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

## TL;DR

This paper explores how biochemical feedback in immune cells exhibits critical slowing down near bifurcation points, using a mapping to the Ising model to quantify response times and hysteresis effects during perturbations.

## Contribution

It introduces a novel application of the Ising universality class to model critical slowing down in biochemical feedback systems, linking theory to experimental immune cell responses.

## Key findings

- Critical slowing down observed near bifurcation points in immune cell models.
- Quenches closer to the critical point lead to slower cellular responses.
- The Kibble-Zurek mechanism predicts hysteresis scaling in cellular responses.

## Abstract

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.