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Biochemical feedback and its application to immune cells II: dynamics and critical slowing down

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Title: Biochemical feedback and its application to immune cells II: dynamics and critical slowing down
Authors: Byrd, Tommy A., Erez, Amir, Vogel, Robert M., Peterson, Curtis, Vennettilli, Michael, Altan-Bonnet, Grégoire, Mugler, Andrew
Source: Phys. Rev. E 100, 022415 (2019)
Publication Year: 2019
Collection: Condensed Matter
Physics (Other)
Quantitative Biology
Subject Terms: Physics - Biological Physics, Condensed Matter - Statistical Mechanics, Quantitative Biology - Molecular Networks
More Details: 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. This mapping allows us to quantify critical slowing down in experiments where we measure the response of T cells to drugs. Specifically, the addition of a drug is equivalent to a sudden quench in parameter space, and we find that quenches that take the cell closer to its critical point result in slower responses. We further demonstrate that our class of biochemical feedback models exhibits the Kibble-Zurek collapse for continuously driven systems, which predicts the scaling of hysteresis in cellular responses to more gradual perturbations. We discuss the implications of our results in terms of the tradeoff between a precise and a fast response.
Comment: 9 pages, 6 figures
Document Type: Working Paper
DOI: 10.1103/PhysRevE.100.022415
Access URL: http://arxiv.org/abs/1902.02444
Accession Number: edsarx.1902.02444
Database: arXiv
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  Data: Phys. Rev. E 100, 022415 (2019)
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  Data: 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. This mapping allows us to quantify critical slowing down in experiments where we measure the response of T cells to drugs. Specifically, the addition of a drug is equivalent to a sudden quench in parameter space, and we find that quenches that take the cell closer to its critical point result in slower responses. We further demonstrate that our class of biochemical feedback models exhibits the Kibble-Zurek collapse for continuously driven systems, which predicts the scaling of hysteresis in cellular responses to more gradual perturbations. We discuss the implications of our results in terms of the tradeoff between a precise and a fast response.<br />Comment: 9 pages, 6 figures
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