Odd dynamics of living chiral crystals.

Active crystals are highly ordered structures that emerge from the self-organization of motile objects, and have been widely studied in synthetic1,2 and bacterial3,4 active matter. Whether persistent  crystalline order can emerge  in groups of autonomously developing multicellular organisms is currently unknown. Here we show that swimming starfish embryos spontaneously assemble into chiral crystals that span thousands of spinning organisms and persist for tens of hours. Combining experiments, theory and simulations, we demonstrate that the formation, dynamics and dissolution of these living crystals are controlled by the hydrodynamic properties and the natural development of embryos. Remarkably, living chiral crystals exhibit self-sustained chiral oscillations as well as various unconventional deformation response behaviours recently predicted for odd elastic materials5,6. Our results provide direct experimental evidence for how non-reciprocal interactions between autonomous multicellular components may facilitate non-equilibrium phases of chiral active matter.

Learning hydrodynamic equations for active matter from particle simulations and experiments.

Recent advances in high-resolution imaging techniques and particle-based simulation methods have enabled the precise microscopic characterization of collective dynamics in various biological and engineered active matter systems. In parallel, data-driven algorithms for learning interpretable continuum models have shown promising potential for the recovery of underlying partial differential equations (PDEs) from continuum simulation data. By contrast, learning macroscopic hydrodynamic equations for active matter directly from experiments or particle simulations remains a major challenge, especially when continuum models are not known a priori or analytic coarse graining fails, as often is the case for nondilute and heterogeneous systems. Here, we present a framework that leverages spectral basis representations and sparse regression algorithms to discover PDE models from microscopic simulation and experimental data, while incorporating the relevant physical symmetries. We illustrate the practical potential through a range of applications, from a chiral active particle model mimicking nonidentical swimming cells to recent microroller experiments and schooling fish. In all these cases, our scheme learns hydrodynamic equations that reproduce the self-organized collective dynamics observed in the simulations and experiments. This inference framework makes it possible to measure a large number of hydrodynamic parameters in parallel and directly from video data.

Publisher Correction: Attachment of the blastoderm to the vitelline envelope affects gastrulation of insects.

In this Letter, the sentence starting: 'For instance, Tribolium and Drosophila inflated are direct targets of the mesoderm…' has been corrected online; see accompanying Amendment.

Attachment of the blastoderm to the vitelline envelope affects gastrulation of insects.

During gastrulation, physical forces reshape the simple embryonic tissue to form the complex body plans of multicellular organisms1. These forces often cause large-scale asymmetric movements of the embryonic tissue2,3. In many embryos, the gastrulating tissue is surrounded by a rigid protective shell4. Although it is well-recognized that gastrulation movements depend on forces that are generated by tissue-intrinsic contractility5,6, it is not known whether interactions between the tissue and the protective shell provide additional forces that affect gastrulation. Here we show that a particular part of the blastoderm tissue of the red flour beetle (Tribolium castaneum) tightly adheres in a temporally coordinated manner to the vitelline envelope that surrounds the embryo. This attachment generates an additional force that counteracts tissue-intrinsic contractile forces to create asymmetric tissue movements. This localized attachment depends on an αPS2 integrin (inflated), and the knockdown of this integrin leads to a gastrulation phenotype that is consistent with complete loss of attachment. Furthermore, analysis of another integrin (the αPS3 integrin, scab) in the fruit fly (Drosophila melanogaster) suggests that gastrulation in this organism also relies on adhesion between the blastoderm and the vitelline envelope. Our findings reveal a conserved mechanism through which the spatiotemporal pattern of tissue adhesion to the vitelline envelope provides controllable, counteracting forces that shape gastrulation movements in insects.

Rheology of Suspensions of Flat Elastic Particles.

We consider a suspension of noninteracting flat elastic particles in a Newtonian fluid. We model a flat shape as three beads, carried along by the flow according to Stokes law, and connected by nonlinear springs, chosen such that the energy is quadratic in the area. In analogy with common dumbbell models involving two beads connected by linear springs, we solve the stochastic equations of motion exactly to compute the constitutive law for the stress tensor of a flat elastic particle suspension. A lower convected time derivative naturally arises as part of the constitutive law, but surprisingly the rheological response in strong extensional and strong contracting flows is similar to that of the classical Oldroyd-B model associated with dumbbell suspensions.

Self-organized shape dynamics of active surfaces.

Mechanochemical processes in thin biological structures, such as the cellular cortex or epithelial sheets, play a key role during the morphogenesis of cells and tissues. In particular, they are responsible for the dynamical organization of active stresses that lead to flows and deformations of the material. Consequently, advective transport redistributes force-generating molecules and thereby contributes to a complex mechanochemical feedback loop. It has been shown in fixed geometries that this mechanism enables patterning, but the interplay of these processes with shape changes of the material remains to be explored. In this work, we study the fully self-organized shape dynamics using the theory of active fluids on deforming surfaces and develop a numerical approach to solve the corresponding force and torque balance equations. We describe the spontaneous generation of nontrivial surface shapes, shape oscillations, and directed surface flows that resemble peristaltic waves from self-organized, mechanochemical processes on the deforming surface. Our approach provides opportunities to explore the dynamics of self-organized active surfaces and can help to understand the role of shape as an integral element of the mechanochemical organization of morphogenetic processes.

Minimal Model of Cellular Symmetry Breaking.

The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry-breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the self-organization of the cell cortex that is based on a hydrodynamic theory of curved active surfaces. Active stresses on this surface are regulated by a diffusing molecular species. We show that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechanochemical instabilities. We discuss the role of external fields in guiding such pattern formation. Our work reveals that key features of cellular symmetry breaking and cell division can emerge in a minimal model via general dynamic instabilities.

Real-time deformability cytometry: on-the-fly cell mechanical phenotyping.

We introduce real-time deformability cytometry (RT-DC) for continuous cell mechanical characterization of large populations (>100,000 cells) with analysis rates greater than 100 cells/s. RT-DC is sensitive to cytoskeletal alterations and can distinguish cell-cycle phases, track stem cell differentiation into distinct lineages and identify cell populations in whole blood by their mechanical fingerprints. This technique adds a new marker-free dimension to flow cytometry with diverse applications in biology, biotechnology and medicine.

Extracting Cell Stiffness from Real-Time Deformability Cytometry: Theory and Experiment.

Cell stiffness is a sensitive indicator of physiological and pathological changes in cells, with many potential applications in biology and medicine. A new method, real-time deformability cytometry, probes cell stiffness at high throughput by exposing cells to a shear flow in a microfluidic channel, allowing for mechanical phenotyping based on single-cell deformability. However, observed deformations of cells in the channel not only are determined by cell stiffness, but also depend on cell size relative to channel size. Here, we disentangle mutual contributions of cell size and cell stiffness to cell deformation by a theoretical analysis in terms of hydrodynamics and linear elasticity theory. Performing real-time deformability cytometry experiments on both model spheres of known elasticity and biological cells, we demonstrate that our analytical model not only predicts deformed shapes inside the channel but also allows for quantification of cell mechanical parameters. Thereby, fast and quantitative mechanical sampling of large cell populations becomes feasible.

Polarized branched Actin modulates cortical mechanics to produce unequal-size daughters during asymmetric division.

The control of cell shape during cytokinesis requires a precise regulation of mechanical properties of the cell cortex. Only few studies have addressed the mechanisms underlying the robust production of unequal-sized daughters during asymmetric cell division. Here we report that unequal daughter-cell sizes resulting from asymmetric sensory organ precursor divisions in Drosophila are controlled by the relative amount of cortical branched Actin between the two cell poles. We demonstrate this by mistargeting the machinery for branched Actin dynamics using nanobodies and optogenetics. We can thereby engineer the cell shape with temporal precision and thus the daughter-cell size at different stages of cytokinesis. Most strikingly, inverting cortical Actin asymmetry causes an inversion of daughter-cell sizes. Our findings uncover the physical mechanism by which the sensory organ precursor mother cell controls relative daughter-cell size: polarized cortical Actin modulates the cortical bending rigidity to set the cell surface curvature, stabilize the division and ultimately lead to unequal daughter-cell size.

Scaling behaviour and control of nuclear wrinkling.

The cell nucleus is enveloped by a complex membrane, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. Here, we characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly when nurse cell nuclei increase in size and display stereotypical wrinkling behavior. A spectral analysis of three-dimensional high-resolution live imaging data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption, providing tuneable physical and biological control parameters for probing mechanical properties of the nuclear envelope. Our findings advance the biophysical understanding of nuclear membrane fluctuations during early multicellular development.

Direct visualization of the subthalamic nucleus and its iron distribution using high-resolution susceptibility mapping.

Histological studies have shown a relatively high iron concentration in the subthalamic nucleus (STN). T2- and T2*-weighted sequences have previously been used to visualize the STN in vivo. The phase information of gradient-echo images reflects the magnetic tissue properties more directly, e.g., iron is more paramagnetic than water. Unfortunately, phase images suffer from non-local effects and orientation dependency. The goal of this study is to delineate the STN more precisely using susceptibility maps, calculated from phase images, which directly index magnetic tissue properties while removing the non-local effects and orientation dependency. Use of 7T MRI enables high spatial resolution with good signal to noise ratio (SNR). Eight healthy subjects were scanned at 7T using a high-resolution 3D gradient-echo sequence. Susceptibility maps were calculated from phase data using a thresholding Fourier approach and a regularization approach using spatial priors. The susceptibility maps clearly distinguish the STN from the adjacent substantia nigra (SN). Their susceptibilities are quantitatively different (0.06 and 0.1 ppm for the STN and SN, respectively). These maps allowed the STN, SN, and the red nucleus to be manually segmented, thus providing 3D visualization of their boundaries. In sum, the STN can be more clearly distinguished from adjacent structures in susceptibility maps than in T2*-weighted images or phase images.

Learning developmental mode dynamics from single-cell trajectories.

Embryogenesis is a multiscale process during which developmental symmetry breaking transitions give rise to complex multicellular organisms. Recent advances in high-resolution live-cell microscopy provide unprecedented insights into the collective cell dynamics at various stages of embryonic development. This rapid experimental progress poses the theoretical challenge of translating high-dimensional imaging data into predictive low-dimensional models that capture the essential ordering principles governing developmental cell migration in complex geometries. Here, we combine mode decomposition ideas that have proved successful in condensed matter physics and turbulence theory with recent advances in sparse dynamical systems inference to realize a computational framework for learning quantitative continuum models from single-cell imaging data. Considering pan-embryo cell migration during early gastrulation in zebrafish as a widely studied example, we show how cell trajectory data on a curved surface can be coarse-grained and compressed with suitable harmonic basis functions. The resulting low-dimensional representation of the collective cell dynamics enables a compact characterization of developmental symmetry breaking and the direct inference of an interpretable hydrodynamic model, which reveals similarities between pan-embryo cell migration and active Brownian particle dynamics on curved surfaces. Due to its generic conceptual foundation, we expect that mode-based model learning can help advance the quantitative biophysical understanding of a wide range of developmental structure formation processes.

Cell lineage-dependent chiral actomyosin flows drive cellular rearrangements in early Caenorhabditis elegans development.

Proper positioning of cells is essential for many aspects of development. Daughter cell positions can be specified via orienting the cell division axis during cytokinesis. Rotatory actomyosin flows during division have been implied in specifying and reorienting the cell division axis, but how general such reorientation events are, and how they are controlled, remains unclear. We followed the first nine divisions of Caenorhabditis elegans embryo development and demonstrate that chiral counter-rotating flows arise systematically in early AB lineage, but not in early P/EMS lineage cell divisions. Combining our experiments with thin film active chiral fluid theory we identify a mechanism by which chiral counter-rotating actomyosin flows arise in the AB lineage only, and show that they drive lineage-specific spindle skew and cell reorientation events. In conclusion, our work sheds light on the physical processes that underlie chiral morphogenesis in early development.

High-throughput cell mechanical phenotyping for label-free titration assays of cytoskeletal modifications.

The mechanical fingerprint of cells is inherently linked to the structure of the cytoskeleton and can serve as a label-free marker for cell homeostasis or pathologic states. How cytoskeletal composition affects the physical response of cells to external loads has been intensively studied with a spectrum of techniques, yet quantitative and statistically powerful investigations in the form of titration assays are hampered by the low throughput of most available methods. In this study, we employ real-time deformability cytometry (RT-DC), a novel microfluidic tool to examine the effects of biochemically modified F-actin and microtubule stability and nuclear chromatin structure on cell deformation in a human leukemia cell line (HL60). The high throughput of our method facilitates extensive titration assays that allow for significance assessment of the observed effects and extraction of half-maximal concentrations for most of the applied reagents. We quantitatively show that integrity of the F-actin cortex and microtubule network dominate cell deformation on millisecond timescales probed with RT-DC. Drug-induced alterations in the nuclear chromatin structure were not found to consistently affect cell deformation. The sensitivity of the high-throughput cell mechanical measurements to the cytoskeletal modifications we present in this study opens up new possibilities for label-free dose-response assays of cytoskeletal modifications.