Oscillation arrest in the mouse somitogenesis clock presumably takes place via an infinite period bifurcation
Zavala-López, E; Santillán, M
Date: 2 August 2011
Article
Journal
arXiv
Publisher
arXiv.org
Related links
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 ...
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 regulatorinputs
act together in an additive rather than in a multiplicative fashion,
and 3) this mechanism for oscillation arrest is compatible whit plentiful experimental
observations.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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