Delayed coupling theory of vertebrate segmentation
arXiv:0812.3276 · doi:10.2976/1.3027088
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.
published online 10 December 2008, Adv. Online Pub. HFSP Journal (free access)
References in corpus (5)
- Time Delay in the Kuramoto Model of Coupled Oscillators
- Oscillations and temporal signalling in cells
- Controlling spatiotemporal chaos in oscillatory reaction-diffusion systems by time-delay autosynchronization
- Molecular Synchronization Waves in Arrays of Allosterically Regulated Enzymes
- Converting genetic network oscillations into somite spatial pattern
Cited by in corpus (18)
- Intercellular Coupling Regulates the Period of the Segmentation Clock
- Spontaneous spiking in an autaptic Hodgkin-Huxley set up
- Collective modes of coupled phase oscillators with delayed coupling
- Mobility induces global synchronization of oscillators in periodic extended systems
- Oscillatory Notch pathway activity in a delay model of neuronal differentiation
- Synchronization Dynamics in the Presence of Coupling Delays and Phase Shifts
- Optimal cellular mobility for synchronization arising from the gradual recovery of intercellular interactions
- Structural and functional networks in complex systems with delay
- Sequential pattern formation governed by signaling gradients
- Modeling delayed processes in biological systems
- Chemical event chain model of coupled genetic oscillators
- Mobility-induced persistent chimera states
- Stochastic Kuramoto oscillators with discrete phase states
- Dickkopf1 - a new player in modelling the Wnt pathway
- Networks of coupled circuits: From a versatile toggle switch to collective coherent behavior
- Nonlinear transient waves in coupled phase oscillators with inertia
- Intrinsic noise, Delta-Notch signalling and delayed reactions promote sustained, coherent, synchronised oscillations in the presomitic mesoderm
- Hybrid reaction-diffusion and clock-and-wavefront model for the arrest of oscillations in the somitogenesis segmentation clock