Oscillation arrest in the mouse somitogenesis clock presumably takes place via an infinite period bifurcation

TL;DR

This paper proposes a minimal mathematical model explaining how oscillations in the mouse somitogenesis clock are halted through an infinite-period bifurcation, aligning with experimental data and involving interactions of feedback loops.

Contribution

It introduces a simple model combining positive and negative feedback loops to explain oscillation arrest via an infinite-period bifurcation in somitogenesis.

Findings

Oscillations are halted through an infinite-period bifurcation.

The model aligns with experimental observations.

Additive interactions of gene regulators are key to arrest mechanism.

Abstract

In this work we address the question of how oscillations are arrested in the mouse somitogenesis clock when the determination front reaches presomitic cells. Based upon available experimental evidence we hypothesize that the mechanism underlying such a phenomenon involves the interaction between a limit cycle (originated by a delayed negative feedback loop) and a bistable switch (originated by a positive feedback loop). With this hypothesis in mind we construct the simplest possible model comprising both negative and positive feedback loops and show that (with a suitable choice of paremeters): 1) it can show an oscillatory behavior, 2) oscillations are arrested via an infinite-period bifurcation whenever the different gene-expression regulator-inputs act together in an additive rather than in a multiplicative fashion, and 3) this mechanism for oscillation arrest is compatible whit plentiful experimental observations.