Delayed coupling theory of vertebrate segmentation

Abstract

Rhythmic and sequential subdivision of the elongating vertebrate embryonic body axis into morphological somites is controlled by an oscillating multicellular genetic network termed the segmentation clock. This clock operates in the presomitic mesoderm (PSM), generating dynamic stripe patterns of oscillatory gene-expression across the field of PSM cells. How these spatial patterns, the clock's collective period, and the underlying cellular-level interactions are related is not understood. A theory encompassing temporal and spatial domains of local and collective aspects of the system is essential to tackle these questions. Our delayed coupling theory achieves this by representing the PSM as an array of phase oscillators, combining four key elements: a frequency profile of oscillators slowing across the PSM; coupling between neighboring oscillators; delay in coupling; and a moving boundary describing embryonic axis elongation. This theory predicts that the segmentation clock's collective period depends on delayed coupling. We derive an expression for pattern wavelength across the PSM and show how this can be used to fit dynamic wildtype gene-expression patterns, revealing the quantitative values of parameters controlling spatial and temporal organization of the oscillators in the system. Our theory can be used to analyze experimental perturbations, thereby identifying roles of genes involved in segmentation.

Modelling Oscillator Synchronisation During Vertebrate Axis Segmentation

“…[10][11][12][13][14]). However, given incomplete knowledge of the governing molecular networks, the seemingly intricate relationship between oscillator coupling and the molecular clocks, and the difficulty in unambiguously parameterising the current models, coarse-grained descriptions of molecular oscillators have recently been considered in which progression through the somitogenesis clock cycle is described by a single variable -the oscillator phase [15][16][17].…”

Random cell movement promotes synchronization of the segmentation clock

“…In the PSM, oscillatory expressions are synchronized among neighboring cells. This synchronized oscillation is necessary for normal segmentation, and disruption of the synchronization results in a defective somite boundary (11-13).Theoretical models of segmentation in vertebrates have been developed to explain the spatiotemporal periodicity of the segmentation process (14-18), the oscillatory expression of segmentation clock genes (19)(20)(21)(22)(23)(24), and the wave-like gene expression observed in the anterior PSM (23,(25)(26)(27)(28)(29). Previous theoretical studies have also addressed mechanisms of synchronization of the segmentation clock between cells (13,24,25,30).…”

Noise and Oscillations in Biological Systems: Multidisciplinary Approach Between Experimental Biology, Theoretical Modelling and Synthetic Biology

“…The spatio-temporal patterns of genetic oscillations have been described by coupled sets of phase oscillators which are arranged in space. 1 The state of a single oscillator is characterized by the phase θ i (t), where i labels the oscillator. The Fig.…”