  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.
