Waves, patterns and bifurcations: a tutorial review on the vertebrate segmentation clock

TL;DR

This review comprehensively covers four decades of biophysical models of the vertebrate segmentation clock, highlighting how oscillatory waves lead to vertebrae patterning and integrating recent advances in molecular and geometric modeling.

Contribution

It offers a unified geometric framework for somitogenesis, connecting classical models with modern molecular and visualization data, and introduces new analytical insights.

Findings

Proposes a geometric description of somitogenesis.

Connects models to embryonic scaling and wave propagation.

Provides new analytical calculations and insights.

Abstract

Proper vertebrae formation relies on a tissue-wide oscillator called the segmentation clock. Individual cellular oscillators in the presomitic mesoderm are modulated by intercellular coupling and external signals, leading to the propagation of oscillatory waves of genetic expression eventually stabilizing into a static pattern. Here, we review 4 decades of biophysical models of this process, starting from the pioneering Clock and Wavefront model by Cooke and Zeeman, and the reaction-diffusion model by Meinhardt. We discuss how modern descriptions followed advances in molecular description and visualization of the process, reviewing phase models, delayed models, systems-level, and finally geometric models. We connect models to high-level aspects of embryonic development from embryonic scaling to wave propagation, up to reconstructed stem cell systems. We provide new analytical calculations and insights into classical and recent models, leading us to propose a geometric description of somitogenesis organized along two primary waves of differentiation.