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How does growth encode form in developing organisms? Many different spatiotemporal growth profiles may sculpt tissues into the same target 3D shapes, but only specific growth patterns are observed in animal and plant development. In particular, growth profiles may differ in their degree of spatial variation and growth anisotropy; however, the criteria that distinguish observed patterns of growth from other possible alternatives are not understood. Here we exploit the mathematical formalism of quasiconformal transformations to formulate the problem of “growth pattern selection” quantitatively in the context of 3D shape formation by growing 2D epithelial sheets. We propose that nature settles on growth patterns that are the “simplest” in a certain way. Specifically, we demonstrate that growth pattern selection can be formulated as an optimization problem and solved for the trajectories that minimize spatiotemporal variation in areal growth rates and deformation anisotropy. The result is a complete prediction for the growth of the surface, including not only a set of intermediate shapes, but also a prediction for cell displacement along those surfaces in the process of growth. Optimization of growth trajectories for both idealized surfaces and those observed in nature show that relative growth rates can be uniformized at the cost of introducing anisotropy. Minimizing the variation of programmed growth rates can therefore be viewed as a generic mechanism for growth pattern selection and may help us to understand the prevalence of anisotropy in developmental programs. Published by the American Physical Society2025 

Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops. However, our quantitative understanding of how cell-level dynamics translate into large-scale morphogenetic flows remains limited. A key challenge is finding the relevant macroscopic variables (order parameters) that retain the essential information about cell-scale structure. To address this challenge, we combine symmetry arguments with a stochastic mean-field model that accounts for the relevant microscopic dynamics. Complementary to previous work on the passive fluid- and solidlike properties of tissue, we focus on the role of actively generated internal stresses. Centrally, we use the timescale separation between elastic relaxation and morphogenetic dynamics to describe tissue shape change in the quasistatic balance of forces within the tissue sheet. The resulting geometric structure—a triangulation in tension space dual to the polygonal cell tiling—proves ideal for developing a mean-field model. All parameters of the coarse-grained model are calculated from the underlying microscopic dynamics. Centrally, the model explains how driven by autonomous active cell rearrangements becomes self-limiting as previously observed in experiments and simulations. Additionally, the model quantitatively predicts tissue behavior when coupled with external fields, such as planar cell polarity and external forces. We show how such fields can sustain oriented active cell rearrangements and thus overcome the self-limited character of purely autonomous active plastic flow. These findings demonstrate how local self-organization and top-down genetic instruction together determine internally driven tissue dynamics. Published by the American Physical Society2025 

Shape changes of epithelia during animal development, such as convergent extension, are achieved through the concerted mechanical activity of individual cells. While much is known about the corresponding large-scale tissue flow and its genetic drivers, fundamental questions regarding local control of contractile activity on the cellular scale and its embryo-scale coordination remain open. To address these questions, we develop a quantitative, model-based analysis framework to relate cell geometry to local tension in recently obtained time-lapse imaging data of gastrulatingDrosophilaembryos. This analysis systematically decomposes cell shape changes and T1 rearrangements into internally driven, active, and externally driven, passive, contributions. Our analysis provides evidence that germ band extension is driven by active T1 processes that self-organize through positive feedback acting on tensions. More generally, our findings suggest that epithelial convergent extension results from the controlled transformation of internal force balance geometry which combines the effects of bottom-up local self-organization with the top-down, embryo-scale regulation by gene expression. 

Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer under actively generated internal tension. To resolve this apparent paradox, we formulate a model in which tissue flow in the tension-dominated regime occurs through adiabatic remodeling of force balance in the network of adherens junctions. We propose that the slow dynamics within the manifold of force-balanced configurations is driven by positive feedback on myosin-generated cytoskeletal tension. Shifting force balance within a tension network causes active cell rearrangements (T1 transitions) resulting in net tissue deformation oriented by initial tension anisotropy. Strikingly, we find that the total extent of tissue deformation depends on the initial cellular packing order. T1s degrade this order so that tissue flow is self-limiting. We explain these findings by showing that coordination of T1s depends on coherence in local tension configurations, quantified by a geometric order parameter in tension space. Our model reproduces the salient tissue- and cell-scale features of germ band elongation duringDrosophilagastrulation, in particular the slowdown of tissue flow after approximately twofold elongation concomitant with a loss of order in tension configurations. This suggests local cell geometry contains morphogenetic information and yields experimentally testable predictions. Defining biologically controlled active tension dynamics on the manifold of force-balanced states may provide a general approach to the description of morphogenetic flow.