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Describing morphogenesis generally consists in aggregating the multiple high-resolution spatiotemporal processes involved into reproducible low-dimensional morphological processes consistent across individuals of the same species or group. In order to achieve this goal, biologists often have to submit movies issued from live imaging of developing embryos either to a qualitative analysis or to basic statistical analysis. These approaches, however, present noticeable drawbacks as they can be time consuming, hence unfit for scale, and often lack standardization and a firm foundation. In this work, we leverage the power of a continuum mechanics approach and flexibility of spectral decompositions to propose a standardized framework for automatic detection and timing of morphological processes. First, we quantify whole-embryo scale shape changes in developing ascidian embryos by statistically estimating the strain rate tensor field of its time-evolving surface without the requirement of cellular segmentation and tracking. We then apply to this data spectral decomposition in space using spherical harmonics and in time using wavelets transforms. These transformations result in the identification of the principal dynamical modes of ascidian embryogenesis and the automatic unveiling of its blueprint in the form of scalograms that tell the story of development in ascidian embryos. 

Describing morphogenesis generally consists in aggregating the multiple high resolution spatiotemporal processes involved into reproducible low dimensional morphological processes consistent across individuals of the same species or group. In order to achieve this goal, biologists often have to submit movies issued from live imaging of developing embryos either to a qualitative analysis or to basic statistical analysis. These approaches, however, present noticeable drawbacks, as they can be time consuming, hence unfit for scale, and often lack standardisation and a firm foundation. In this work, we leverage the power of a continuum mechanics approach and flexibility of spectral decompositions to propose a standardised framework for automatic detection and timing of morphological processes. First, we quantify whole-embryo scale shape changes in developing ascidian embryos by statistically estimating the strain-rate tensor field of its time-evolving surface without the requirement of cellular segmentation and tracking. We then apply to this data spectral decomposition in space using spherical harmonics and in time using wavelets transforms. These transformations result in the identification of the principal dynamical modes of ascidian embryogenesis and the automatic unveiling of its blueprint in the form of spectograms that tell the story of development in ascidian embryos. 

Abstract The metabolic activity of soil microbiomes plays a central role in carbon and nitrogen cycling. Given the changing climate, it is important to understand how the metabolism of natural communities responds to environmental change. However, the ecological, spatial, and chemical complexity of soils makes understanding the mechanisms governing the response of these communities to perturbations challenging. Here, we overcome this complexity by using dynamic measurements of metabolism in microcosms and modeling to reveal regimes where a few key mechanisms govern the response of soils to environmental change. We sample soils along a natural pH gradient, construct >1500 microcosms to perturb the pH, and quantify the dynamics of respiratory nitrate utilization, a key process in the nitrogen cycle. Despite the complexity of the soil microbiome, a minimal mathematical model with two variables, the quantity of active biomass in the community and the availability of a growth-limiting nutrient, quantifies observed nitrate utilization dynamics across soils and pH perturbations. Across environmental perturbations, changes in these two variables give rise to three functional regimes each with qualitatively distinct dynamics of nitrate utilization over time: a regime where acidic perturbations induce cell death that limits metabolic activity, a nutrientlimiting regime where nitrate uptake is performed by dominant taxa that utilize nutrients released from the soil matrix, and a resurgent growth regime in basic conditions, where excess nutrients enable growth of initially rare taxa. The underlying mechanism of each regime is predicted by our interpretable model and tested via amendment experiments, nutrient measurements, and sequencing. Further, our data suggest that the long-term history of environmental variation in the wild influences the transitions between functional regimes. Therefore, quantitative measurements and a mathematical model reveal the existence of qualitative regimes that capture the mechanisms and dynamics of a community responding to environmental change. 

ABSTRACT Inspired by Waddington's illustration of an epigenetic landscape, cell-fate transitions have been envisioned as bifurcating dynamical systems, wherein exogenous signaling dynamics couple to the enormously complex signaling and transcriptional machinery of a cell to elicit qualitative transitions in its collective state. Single-cell RNA sequencing (scRNA-seq), which measures the distributions of possible transcriptional states in large populations of differentiating cells, provides an alternate view, in which development is marked by the variations of a myriad of genes. Here, we present a mathematical formalism for rigorously evaluating, from a dynamical systems perspective, whether scRNA-seq trajectories display statistical signatures consistent with bifurcations and, as a case study, pinpoint regions of multistability along the neutrophil branch of hematopoeitic differentiation. Additionally, we leverage the geometric features of linear instability to identify the low-dimensional phase plane in gene expression space within which the multistability unfolds, highlighting novel genetic players that are crucial for neutrophil differentiation. Broadly, we show that a dynamical systems treatment of scRNA-seq data provides mechanistic insights into the high-dimensional processes of cellular differentiation, taking a step toward systematic construction of mathematical models for transcriptomic dynamics. 

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 towardsboththese 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. 

Pattern formation of biological structures involves the arrangement of different types of cells in an ordered spatial configuration. In this study, we investigate the mechanism of patterning the Drosophila eye epithelium into a precise triangular grid of photoreceptor clusters called ommatidia. Previous studies had led to a long-standing biochemical model whereby a reaction-diffusion process is templated by recently formed ommatidia to propagate a molecular prepattern across the eye. Here, we find that the templating mechanism is instead, mechanochemical in origin; newly born columns of differentiating ommatidia serve as a template to spatially pattern flows that move epithelial cells into position to form each new column of ommatidia. Cell flow is generated by a source and sink, corresponding to narrow zones of cell dilation and contraction respectively, that straddle the growing wavefront of ommatidia. The newly formed lattice grid of ommatidia cells are immobile, deflecting, and focusing the flow of other cells. Thus, the self-organization of a regular pattern of cell fates in an epithelium is mechanically driven. 

Organismal development is a complex process, involving a vast number of molecular constituents interacting on multiple spatio-temporal scales in the formation of intricate body structures. Despite this complexity, development is remarkably reproducible and displays tolerance to both genetic and environmental perturbations. This robustness implies the existence of hidden simplicities in developmental programs. Here, using the Drosophila wing as a model system, we develop a new quantitative strategy that enables a robust description of biologically salient phenotypic variation. Analyzing natural phenotypic variation across a highly outbred population and variation generated by weak perturbations in genetic and environmental conditions, we observe a highly constrained set of wing phenotypes. Remarkably, the phenotypic variants can be described by a single integrated mode that corresponds to a non-intuitive combination of structural variations across the wing. This work demonstrates the presence of constraints that funnel environmental inputs and genetic variation into phenotypes stretched along a single axis in morphological space. Our results provide quantitative insights into the nature of robustness in complex forms while yet accommodating the potential for evolutionary variations. Methodologically, we introduce a general strategy for finding such invariances in other developmental contexts.