Search

Embryonic development hinges on effective coordination of molecular events across space and time. Waves have recently emerged as constituting an ubiquitous mechanism that ensures rapid spreading of regulatory signals across embryos, as well as reliable control of their patterning, namely, for the emergence of body plan structures. In this article, we review a selection of recent quantitative work on signaling waves and present an overview of the theory of waves. Our aim is to provide a succinct yet comprehensive guiding reference for the theoretical frameworks by which signaling waves can arise in embryos. We start, then, from reaction-diffusion systems, both static and time dependent; move to excitable dynamics; and conclude with systems of coupled oscillators. We link these theoretical models to molecular mechanisms recently elucidated for the control of mitotic waves in early embryos, patterning of the vertebrate body axis, micropattern cultures, and bone regeneration. Our goal is to inspire experimental work that will advance theory in development and connect its predictions to quantitative biological observations.

Understanding the mechanisms of embryonic cell cycles is a central goal of developmental biology, as the regulation of the cell cycle must be closely coordinated with other events during early embryogenesis. Quantitative imaging approaches have recently begun to reveal how the cell cycle oscillator is controlled in space and time, and how it is integrated with mechanical signals to drive morphogenesis. Here, we discuss how the Drosophila embryo has served as an excellent model for addressing the molecular and physical mechanisms of embryonic cell cycles, with comparisons to other model systems to highlight conserved and species-specific mechanisms. We describe how the rapid cleavage divisions characteristic of most metazoan embryos require chemical waves and cytoplasmic flows to coordinate morphogenesis across the large expanse of the embryo. We also outline how, in the late cleavage divisions, the cell cycle is inter-regulated with the activation of gene expression to ensure a reliable maternal-to-zygotic transition. Finally, we discuss how precise transcriptional regulation of the timing of mitosis ensures that tissue morphogenesis and cell proliferation are tightly controlled during gastrulation., Competing Interests: Competing interests The authors declare no competing or financial interests., (© 2021. Published by The Company of Biologists Ltd.)

Early embryogenesis of most metazoans is characterized by rapid and synchronous cleavage divisions. Chemical waves of Cdk1 activity were previously shown to spread across Drosophila embryos, and the underlying molecular processes were dissected. Here, we present the theory of the physical mechanisms that control Cdk1 waves in Drosophila The in vivo dynamics of Cdk1 are captured by a transiently bistable reaction-diffusion model, where time-dependent reaction terms account for the growing level of cyclins and Cdk1 activation across the cell cycle. We identify two distinct regimes. The first one is observed in mutants of the mitotic switch. There, waves are triggered by the classical mechanism of a stable state invading a metastable one. Conversely, waves in wild type reflect a transient phase that preserves the Cdk1 spatial gradients while the overall level of Cdk1 activity is swept upward by the time-dependent reaction terms. This unique mechanism generates a wave-like spreading that differs from bistable waves for its dependence on dynamic parameters and its faster speed. Namely, the speed of "sweep" waves strikingly decreases as the strength of the reaction terms increases and scales as the powers 3/4, -1/2, and 7/12 of Cdk1 molecular diffusivity, noise amplitude, and rate of increase of Cdk1 activity in the cell-cycle S phase, respectively. Theoretical predictions are supported by numerical simulations and experiments that couple quantitative measurements of Cdk1 activity and genetic perturbations of the accumulation rate of cyclins. Finally, our analysis bears upon the inhibition required to suppress Cdk1 waves at the cell-cycle pause for the maternal-to-zygotic transition., Competing Interests: The authors declare no conflict of interest.

In most metazoans, embryonic development is orchestrated by a precise series of cellular behaviors. Understanding how such events are regulated to achieve a stereotypical temporal progression is a fundamental problem in developmental biology. In this review, we argue that studying the regulation of the cell cycle in early embryonic development will reveal novel principles of how embryos accurately measure time. We will discuss the strategies that have emerged from studying early development of Drosophila embryos. By comparing the development of flies to that of other metazoans, we will highlight both conserved and alternative mechanisms to generate precision during embryonic development., (Copyright © 2016 Elsevier Ltd. All rights reserved.)