Lumen formation during tubulogenesis requires the large-scale redistribution of cellular material, but the in vivo mechanisms remain unclear. Using the ascidian notochord as a tractable model, we show that actomyosin contractility orchestrates sequential, spatially distinct modes of cortical and cytoplasmic transport to promote lumen initiation and growth: lateral actomyosin centralizes apical determinants on cell contacts to position apical lumens; cyclic detachment and inward contraction of actomyosin bundles from a basal equatorial contractile ring drives internalization and transport of basal membranes toward the apical lumen surface to enable lumen growth. Basal membrane internalization/transport and lumen growth require both Ezrin/Radixin/Moesin (ERM) proteins and extracellular matrix (ECM). ERM promotes equatorial contractility and transmits inward contractile forces to basal membranes, while broad attachment to ECM resists inward forces to promote equatorial detachment. These findings reveal how cells integrate cortical and cytoplasmic modes of transport, driven by actomyosin contractility, to enable rapid lumen formation and likely other types of cellular remodeling.

Abstract A key question in cell biology is how cell-scale organization emerges from a given set of molecular players and rules of interaction. Given its multiscale nature, addressing this question requires a combination of experimental perturbation, mathematical modeling, and parameter inference. We leverage recent advances in each of these fields, focusing in particular on neural-network methods for simulation-based inference, to study how cell-scale patterns of Rho GTPase activity are defined by molecular-scale activator-inhibitor interactions with filamentous actin. Using an existing model of this interaction, we demonstrate that an over-expressive, regularized classification neural network can approximate the likelihood of data arising from a particular parameter set. We show that variations in F-actin assembly dynamics can be inferred directly from experimental data, but only if the network is made less sensitive to model misspecification. We use our approach to interpret perturbation experiments in which increasing RhoGAP coexpression increases the frequency and coherence of Rho activity waves in frog eggs. After showing that the known functions of RhoGAP are insufficient to explain experimentally-observed dynamics, we use neural methods to suggest an alternative pathway by which RhoGAP could decrease filament nucleation rates to sustain waves. Our work yields specific, experimentally-testable predictions and illustrates how a combination of traditional forward models and modern inference tools can aid in unraveling mechanisms of self-organization.

Studies of PAR polarity have emphasized a paradigm in which mutually antagonistic PAR proteins form complementary polar domains in response to transient cues. A growing body of work suggests that the oligomeric scaffold PAR-3 can form unipolar asymmetries without mutual antagonism, but how it does so is largely unknown. Here, we combine single-molecule analyses and modeling to show how the interplay of two positive feedback loops promotes dynamically stable unipolar PAR-3 asymmetries in early C. elegans embryos. First, the intrinsic dynamics of PAR-3 membrane binding and oligomerization encode negative feedback on PAR-3 dissociation. Second, membrane-bound PAR-3 promotes its own recruitment through a mechanism that requires the anterior polarity proteins PAR-6 and PKC-3. Using a kinetic model tightly constrained by our experimental measurements, we show that these two feedback loops are individually required and jointly sufficient to encode dynamically stable and locally inducible unipolar PAR-3 asymmetries in the absence of posterior inhibition. Given the central role of PAR-3, and the conservation of PAR-3 membrane-binding, oligomerization, and core interactions with PAR-6 and PKC-3, these results have widespread implications for PAR-mediated polarity in metazoa.

Biological systems can display diverse patterns of self-organization, even when built on conserved networks of interaction between molecular species. In these cases, reaction-diffusion equations provide a valuable tool to learn how new dynamics could emerge from quantitative tuning of parameters. Bringing these models into quantitative correspondence with biological data remains an outstanding challenge, especially when the data manifest heterogeneities that are difficult to account for mathematically. One particular example occurs in cell biology, where the membrane-bound regulatory protein RhoA interacts with the filamentous actin cortex in an activator-inhibitor loop. Though this core biochemical circuit is conserved across multiple cell types in different organisms, it produces different patterns of RhoA activity in different contexts, from traveling waves in starfish to transient pulses in Caenorhabditis elegans. To understand how this variation emerges, we develop an activator-inhibitor model that accounts explicitly for actin assembly and heterogeneity. By fitting the model to summary statistics of experimental data, subject to known parameter constraints, we show that F-actin assembly dynamics tune the spatiotemporal patterns of RhoA activity. A minimal representation of these dynamics reveals how directional transport (via polymerization) combines with stochasticity in F-actin number and orientation to produce the observed patterns. This work sheds light on how phenotypic diversity arises from heterogeneity and anisotropy, with important implications for the next generation of activator-inhibitor models.

Studies of PAR polarity have emphasized a paradigm in which mutually antagonistic PAR proteins form complementary polar domains in response to transient cues. A growing body of work suggests that the oligomeric scaffold PAR-3 can form unipolar asymmetries without mutual antagonism, but how it does so is largely unknown. Here we combine single molecule analysis and modeling to show how the interplay of two positive feedback loops promotes dynamically stable unipolar PAR-3 asymmetries in early C. elegans embryos. First, the intrinsic dynamics of PAR-3 membrane binding and oligomerization encode negative feedback on PAR-3 dissociation. Second, membrane-bound PAR-3 promotes its own recruitment through a mechanism that requires the anterior polarity proteins PAR-6 and PKC-3. Using a kinetic model tightly constrained by our experimental measurements, we show that these two feedback loops are individually required and jointly sufficient to encode dynamically stable and locally inducible unipolar PAR-3 asymmetries in the absence of posterior inhibition. Given the central role of PAR-3, and the conservation of PAR-3 membrane-binding, oligomerization, and core interactions with PAR-6/PKC-3, these results have widespread implications for PAR-mediated polarity in metazoa.

Carrier-assisted diffusion and cytoneme transport have been postulated to disperse Hedgehog across diverse embryonic tissues, yet their relative contributions to patterning mesenchymal tissues remains poorly understood. Here, we combine novel signaling assays with quantitative microscopy to establish exosome secretion as a predominant and adaptable mechanism for Sonic Hedgehog (Shh) dispersal. Introducing a novel synchronous release system to visualize Shh trafficking in embryonic tissues, we demonstrate that Shh traffics through the exosome biogenesis pathway in the limb bud mesenchyme. Shh-bound exosomes diffuse through the extracellular space, and can also bind and travel along cytonemes, providing a potential mechanism for directed and/or long-range transport. Using a synthetic patterning assay, we show that exosome secretion is essential to establish short-range Shh gradients in vitro. We propose that exosome-based Shh secretion, combined with different modes of extracellular transport, provides a tunable mechanism to sculpt Shh gradients on different length and time scales, across different embryonic tissues. ### Competing Interest Statement The authors have declared no competing interest.

Cell polarization, migration, and cytokinesis rely on flows of the cell cortex, a network of actin filaments, cross-linkers, and motors beneath the plasma membrane of animal cells. While actin network architecture, assembly dynamics, and motor activity are known to be important for cortical flows, how their modulation tunes macroscopic flow dynamics remains poorly quantified in vivo. Here, we use quantitative microscopy to constrain agent-based simulations that account for filament assembly, crosslinking, and motor activity. We calibrate the model to reproduce steady-state flows in polarized C. elegans zygotes and then challenge it to predict the results of RNA interference (RNAi) experiments. Our model predicts, and experiments largely confirm, a biphasic dependence of flow speed on microscopic rates of actin filament assembly and crosslinking. This biphasic dependence reflects a competition between the tendencies of perturbations to disrupt both transmission of and resistance to cortical forces. Our results provide new insights into how variations in microscopic features shape the emergent dynamics of the cell cortex. By establishing a well-calibrated model of cortical flow in a highly tractable model cell, we also provide a foundation for future studies of microscopic origins and biological control of cortical contractility and flow in vivo. ### Competing Interest Statement The authors have declared no competing interest.

Cell polarization relies on long-range cortical flows, which are driven by active stresses and resisted by the cytoskeletal network. While the general mechanisms that contribute to cortical flows are known, a quantitative understanding of the factors that tune flow speeds has remained lacking. Here, we combine physical simulation, representation learning, and theory to elucidate the role of actin turnover in cortical flows. We show how turnover tunes the actin density and filament curvature and use representation learning to demonstrate that these quantities are sufficient to predict cortical flow speeds. We extend a recent theory for contractility to account for filament curvature in addition to the nonuniform distribution of crosslinkers along actin filaments due to turnover. We obtain formulas that can be used to fit data from simulations and microscopy experiments. Our work provides insights into the mechanisms of contractility that contribute to cortical flows and how they can be controlled quantitatively.

ABSTRACT The intricate three-dimensional (3D) structures of multicellular organisms emerge through genetically encoded spatio-temporal patterns of mechanical stress. Cell atlases of gene expression during embryogenesis are now available for many organisms, but connecting these to the mechanical drivers of embryonic shape requires physical models of multicellular tissues that identify the relevant mechanical and geometric constraints, and an ability to measure mechanical stresses at single-cell resolution over time. Here we report significant steps towards both these goals. We describe a new mathematical theory for the mechanics of 3D multicellular aggregates involving the quasi-static balance of cellular pressures, surface tensions, and line tensions. Our theory yields a quantitatively accurate low-dimensional description for the time-varying geometric dynamics of 3D multicellular aggregates and, through the solution of a mechanical inverse problem, an image-based strategy for constructing spatio-temporal maps of the mechanical stresses driving morphogenesis in 3D. Using synthetic image data, we confirm the accuracy and robustness of our geometric and mechanical approaches. We then apply these approaches to segmented light sheet data, representing cellular membranes with isotropic resolution, to construct a 3D mechanical atlas for ascidian gastrulation. The atlas captures a surprisingly accurate low-dimensional description of ascidian gastrulation, revealing the adiabatic nature of the underlying mechanical dynamics. Mapping the inferred forces onto the invariant embryonic lineage reveals a rich correspondence between dynamically evolving cell states, patterns of cell division, and local regulation of cellular pressure and contractile stress. Thus, our mechanical atlas reveals a new view of ascidian gastrulation in which lineage-specific control over a complex heterogenous pattern of cellular pressure and contractile stress, integrated globally, governs the emergent dynamics of ascidian gastrulation.

For a group of cells to migrate together, each cell must couple the polarity of its migratory machinery with that of the other cells in the cohort. Although collective cell migrations are common in animal development, little is known about how protrusions are coherently polarized among groups of migrating epithelial cells. We address this problem in the collective migration of the follicular epithelial cells in Drosophila melanogaster. In this epithelium, the cadherin Fat2 localizes to the trailing edge of each cell and promotes the formation of F-actin-rich protrusions at the leading edge of the cell behind. We show that Fat2 performs this function by acting in trans to concentrate the activity of the WASP family verprolin homolog regulatory complex (WAVE complex) at one long-lived region along each cell's leading edge. Without Fat2, the WAVE complex distribution expands around the cell perimeter and fluctuates over time, and protrusive activity is reduced and unpolarized. We further show that Fat2's influence is very local, with sub-micron-scale puncta of Fat2 enriching the WAVE complex in corresponding puncta just across the leading-trailing cell-cell interface. These findings demonstrate that a trans interaction between Fat2 and the WAVE complex creates stable regions of protrusive activity in each cell and aligns the cells' protrusions across the epithelium for directionally persistent collective migration.

Pulsatile RhoA dynamics underlie a wide range of cell and tissue behaviors. The circuits that produce these dynamics in different cells share common architectures based on fast positive and delayed negative feedback through F-actin, but they can produce very different spatiotemporal patterns of RhoA activity. However, the underlying causes of this variation remain poorly understood. Here we asked how this variation could arise through modulation of actin network dynamics downstream of active RhoA in early Caenorhabditis elegans embryos. We find that perturbing two RhoA effectors-formin and anillin-induce transitions from nonrecurrent focal pulses to either large noisy oscillatory pulses (formin depletion) or noisy oscillatory waves (anillin depletion). In both cases these transitions could be explained by changes in local F-actin levels and depletion dynamics, leading to changes in spatial and temporal patterns of RhoA inhibition. However, the underlying mechanisms for F-actin depletion are distinct, with different dependencies on myosin II activity. Thus, modulating actomyosin network dynamics could shape the spatiotemporal dynamics of RhoA activity for different physiological or morphogenetic functions.

Asymmetric distributions of peripheral membrane proteins define cell polarity across all kingdoms of life. Non-linear positive feedback on membrane binding is essential to amplify and stabilize these asymmetries, but how specific molec-ular sources of non-linearity shape polarization dynamics remains poorly understood. Here we show that the ability to oligomer-ize, which is common to many peripheral membrane proteins, can play a profound role in shaping polarization dynamics in simple feedback circuits. We show that size-dependent binding avidity and mobility of membrane-bound oligomers endow po-larity circuits with several key properties. Size-dependent membrane binding avidity confers a form of positive feedback on the accumulation of oligomer subunits. Although insufficient by itself, this sharply reduces the amount of additional feedback required for spontaneous emergence and stable maintenance of polarized states. Size-dependent oligomer mobility makes symmetry breaking and stable polarity more robust with respect to variation in subunit diffusivities and cell sizes, and slows the approach to a final stable spatial distribution, allowing cells to "remember"polarity boundaries imposed by transient external cues. Together, these findings reveal how oligomerization of peripheral membrane proteins can provide powerful and highly tunable sources of non-linear feedback in biochemical circuits that govern cell surface polarity. Given its prevalence and wide-spread involvement in cell polarity, we speculate that self-oligomerization may have provided an accessible path to evolving sim-ple polarity circuits.

The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate, and transmit mechanical forces. The cortex exhibits a wide range of dynamic behaviours, from generating pulsatory contractions and travelling waves to forming organised structures. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, the emergent dynamics of this mechanochemical system is poorly understood. Here we develop a reaction-diffusion model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active actomyosin gel, to investigate how the interplay between chemical signalling and mechanical forces regulate stresses and patterns in the cortex. We demonstrate that mechanochemical feedback in the cortex acts to destabilise homogeneous states and robustly generate pulsatile contractions. By tuning active stress in the system, we show that the cortex can generate propagating contraction pulses, form network structures, or exhibit topological turbulence.

The actin cytoskeleton is a soft, structural material that underlies biological processes such as cell division, motility, and cargo transport. The cross-linked actin filaments self-organize into a myriad of architectures, from disordered meshworks to ordered bundles, which are hypothesized to control the actomyosin force generation that regulates cell migration, shape, and adhesion. Here, we use fluorescence microscopy and simulations to investigate how actin bundle architectures with varying polarity, spacing, and rigidity impact myosin II dynamics and force generation. Microscopy reveals that mixed-polarity bundles formed by rigid cross-linkers support slow, bidirectional myosin II filament motion, punctuated by periods of stalled motion. Simulations reveal that these locations of stalled myosin motion correspond to sustained, high forces in regions of balanced actin filament polarity. By contrast, mixed-polarity bundles formed by compliant, large cross-linkers support fast, bidirectional motion with no traps. Simulations indicate that trap duration is directly related to force magnitude and that the observed increased velocity corresponds to lower forces resulting from both the increased bundle compliance and filament spacing. Our results indicate that the microstructures of actin assemblies regulate the dynamics and magnitude of myosin II forces, highlighting the importance of architecture and mechanics in regulating forces in biological materials.

The way in which interactions between mechanics and biochemistry lead to the emergence of complex cell and tissue organization is an old question that has recently attracted renewed interest from biologists, physicists, mathematicians and computer scientists. Rapid advances in optical physics, microscopy and computational image analysis have greatly enhanced our ability to observe and quantify spatiotemporal patterns of signalling, force generation, deformation, and flow in living cells and tissues. Powerful new tools for genetic, biophysical and optogenetic manipulation are allowing us to perturb the underlying machinery that generates these patterns in increasingly sophisticated ways. Rapid advances in theory and computing have made it possible to construct predictive models that describe how cell and tissue organization and dynamics emerge from the local coupling of biochemistry and mechanics. Together, these advances have opened up a wealth of new opportunities to explore how mechanochemical patterning shapes organismal development. In this roadmap, we present a series of forward-looking case studies on mechanochemical patterning in development, written by scientists working at the interface between the physical and biological sciences, and covering a wide range of spatial and temporal scales, organisms, and modes of development. Together, these contributions highlight the many ways in which the dynamic coupling of mechanics and biochemistry shapes biological dynamics: from mechanoenzymes that sense force to tune their activity and motor output, to collectives of cells in tissues that flow and redistribute biochemical signals during development.

During cytokinesis, animal cells rapidly remodel the equatorial cortex to build an aligned array of actin filaments called the contractile ring. Local reorientation of filaments by active equatorial compression is thought to underlie the emergence of filament alignment during ring assembly. Here, combining single molecule analysis and modeling in one-cell C. elegans embryos, we show that filaments turnover is far too fast for reorientation of individual filaments by equatorial compression to explain the observed alignment, even if favorably oriented filaments are selectively stabilized. By tracking single formin/CYK-1::GFP particles to monitor local filament assembly, we identify a mechanism that we call filament-guided filament assembly (FGFA), in which existing filaments serve as templates to orient the growth of new filaments. FGFA sharply increases the effective lifetime of filament orientation, providing structural memory that allows cells to build highly aligned filament arrays in response to equatorial compression, despite rapid turnover of individual filaments.

Germ granules, also known as P granules in Caenorhabditis elegans, are phase-separated cellular bodies that are frequently found at the perinuclear region of germ cell nuclei in various animals. However... P granules are phase-separated liquid droplets that play important roles in the maintenance of germ cell fate in Caenorhabditis elegans. Both the localization and formation of P granules are highly dynamic, but mechanisms that regulate such processes remain poorly understood. Here, we show evidence that the VASA-like germline RNA helicase GLH-1 couples distinct steps of its ATPase hydrolysis cycle to control the formation and disassembly of P granules. In addition, we found that the phenylalanine-glycine-glycine repeats in GLH-1 promote its localization at the perinucleus. Proteomic analyses of the GLH-1 complex with a GLH-1 mutation that interferes with P granule disassembly revealed transient interactions of GLH-1 with several Argonautes and RNA-binding proteins. Finally, we found that defects in recruiting the P granule component PRG-1 to perinuclear foci in the adult germline correlate with the fertility defects observed in various GLH-1 mutants. Together, our results highlight the versatile roles of an RNA helicase in controlling the formation of liquid droplets in space and time.

Global tissue tension anisotropy has been shown to trigger stereotypical cell division orientation by elongating mitotic cells along the main tension axis. Yet, how tissue tension elongates mitotic cells despite those cells undergoing mitotic rounding (MR) by globally upregulating cortical actomyosin tension remains unclear. We addressed this question by taking advantage of ascidian embryos, consisting of a small number of interphasic and mitotic blastomeres and displaying an invariant division pattern. We found that blastomeres undergo MR by locally relaxing cortical tension at their apex, thereby allowing extrinsic pulling forces from neighboring interphasic blastomeres to polarize their shape and thus division orientation. Consistently, interfering with extrinsic forces by reducing the contractility of interphasic blastomeres or disrupting the establishment of asynchronous mitotic domains leads to aberrant mitotic cell division orientations. Thus, apical relaxation during MR constitutes a key mechanism by which tissue tension anisotropy controls stereotypical cell division orientation.