Instability of CII is needed for efficient switching between lytic and lysogenic development in bacteriophage 186

Abstract The CII protein of temperate coliphage 186, like the unrelated CII protein of phage λ, is a transcriptional activator that primes expression of the CI immunity repressor and is critical for efficient establishment of lysogeny. 186-CII is also highly unstable, and we show that in vivo degradation is mediated by both FtsH and RseP. We investigated the role of CII instability by constructing a 186 phage encoding a protease resistant CII. The stabilised-CII phage was defective in the lysis-lysogeny decision: choosing lysogeny with close to 100% frequency after infection, and forming prophages that were defective in entering lytic development after UV treatment. While lysogenic CI concentration was unaffected by CII stabilisation, lysogenic transcription and CI expression was elevated after UV. A stochastic model of the 186 network after infection indicated that an unstable CII allowed a rapid increase in CI expression without a large overshoot of the lysogenic level, suggesting that instability enables a decisive commitment to lysogeny with a rapid attainment of sensitivity to prophage induction.

simulation of hybrid stochastic-deterministic models using the 'next reaction' variant of Gillespie's algorithm (1) was written in C++ with an API written for R to facilitate model specification. Software is available on request.
The reactions included in the model are listed in Supplementary Table 1 and describe regulation of the lytic (pR), lysogenic (pL) and establishment (pE) promoters by the products of the lytic transcript (Apl and CII) and by the product of the lysogenic transcript (CI). Variants from the wildtype phage were simulated by simple adjustments to the parameters as listed in Supplementary Table 2. The trans-pE-lacZ reporter strains were modelled as a CInetwork, taking the hazard for production of pE transcripts as proportional to LacZ activity, with equality when both are normalised by maximum promoter activity. In Figure 7 (main text), the rate of production/loss of CI was calculated directly at each time point as the value of equation 8 in Supplementary Table 1. Regulation of pR and pL activity by the repressor CI is non-trivial, involving both multimerisation of the transcription factor at the DNA and transcriptional interference between the promoters. A detailed model of both processes has previously been described (2)(3) and was fit to population measurements of promoter activity for inducible concentrations of CI (4). For simplicity and clarity in this context, however, we chose instead to fit that data using Hill equations in the concentration of CI (equations 3 and 5 in Supplementary Table 1). The best least squares fit to the experimental data is shown in Supplementary Figure 1.
Estimates for many of the other parameters have been determined previously. The degradation rate of CII was from (5), and the rates of loss of CI and Apl were assumed to be dilution limited. Promoter firing rates for pR and pL were from (2), with that for pE being estimated similarly by comparing promoter strengths.
CII activation of the pE promoter was modelled as a Hill function with parameters fit to in vitro transcription data (5). Apl repression was assumed to act equally on pR and pL, with parameters from a fit of 7-site gel shift data (6).
The protein translation rates and transcript degradation rates could not be determined from elsewhere.
For the translation rates, we noted that over a broad range of parameters, simulations of the steady-state behaviour of lysogenic phage (corresponding to the variants in main text Fig. 5A) and of the trans-pE reporter strains (main text Fig. 6A) showed average behaviour that closely matched that of the equivalent deterministic model. As such, we were able to fit these parameters to reproduce the experimental data ( Fig. 7A) by solving the equivalent deterministic model at steady state. A weighted least squares scheme was used in which residual errors were generally assumed to scale with the magnitude of the model output.
Specifically, the following equation was minimised: where [ ] ( ) is the average total concentration of CI in each of the three lysogen variants, and [ ] ( ) and [ ] ( , ) are, respectively, the average values of trans-pE activity (normalised by maximum pE activity) for each of the eight trans-pE reporter variants. We had no data with which to fit the transcript degradation rates, so made them all equal, choosing a value typical of mRNA half-lives observed in E. coli (7). We note that within a biologically feasible range, the transcript degradation rates had little influence on the model outputs of interest.