During embryogenesis, the earliest cell fate decision is often linked to nuclear positioning, whose control arises from the integration of the cell cycle oscillator and associated cytoskeletal dynamics. Yet, the mechanisms that ensure that the correct number of nuclei move to the appropriate place remain poorly understood. Here, using light sheet microscopy, we show that in Drosophila embryos spindle orientation controls which nuclei migrate towards the cortex and which remains inside the embryo, thereby determining nuclear fate and the number of cells undergoing development. Combining computational methods inspired by integral geometry and manipulations of cell cycle genes, we show that spindle orientation is controlled by topological spindle-spindle interactions and not by internuclear distance. Using arguments describing the behavior of space-filling systems, we develop a theory for topological dependency in microtubule structures. Our work shows how topological interplay of microtubule mechanics can ensure robust control of density and cell fate determination.

Living organisms develop their shape through the interplay of gene expression and mechanics. While atlases of static samples characterize cell fates and gene regulation, understanding dynamic shape changes requires live imaging. Here we present DynamicAtlas: a 'morphodynamic atlas' of live and static datasets from 500 Drosophila melanogaster embryos (wild type and 18 mutants), aligned to a common morphological timeline. Surprisingly, characterizing wild-type surface tissue flows reveals distinct 'morphodynamic modules'-time periods in which the global pattern of motion is stationary-corresponding to key developmental stages. Mutant analysis shows stationary flow patterns depend on genes that break spatial symmetry along the dorsal-ventral axis. Temperature perturbations indicate that morphodynamic modules change in response to accumulated tissue deformation, rather than elapsed time. Extending our approach to the embryonic Drosophila midgut, we find modules in covariant measures of the dynamic three-dimensional surface. DynamicAtlas provides a high-resolution framework for studying shape formation across living systems.

During embryogenesis, the first cell fate decision - whether the cell participates in development of the embryo or not - is often linked to the positioning of the nucleus. The cell cycle oscillator and associated cytoskeletal dynamics contribute to the control of nuclear positioning. Yet, the mechanisms that ensure that the correct number of nuclei move to their appropriate place remain poorly understood. Here, we show that the orientation of the mitotic spindle controls the first fate decision in Drosophila embryos using light sheet microscopy experiments. Combining computational methods inspired by integral geometry, manipulation of cell cycle genes and investigation of the relationship between geometry and topology, we show that spindle orientation is controlled by topological interactions and not by internuclear distance. Leveraging physics of space-filling systems, we develop a theory for topological dependency in microtubule structures. Our work shows how topological interplay of microtubule mechanics can ensure robust control of nuclear density and determine cell fate.

Drosophila border cell clusters model collective cell migration. Airyscan super-resolution microscopy enables fine-scale description of cluster shape and texture. Here we describe how to convert Airyscan images of border cell clusters into 3D models of the surface and detect regions of convex and concave curvature. We use spectral decomposition analysis to compare surface textures across genotypes to determine how genes of interest impact cluster surface geometry. This protocol applies to border cells and could generalize to additional cell types.For complete details on the use and execution of this protocol, please refer to Gabbert et al.1

Morphogenesis is the process whereby the body of an organism develops its target shape. The morphogen BMP is known to play a conserved role across bilaterian organisms in determining the dorsoventral (DV) axis. Yet, how BMP governs the spatio-temporal dynamics of cytoskeletal proteins driving morphogenetic flow remains an open question. Here, we use machine learning to mine a morphodynamic atlas of Drosophila development, and construct a mathematical model capable of predicting the coupled dynamics of myosin, E-cadherin, and morphogenetic flow. Mutant analysis shows that BMP sets the initial condition of this dynamical system according to the following signaling cascade: BMP establishes DV pair-rule-gene patterns that set-up an E-cadherin gradient which in turn creates a myosin gradient in the opposite direction through mechanochemical feedbacks. Using neural tube organoids, we argue that BMP, and the signaling cascade it triggers, prime the conserved dynamics of neuroectoderm morphogenesis from fly to humans.

A common motif in biology is the arrangement of cells into tubes, which further transform into complex shapes. Traditionally, analysis of dynamic tissues has relied on inspecting static snapshots, live imaging of cross-sections or tracking isolated cells in three dimensions. However, capturing the interplay between in-plane and out-of-plane behaviors requires following the full surface as it deforms and integrating cell-scale motions into collective, tissue-scale deformations. Here, we present an analysis framework that builds in toto maps of tissue deformations by following tissue parcels in a static material frame of reference. Our approach then relates in-plane and out-of-plane behaviors and decomposes complex deformation maps into elementary contributions. The tube-like surface Lagrangian analysis resource (TubULAR) provides an open-source implementation accessible either as a standalone toolkit or as an extension of the ImSAnE package used in the developmental biology community. We demonstrate our approach by analyzing shape change in the embryonic Drosophila midgut and beating zebrafish heart. The method naturally generalizes to in vitro and synthetic systems and provides ready access to the mechanical mechanisms relating genetic patterning to organ shape change.

Septins self-assemble into polymers that bind and deform membranes in vitro and regulate diverse cell behaviors in vivo . How their in vitro properties relate to their in vivo functions is under active investigation. Here we uncover requirements for septins in detachment and motility of border cell clusters in the Drosophila ovary. Septins and myosin colocalize dynamically at the cluster periphery and share phenotypes, but surprisingly do not impact each other. Instead, Rho independently regulates myosin activity and septin localization. Active Rho recruits septins to membranes while inactive Rho sequesters septins in the cytoplasm. Mathematical analyses reveal how manipulating septin expression alters cluster shape and surface geometry. This study shows that the level of septin expression regulates surface properties at different scales. This work suggests that downstream of Rho, septins tune surface deformability while myosin controls contractility, the combination of which govern cluster shape and movement.

The actomyosin cytoskeleton is a crucial driver of morphogenesis. Yet how the behavior of large-scale cytoskeletal patterns in deforming tissues emerges from the interplay of geometry, genetics, and mechanics remains incompletely understood. Convergent extension in Drosophila melanogaster embryos provides the opportunity to establish a quantitative understanding of the dynamics of anisotropic non-muscle myosin II. Cell-scale analysis of protein localization in fixed embryos suggests that gene expression patterns govern myosin anisotropy via complex rules. However, technical limitations have impeded quantitative and dynamic studies of this process at the whole embryo level, leaving the role of geometry open. Here, we combine in toto live imaging with quantitative analysis of molecular dynamics to characterize the distribution of myosin anisotropy and the corresponding genetic patterning. We found pair rule gene expression continuously deformed, flowing with the tissue frame. In contrast, myosin anisotropy orientation remained approximately static and was only weakly deflected from the stationary dorsal-ventral axis of the embryo. We propose that myosin is recruited by a geometrically defined static source, potentially related to the embryo-scale epithelial tension, and account for transient deflections by cytoskeletal turnover and junction reorientation by flow. With only one parameter, this model quantitatively accounts for the time course of myosin anisotropy orientation in wild-type, twist, and even-skipped embryos, as well as embryos with perturbed egg geometry. Geometric patterning of the cytoskeleton suggests a simple physical strategy to ensure a robust flow and formation of shape.

Turbulence is hard to control. Many experimental methods have been developed to generate this elusive state of matter, leading to fundamental insights into its statistical and structural features as well as its onset. In all cases, however, the material boundaries of the experimental apparatus pose a challenge for understanding what the turbulence has been fed and how it would freely evolve. Here we build and control a confined state of turbulence using elemental building blocks—vortex rings. We create a stationary and isolated blob of turbulence in a quiescent environment, initiated and sustained solely by vortex rings. We assemble a full picture of its three-dimensional structure, onset, energy budget and tunability. The incoming vortex rings can be endowed with conserved quantities, such as helicity, which can then be controllably transferred to the turbulent state. Our one-eddy-at-a-time approach opens the possibility for sculpting turbulent flows much as a state of matter, placing the turbulent blob at the targeted position, localizing it and ultimately harnessing it. Turbulence is generated in a quiescent environment using vortex rings as building blocks.

This paper is associated with a video winner of a 2022 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2022.GFM.V0008

During morphogenesis, diverse cell-scale and tissue-scale processes couple to dynamically sculpt organs. In this coupling, genetic expression patterns and biochemical signals regulate and respond to mechanical deformations to ensure reproducible and robust changes in tissue geometry. A long-standing approach to characterize these interactions has been the construction of expression atlases, and these atlases have necessarily relied on fixed snapshots of embryogenesis. Addressing how expression profiles relate to tissue dynamics, however, requires a scheme for spatiotemporal registration across different classes of data that incorporates both live samples and fixed datasets. Here, we construct a morphodynamic atlas that unifies fixed and live datasets – from gene expression profiles to cytoskeletal components – into a single, morphological consensus timeline. This resource and our computational approach to global alignment facilitate hypothesis testing using quantitative comparison of data both within and across ensembles, with resolution in both space and time to relate genes to tissue rearrangement, cell behaviors, and out-of-plane motion. Examination of embryo kinematics reveals stages in which tissue flow patterns are quasi-stationary, arranged as a sequence of ‘morphodynamic modules’. Temperature perturbations tune the duration of one such module – during body axis elongation – according to a simple, parameter-free scaling in which the total integrated tissue deformation is achieved at a temperature-dependent rate. By extending our approach to visceral organ formation during later stages of embryogenesis, we highlight how morphodynamic atlases can incorporate complex shapes deforming in 3D. In this context, morphodynamic modules are reflected in some, but not all, measures of tissue motion. Our approach and the resulting atlas opens up the ability to quantitatively test hypotheses with resolution in both space and time, relating genes to tissue rearrangement, cell behaviors, and organ motion.

Organ architecture is often composed of multiple laminar tissues arranged in concentric layers. During morphogenesis, the initial geometry of visceral organs undergoes a sequence of folding, adopting a complex shape that is vital for function. Genetic signals are known to impact form, yet the dynamic and mechanical interplay of tissue layers giving rise to organs' complex shapes remains elusive. Here, we trace the dynamics and mechanical interactions of a developing visceral organ across tissue layers, from subcellular to organ scale in vivo. Combining deep tissue light-sheet microscopy for in toto live visualization with a novel computational framework for multi-layer analysis of evolving complex shapes, we find a dynamic mechanism for organ folding using the embryonic midgut of Drosophila as a model visceral organ. Hox genes, known regulators of organ shape, control the emergence of high-frequency calcium pulses. Spatiotemporally patterned calcium pulses trigger muscle contractions via myosin light chain kinase. Muscle contractions, in turn, induce cell shape change in the adjacent tissue layer. This cell shape change collectively drives a convergent extension pattern. Through tissue incompressibility and initial organ geometry, this in-plane shape change is linked to out-of-plane organ folding. Our analysis follows tissue dynamics during organ shape change in vivo, tracing organ-scale folding to a high-frequency molecular mechanism. These findings offer a mechanical route for gene expression to induce organ shape change: genetic patterning in one layer triggers a physical process in the adjacent layer - revealing post-translational mechanisms that govern shape change.

Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane bending elasticity. Their open edges and micrometer-length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. Here, we find that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped surfaces with complex edge structures. The saddle-shaped membranes are well approximated by Enneper’s minimal surfaces. Theoretical modeling demonstrates that their formation is driven by increasing the positive Gaussian modulus, which in turn, is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to diverse topologically distinct structures, including shapes similar to catenoids, trinoids, four-noids, and higher-order structures. At long timescales, we observe the formation of a system-spanning, sponge-like phase. The unique features of colloidal membranes reveal the topological transformations that accompany coalescence pathways in real time. We enhance the functionality of these membranes by making their shape responsive to external stimuli. Our results demonstrate a pathway toward control of thin elastic sheets’ shape and topology—a pathway driven by the emergent elasticity induced by compositional heterogeneity.

Mixtures of filaments and molecular motors form active materials with diverse dynamical behaviors that vary based on their constituents' molecular properties. To develop a multiscale of these materials, we map the nonequilibrium phase diagram of microtubules and tip-accumulating kinesin-4 molecular motors. We find that kinesin-4 can drive either global contractions or turbulentlike extensile dynamics, depending on the concentrations of both microtubules and a bundling agent. We also observe a range of spatially heterogeneous nonequilibrium phases, including finite-sized radial asters, 1D wormlike chains, extended 2D bilayers, and system-spanning 3D active foams. Finally, we describe intricate kinetic pathways that yield microphase separated structures and arise from the inherent frustration between the orientational order of filamentous microtubules and the positional order of tip-accumulating molecular motors. Our work reveals a range of novel active states. It also shows that the form of active stresses is not solely dictated by the properties of individual motors and filaments, but is also contingent on the constituent concentrations and spatial arrangement of motors on the filaments.

Lattices of interacting gyroscopes naturally support band gaps and topologically protected wave transport along material boundaries. Recently the authors and their collaborators found that amorphous arrangements of such coupled gyroscopes also support nontrivial topological phases. In contrast to periodic systems, for which there is a comprehensive understanding and predictive framework for band gaps and band topology, the theory of spectral gaps and topology for amorphous materials remains less developed. Here we use experiments, numerics, and analytic tools to address the relationship between local interactions and nontrivial topology. We begin with a derivation of the equations of motion within the framework of symplectic mechanics. We then present a general method for predicting whether a gap exists and for approximating the Chern number using only local features of a network, bypassing the costly diagonalization of the system's dynamical matrix. Finally we study how strong disorder interacts with band topology in gyroscopic metamaterials and find that amorphous gyroscopic Chern insulators exhibit similar critical behavior to periodic lattices. Our experiments and simulations additionally reveal a topological Anderson insulation transition, wherein disorder drives a trivial phase into a topological one.

How organs achieve their final shape is a problem at the interface between physics and developmental biology. Organs often involve multiple interacting tissue layers that must be coordinated to orchestrate the complex shape changes of development. Intense study uncovered genetic, and physical ingredients driving the form of mono layer tissue. Yet, tracing dynamics across tissue layers, and scales – from cell to tissue, to entire organs – remains an outstanding challenge. Here, we study the midgut of Drosophila embryos as a model visceral organ, to reconstruct in toto the dynamics of multi-layer organ formation in vivo . Using light-sheet microscopy, genetics, computer vision, and tissue cartography, we extract individual tissue layers to map the time course of shape across scales from cells to organ. We identify the kinematic mechanism driving the shape change due to tissue layer interactions by linking out-of-plane motion to active contraction patterns, revealing a convergent extension process in which cells deform as they flow into deepening folds. Acute perturbations of contractility in the muscle layer using non-neuronal optogenetics reveals that these contraction patterns are due to muscle activity, which induces cell shape changes in the adjacent endoderm layer. This induction cascade relies on high frequency calcium pulses in the muscle layer, under the control of hox genes. Inhibition of targets of calcium involved in myosin phosphorylation abolishes constrictions. Our study of multi-layer organogenesis reveals how genetic patterning in one layer triggers a dynamic molecular mechanism to control a physical process in the adjacent layer, to orchestrate whole-organ shape change.