cycle.

The cell cortex is a highly dynamic network of cytoskeletal filaments in which motor proteins induce active cortical stresses which in turn drive dynamic cellular processes such as cell motility, furrow formation or cytokinesis during cell division. Here, we develop a three-dimensional computational model of a cell cortex in the viscous limit including active cortical flows. Combining active gel and thin shell theory, we base our computational tool directly on the force balance equations for the velocity field on a discretized and arbitrarily deforming cortex. Since our method is based on the general force balance equations, it can easily be extended to more complex biological dependencies in terms of the constitutive laws or a dynamic coupling to a suspending fluid. We validate our algorithm by investigating the formation of a cleavage furrow on a biological cell immersed in a passive outer fluid, where we successfully compare our results to axi-symmetric simulations. We then apply our fully three-dimensional algorithm to fold formation and to study furrow formation under the influence of non-axisymmetric disturbances such as external shear. We report a reorientation mechanism by which the cell autonomously realigns its axis perpendicular to the furrow plane thus contributing to the robustness of cell division under realistic environmental conditions.

Lumen formation plays an essential role in the morphogenesis of tissues during development. Here we review the physical principles that play a role in the growth and coarsening of lumens. Solute pumping by the cell, hydraulic flows driven by differences of osmotic and hydrostatic pressures, balance of forces between extracellular fluids and cell-generated cytoskeletal forces, and electro-osmotic effects have been implicated in determining the dynamics and steady-state of lumens. We use the framework of linear irreversible thermodynamics to discuss the relevant force, time and length scales involved in these processes. We focus on order of magnitude estimates of physical parameters controlling lumen formation and coarsening.