Critical slowing down in biochemical networks with feedback

Tommy A. Byrd, Amir Erez, Robert M. Vogel, Curtis Peterson, Michael Vennettilli, Grégoire Altan-Bonnet, Andrew Mugler

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Near a bifurcation point, the response time of a system is expected to diverge due to the phenomenon of critical slowing down. We investigate critical slowing down in well-mixed stochastic models of biochemical feedback by exploiting a mapping to the mean-field Ising universality class. We analyze the responses to a sudden quench and to continuous driving in the model parameters. In the latter case, we demonstrate that our class of models exhibits the Kibble-Zurek collapse, which predicts the scaling of hysteresis in cellular responses to gradual perturbations. We discuss the implications of our results in terms of the tradeoff between a precise and a fast response. Finally, we use our mapping to quantify critical slowing down in T cells, where the addition of a drug is equivalent to a sudden quench in parameter space.

Original languageAmerican English
Article number022415
JournalPhysical Review E
Issue number2
StatePublished - 26 Aug 2019
Externally publishedYes

Bibliographical note

Funding Information:
We thank Anushya Chandran for helpful communications. This work was supported by Simons Foundation Grant No. 376198 (T.A.B. and A.M.), Human Frontier Science Program Grant No. LT000123/2014 (Amir Erez), National Science Foundation Research Experiences for Undergraduates Grant No. PHY-1460899 (C.P.), National Institutes of Health (NIH) Grants No. R01 GM082938 (A.E.) and No. R01 AI083408 (A.E., R.V., and G.A.-B), and the NIH National Cancer Institute Intramural Research programs of the Center for Cancer Research (A.E. and G.A.-B.).

Publisher Copyright:
© 2019 American Physical Society.


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