Figure 2.

The E. coli stress response network employs queueing as a signaling mechanism to ensure the most rapid response possible to adverse conditions. (A) Certain types of stress cause the accumulation of a large amount of aberrant proteins, which are targeted for rapid degradation and compete with the master stress regulator, σ^s, for a limited amount of ClpXP machinery. This leads to a decrease in the effective degradation rate of σ^s, allowing it to build up rapidly and initiate an immediate response. See the Supplementary Information for a precise definition of the model and for simulation details. (B) For a stochastic queueing model with 100 ClpXP molecules that each have processing rate μ=10 min⁻¹, with cells dividing every 20 min, a scan of the mean steady-state level of σ^s with respect to the stress level (mistranslated protein production rate λ_m) demonstrates a very sensitive response of the system once the system has crossed the balance point (respectively colored dashed lines). Different σ^s basal production rates λ_σs are indicated in the figure. (C) The dynamic response of σ^s to a 10-min pulse of stress demonstrates that queueing provides for a very fast and dynamic response. Importantly, the response is highly specific temporally, as σ^s only remains at a high level during the time that excess aberrant proteins are around. We assume the basal rate λ_σs=500 min⁻¹, while λ_m=1000 min⁻¹ during the pulse of stress but λ_m=0 min⁻¹ otherwise. (Inset) The mean response amplitude of σ^s to a periodic stress is strongest, especially at fast frequencies, when the system is on average near balance or slightly overloaded. The rate λ_m is taken to be a constant plus a sinusoid with amplitude 100 min⁻¹ and given frequency. (D) The adaptive response leads to positive correlations between σ^s and mistranslated protein levels for a broad range of parameters, peaking near the balance point (respectively colored dashed lines). Parameters are the same as those used in (B).