Foci, waves, excitability : self-organization of phase waves in a model of asymmetrically coupled embryonic oscillators
Bibliographic record
Abstract
The ‘segmentation clock’ is an emergent embryonic oscillator that controls the periodic formation of vertebrae precursors (or somites). It relies on the self-organization at the Pre Somitic Mesoderm (PSM) level of multiple coupled cellular oscillators. Dissociation-reaggregation experiments have further revealed that ensembles made of such cellular oscillators self-organize into an oscillatory bidimensional system, showing concentric waves around multiple foci. Here, we systematically study the dynamics of a two dimensional lattice of phase oscillators locally coupled to their nearest neighbors through a biharmonic coupling function, of the form sin θ + Λ sin 2 θ . This coupling was inferred from the Phase Response Curve (PRC) of entrainment experiments on cell cultures, leading to the formulation of a minimal Elliptic Radial Isochron Cycle (ERIC) phase model. We show that such ERIC-based coupling parsimoniously explains the emergence of self-organized concentric phase wave patterns around multiple foci, for a range of weak couplings and wide distributions of initial random phases, closely mimicking experimental conditions. We further study extended modalities of this problem to derive an atlas of possible behaviours. In particular, we predict the dominant observation of spirals over target wave patterns for initial phase distributions wider than approximately π . Since PSM cells further display properties of an excitable system, we also introduce excitability into our simple model, and show that it also supports the observation of concentric phase waves for the conditions of the experiment. Our work suggests important modifications that can be made to the simple phase model with Kuramoto coupling, that can provide further layers of complexity and can aid in the explanation of the spatial aspects of self-organization in the segmentation clock.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".