Tunable stochastic pulsing in the Escherichia coli multiple antibiotic resistance network from interlinked positive and negative feedback loops

Abstract

Cells live in uncertain, dynamic environments and have many mechanisms for sensing and responding to changes in their surroundings. However, sudden fluctuations in the environment can be catastrophic to a population if it relies solely on sensory responses, which have a delay associated with them. Cells can reconcile these effects by using a tunable stochastic response, where in the absence of a stressor they create phenotypic diversity within an isogenic population, but use a deterministic response when stressors are sensed. Here, we develop a stochastic model of the multiple antibiotic resistance network of Escherichia coli and show that it can produce tunable stochastic pulses in the activator MarA. In particular, we show that a combination of interlinked positive and negative feedback loops plays an important role in setting the dynamics of the stochastic pulses. Negative feedback produces a pulsatile response that is tunable, while positive feedback serves to amplify the effect. Our simulations show that the uninduced native network is in a parameter regime that is of low cost to the cell (taxing resistance mechanisms are expressed infrequently) and also elevated noise strength (phenotypic variability is high). The stochastic pulsing can be tuned by MarA induction such that variability is decreased once stresses are sensed, avoiding the detrimental effects of noise when an optimal MarA concentration is needed. We further show that variability in the expression of MarA can act as a bet hedging mechanism, allowing for survival in time-varying stress environments, however this effect is tunable to allow for a fully induced, deterministic response in the presence of a stressor.

Figure 1. The marRAB operon and stochastic modeling results.

(A) Schematic representation of the marRAB operon encoding marR (R, repressor) and marA (A, activator). MarA and two copies of the MarR₂ dimer bind to the marRAB operator; salicylate and other aromatic compounds allosterically inhibit repression by MarR₂. (B) Stochastic simulations of the uninduced marRAB operon show stochastic pulses in MarA and MarR₂ protein expression. Pulses correspond to times when promoter is in the active state, i.e. one MarA and no MarR₂ molecules are bound to the marRAB promoter. (C) Stochastic simulations of the marRAB operon induced with 5 mM salicylate. MarR₂ levels shown in (B) and (C) include the dimeric form of the protein both with and without salicylate bound. Note the difference in y-axis scale between the uninduced and induced simulations.

Figure 2. Stochastic pulsing mediated by interlinked positive and negative feedback and tuned by inducer levels.

(A) Schematic representation of the four variants of the marRAB network studied. The Wildtype case has binding sites for MarA and MarR₂, Only Positive eliminates both binding sites for MarR₂, Only Negative eliminates the MarA binding site, and No Feedback has constant, constitutive expression. (B) Stochastic simulations of the four network variants. Noise amplification is observed in the Only Positive variant, transcriptional bursting appears in the Only Negative case, and both characteristics are combined to create high-amplitude stochastic pulsing in the Wildtype network. (C) Coefficient of variation (CV, std/mean) of MarA as a function of salicylate concentration. Constant noise is observed for the variants that do not respond to salicylate (Only Positive and No Feedback). The salicylate-responsive variants (Wildtype and Only Negative) show a decrease in CV upon induction. (D) Noise strength (var/mean) of MarA as a function of salicylate. Error bars in (C) and (D) show standard deviation across 100 replicates.

Figure 3. Positive and negative feedback strengths place the system in a low cost, high noise regime.

(A) Cost of MarA expression as a function of the activator and repressor association rates, k_a and k_r. (B) Noise strength (var/mean) as a function of k_a and k_r. White circles in (A) and (B) show the nominal Wildtype system parameters. Data show mean values of five replicates.

Figure 4. Stochastic pulsing acts as a bet hedging strategy.

(A) Competitive growth simulation with Wildtype and Reduced Noise network variants. Gray bars show the antibiotic stress profile as a function of time, with heights indicating the antibiotic concentration. Antibiotic is introduced randomly with a probability of 0.5. In other words, there is a 50% chance of the antibiotic being introduced. Note that the Wildtype network is at an advantage when concentrations of antibiotic jump from off to high in a short time span. (B) Final proportion of Wildtype and Reduced Noise cells as a function of the probability of antibiotic exposure in a fluctuating environment. (C) Final proportion of Wildtype and Reduced Noise cells as a function of antibiotic concentration in a constant environment. Error bars show standard deviation over three runs. (D) Proportion of surviving cells after a pulse of antibiotic. Simulations are of 10,000 cells. Error bars show standard deviation over five runs.