Introduction Small noncoding RNAs (sRNAs) have been demonstrated in recent years to play central regulatory roles in prokaryotes and eukaryotes [1–4]. Organisms that use sRNAs in post-transcriptional regulation range from bacteria to mammals. Interestingly, sRNAs are predominantly implicated in regulating critical pathways, such as stress responses in bacteria [5–15], or developmental timing and cell differentiation in plants and metazoans [16,17]. Despite the recent surge of interest in sRNAs, their regulatory role in bacteria has actually been a subject of research for the last several decades. Early on, sRNAs were mainly recognized for their specialized roles in controlling the transposition of insertion elements [18,19], in regulating plasmid copy number during plasmid replication [20–23], and in mediating plasmid maintenance through the toxin-antidote system [24]. Those sRNAs studied are encoded on the antisense strand and in cis with their targets [23,25], to which they bind through perfect base-pairing. This class of sRNAs will be referred to hereafter as antisense RNAs. In accord with their biological functions [25], some of these antisense RNAs are metabolically stable (e.g., the ones controlling transposition [26]), whereas others are very unstable (such as the ones controlling plasmid copy number [27,28]). For the latter, it has been demonstrated that the strength of inhibition is strongly related to the binding rate, rather than the binding affinity, of the antisense RNA and its target [29,30]. Until recently, only a few cases involving regulation by trans-encoded sRNA were known [31,32]. The advent of large-scale experimental techniques [33–36] and bioinformatic methods [35,37–39] has led to the identification and the subsequent verification of numerous such sRNAs in a variety of bacterial species in the past five years. Currently, there are over 70 such sRNAs identified in Escherichia coli [6,8,40]. Like regulatory proteins, these sRNAs can regulate the expression of multiple target genes, and are themselves regulated by one or more transcription factors. They have been implicated in the regulation of important pathways including oxidative response [15], osmotic response [13,32], acid response [9,10], quorum sensing [7], SOS response to DNA damage [11], glucose-phosphate stress[14], and more [5,6,8]. The mechanisms by which trans-acting sRNAs exert their effect are diverse. Most act by binding to the 5′ untranslated region (UTR) of a target mRNA [2,3,6], with specificity achieved through (often imperfect) base-pairing between the two RNA molecules. Upon binding, these sRNAs can reduce the efficiency of translation initiation—e.g., by interfering with ribosomal binding—or the stability of the target mRNA. Among these sRNAs that down-regulate their targets are RyhB (regulator of iron metabolism) [41–44], OxyS (oxidative stress) [15], and MicC and MicF (osmotic stress) [13,32]. In contrast, RprA and DsrA promote translation of their target, rpoS (encoding the stationary phase sigma factor σs) [5], whereas GadY— the only sRNA in E. coli known to bind the 3′-UTR of its target— stabilizes its target [10]. A large class of trans-acting sRNAs bind tightly to the RNA chaperone Hfq, a highly abundant protein that also binds the target mRNA in a number of cases studied [15,45–48]. Binding to Hfq may protect these sRNA molecules from degradation in the absence of their mRNA targets [42,49–51]. Hfq has also been shown to facilitate the pairing of an sRNA with its target mRNA [43,52], leading to the inhibition of translational initiation. In turn, pairing of the sRNA and mRNA exposes both molecules to rapid degradation [42,43,49,53]. Importantly, the interaction between the sRNA and its target is noncatalytic in nature, since a given sRNA molecule may be degraded along with its target, instead of being used to regulate other targets [42]. Some antisense RNAs can also interact with their targets in a noncatalytic fashion. For example, the antisense RNA RNA-OUT forms a highly stable complex with its target RNA-IN, encoding the IS10 transposase [54]. With a half-life of over 2 h for this complex [55,56], the active antisense RNA may be regarded as irreversibly “consumed” by its target once the two bind. A similar stability is shown by CopA and its mRNA target [57], which codes for the R1 plasmid replication initiation protein RepA [28]. Although the extended base-pairing between the antisense RNA and its target eventually exposes the sRNA–mRNA complex to degradation by RNase III, this coupled degradation has little effect on repression itself [56,58]. Thus, for this class of sRNA regulators, repression is implemented by the irreversible sRNA–target complex formation, which is also noncatalytic. The noncatalytic nature of sRNA–target interaction is qualitatively different from the catalytic effect of many protein regulators on the expression of their targets (e.g., protein regulators are not consumed upon regulating their targets). It is then interesting to ask whether sRNA-mediated regulation has special features distinct from protein-mediated regulation. Here we address this question using a combination of experimental and theoretical approaches. First, we describe the results of theoretical analysis that predicts a number of novel features for noncatalytic gene regulation by sRNAs. These features include a tunable threshold-linear expression pattern, a robust noise resistance characteristic, and a built-in capability for hierarchical cross-talk. These predictions are validated by a series of detailed experiments that quantified the regulatory effects exerted by the trans-acting sRNA, RyhB, on several targets in E. coli. We further extended the experiments to characterize the regulatory effect of the antisense RNA, RNA-OUT, to test the prediction that the novel features described above depended only on the noncatalytic nature of gene regulation and not necessarily on the degradation of the regulators themselves. Results Theoretical Analysis of the Noncatalytic Mode of Gene Regulation The noncatalytic nature of sRNA-mediated gene regulation suggests a novel threshold-linear mode of action, by which the expression of a target gene is silenced below a threshold, and is gradually activated above it (Figure 1). Consider first a case where sRNA and mRNA are co-degraded in a one-to-one fashion. In this case, if the transcription rate for the target mRNA (αm) is below that for the sRNA (αs) (Figure 1A), then most of the targets are expected to pair with the sRNAs and be rapidly degraded, as suggested recently by Lenz et al. [7]. Conversely, if the transcription rate of the mRNA exceeds that of the sRNA (Figure 1B), then most of the sRNAs are expected to turnover, whereas the unconsumed mRNAs are free to be translated into proteins. In the latter regime, the expressed protein level would reflect the difference between the two transcription rates. This scenario is summarized by the blue line in Figure 1C, where the steady state mRNA level of the target gene (m) is plotted against its transcription rate (αm). Messenger RNAs are expected to accumulate only if the target transcription rate exceeds the threshold, which is given by the transcription rate of the sRNA αs (vertical dashed line). Figure 1 Threshold-Linear Response of a Target Gene (A) and (B) depict an idealized model for the interaction between mRNAs of a target gene and sRNAs. If the sRNA transcription rate is larger than that of the target (A), then gene expression is silenced, whereas if sRNA is transcribed less efficiently than its target (B), the residual unbound mRNAs code for proteins. (C) Predicted response curve of a target gene. The blue line depicts the idealized threshold-linear mode of regulation in which gene expression is completely silenced if the target transcription rate is below a threshold set by the transcription rate of the sRNA (indicated by the dashed line). Above this threshold, gene expression increases linearly with the difference between the mRNA and sRNA transcription rates. The idealized scenario is expected when binding between sRNA and mRNA occurs extremely rapidly. The red line is the actual response expected according to Equation 2, using the estimated parameters of Table 1, column 3 for αs = 1 nM/min. Table 1 Model Parameters: Definitions and Estimated Values The above qualitative prediction can be formulated quantitatively via a simple kinetic model for sRNA-mediated gene silencing. The model is cast in terms of two mass-action equations [7,59] for the cellular concentrations of the sRNA (s) and its target mRNA (m) In this model, transcription of mRNAs and sRNAs are characterized by the rates αm and αs, and their turnover by rates βm and βs respectively. The coupled degradation between sRNA and its target is described through a second-order kinetic constant k. The levels of Hfq and any endoribonuclease involved are assumed to be at saturation and are not tracked explicitly. The predicted pattern of gene expression is obtained by solving Equation 1 in the steady state, with the steady state mRNA level expressed in terms of the two control variables, αm and αs, and an effective parameter λ = βmβs/k. The latter, being the ratio of the spontaneous and mutual turnover rates, characterizes the rate of mRNA turnover that is not due to the sRNA, and is referred to below as the leakage rate; it is a (inverse) measure of the strength of sRNA–mRNA interaction. For strong, rapid sRNA–mRNA interactions, the leakage rate is small and the solution (Equation 2) is given approximately by In the absence of leakage (i.e., λ = 0), Equation 3 is just the threshold-linear function depicted by the blue line of Figure 1C. For small but finite λ, the mRNA level is somewhat larger, especially near the threshold (where the denominators of the λ terms become small). Thus, leakage makes the transition smoother, as illustrated by the red line of Figure 1C, but does not change the qualitative feature of the threshold-linear form. We note that the value of the threshold (αs) is set by the sRNA transcription rate and is hence a dynamic variable that is controllable by the genetic circuit (rather than a fixed quantity such as the binding affinity encoded by the genomic sequence.) In particular, the threshold value is not affected by the strength of the interaction parameter k (as long as the leakage λ is reasonably small to preserve the threshold-linear form). More generally, it is possible that degradation of the mRNA in the complex does not always lead to the degradation of the sRNA. Suppose that a fraction p k R); see the large k T/k R region of Figure 4C, where the expression of geneT (increasing αT/αR) indirectly activates geneR by relieving the sRNA repression. Conversely, a strongly interacting target (e.g., geneR, with a large k R) is expected to be much less affected by a weakly interacting one (e.g., geneT, with k T < k R). Thus, in the small k T/k R region of Figure 4C, the expression of geneR remains suppressed even when geneT is highly expressed. Interestingly, our calculation predicts that for large k T/k R, the response of geneR to changes in the transcription rate of geneT may be very sharp. For example, the data of Figure 4C allow for an effective Hill coefficient ∼10 for k T/k R ≈ 2. Thus, the sensitivity of the sRNA-mediated repression may be translated into sensitivity in the indirect interaction between its targets. Discussion The “standard model” of gene regulation in bacteria primarily involves transcriptional initiation control by one or more regulatory proteins. Solid understanding of the key mechanistic ingredients of transcriptional regulation [70], stemmed from decades of research in molecular biology, leads to a reasonable quantitative description [71–73]. Although such a framework for sRNA is still lacking, the successful description of our experimental results by the simple kinetic model (Equation 1) for sRNA-mediated regulation prompted us to use this model to compare between the two modes of regulation. sRNA Regulation Is Subject to Dynamic Control Analysis of a simple model of protein-mediated gene regulation (Text S1) predicts that regardless of whether a protein regulator acts as a transcriptional repressor or as a catalyst of mRNA degradation, target expression always increases linearly with the promoter activity. The ratio between expression levels at different concentrations of the regulator is independent of the target activity (Figure 5B). Thus, one can safely talk about the strength of repression in term of the fold-change in gene expression in the presence and absence of the repressor without referring to the rate of target transcription. Figure 5 Comparison between sRNA- and Protein-Mediated Repression (A) Steady-state solution of model (1), with the estimated parameters of Table 1. The strength of sRNA repression decreases as the target transcription increases. (B) Steady-state solution of a model for protein regulators (Supporting Text S1), where the strength of repression is independent of target transcription rate. (C) Temporal behavior in a single stochastic simulation [94] of the expression of two model genes, geneA (blue line) and geneP (red), regulated by sRNA and protein regulators respectively. For geneA we set α A = 1/min and kA = 0.02/min, while for geneP we have αP = 0.0043/min and kP = 0. All other parameters are taken from Table 1 and are identical for both genes. This choice of parameters makes the mean mRNA levels of the two genes equal. The bursty nature of the noise for geneP is compared with the smooth fluctuations exhibited by geneA. This is, however, not the case for the threshold-linear mode that characterizes sRNA-mediated regulation. Here the fold-change depends not only on the presence of the repressor, but also on the transcription of the target (Figure 5A, arrows). For the same degree of repressor transcription (e.g., compare the red and blue lines), the fold repression could be small (e.g., 2-fold) above the threshold and large (e.g., 25-fold) below the threshold. This property may have functional consequences: sRNA may serve to tightly shutdown a gene that is repressed by other means. However, at circumstances that allow for high expression of the target, sRNA expression may exert virtually no effect. Moreover, in the threshold-linear mode of sRNA-mediated gene regulation, the onset of repression is set by comparison of transcription rates between sRNA and its target. As a result, the threshold value is dynamically tunable through controlling the rate of sRNA transcription. In contrast, protein–operator binding affinity, which controls the onset of repression in protein-mediated regulation, is fixed genetically by the operator sequence. Dynamic control of the latter would require other cofactor(s) and auxiliary binding sites and become more elaborate to implement. Of course, the more complex mode of control described here for sRNA can, in principle, be realized through more complex promoters involving more complex protein–protein interactions [74]. Also, features of sRNA-mediated regulation discussed here may also be realized by proteins that regulate the proteolysis of their targets in noncatalytic ways. In the latter case however, the steady co-degradation of protein regulators may pose a substantial metabolic load. In a number of cases studied, a sRNA serves as a node in a regulatory cascade. Expression of the sRNA may be controlled by protein regulator that senses (directly or indirectly) an environmental signal. For example, the Ferric Uptake Regulator (Fur) is activated by free Fe2+ ions and negatively regulates transcription of RyhB, which in turn regulates targets whose expressions are required when Fe2+ is abundant in the cytoplasm [41,60]. Our results suggest that sRNA regulators may be more than a simple “inverter” of such a protein regulator. sRNA regulators could act, for example, as a “stress-relief valve.” In the iron example, whereas Fur senses levels of Fe2+ continuously (through rapid equilibration between Fur and Fur–Fe2+), we predict that targets of RyhB will only be expressed when the Fe2+ level crosses some threshold. This threshold can be set dynamically for each target by regulators controlling its transcription. Recently it has been suggested that targets of microRNA regulation in eukaryotes may be classified as “switch,” “tuning,” and “neutral” targets, depending on their response to microRNA level [75,76]. In the framework presented here, these classes correspond to targets whose transcription rate is well below, near, or well above that of the RNA regulator. We emphasize, however, that the threshold-linear picture we draw is only applicable if the level of the free RNA regulator is affected by its interaction with its targets, i.e., for regulators that operate in the noncatalytic mode. This is yet to be established for microRNAs in eukaryotes. sRNAs May Exhibit Tight Repression of Fluctuations Our model predicts that deep in the repressed state, the sRNAs strongly repress variations in protein expression. The effect of noise on gene expression is a subject of extensive current research [77–80]. We studied this effect theoretically by generalizing the model (Equation 1) to incorporate stochastic fluctuations (Text S1). In Figure 5C, we compare results of stochastic simulations for two genes with the same low mean protein expression: geneA is silenced by a sRNA, and geneP is repressed transcriptionally by a protein regulator. In general, we predict a much-reduced variance in protein level for sRNA-mediated regulation (Text S1). This can be understood by inspecting the time courses of protein expression (Figure 5C). With the protein regulator (red curve), any leakage in transcription is amplified through translation, resulting in large bursts of protein expression, as was recently observed experimentally [81,82]. With the sRNA (blue curve), gene expression is expected to be much smoother, because mRNA molecules are rarely translated. This difference in the noise properties may be very important in situations where a large burst of proteins will switch a cell from one stable state to another. In cases such as stress responses where unintentional entry into the alternative state may be harmful and spontaneous switching is to be avoided, sRNA-mediated regulation might possess a distinct advantage. Attenuation of noise by decreased burst size may also be accomplished by eukaryotic microRNAs [76], through a decrease in mRNA stability or inhibition of translation. sRNA Regulation May Be Highly Sensitive sRNA-mediated regulation was predicted to be ultrasensitive to small changes in sRNA expression near the threshold [7]. A common measure for the abruptness of a transition, referred to as the “sensitivity,” is the maximal slope of the response curve, m(αs), in a double-log plot. From the solution (Equation 2), we find this sensitivity to be given by , which quantifies our statement that lower leakage makes a sharper transition, and also predicts a sharper transition for highly expressed targets. For sRNA regulators described by the parameters of Table 1, we find the sensitivity to be given approximately by 2.5 for αm = 1 nM/min, and 4.3 for αm = 3 nM/min . In comparison, the sensitivity of a protein repressor is bounded by the Hill coefficient, which is typically ≤2, although higher sensitivity (3∼4) can also be accomplished via, e.g., DNA looping [73]. On the other hand, much higher sensitivity can be achieved by processes such as those with zeroth-order kinetics [83]. Hierarchical Cross-Talk between Targets of sRNA Our data demonstrate how the activity of a strong target of RyhB may influence the expression of another target. In particular, we show that over-expression of a plasmid-borne target relieves completely the strong sRNA repression of its chromosomal target. Generalizing our kinetic model offers a simple intuitive picture (Figure S1). A weak sRNA target (geneR) is completely repressed by the sRNA when another, stronger target (geneT, with k T ≫ k R ) is not expressed (Figure S1A). Expression of the latter captures a significant portion of the sRNAs, thus allowing some mRNA molecules of geneR to be translated into proteins (Figure S1B). On the other hand, expression of another target weaker than geneR may not attract enough sRNA to affect the expression of geneR (unpublished data). In the context of a single target, our model predicts that the strength of the sRNA–target interaction influences only the smoothness of the transition, but not the threshold value of the threshold-linear expression pattern. However, when multiple targets are expressed simultaneously, the different mRNA species are expected to compete for association with the same pool of sRNA, and the relative interaction strength becomes a key determinant of the complex interactions that ensue. The interaction strength of the different targets sets their relative position in the cross-talk hierarchy, where targets of a given binding strength affect—but are not affected by—targets of lower binding strength. Through quantitative characterization of gene regulation for two distinct classes of sRNA regulators, we have shown that sRNA-mediated regulation has many functional properties that are fundamentally different from the classical, protein-mediated mode of gene regulations. Analysis of our model suggests that sRNAs may offer tight regulation below the threshold (repressing the average expression and reducing fluctuations) accompanied by derepression away from the threshold. Taken together, this suggests that sRNAs working in the threshold-linear mode may be particularly suitable for a “stress-relief” mechanism, where no action is elicited until a tolerance threshold is exceeded. Knowledge of these properties is essential to an integrated understanding of gene regulatory systems, and may inspire the design and synthesis of novel genetic circuits [84] with properties difficult to obtain by using regulatory proteins alone. Materials and Methods Strains and plasmids. All experiments were performed with BW-RI cells derived from E. coli K-12 BW25113 [85], with the transfer of the spr-lacI-tetR cassette from DH5α-ZI cells [62] by phage P1 transduction. This cassette provides the constitutive expression of lacI and tetR genes [62]. For some experiments, ryhB and/or sodB were deleted from BW-RI [85]. These strains were then transformed by the following target and source plasmids. All strains and plasmids used are summarized in Table 2. pZE12-luc, whose copy number has been estimated at 50–70 copies [62], was used to make the target plasmid pZE12S. Using site-directed mutagenesis, an EcoRI site was created by adding GAAT immediately downstream of +1 of the PLlac-O1 promoter. The region between the newly created EcoRI site and the resident EcoRI site 6 bp upstream of RBS was then deleted by EcoRI digestion and subsequent religation, yielding pZE12-lucM. The KpnI-XbaI flanking luc gene in pZE12-lucM was replaced by the gfpmut3b structure gene [86]. This yields pZE12G, which harbors the PLlac-O1:gfpmut3b construct with a 5′-UTR defined by an EcoRI site immediately downstream of +1 and a KpnI site immediately upstream of the translation start of gfpmut3b. The 15-base sequence sandwiched by the EcoRI and KpnI sites, ATTAAAGAGGAGAAA, contains an RBS indicated by the underlined bases. The 5′-UTR from the control region of sodB (crsodB, from −1 to +88 relative to the transcriptional start site of sodB and including the first 11 codons) was cloned into the EcoRI and KpnI sites of pZE12G, yielding pZE12S. pZE12S therefore contains the ColE1 ori, the PLlac-O1 promoter [62], and crsodB fused to the coding sequence of the gfpmut3b gene. Similarly, the control region of is10in (from +1 to +36) was substituted for crsodB in pZE12S, yielding pZE12IS. To improve the expression level, the RBS in the is10in control region was modified by changing TC (+16 to +17) to GG. Three sRNA-source plasmids (pZA30R, pZA31R, and pZA31O), were derived from the pZA31-luc plasmid, which has been estimated to maintain at 20–30 copies per cell [62]. Each contains the p15A replication ori and is marked by chloramphenicol resistance. First, a NdeI site was added immediately downstream the +1 of the luc gene by inserting ATG between +2 and +3, and a BamHI site was added downstream of luc by inserting ATC between the 1,772th and 1,773th nucleotides, yielding pZA31-lucNB. For pZA31R, the ryhB gene (from +1 to +96 cloned directly from E. coli K-12) was ligated into the NdeI/BamHI sites of pZA31-lucNB, replacing the luc gene. For pZA30R, the PLtet-O1 promoter and the luc gene of pZA31-lucNB were replaced by PryhB:ryhB (from −62 to +96 cloned directly from E. coli K-12 MG1655), which contains the ryhB gene and its native promoter. Finally, for pZA31O, the is10out gene (from +1 to +103) was substituted for the luc gene in pZA31-lucNB. In addition, we transferred the target crsodB-gfp to the attP site of strain ZZS00 (ryhB−) chromosome using the method of Diederich et al. [87]. Briefly, a SalI/BamHI-flanked PLlac-O1: crsodB-gfpmut3b containing the downstream terminator was cloned into the same sites of pLDR10 containing the attachment site attP and encoding the chloramphenicol (Cm) resistance. The recombinant plasmid was digested with NotI and the larger portions of the plasmids containing the fragment of interest but not the ori were religated. The circular DNA molecules were transformed into ZZS00 cells expressing the int gene contained in pLDR8, a helper plasmid bearing a temperature-sensitive ori and encoding the kanamycin (Km) resistance. The transformations were applied on LB+Ap plates that were incubated at 42 °C. The transformants were tested for sensitivity to Cm and Km. The ampicillin (Ap)-resistant but Cm- and Km-sensitive transformants were identified as the clones that carry the DNA fragment of interest at the attP site of E. coli chromosome. Medium, growth, measurements. BW-RI strains each containing the target and/or source plasmids were grown in M63 minimal media with 0.5% glucose, and standard concentrations of the appropriate antibiotics. The overnight cultures were diluted into fresh M63 media (OD600 ≈ 0.002) containing the appropriate antibiotics as well as varying amounts of the inducers (aTc, IPTG, FeSO4) in the wells of 48-well plates. The plates were incubated with shaking at 37 °C and taken for OD600 and fluorescence measurements every hour for up to 12 h (until a final OD600 of 0.2–0.3) using a TECAN Genios-Pro plate reader (http://www.tecan.com). Each measurement was repeated 3–6 times and the data were analyzed as discussed below. For RT-PCR measurements, overnight cultures were used to inoculate M63 medium with 0.5% glucose, standard concentrations of the appropriate antibiotics, and various concentrations of inducers to an initial OD600 of 0.001 and grown in 48-well plates in a 37 °C incubator. OD600 and GFP fluorescence were monitored periodically (if applicable). When OD600 of these cultures reached 0.3–0.5, approximately 109 cells of each culture were harvested in a microcentrifuge at 4 °C, treated with 10 mg/ml lysozyme in TE buffer (pH = 8.0) and total RNA was collected using an Absolutely RNA miniprep kit (Stratagene; http://www.stratagene.com). The prepared samples were then treated with Turbo DNA-free DNase (Ambion; http://www.ambion.com), and PCR controls were performed on each sample to verify the absence of contaminating DNA. cDNA was prepared with 1 μg of RNA from each sample using Superscript III First Strand Synthesis system (Invitrogen; http://www.invitrogen.com). Dilutions of the resulting samples were then used as the template in PCR reactions using iQ SYBR Green Supermix (Bio-Rad; http://www.bio-rad.com) in a Smart Cycler thermal cycler (Cepheid; http://www.cepheid.com). To measure expression from a chromosomal target, cells were grown overnight in minimal media with antibiotics. Cultures were then diluted to OD600 = 0.001, and grown in a 12-well plate with 3 ml of culture in each well, with appropriate antibiotics and inducers. To determine the growth rate, OD600 was measured every 60 min. Cultures were grown at 37 °C with constant shaking until they reach OD600 = 0.3, at which time 1.7 ml of each culture was spun down and resuspended in 1 ml phosphate buffer solution (PBS). GFP fluorescence was measured using a Becton-Dickinson FACSCalibur flow cytometer with a 488-nm argon excitation laser and a 515- to 545-nm emission filter (FL1) at a low flow rate. Photomultiplier tube (PMT) voltage was set to 950 V, and a linear amplifier was set at 9.5×. Forward scatter and fluorescence values were collected for 50,000 cells. Data analysis. To obtain gene expression patterns for the different strains, we averaged (for each time point) the data obtained from the different repeats for each combination of strain and inducers. First, the cell doubling rate (μ) was obtained as the slope of a linear fit of log2(OD600) versus time for each strain and condition; this yielded a doubling time of ∼2 h for most strains. Next, for all of the time points concerning each strain and condition, we plotted the average fluorescence versus average OD600 on linear-linear plot and extracted the slope (f). In Figure S2 we show, for example, GFP fluorescence against OD600 for the ryhB − strain (ZZS21), together with the fitted slopes. Each slope gave the average fluorescence per growing cell (in unit of relative fluorescence units (RFU)/OD) for that strain and the corresponding growth condition. The raw fluorescence production rate per cell was computed as fμ(1 + μτ) [88], upon taking into account of the maturation kinetics of GFPmut3 (maturation half-life τ of ∼30 min) [86]. We then subtracted away from this raw rate the background fluorescence production rate, obtained in the same way from data collected from our negative control strain BW-NULL. This yielded the rate of GFP production synthesis from PLlac-O1, and is referred to as the GFP expression. The results were plotted in Figure S3 at each IPTG level for different levels of RyhB expression, via the PLtet-O1 promoter controlled by the amount of aTc in the growth medium. To fit the experimental data with the steady-state solution (Equation 2), we assume that the GFP expression defined above is proportional to m, the steady-state mRNA level, i.e., GFP expression = bm, where b reflects the rate of GFP translation and maturation. Then, Equation 2 can be written in the following way, where is the GFP expression in the absence of the sRNA, referred to as the promoter activity and set by the IPTG concentration, is proportional to the transcription rate of the sRNA (and therefore takes different values for different experiments); and is proportional to the leakage parameter (defined in Results). The latter is independent of the sRNA activity, and should be chosen once for all experiments. We fitted the data to f(a,a a,a λ) using a standard Levenberg-Marquardt algorithm implemented in MATLAB (MathWorks; http://www.mathworks.com), with the least-square error defined as The values of the best-fit parameters obtained are given in Table S1 in terms of 0.5 confidence intervals. Estimation of model parameters. The values of the model parameters can be estimated from various experiments. Consider first RyhB and its targets [41,42]. In the absence of its targets, the Hfq-bound sRNA RyhB is very stable, with a half-life of ∼30 min [42,49], yielding βs ∼ 1/50 min−1. Similarly, from the half-life of ∼6 min for sodB mRNA [42] in the absence of RhyB, we have βm ∼ 1/10 min−1 . Moreover, DNA microarray experiments [69,89] indicated approximately 10–20 copies/cell for the sdhCDAB and sodB mRNA in rich medium (where iron is abundant and RyhB is expected to be repressed). This suggests a target transcription rate (αm) of ∼ 1 nM/min in the state where mRNA is expressed. In general, αm is controlled by various cellular signals (e.g., sdhCDAB by Crp-cAMP) and can typically vary ∼10-fold. (The DNA microarray study of Zhang et al. [69] showed approximately 5-fold change in sdhCDAB and sodB mRNA levels under various physiological conditions.) On the other hand, the activity of the RyhB promoter has a broad range, since it is strongly regulated by Fur-Fe2+ whose concentration can vary over 1000-fold [61]. We model the latter by allowing αs to take on the range from 0.1/min to 10/min. Finally the coupled degradation rate k can also be deduced from the results of Masse et al. [42] (assuming p of order 1). Because RyhB is shown to disappear in the presence of its targets within 3 min, then by using an estimated target mRNA concentration of 20 nM, we find 1/50 (nM min) −1, which is close to the diffusion-limited association rate for typical small proteins [90,91] and is similar to what has been observed directly for the sRNA OxyS and its target fhlA [92], as well as for the antisense hok/sok pair [93]. Finally, we consider RNA-OUT and its target, the mRNA of is10in. RNA-OUT itself is extremely stable, with a half-life dictated by dilution due to growth βs ∼ 0.02 min−1 [26], while the half-life of is10in mRNA is typical to bacterial mRNA (2–3 min, βm ∼ 0.3 [64]). Binding of RNA-OUT to its target mRNA is characterized by a second-order binding constant in the range of k ∼ 1/50–1/20 (nM min) −1. The pOUT promoter is a typical promoter, and we assume that αs is not very different from that of RyhB [65]. The pIN promoter, on the other hand, is atypically weak, and is only enhanced 10-fold upon methylation [65–67]. Values of the model parameters are summarized in Table 1. Supporting Information Figure S1 Model for Indirect Interaction between Different Targets of a sRNA, in the Case k T ≫ k R When geneT is not expressed, the sRNA silences the expression of geneR. When geneT is expressed, most sRNA molecules bind and degrade with mRNAs of geneT, allowing mRNAs of geneR to be translated into proteins. (63 KB PDF) Click here for additional data file. Figure S2 Example for Raw Data, Used to Compile Figure 2A GFP fluorescence is plotted against OD600 for the RyhB-less strain (ZZS21) containing the plasmid borne PLlac-O1:crsodB-gfp reporter. Lines are given by a linear fit. The slope of each line was used to define the GFP expression. (55 KB PDF) Click here for additional data file. Figure S3 Example for Raw Data, Used to Compile Figure 2A GFP expression for strains (ZZS23) harboring PLtet-O1:ryhB on a plasmid, in addition to the PLlac-O1:crsodB-gfp reporter. The IPTG dependence of GFP expression (defined from plots such as Figure S2) is plotted for different degrees of RyhB expression. The latter is controlled by the level of the inducer aTc in the growth medium as indicated by the legend. (46 KB PDF) Click here for additional data file. Figure S4 Repression Strength of RyhB Depends on the Transcription Rate of the Target The fluorescence levels of cells carrying a plasmid coding for the target, PLlac−O1:crsodB-gfp, was measured as in Figure 2A, for strains ZZS21 (no ryhB) and ZZS23 (plasmid-borne ryhB). The fold of repression (vertical axis) is defined as the ratio between the two. The repression effect of RyhB is diminished at higher levels of IPTG, corresponding to higher transcription rates of the target. (45 KB PDF) Click here for additional data file. Table S1 Best-Fit Parameters of the Data in Figure 2A to Model (Equation 1), Given in Terms of 50% Confidence Interval See Material and Methods for a detailed description of the fitting procedure. (13 KB PDF) Click here for additional data file. Table S2 Best-Fit Parameters of the Data in Figure 3A to Model (Equation 1), Given in Terms of 50% Confidence Interval See Material and Methods for a detailed description of the fitting procedure. (13 KB PDF) Click here for additional data file. Table S3 Naming Scheme for Strains Used in this Study (13 KB PDF) Click here for additional data file. Text S1 Detailed Description of Models and Derivation of Analytical Results (120 KB PDF) Click here for additional data file. Accession Numbers The GenBank (http://www.ncbi.nlm.nih.gov/Genbank/) accession numbers for the genes and gene products discussed in this paper are ryhB (GeneID: 2847761), sodB (GeneID: 944953), fumA (GeneID: 2955664), fur (GeneID: 945295), hfq (GeneID: 948689), oxyS (GeneID: 2847701), micC (GeneID: 2847713), micF (GeneID: 2847742), rprA (GeneID: 2847671), dsrA (GeneID: 946470), rpoS (GeneID: 947210), gadY (GeneID: 2847729).