Active degradation of MarA controls coordination of its downstream targets

Several key transcription factors have unusually short half-lives compared to other cellular proteins. Here, we explore the utility of active degradation in shaping how the multiple antibiotic resistance activator MarA coordinates its downstream targets. MarA controls a variety of stress response genes in Escherichia coli. We modify its half-life either by knocking down the protease that targets it via CRISPRi or by engineering MarA to protect it from degradation. Our experimental and analytical results indicate that active degradation can impact both the rate of coordination and the maximum coordination that downstream genes can achieve. In the context of multi-gene regulation, trade-offs between these properties show that perfect information fidelity and instantaneous coordination cannot coexist.

base-pairs after the transcriptional start site of the lon gene. This sequence has a single mutation (underlined letter) at the 14th base-pair. This decreases its repression and causes leaky expression of lon to avoid producing off-target phenotypic changes such as increased filamentation (Fig. S1).

Western Blots
To determine the half-life of both wild type MarA under CRISPRi knockdown of Lon protease and MarA fusion protein, we grew cultures of both systems overnight and then diluted them 1:100 in 30 ml LB. Cells were grown for 4 hours and then spectinomycin (100 µg/ml) was added to stop protein synthesis. 1 ml of the culture was collected at different time points (0, 5, 10, 15 and 30 minutes). Cells were harvested at 13,000 rpm for 3 minutes and the supernatant was removed in order to extract total proteins. The cell pellets were resuspended with 4% SDS and shaken for 15 minutes at 37 • C. Glass beads (0.1 mm) were added and the samples were vortexed for 10 seconds and incubated on ice for 10 seconds three times. Anti-MarA antibody was used to detect the presence of MarA or MarA fusion protein. Membranes were probed first with 1:3000 of rabbit anti-MarA antibodies generously provided by Valerie Duval, Laura McMurry, and Stuart Levy [4]. Primary antibodies were detected using the secondary Peroxidase-AffiniPure Goat Anti-Rabbit IgG.

Analytic solutions for variance and mutual information over time
Following the methods outlined in [5] we derived the exact analytical solutions for the models described in the text. This allowed us to describe how variance evolves as a function of time for the input X and its two downstream targets Y and Z.
Next, in order to quantify how coordinated diversity of two downstream genes evolves over time we compute the mutual information between the two genes as a function of time. To compute this, we first calculate the covariance over time.
Next, the correlation of Y and Z is calculated by combining equations 2, 3, and 4 as :

ar{y(t)}V ar{z(t)}
This is then converted to mutual information by the following equivalence Note this analytical conversion assumes Gaussian statistics for the underlying stochastic differential equations.

Analytic solutions for variance and mutual information over time with scaled variance
The solutions to the equations as illustrated in Figure 3 in the main text are similar to that in Figure  2 except the variance is constrained as a function of correlation time τ .

Modified model incorporating growth rate
To consider the effects of growth rate on the system we modified Eqn. 7 to include terms modeling the exponential growth of a bacterial microcolony.
where N cells is the starting number of cells, t div is the division time (or length of cell cycle) in minutes. τ x is the correlation time of the activator, while t is measured in minutes.

Parameters
Parameter Value Definition λ x range from 1 to 100 half-life of x τ x λx log (2) correlation-time of x τ y 30.0 log (2) correlation-time of y τ z 30.0 log (2) correlation-time of z g y 0.1τ y dose response gain of x on y g z 0.1τ z dose response gain of x on z The correlation time of y and z was assumed to scale from the average division time of E. coli as 30 minutes [6] as they are both stable proteins. The gain of each promoter was an approximation of acrAB and inaA promoters at wild-type levels of MarA [7].