CsrA and its regulators control the time-point of ColicinE2 release in Escherichia coli

The bacterial SOS response is a cellular reaction to DNA damage, that, among other actions, triggers the expression of colicin - toxic bacteriocins in Escherichia coli that are released to kill close relatives competing for resources. However, it is largely unknown, how the complex network regulating toxin expression controls the time-point of toxin release to prevent premature release of inefficient protein concentrations. Here, we study how different regulatory mechanisms affect production and release of the bacteriocin ColicinE2 in Escherichia coli. Combining experimental and theoretical approaches, we demonstrate that the global carbon storage regulator CsrA controls the duration of the delay between toxin production and release and emphasize the importance of CsrA sequestering elements for the timing of ColicinE2 release. In particular, we show that ssDNA originating from rolling-circle replication of the toxin-producing plasmid represents a yet unknown additional CsrA sequestering element, which is essential in the ColicinE2-producing strain to enable toxin release by reducing the amount of free CsrA molecules in the bacterial cell. Taken together, our findings show that CsrA times ColicinE2 release and reveal a dual function for CsrA as an ssDNA and mRNA-binding protein, introducing ssDNA as an important post-transcriptional gene regulatory element.


Supplementary Tables
LexA binding sequence altered on pMO3 to achieve weaker LexA binding, resulting in pMO5 Same as C REP1 , only the origin of replication on pMO3 has been changed to p15A to achieve a lower copy number of 13 copies per cell -pMO8 This study S REP2 BZB 1011 pMO8 Same as S REP1 , only the origin of replication on pMO3 has been changed to p15A to achieve a lower copy number of 13 copies per cell -> pMO8 This study  Table S4. Sequences of genetic elements. The first three rows depict sequence changes in the LexA binding site (two overlapping LexA binding SOS boxes) on the pMO3 reporter plasmid, leading to altered LexA binding (pMO4, pMO5). The following three rows show the changes made in the CsrA binding site within the second mRNA loop (which also includes the ribosome binding site of the cel gene and the GGA motif recognized by CsrA) that potentiate (pMO6) or weaken (pMO7) CsrA binding (Fig 2d). The following three rows list the sequences of RNA oligos used for CsrA binding studies (Methods, Fig 2d) and include the alterations in the CsrA binding site mentioned above. The last three rows give the sequences of the 89-bp ssDNA oligos used to study binding of CsrA to ssDNA by gel shift analysis (Methods). Bases highlighted in green correspond to sequence changes. Bases shown in boldface highlight the GGA motif required for CsrA binding as present within the second mRNA (plasmid), RNA oligo or ssDNA oligo loop. We confirmed the appropriate formation of secondary structures of these oligos using Mfold (10) Fig S6: cea-cel delay-time distributions and average cea-cel delay-times for different ssDNA production rates and strains. The S REP1 strain does not produce ssDNA, and is plotted (in green) only for the purpose of direct comparison with the C REP1 strain. If no ssDNA is produced ( D = 0), we find that the C REP1 strain shows a broader cea-cel delay-time distribution, compared to the cases with ssDNA production. The wild-type strain C WT does not lyse at all during the SOS signal for  D = 0. If we increase the ssDNA production rate, we find the experimentally observed behaviour that the C REP1 strain shows very short cea-cel delays. In the wild-type strain, a certain threshold rate of ssDNA production is required to induce a significant level of lysis, emphasizing the importance of ssDNA for toxin release. Ensemble size: 2000 realisations.

Fig S7:
Average of the time evolution of the CsrA and long mRNA abundance for different ssDNA production rates and strains. Between t=200 and t=500, the system is subject to an SOS signal. In all cases, the SOS signal initiates a decrease in CsrA abundance from a previously stable level. This level is determined by the production, binding, and degradation rates of CsrA and its complex partners. As higher CsrA levels take longer and are also less likely to decrease to zero, they also directly affect the duration of the average cea-cel delay-time. The three plots for  D = 0 also show a single trajectory of long mRNA and CsrA in light green and light red, respectively. Ensemble size: 2000 realisations.

Fig S8:
Cell lysis after induction with 0.25 µg/ml MitC. C REP1 lyses on average 87 (± 3.9) min after induction with MitC, C WT lyses considerably later at 150 (± 6.9) min. For C REP1 , mean cell lysis nearly coincides with the T ONcea at 69.71 ± 0.77 min(7) (red line). This interval between T ONcea constitutes the delay between the SOS signal (MitC induction) and the start of cea gene expression. In our theoretical model, this initial delay is very short, as the system here switches directly from the pre-SOS signal 'OFF' state into the post-SOS signal 'ON' state. Hence, the red line also depicts the time-point of this switch (0 min in Fig  4).

Fig S9:
Importance of ssDNA production from the toxin producing plasmid (pColE2-P9) for toxin release in the wild-type strain C WT . Left: Simulations for ColicinE2 expression from the pColE2-P9 plasmid with a plasmid copy number of ~20 in the absence ( D = 0) and presence ( D = 7) of ssDNA. Right: Simulations for ColicinE2 expression from the pColE2-P9 plasmid with a plasmid copy number of only 1 in the absence ( D = 0) and presence ( D = 7) of ssDNA. Here, the simulation lacking ssDNA production would resemble toxin production from a chromosomally encoded ColicinE2 operon. The biological phenomenon we wish to describe by means of a quantitative theoretical model is the regulation of ColicinE2 release in E. coli. ColicinE2 is a bacterial toxin encoded by the gene cea, which is part of the ColicinE2 operon located on a plasmid. This operon also contains genes for an immunity protein (cei gene) and a lysis protein (cel gene). The lysis protein is part of the operon as cell lysis is the only way to release the toxin into the environment. Since lysis also means the death of the cell, the release of ColicinE2 is highly regulated. Previous studies have revealed the regulatory components controlling ColicinE2 production and release on both the transcriptional and post-transcriptional levels: • The transcription of the operon is regulated by the repressor LexA, which is part of the E. coli SOS response regulatory network [1,2]. Stressful events, such as DNA damage activate a SOS response system [1], which stochastically triggers the transcription of the operon by degradation of LexA. Once transcription starts, two mRNA transcripts are produced: short mRNA, containing only the toxin and immunity protein, and long mRNA, which contains also the lysis protein [3].
• The post-transcriptional regulation (see Fig. 1 and also Fig. S3) acts on the long mRNA only. To our knowledge, its only regulator is the protein CsrA, which binds to the Shine-Dalgarno sequence that is located on the long mRNA between the sequences coding for the immunity and lysis proteins [3]. When a CsrA protein binds to long mRNA and thus forms a complex with it, the gene for the lysis protein can no longer be translated, and thus the cell does not lyse [3]. By preventing lysis protein expression, CsrA regulates the release of ColicinE2. The abundance of CsrA itself is known to be regulated by the two CsrA-sequestering short RNAs (sRNAs) CsrB and CsrC, which both have several CsrA binding sites [4,5]. Our current study suggests that, in addition, rings of single-stranded DNA (ssDNA) also sequester CsrA, and therefore represent a novel CsrA regulator. This ssDNA is created as an intermediate during the rolling circle replication of the ColicinE2 plasmids.
A particular example for the importance of these regulatory interactions is the delay between production and release of ColicinE2, which has recently been studied experimentally [6]: The translation of lysis proteins from long mRNA (and therefore lysis itself) can only start if there are free long mRNAs, that is, long mRNAs that are not bound to CsrA. From what is known about CsrA interactions, we assume in our biochemical model that a CsrA molecule can no longer regulate long mRNA when it is either sequestered, or degraded. Previous studies [7] show that CsrA is highly abundant during growth phase, mainly in form of CsrA complexes. When an SOS response is triggered, however, the production of long mRNA increases such that free CsrA abundance decreases, and eventually lysis proteins are translated from free long mRNA. This process does not happen instantaneously: Due to stochasticity in the SOS response system and the time it takes to produce, bind or degrade the regulatory components involved, we find a delay between the expression of the unregulated cea gene (part of the short mRNA) and the CsrA-regulated cel gene (part of the long mRNA). This delay is presumably not just a byproduct of regulation, but has also a biological function: It gives the cell time to accumulate ColicinE2, and thus allows for higher toxin concentrations upon the release. Moreover, it presumably also acts as a safety buffer, which prevents premature cell lysis, for instance due to fluctuations in the system [6]. In contrast to the abundances of the regulatory components, the cea-celdelay is a quantity that can readily be measured experimentally by reporter plasmids inserted in the E. coli cells. These reporter plasmids carry the ColicinE2 operon, but the toxin (cea) and lysis (cel) gene are replaced by two different fluorescence protein genes (CFP and YFP). Since only these two 2 number of number of strain reporter plasmids pColE2P9 plasmids ssDNA ≈ 20 accumulates C WT -≈ 20 accumulates Table S5: The five different strains and the abundance of the genetic elements that differentiate them [8].
genes are replaced, the reporter plasmids have the same promoter as the ColicinE2 plasmid, and the long mRNA transcript of the reporter plasmid has the same CsrA binding site as the original long mRNA. Consequently, a reporter plasmid behaves like the ColicinE2 plasmid, but produces two types of fluorescence proteins instead of toxin and lysis proteins. Therefore, upon introducing reporter plasmids to an E. coli cell, one can measure the time points of production of the corresponding fluorescence proteins; these measured time points then coincide with the time points of toxin and lysis protein production. In this study, we use two reporter plasmid types, which differ by their mean abundance in the cell: type 1 (pMO3) accumulates to about 55 plasmids per cell, whereas type 2 (pMO8) only to about 13 plasmids per cell.
With three different plasmid types, the original and the two reporter plasmids, we can construct five different strains (see also Table S5): First, the wild-type strain, C WT , which carries only ColicinE2 plasmids. Inserting reporter plasmids to this strain creates, depending on the reporter plasmid type inserted, either a strain called C REP1 or a strain called C REP2 . Completely replacing the ColE2 plasmid with one of the reporter plasmid types creates another two strains, referred to as S REP1 and S REP2 . Our experiments show that the plasmid types also differ in the production of ssDNA: cells carrying the ColicinE2 plasmid do accumulate ssDNA (see Fig. 3), while this is not the case for the S REP1 and S REP2 strain cells, which only contain reporter plasmids (see Fig. 3

and Supplementary Information).
As discussed in detail in section 2, we will use mathematical modelling to infer the delay of the wild-type strain from the delay measured in the other strains containing the reporter plasmid. Before doing so, we recapitulate the main experimental findings on the delay-times in the bacterial strains containing the reporter plasmid.
In our experiments (see main text) we found that the C REP1 strain shows no significant delay between cea and cel gene expression, whereas the S REP1 strain has a significant mean delay of 75 minutes. Moreover, we observed that the S REP1 strain has a broad delay-time distribution around this mean value. This raised the question as to the source of this difference. The C REP1 and S REP1 strains differ only in their plasmid composition and are both genetically identical (see Table S5). From this we conclude that the presence of ColicinE2 plasmids in the C REP1 strain introduces further regulatory elements (compared to the reporter plasmids), which are responsible for the shorter cea-cel delay times compared to the S REP1 strain. The reporter and the ColicinE2 plasmids contain the same regulatory sequences (see Methods), which means that the additional regulatory elements cannot be different mRNA transcripts specifically produced by the ColicinE2 plasmid.
From what is known about the two plasmids and the regulatory network of ColicinE2 (see above), two mechanisms could in principle account for the shorter delay times in C REP1 , which are: First, additional production of CsrA sequestering long mRNA due to the larger plasmid copy number, and second, the accumulation of ssDNA which, as our study shows, can also sequester CsrA.

Mathematical model of the ColicinErelease
In the following, we develop a mathematical model that enables us to investigate the regulation of ColicinE2 release in all five strains (C REP1 , C REP2 , C WT , S REP1 , and S REP2 ). The model accounts for all necessary regulatory components, including the ssDNA and the different plasmid compositions. We validate this model by reproducing the experimentally observed delay time distributions for the S REP1 strain. Variation of ssDNA production in the model then allows us to quantify the impact of ssDNA production and plasmid copy number on the cea-cel delay. Moreover, the model enables us to infer the behaviour of the C WT strain, for which the cea-cel delay cannot be directly measured experimentally. The inferred behaviour can be validated by comparison with experimentally measured lysis times, see Fig.  S8. Several experimental studies defined and probed the regulatory networks and components involved in E. coli SOS responses, as well as Col-icinE2 production and release [1,3,6,8]. Starting from these experimental results, the regulatory interactions have also been studied using mathematical models [2,[9][10][11]: For the transcriptional regulation network of the E. coli SOS response system, a stochastic model has been presented, which is able to reproduce the distribution of stochastic SOS activity peaks [2]. For the post-transcriptional regulation of ColicinE2 release, we recently introduced a hierarchical three-component model [9] involving long mRNA, CsrA, and an effective sRNA. This model was also combined with the stochastic SOS signal model from Ref. [2] to emulate the response of ColicinE2-producing bacteria to external stress. With this combined approach, the model shows that sRNA reduces internal fluctuations and helps controlling the level of CsrA. Moreover, the model predicts stochastically distributed delays between SOS signal and lysis, which is also seen in experiments with the S REP1 strain.
In this section, we extend our previous model [9], taking into account the new experimental findings presented in the main text. In particular, we incorporate the additional regulator ssDNA as well as the different plasmid copy numbers and types. For this step, it is important to know the derivation of the previous, three-component model, which is why we outline the derivation of the previous model as we develop our new model from scratch. For a detailed derivation of the three-component model, we refer the reader to Ref. [9].

Regulatory network
Our goal is to design a stochastic model that enables us to investigate the dynamics of the regulatory networks involved the SOS response and the ensuing synthesis and release of ColicinE2. To this end, we first formulate the interactions of the regulatory components as a set of (deterministic) differential equations, that is, as a mass-action model. This approach disregards any spatial effects and considers the system as well mixed.
Extending our previous study [9], we build a mass-action model for the SOS response, and the regulatory network for ColicinE2 production and release from the following assumptions and properties of the components (see also Fig. S3): • The abundances of long mRNA, CsrA and effective single-bindingsite sRNA (see below) are denoted by M, A and S, respectively. These abundances give the number of free components, that is, the number of long mRNA, CsrA and sRNA molecules that are not bound in a complex. Moreover, P COL and P REP denote the copy number of ColicinE2 and the reporter plasmids, respectively (there is no need to distinguish between the two reporter plasmid types for P REP as they do not occur in the same cell at the same time).
• The response to external stress ("SOS response") is regulated by the LexA/RecA system [1], which we incorporate into our model using the differential equations given in Ref. [2]. This model accounts for the production, degradation and (un)binding of the proteins LexA (L) and RecA (R), the mRNAs they are translated from (M l and M r , respectively), as well as the number of repressed promoters controlling the transcription of these mRNAs (B l and B r , respectively). In this system, LexA acts as repressor: as long as a LexA protein is bound to the promoter region of the RecA or LexA operon, no mRNA is produced. The number of repressed RecA and LexA promoters increases if LexA binds to an unrepressed promoter, and decreases as it unbinds. Therefore, the differential equations for B l and B r contain two terms each: a production term proportional to the abundances of LexA and unrepressed promoters, and a degradation term proportional to the number of repressed promoters. In an E. coli cell, there is only one promoter for each LexA and RecA, which means that B l and B r can take either the values 0 or 1. The differential equations then read where the k ± denote the attachment and detachment rates of LexA to/from the promoter indicated by the subscript. From unrepressed promoters the respective mRNA is transcribed, and hence, the mRNA production depends linearly on the number of unrepressed promoters. Once produced, the mRNA can spontaneously degrade. Therefore, the differential equations for the mRNAs also contain two terms each, and read: where α and δ give the per capita production and degradation rate of the component indicated by the subscript. These mRNAs are translated to RecA and LexA proteins, respectively. Hence, the production terms of the two proteins are proportional to the respective mRNA abundance. The number of proteins decreases by spontaneous degradation. As the abundance of RecA is only affected by these two processes, its differential equation reads: where α R and δ R denote the per capita production and degradation rate of RecA. Since LexA acts as regulator in the LexA/RecA-system, its abundance is also affected by the interactions with the promoters. Consequently, the terms from eqs. (1) and (2) appear in the differential equation for LexA, but with opposite sign. Moreover, in case of an SOS signal, RecA depletes LexA, motivating an additional degradation term bilinear in L and R, with the degradation constant c p . Apart from these interactions with the LexA/RecA-system, LexA is also the repressor of the colicin operon. Therefore, the LexA/RecA SOS response system interacts with the regulatory system of ColicinE2 production and release via B, the number of repressed promoters of the ColicinE2 operon. Its differential equation contains two terms analogous to the LexA and RecA promoters: where the k ± P denote the attachment and detachment rates of LexA repressor to/from the ColicinE2 promoter. Unlike B r and B l , B can take values between 0 and P COL + P REP . The terms from eq. (6) apppear, again with opposite sign, also in the differential equation for LexA, which, altogether, reads where α L and δ L give the per capita production and degradation rate of LexA. For a detailed discussion of these equations, we refer to Ref. [2]. Note that the SOS response system, eqs. (1)- (7), interacts with the ColicinE2 regulatory network only through the parameter B (see also next bullet point).
• The total production rate of long mRNA in the cell is proportional to the number of unrepressed ColicinE2 promoters in the cell. This number is given by the total number of plasmids in the cell, P COL + P REP , minus B, the number of promoters with the repressor LexA bound to it. Hence, the production rate of long mRNA reads where α M is the production rate per unrepressed promoter. Note that considering different plasmid types generalizes our earlier work presented in Ref. [9].
• CsrA is produced at a constant rate, α A .
• The ColicinE2 system has two different regulatory sRNAs: CsrB and CsrC. Apart from having different numbers of CsrA binding sites and slightly different half-lifes, their mode of binding with CsrA is very similar. Hence, we assume that we can describe their regulatory impact by a single effective sRNA with corresponding effective parameters (see Ref. [9] for details). Using effective sRNAs in a mathematical model is indeed supported by experiments, which show that the knock-out of either CsrB or CsrC causes a compensating overproduction of the other sRNA (see the main text, and Ref. [5]). This compensation is a natural consequence of a positive regulatory effect of CsrA abundance to sRNA production (see bullet point below), and highlights the functional equivalence of CsrB and CsrC. In Ref. [9] we also showed that this effective sRNA, which contains N ≈ 10 CsrA binding sites is equivalent to N effective single-binding-site sRNAs. This drastically reduces the mathematical complexity of the model.
• Several studies found that the production of CsrB and CsrC is indirectly regulated by the abundance of CsrA via the BarA/UvrYsystem [3][4][5]. Since the details of this interaction are largely unknown, we model this positive regulation with an sRNA production rate that is a linear function of the CsrA abundance. In addition to this linear term, we also introduce a constant baseline production term, since studies show that sRNAs are also produced (at very low levels) in the absence of free CsrA [5]. Both production terms contain a factor N, as we consider effective single-binding-site sRNAs in our model (see the previous bullet point). The production term of the effective single-binding-site sRNAs thus reads with the baseline production rate α S,0 , the linear coupling coefficient α S,c , and the abundance of CsrA proteins A. Note that we did not consider the positive feedback of CsrA on sRNA production in Ref. [9].
• The degradation rates of long mRNA, CsrA and the effective sRNA are each proportional to their respective abundance, and read δ M M, δ A A and δ S S, respectively.
• CsrA can bind to both long mRNA and the effective sRNA, and thus forms CsrA-long mRNA and CsrA-sRNA complexes (C MA and C SA , respectively). In line with previous studies [12,13] and our threecomponent model [9], we assume that the formation and disassembly of these complexes is much faster than the other processes involved in post-transcriptional regulation. Therefore, we can employ adiabatic elimination, ∂ t C MA ≡ 0 and ∂ t C SA ≡ 0. In Ref. [9], we show that this enables us to combine the formation, disassembly and degradation of the complexes into effective binding parameters, k M and k S . As a consequence, we can solve for the complex abundances, C MA and C SA , and eliminate them from our set of differential equations (see Ref. [9] for details).
• The precise mechanism for the degradation of CsrA-sRNA and CsrAlong mRNA complexes is not known. Here, we assume that CsrA dimers are always degraded once their complex partner is degraded (in other words: CsrA cannot "survive" the degradation of its partner).
• CsrA is a main regulator in growing E. coli cells, which is known to bind to over 700 different targets [14,15]. In the Supplementary Information of Ref. [9] we show how one can eliminate the many targets of CsrA to obtain a reduced system, which contains only the components that are changed by the processes the model focusses on (in this case: SOS-induced production and release of ColicinE2). In the mathematical model presented in this section, we reduce the system to three CsrA targets: long mRNA, sRNA, and (see below) ssDNA. In agreement with experiments [7], the production rate of the effective sRNA is large compared to the production of long mRNA and ssDNA, such that the vast majority of sequestered CsrA proteins is bound to sRNA.
• The short mRNA is not regulated by CsrA, and hence not part of the regulatory network. However, our experiments use the translation of short mRNA (specifically, the translation of the cea gene) as proxy for promoter activity in the S REP1 , S REP2 , C REP1 , and C REP2 strain.
To enable the experimental validation of our model, we include the production of short mRNA in our model. Due to the lack of regulation, the corresponding differential equation is decoupled from M, A and S, and reads (with ∂M short ∂t ≡ ∂ t M short ) where α M short and δ M short are the rate constants for production and per-capita degradation, respectively.

9
The properties and assumptions of the SOS response and the ColicinE2 regulatory system we listed above have already been used (if not stated otherwise) in the combined model for SOS response and ColicinE2 regulation presented in Ref. [9].
ssDNA as regulatory component: In the main text, we show experimentally that single-stranded DNA (ssDNA) serves as a component of post-transcriptional regulation of ColicinE2 production and release. Since this is a novel and, so far, an undocumented role of ssDNA, we briefly discuss how it acts as a regulator for CsrA in an E. coli cell. ssDNA is an intermediate in the rolling circle replication mechanism of the ColicinE2 plasmid: The plasmid consists of double-stranded DNA (dsDNA). The first step in its replication is the production of a ring-shaped ssDNA transcript. These transcripts are produced both in absence and presence of an SOS signal (Fig. S5), which means that ssDNA production is constant. It is assumed that once a ring of ssDNA is completed, it detaches from the plasmid and diffuses freely through the cell. During this time, it is converted to double-stranded DNA, which eventually results in a new plasmid. Between the detachment of the single-stranded ring and the formation of a new plasmid, the ssDNA acts as a regulator of CsrA: Since the ssDNA includes the coding sequences present in the long mRNA, CsrA can bind to the Shine-Dalgarno sequence of the cel gene located on the ssDNA, and thus forms an ssDNA-CsrA complex. This allows the ssDNA to regulate free CsrA levels by sequestration, similar to the CsrA regulation by sRNA. In our mathematical model, we account for these properties of ssDNA as follows: • The production rate of ssDNA is assumed to be proportional to the number of ColicinE2 plasmids, P COL , as it is an intermediate product of the rolling circle replication mechanism of the ColicinE2 plasmid. It reads with the per plasmid production rate constant α D .
• The degradation of ssDNA is proportional to the ssDNA abundance, D, and thus reads with the per capita degradation rate constant is δ D .
• The ssDNA has two binding sites for a CsrA dimer (see Methods of the main text), and thus can form a complex, C DA , with it. Complex formation occurs with rate k + D , and the complexes dissociate into ssDNA and a CsrA dimer with rate k − D . Apart from disassembly, we also include the possibility that a CsrA-ssDNA-complex can spontaneously degrade (meaning that both CsrA and ssDNA are degraded at the same time) by introducing the per capita rate δ DA . The abundance of complexes is denoted by C DA .
Taken together, we can now formulate a set of differential equations, which allows us to quantify these interactions. These interactions are also illustrated as a biochemical network in Fig. S3.
We begin with the differential equation for the time evolution of the long mRNA, M. From the properties collected above, we conclude that this equation must contain three terms: The first term describes the production of long mRNA, which is proportional to the number of unrepressed promoters. This number is calculated from the difference between the total plasmid copy number, P COL + P REP , and the number of repressed promoters, B. The abundance of long mRNA is reduced by a second and a third term: The second term describes the spontaneous degradation of long mRNA, and is proportional to its abundance, M. The third term is bi-linear (that is, it is proportional to A and M) and represents the effective coupled degradation of long mRNA in complexes with CsrA. This term combines the binding of CsrA to long mRNA, the dissociation of this complex, and its degradation in an effective binding parameter k M . The three terms read: The derivation of the effective coupled degradation in the third term is described in detail in Ref. [9]; an analogous derivation for the ssDNA is given below. The B in the first term is determined by the LexA/RecA subsystem of the SOS response, in particular by eq. (6). The differential equation for the time evolution of the effective singlebinding-site sRNA, S, consists of terms very similar to that for long mRNA. Two terms account for spontaneous and effective coupled degradation, respectively, and are structurally the same as in eq. (12). This is due to the fact that the sRNAs regulate CsrA in the same way as CsrA regulates the long mRNA, by forming complexes. The production term is, however, different, and contains two parts: The first part, α S,0 , describes a constant baseline production, which ensures the production of sRNAs in the absence of CsrA. The second part depends linearly on the abundance of free CsrA, and thus accounts for the positive regulatory function of CsrA for the sRNAs. Taken together, these four terms give the differential equation for S: Having described the two partners of CsrA, we now turn to the differential equation for CsrA itself. Again, this equation has a very similar structure to eqs. (12) and (13): An, in this case constant, production term, as well as a term for spontaneous degradation. Here, however, we have more than one coupled degradation term, since CsrA can bind to more than one component: long mRNA (M), sRNAs (S), and ssDNA (D). The effective coupled degradation terms for long mRNA and sRNA are exactly the same as in eqs. (12) and (13), respectively. This reflects the fact that the formation of a long-mRNA/CsrA-or sRNA/CsrA-complex has for both complex partners the same consequence, that is, it reduces the abundance of free CsrA by 1. The coupled degradation part is also responsible for the hierarchical regulation, which we discussed in [9]: The actual regulation target, long mRNA (M), exclusively binds to CsrA; the sRNAs affects the free long mRNA level only indirectly by sequestering the CsrA and thus "regulating the regulator". Moreover, we also have to account for ssDNA/CsrA-complexes. Since we have not derived an effective coupled degradation for this complex yet, we explicitly account for its formation and disassembly. This means that we have to include two terms that account for the decrease of free CsrA due to the formation of ssDNA/CsrA-complexes and the increase of free CsrA when such a complex disassembles. Altogether, the differential equation for CsrA reads where C DA is the abundance of ssDNA/CsrA-complexes, and k ± D the complex binding and disassembly rate, and the terms containing the novel regulator ssDNA are highlighted in red. Note that we consider the ssDNA to have only one binding site for CsrA in our model. We account for the second binding site analogously to the many binding sites of the sRNA, that is by assuming D to be an effective, single binding site ssDNA, with an effective production rate fitted to experimental data.
The two ssDNA terms highlighted in red also appear in the differential equation for D, since the formation and disassembly of ssDNA/CsrAcomplexes in-and decreases also the abundances of ssDNA. The spontaneous degradation is accounted for by a separate degradation term, already known from the differential equations of the other components. The production term of ssDNA is proportional to P COL , the number of ColicinE2 plasmids in the cell, since ssDNA is an intermediate of the ColicinE2 plasmid replication. The differential equation for ssDNA therefore reads We are still left with the dynamics of the ssDNA-CsrA-complexes, C DA . The "production" term of the ssDNA/CsrA-complexes is the binding term already known from eqs. (15) and (14), but in this case with a positive sign. The number of complexes is reduced by complex disassembly, which is accounted for by the term k − D C DA that also appears in eqs. (15) and (14) with a different sign. Apart from complex disassembly, the complexes can be degraded (in the sense that the complexes and their components are destroyed) spontaneously, which is given by a spontaneous degradation term. Taken together, the differential equation for ssDNA reads Effective coupled degradation of ssDNA and CsrA: In the discussion of the ssDNA properties, we saw that ssDNA also has a Shine-Dalgarno sequence, just as the long mRNA. This suggests that we can make the same assumptions for the CsrA-ssDNA-complex as we did for the CsrAlong-mRNA-complex. In the following, we proceed analogously to the simplification of the hierarchical three component model (see Ref. [9]), and assume fast dynamics of complexes. Adiabatic elimination (∂ t C DA ≡ 0) yields with the effective binding parameter By inserting eq. (17) into eqs. (14)-(16), we get our final set of differential equations, which includes all four components: The new regulative component ssDNA acts in the same fashion as the sRNA by binding CsrA. Compared to the original three component system, eqs. (12)- (14), the extension with ssDNA therefore resulted in a system of equations with the same types of terms (source term, spontaneous degradation, coupled degradation). We use eqs. (18)-(21) to study gene expression dynamics for all three different strains. This is done by adjusting the corresponding values for P COL and P REP , see section 3. Moreover, we investigate the impact of ssDNA on the regulation of ColicinE2 production and release.

Parameter values
For the parameters associated with long mRNA, CsrA and the effective sRNA, we adjusted the values that we determined in our previous study ( [9]) according to new measurements. In particular, they were chosen such that they are in accordance with our own experimental measurements (k M and k S ) or other studies (see below). In particular, the rates read (given per E. coli cell volume, and using the shorthand notation "#" for molecule numbers): The three degradation rates (δ M , δ S , δ A ) were determined in previous, experimental studies [5,7]. The production rates (α A , α S,c , α M ) were fitted such that they reproduce component abundances from experimental studies [7]. The baseline production for the sRNAs, α S,0 N, is set to a low value, as only few sRNAs are produced in the absence of CsrA [5]. In Ref. [9] we showed that a Poisson-distributed plasmid copy number gives very similar results to a fixed plasmid copy number. This is due to the fact that plasmid replication happens on larger timescales than the regulatory interactions considered in our model. We retain this simplifying assumption, and set the number of ColicinE2 plasmids constant at P COL = 20, which is the average value [8]. For the reporter plasmids in the C REP1 , C REP2 , S REP1 and S REP2 strains, we take for type 1 the average copy number P REP = 55 [16], and for type 2 the average copy number P REP = 13, which we both also assume constant.
Adding ssDNA dynamics to the system introduces three new effective rates, α D , δ D , and k D . We assume that the ssDNA and the mRNA are equally stable, and therefore use the same degradation rate constants for both: In combination with the K D -value measurements for ssDNA we could determine the coupled degradation constant to Finally, we have to define the value for the production rate constant of ssDNA, α D , which has not been explicitly measured yet. However, our experimental data suggests that ssDNA accumulates abundances about an order of magnitude larger than long mRNA. From fitting the ssDNA production to this rough abundance relation, and also to measured delaytimes, we obtain α D = 7 min −1 · plasmid −1 .
To study the influence of ssDNA on the cea-cel delay, we varied the value of α D between 0 and 9, see Fig. S6 and S7. For the validation of our model, we also tested various values of α S,c and α M (data not shown). These tests showed that, in general, the model is robust to parameter variations, in the sense that changing a parameter value by a few percent only had minor consequences for the resulting delay times and component abundances.

Simulation results
The differential equations eqs. (18)-(21) give, in combination with the SOS response model, eqs. (1)-(7) (see [2]), a description of the regulatory interactions governing ColicinE2 production. They enable us to study steady states and the deterministic dynamics of gene expression for all five strains. However, the SOS response [2] shows an inherent stochasticity: The ColicinE2 promoter is not activated permanently during an SOS signal, but in stochastically appearing bursts of activity. Moreover, most of the regulatory components like long mRNA occur in low abundances, such that also intrinsic demographic fluctuations in the ColicinE2 regulatory system become important. We can study stochastic effects like these by formulating the deterministic dynamics described in eqs. (1)-(7) and eqs. (18)-(21) as a stochastic process. To this end, we consider each component (M, S, A and D, as well as the components of the SOS response system) as random variables that are changed by stochastic events like production or degradation of molecules. Each of these events occurs at an average rate that equals the corresponding term in the mass action model. For instance, the effective coupled degradation of a long mRNA and CsrA happens at a rate k M M · A (see eq. (18)), which decreases both the abundance of long mRNA (M) and the abundance of CsrA (A) by 1. By defining all remaining stochastic production, degradation and binding events in the system this way, we obtain a description of the SOS response and ColicinE2 regulatory system as a stochastic (Markov) process. We then use the Gillespie algorithm [17] to implement the stochastic process as a stochastic simulation. This simulation enables us to produce stochastically correct realisations of the temporal evolution of the system's random variables. The results from sufficiently large ensembles of these realisations is then the basis for the validation of the theory by experimental data.
In our simulations, we followed the scheme already developed in Ref. [9]: We initiate the system in a non-SOS state, where the parameter c p in eq. (6) of the SOS response system (see also Ref. [2]) is set to 0, that is, RecA does not cleave LexA. Therefore, B, the number of unrepressed promoters, is low (1 for S REP2 , 2 for C WT , 3 for C REP2 , 4 for S REP1 , and 5 for C REP1 ). After 200 minutes, we mimic the effect of an SOS signal by increasing the parameter c p , such that RecA catalyses the degradation of LexA, which acts as repressor for the ColicinE2 operon. This has the effect that the production of both long and short mRNA immediately increases. The SOS signal is stopped again at t = 500 minutes. For each set of parameters, this scheme is repeated 2000 times in order to obtain an ensemble of 2000 realisations.
To be able to compare these simulation results with experiments, we have to give an appropriate definition of the cea-cel delay in the simulations. As the beginning of "cea expression", we define the point in time at which the short mRNA level rises to two times its value before the SOS signal started. Our simulations show that the CsrA abundance decreases during the SOS signal, as more CsrA-sequestering long mRNA is produced. Once there is no free CsrA left, we find free long mRNA in the system. We define the first point in time at which more than 8 free long mRNAs exist in the system as "cel expression". This definition accounts for the fact that in general fewer lysis proteins are produced than toxin proteins [8].
In the experiment, the expression of cea and cel are defined by the point in time the respective fluorescence intensity reaches five times its basal (i.e. pre-SOS) level. Therefore, the expression times are determined by the appearance of proteins in the experiment, but by the appearance of mRNAs in the stochastic simulations. We choose the different definition of the delay in the simulations, as the specific biochemical rates of many processes involving the mRNAs and proteins are largely unknown, and have to be fitted according to observed abundances. If we included the translation of short and long mRNA to toxin, lysis and fluorescence proteins used in the experimental study into our model as well, we would add several new parameters that require fitting to our mathematical model, without getting a more precise definition of the thresholds that determine the delay. Moreover, comparing a delay in the production of mRNAs with a delay in the production of proteins is valid in our case, since both fluorescence proteins have very similar maturation times [6], and since we are interested in the relative rather than the absolute times of protein expression.
For the C WT strain, we cannot compare the cea-cel delay-time from our simulations with experimental results due to the lack of reporter plasmids (see main text). To still be able to validate our stochastic simulations with experimental data in this case, we use the time between the beginning of the SOS response and cell lysis (referred to as "lysis time"), which we also measured in experiments (see Fig. S8). The absolute values of the lysis time will differ between our simulations and experiments, as the simulations do not account for maturation times and other processes of equal duration in all three strains. Therefore, we do not compare lysis times themselves, but the differences of the C REP1 and C WT strain's lysis times, which eliminates these constant factors.
In the following, we discuss the results of our stochastic simulations for the experiments presented in the main text.

The role of CsrA
As a first step to validate the mathematical model for the S REP1 strain (that is, with no ssDNA in the system), we test the role of CsrA for the cea-cel delay. The corresponding experiment varied the binding affinity of CsrA to long mRNA, see Fig. 2E in the main text. Specifically, the experiment measured the average cea-cel delay-time for the original S REP1 strain, and stochastic simulations of the model described in eqs. (18)-(21) to study the origin of this difference and the effects of ssDNA production. Moreover, we infer the cea-cel delay in the C WT strain from this analysis, which cannot be measured directly in experiments. To this end, we modelled the five strains in our simulations by setting P COL and P REP to the corresponding values (see Table S5): P COL = 20 and P REP = 0 for C WT , P COL = 20 and P REP = 55 for C REP1 , P COL = 20 and P REP = 13 for C REP2 , P COL = 0 and P REP = 55 for the S REP1 strain, and P COL = 0 and P REP = 13 for the S REP2 strain. For each strain, we simulated 2000 realisations for different ssDNA production rates (α D ) to investigate the role of this novel regulatory component. The results of these simulations are depicted in the form of cea-cel delay-time histograms in Fig. S6, in which we, for a clear and concise discussion, only depict the results for the C REP1 , S REP1 , and C WT strains.
As we showed in section 1, only two factors can in principle be responsible for the different cea-cel delays: The total plasmid copy number, and the production of ssDNA. To separately study the influence of total plasmid copy number in the strains, we first analyse the case of no ssDNA production (α D = 0). The delay-time histograms of the three strains for this case are depicted in the first column of Fig. S6. Comparing the histograms, we find that the total plasmid copy number has a significant effect: The cea-cel delay distribution of the C REP1 strain (75 plasmids in total) has a shorter tail and a more pronounced peak at short lysis times compared to the distribution of the S REP1 strain (55 plasmids in total), and the C WT strain (with only 20 plasmids) shows almost no lysis at all. The average delay-time of the S REP1 strain (68 minutes) is in good agreement with experimental values (see Fig. 2E). For the other strains, however, the results do not match: The C REP1 strain has a mean delay time of 24.1minutes, which is significantly larger than the value we find in our experiments. Our experiments also find that the wild-type indeed does lyse after SOS responses (see Fig. S8), while the histogram of C WT predicts no lysis. These results for α D = 0 show that the plasmid copy number does not suffice to explain the quantitative and (for the wild-type) qualitative behaviour found in our experiments. However, it already accounts for significant differences in the cea-cel delay-time distributions between the strains.
Before we study the additional effects of ssDNA, we discuss the origin of these differences in the cea-cel delay-time distributions. To this end, we consider the time evolution of the average levels of free CsrA and long mRNA, which are depicted for α D = 0 in the first column of Fig. S7. We find for all three strains that, after the initial equilibration, the average number of CsrA molecules remains at a constant value before an SOS response (t < 200 min), which results from the interactions of CsrA with all its binding partners. Before an SOS signal, the three strains exhibit roughly the same average CsrA level. This changes after the response to an SOS signal (200 min < t < 500 min), which reduces the average CsrA level in all three strains: The C REP1 strain, containing 75 plasmids, has the lowest CsrA levels, whereas the wild-type strain with only 20 plasmids has a significantly higher level.
Comparing the CsrA and long mRNA levels with the corresponding ceacel delay-time distributions in Fig. S6 shows that the different cea-cel delay time distributions are correlated with the average levels of free CsrA (and free long mRNA): The lower the average CsrA level during a SOS signal, the shorter the average cea-cel delay-time, and the narrower the delay-time distribution. We can explain this correlation in our mathematical model by the fact that long mRNA production increases in form of stochastic bursts during SOS responses (see section 2). The long mRNAs produced during these bursts must first sequester free CsrA, before their abundance is high enough to produce lysis proteins from it. For the C WT strain, the CsrA level during the SOS response is too high to be sequestered enough by stochastic long mRNA bursts (see Fig. S7 and Fig. S6). For the S REP1 and the C REP1 strain, however, CsrA levels reach a sufficiently low average abundance during an SOS response that stochastic bursts of free long mRNA are possible, and eventually lysis protein is produced. The average level of free CsrA therefore determines the probability and hence the timing of lysis.
In Fig. S7 we can also see that the single trajectories of CsrA abundance differ qualitatively between the three strains: The trajectories of the C REP1 strain show large and abrupt deviations from the mean value, whereas the abundance of CsrA is closer to the mean in the C WT strain. The reason for this difference is the plasmid copy number in each strain: The more plasmids with LexA-regulated promoters, the more CsrA-sequestering elements are produced during an SOS response, and thus the more susceptible the system will be to stochastic bursts in the SOS response, increasing the probability of lysis. We already discussed in the previous paragraph that the number of plasmids also strongly affects the average level of free CsrA, as more plasmids cause a larger average number of promoters to be unrepressed. This effect is due to the fact that the repressor of the ColicinE2 operon, LexA, stochastically binds to and dissociates from the promoter, and thus triggers long mRNA production for short times even in the absence of an SOS signal. The more plasmids present, the larger the number of (transiently) derepressed promoters, and hence the more CsrA-sequestering long mRNA the cell contains. These relations explain the differences in the cea-cel delay between the three strains.
Finally, in order to characterise the additional effect of ssDNA, we consider the plots with ssDNA production (that is, with α D > 0) in Fig. S6. As the ssDNA production rate α D increases from 0, the average delay times in the C REP1 and C WT strain decrease, and also several cells in the C WT strain lyse (see the C WT histogram for α D = 1 in Fig. S6). We attribute this to the fact that increasing α D results in lower average CsrA levels in the C REP1 and C WT strain, see Fig. S7. Consequently, the average cea-cel delay-times in Fig. S6 decrease, and lysis of C WT bacteria becomes possible. The S REP1 strain, which contains no ssDNA-producing ColicinE2 plasmid, but only reporter plasmids, is not affected by the increase of this parameter. The experimentally observed difference in mean delay times of the C REP1 and S REP1 strain occur when the ssDNA production rate reaches α D = 7 (see Fig. S6). At this rate, also the C WT shows a broad cea-cel delay distribution. For the C WT strain, we cannot compare the average cea-cel delay-time from our simulations with experimental results, but have to use the lysis time. For α D = 7, this difference is in the same order of magnitude as the experimental results (see Fig. S8). If the ssDNA production rate becomes too high, large fractions of the cell ensemble lyse even in the absence of an SOS signal, which is not seen for the C REP1 strain in experiments.
Taken together, these results show that the additional sequestration of CsrA by ssDNA is required for cell lysis in the C WT strain, and hence necessary to produce the experimentally observed cea-cel delays. Therefore, ssDNA plays a key role in the regulation of ColicinE2 release.

sRNA knock-out mutants
In the main text we also discuss experiments with different sRNA knockout mutant strains, see Fig. S4. While the two single knock-out cases (no CsrB or no CsrC) are automatically accounted for by the effective sRNA (see the bullet points on sRNA in section 2), the special case of the double sRNA knock-out mutant corresponds to setting α S,0 ≡ α S,c ≡ 0 in eq. (19) of our model. This means that no sRNA would be produced, which is the main CsrA-sequestering element in our mathematical model. Therefore, our model predicts a large abundance of free CsrA for the double sRNA knock-out case, and hence a significantly larger cea-cel delay. However, we do not see this behaviour in our experiments (see Figs. S2 and S4), which in contrast show shorter average cea-cel delay-times in the double knock-out mutant. These experimental results indicate that, in the absence of the two sRNAs, yet unknown regulatory mechanisms become important. In the derivation of our mathematical model (see section 2), we eliminated any subordinate targets for CsrA, and focussed on the main CsrA-sequestering elements in E. coli, the sRNAs CsrB and CsrC [7]. Hence, adjusting our model for the double sRNA knock-out mutant would first require to experimentally investigate the detailed interactions and components of the yet unknown regulatory mechanisms, and then to replace the S component and its interactions correspondingly in the model. As the double knock-out mutant is not part of our investigation of the cea-cel delay-time in the main text, we do not further extend our model for this very special case. In all other strains and mutants discussed in the main text and the Supplementary Information, sRNAs are produced and also are the main CsrA regulator. Therefore, the aforementioned differences between theoretical model and experimental observations that arise with the double sRNA knock-out mutant do not affect any statements we derive for the single knock-out or original strains using our model, eqs. (18)-(21).