Dynamic morphoskeletons in development

Optimal Control of Short-Time Attractors in Active Nematics

Objective Eulerian coherent structures (OECSs) and instantaneous Lyapunov exponents (iLEs) govern short-term material transport in fluid flows as Lagrangian coherent structures and the finite-time Lyapunov exponent do over longer times. Attracting OECSs and iLEs reveal short-time attractors and are computable from the Eulerian rate-of-strain tensor. Here, we devise for the first time an optimal control strategy to create short-time attractors in compressible, viscosity-dominated active nematic flows. By modulating the active stress intensity, our framework achieves a target profile of the minimum eigenvalue of the rate-of-strain tensor, controlling the location and shape of short-time attractors. We show that our optimal control strategy effectively achieves desired short-time attractors while rejecting disturbances. Combining optimal control and coherent structures, our work offers a new perspective to steer material transport in compressible active nematics, with applications to morphogenesis and synthetic active matter.

Evo-Devo Mechanobiology: The Missing Link

While the modern framework of evolutionary development (evo-devo) has been decidedly genetic, historic analyses have also considered the importance of mechanics in the evolution of form. With the aid of recent technological advancements in both quantifying and perturbing changes in the molecular and mechanical effectors of organismal shape, how molecular and genetic cues regulate the biophysical aspects of morphogenesis is becoming increasingly well studied. As a result, this is an opportune time to consider how the tissue-scale mechanics that underlie morphogenesis are acted upon through evolution to establish morphological diversity. Such a focus will enable a field of evo-devo mechanobiology that will serve to better elucidate the opaque relations between genes and forms by articulating intermediary physical mechanisms. Here, we review how the evolution of shape is measured and related to genetics, how recent strides have been made in the dissection of developmental tissue mechanics, and how we expect these areas to coalesce in evo-devo studies in the future.

A mechanochemical model recapitulates distinct vertebrate gastrulation modes

During vertebrate gastrulation, an embryo transforms from a layer of epithelial cells into a multilayered gastrula. This process requires the coordinated movements of hundreds to tens of thousands of cells, depending on the organism. In the chick embryo, patterns of actomyosin cables spanning several cells drive coordinated tissue flows. Here, we derive a minimal theoretical framework that couples actomyosin activity to global tissue flows. Our model predicts the onset and development of gastrulation flows in normal and experimentally perturbed chick embryos, mimicking different gastrulation modes as an active stress instability. Varying initial conditions and a parameter associated with active cell ingression, our model recapitulates distinct vertebrate gastrulation morphologies, consistent with recently published experiments in the chick embryo. Altogether, our results show how changes in the patterning of critical cell behaviors associated with different force-generating mechanisms contribute to distinct vertebrate gastrulation modes via a self-organizing mechanochemical process.

Mechanochemical Active Feedback Generates Convergence Extension in Epithelial Tissue

Convergence extension, the simultaneous elongation of tissue along one axis while narrowing along a perpendicular axis, occurs during embryonic development. A fundamental process that contributes to shaping the organism, it happens in many different species and tissue types. Here, we present a minimal continuum model, that can be directly linked to the controlling microscopic biochemistry, which shows spontaneous convergence extension. It is comprised of a 2D viscoelastic active material with a mechanochemical active feedback mechanism coupled to a substrate via friction. Robust convergent extension behavior emerges beyond a critical value of the activity parameter and is controlled by the boundary conditions and the coupling to the substrate. Oscillations and spatial patterns emerge in this model when internal dissipation dominates over friction, as well as in the active elastic limit.

The evolution of gastrulation morphologies

During gastrulation, early embryos specify and reorganise the topology of their germ layers. Surprisingly, this fundamental and early process does not appear to be rigidly constrained by evolutionary pressures; instead, the morphology of gastrulation is highly variable throughout the animal kingdom. Recent experimental results demonstrate that it is possible to generate different alternative gastrulation modes in single organisms, such as in early cnidarian, arthropod and vertebrate embryos. Here, we review the mechanisms that underlie the plasticity of vertebrate gastrulation both when experimentally manipulated and during evolution. Using the insights obtained from these experiments we discuss the effects of the increase in yolk volume on the morphology of gastrulation and provide new insights into two crucial innovations during amniote gastrulation: the transition from a ring-shaped mesoderm domain in anamniotes to a crescent-shaped domain in amniotes, and the evolution of the reptilian blastoporal plate/canal into the avian primitive streak.

Reconstruction of distinct vertebrate gastrulation modes via modulation of key cell behaviors in the chick embryo

The morphology of gastrulation driving the internalization of the mesoderm and endoderm differs markedly among vertebrate species. It ranges from involution of epithelial sheets of cells through a circular blastopore in amphibians to ingression of mesenchymal cells through a primitive streak in amniotes. By targeting signaling pathways controlling critical cell behaviors in the chick embryo, we generated crescent- and ring-shaped mesendoderm territories in which cells can or cannot ingress. These alterations subvert the formation of the chick primitive streak into the gastrulation modes seen in amphibians, reptiles, and teleost fish. Our experimental manipulations are supported by a theoretical framework linking cellular behaviors to self-organized multicellular flows outlined in detail in the accompanying paper. Together, this suggests that the evolution of gastrulation movements is largely determined by changes in a few critical cell behaviors in the mesendoderm territory across different species and controlled by a relatively small number of signaling pathways.

A Review of Mathematical and Computational Methods in Cancer Dynamics

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems medicine. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems, and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.

Active flows and deformable surfaces in development

We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients- active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.

Cellular processes driving gastrulation in the avian embryo

Gastrulation consists in the dramatic reorganisation of the epiblast, a one-cell thick epithelial sheet, into a multilayered embryo. In chick, the formation of the internal layers requires the generation of a macroscopic convection-like flow, which involves up to 50,000 epithelial cells in the epiblast. These cell movements locate the mesendoderm precursors into the midline of the epiblast to form the primitive streak. There they acquire a mesenchymal phenotype, ingress into the embryo and migrate outward to populate the inner embryonic layers. This review covers what is currently understood about how cell behaviours ultimately cause these morphogenetic events and how they are regulated. We discuss 1) how the biochemical patterning of the embryo before gastrulation creates compartments of differential cell behaviours, 2) how the global epithelial flows arise from the coordinated actions of individual cells, 3) how the cells delaminate individually from the epiblast during the ingression, and 4) how cells move after the ingression following stereotypical migration routes. We conclude by exploring new technical advances that will facilitate future research in the chick model system.