Phenotypic Heterogeneity in Mycobacterial Stringent Response
Sayantari Ghosh, Kamakshi Sureka, Bhaswar Ghosh, Indrani Bose, Joyoti Basu, Manikuntala Kundu
aa r X i v : . [ q - b i o . S C ] F e b Phenotypic Heterogeneity in Mycobacterial Stringent Response
Sayantari Ghosh , Kamakshi Sureka , Bhaswar Ghosh , Indrani Bose ∗ , Joyoti Basu , Manikuntala Kundu Department of Physics, Bose Institute, Kolkata, India, Department Of Chemistry, Bose Institute, Kolkata, India, Centre for AppliedMathematics and Computational Science , Saha Institute of Nuclear Physics, Kolkata, India ∗ E-mail: [email protected]
AbstractBackground:
A common survival strategy of microorganisms subjected to stress involves the generationof phenotypic heterogeneity in the isogenic microbial population enabling a subset of the population to surviveunder stress. In a recent study, a mycobacterial population of
M. smegmatis was shown to develop phenotypicheterogeneity under nutrient depletion. The observed heterogeneity is in the form of a bimodal distribution ofthe expression levels of the Green Fluorescent Protein (GFP) as reporter with the gfp fused to the promoter ofthe rel gene. The stringent response pathway is initiated in the subpopulation with high rel activity.
Results:
In the present study, we characterise quantitatively the single cell promoter activity of the threekey genes, namely, mprA, sigE and rel , in the stringent response pathway with gfp as the reporter. The origin ofbimodality in the GFP distribution lies in two stable expression states, i.e., bistability. We develop a theoreticalmodel to study the dynamics of the stringent response pathway. The model incorporates a recently proposedmechanism of bistability based on positive feedback and cell growth retardation due to protein synthesis. Basedon flow cytometry data, we establish that the distribution of GFP levels in the mycobacterial population at anypoint of time is a linear superposition of two invariant distributions, one Gaussian and the other lognormal, withonly the coefficients in the linear combination depending on time. This allows us to use a binning algorithmand determine the time variation of the mean protein level, the fraction of cells in a subpopulation and also thecoefficient of variation, a measure of gene expression noise.
Conclusions:
The results of the theoretical model along with a comprehensive analysis of the flow cytometrydata provide definitive evidence for the coexistence of two subpopulations with overlapping protein distributions.
Background
Microorganisms are subjected to a number of stresses during their lifetime. Examples of such stresses are: depletionof nutrients, environmental fluctuations, lack of oxygen, application of antibiotic drugs etc. Microorganisms takerecourse to a number of strategies for survival under stress and adapting to changed circumstances [1–4]. Aprominent feature of such strategies is the generation of phenotypic heterogeneity in an isogenic microbial population.The heterogeneity is advantageous as it gives rise to variant subpopulations which are better suited to persist understress. Bistability refers to the appearance of two subpopulations with distinct phenotypic characteristics [5, 6]. Inone of the subpopulations, the expression of appropriate stress response genes is initiated resulting in adaptation .There are broadly two mechanisms for the generation of phenotypic heterogeneity [7, 8]. In “responsive switching”cells switch phenotypes in response to perturbations associated with stress. In the case of “spontaneous stochasticswitching”, transitions occur randomly between the phenotypes even in the absence of stress. Responsive switchingmay also have a stochastic component as fluctuations in the level of a key regulatory molecule can activate theswitch once a threshold level is crossed [1, 3, 5, 6].The pre-existing phenotypic heterogeneity, an example of the well-known “bet-hedging-strategy”, keeps the pop-ulation in readiness to deal with future calamities. Using a microfluidic device, Balaban et al. [9] have demonstratedthe existence of two distinct subpopulations, normal and persister, in a growing colony of
E. coli cells. The persistersubpopulation constitutes a small fraction of the total cell population and is distinguished from the normal subpop-ulation by a reduced growth rate. Since killing by antibiotic drugs like ampicillin depends on the active growth ofcell walls, the persister cells manage to survive when the total population is subjected to antibiotic treatment. Thenormal cells, with an enhanced growth rate are, however, unable to escape death. Once the antibiotic treatmentis over, some surviving cells switch from the persister to the normal state so that normal population growth isresumed [9, 10]. A simple theoretical model involving transitions between the normal and persister phenotypesexplains the major experimental observations well [9, 11]. In the case of environmental perturbations, Thattai andOudenaarden [12] have shown through mathematical modelling that a dynamically heterogeneous bacterial pop-ulation can under certain circumstances achieve a higher net growth rate conferring a fitness advantage than ahomogeneous one. Mathematical modelling further shows that responsive switching is favoured over spontaneousswitching in the case of rapid environmental fluctuations whereas the reverse is true when environmental perturba-tions are infrequent [7]. Another theoretical prediction that cells may tune the switching rates between phenotypesto the frequency of environmental changes has been verified in an experiment by Acar et al. [13] involving an en-gineered strain of S. cerevisiae which can switch randomly between two phenotypes. The major feature of all suchstudies is the coexistence of two distinct subpopulations in an isogenic population and their interconversions in thepresence/absence of stress. Bistability, i.e., the partitioning of a cell population into two distinct subpopulations1as been experimentally observed in a number of cases [1,3,5]. Some prominent examples include: lysis/lysogeny inbacteriophage λ [14], the activation of the lactose utilization pathway in E. coli [15] and the galactose utilizationgenetic circuit in S. cerevisiae [16], competence development in
B. subtilis [6, 17, 18] and the stringent response inmycobacteria [19].The mycobacterial pathogen
M. tuberculosis , the causative agent of tuberculosis, has remarkable resilienceagainst various physiological and environmental stresses including that induced by drugs [20–22]. On tubercularinfection, granulomas form in the host tissues enclosing the infected cells. Mycobacteria encounter a changed physicalenvironment in the confined space of granulomas with a paucity of life-sustaining constituents like nutrients, oxygenand iron [23, 24]. The pathogens adapt to the stressed conditions and can survive over years in the so-calledlatent state. In vitro too,
M. tuberculosis has been found to persist for years in the latent state characterised bythe absence of active replication and metabolism [25]. Researchers have developed models simulating the possibleenvironmental conditions in the granulomas. One such model is the adaptation to nutrient-depleted stationary phase[26]. The processes leading to the slowdown of replicative and metabolic activity constitute the stringent response.In mycobacteria, the expression of rel initiates the stringent response which leads to persistence. The importance ofRel arises from the fact that it synthesizes the stringent response regulator ppGpp (guanosine tetraphosphate) [27]and is essential for the long-term survival of
M. tuberculosis under starvation [28] and for prolonged life of the bacilliin mice [29].Key elements of the stringent response and the ability to survive over long periods of time under stress are sharedbetween the mycobacterial species
M. tuberculosis and
M. smegmatis [30]. Recent experiments provide knowledge ofthe stress signaling pathway in mycobacteria linking polyphosphate (poly P), the two-component system MprAB,the alternate sigma factor SigE and Rel [31]. In an earlier study [19], we investigated the dynamics of rel-gfp expression ( gfp fused with rel promoter) in
M. smegmatis grown upto the stationary phase with nutrient depletionserving as the source of stress. In a flow cytometry experiment, we obtained evidence of a bimodal distribution inGFP levels and suggested that positive feedback in the stringent response pathway and gene expression noise areresponsible for the creation of phenotypic heterogeneity in the mycobacterial population in terms of the expressionof rel-gfp . Positive feedback gives rise to bistability [5, 6], i.e., two stable expression states corresponding to lowand high GFP levels. We further demonstrated hysteresis, a feature of bistability, in rel-gfp expression. Themathematical model developed by us to study the dynamics of the stringent response pathway predicted bistabilityin a narrow parameter regime which, however, lacks experimental support. In general, to obtain bistability a genecircuit must have positive feedback and cooperativity in the regulation of gene expression. Recently, Tan et al. [32]have proposed a new mechanism by which bistability arises from a noncooperative positive feedback circuit andcircuit-induced growth retardation. The novel type of bistability was demonstrated in a synthetic gene circuit.The circuit, embedded in a host cell, consists of a single positive feedback loop in which the protein product X ofa gene promotes its own synthesis in a noncooperative fashion. The protein decay rate has two components, thedegradation rate and the dilution rate due to cell growth. In the circuit considered, production of X slows downcell growth so that at higher concentrations of X, the rate of dilution of X is reduced. This generates a secondpositive feedback loop since increased synthesis of X proteins results in faster accumulation of the proteins so thatthe protein concentration is higher. The combination of two positive feedback loops gives rise to bistability in theabsence of cooperativity. A related study by Klumpp et al [33] has also suggested that cell growth inhibition by aprotein results in positive feedback.
Results
In this paper, we develop a theoretical model incorporating the effect of growth retardation due to protein synthesis[32, 34]. We provide some preliminary experimental evidence in support of the possibility. In our earlier study [19],bimodality in the rel-gfp expression levels was observed. As a control, GFP expression driven by the constitutive hsp60 promoter was monitored as a function of time. A single bright population was observed at different times ofgrowth (Figure S4 of [19]). The unimodal rather than bimodal distribution ruled out the possibility that clumpingof mycobacterial cells and cell-to-cell variation of plasmid copy number were responsible for the observed bimodalfluorescence intensity distribution of rel promoter driven GFP expression. In the present study, we perform flowcytometry experiments to monitor mprA-gfp and sigE-gfp expression levels. The distribution of GFP levels in eachcase is found to be bimodal. We determine the probability distributions of the two subpopulations associated withlow and high expression levels at different time points in the three cases of mprA-gfp , sigE-gfp and rel-gfp expression.In each case, the total distribution is a linear combination of two invariant distributions with the coefficients in thelinear combination depending on time. The results of hysteresis experiments are also reported.2 prA mprBMprA MprB MprB−PMprA−P sigE SigE rel Rel PPP mprAB
Phospho−transferpoly−Pppk1 [Phosphate Starvation]sigE relMprB
Figure 1. Schematic diagram of the stringent response pathway in
M. smegmatis activated undernutrient depletion.
MprB-P and MprA-P are the phosphorylated forms of MprB and MprA respectively. PolyP serves as the phosphate donor in the conversion of MprB to MprB-P.
Mathematical modeling of the stress response pathway
Figure 1 shows a sketch of the important components of the stress response pathway in
M. smegmatis subjected tonutrient depletion [19, 31]. The operon mprAB consists of two genes mprA and mprB which encode the histidinekinase sensor MprB and its partner the cytoplasmic response regulator MprA respectively. The protein pair respondsto environmental stimuli by initiating adaptive transcriptional programs. Polyphosphate kinase 1 (PPK1) catalysesthe synthesis of polyphosphate (poly P) which is a linear polymer composed of several orthophosphate residues.Mycobacteria possibly encounter a phosphate-limited environment in macrophages. Sureka et al. [31] proposedthat poly P could play a critical role under ATP depletion by providing phosphate for utilisation by MprAB. Arecent experiment [34] on a population of
M. tuberculosis has established that the MTB gene ppk1 is significantlyupregulated due to phosphate starvation resulting in the synthesis of inorganic poliphosphate (poly P). The two-component regulatory system SenX3-RegX3 is known to be activated on phosphate starvation in both
M. smegmatis [35] and
M. tuberculosis [34]. In the latter case, RegX3 has been shown to regulate the expression of ppk1 , afeature expected to be shared by
M. smegmatis . In both the mycobacterial populations, poly P regulates thestringent response via the mprA-sigE-rel pathway [31]. In our experiments, nutrient depletion possibly gives riseto phosphate starvation. On activation of the mprAB operon, MprB autophosphorylates itself with poly P servingas the phosphate donor [31, 34]. The phosphorylated MprB-P phosphorylates MprA via phosphotransfer reactions.There is also evidence that MprB functions as a MprA-P (phosphorylated MprA) phosphatase. MprA-P binds thepromoter of the mprAB operon to initiate transcription. A positive feedback loop is functional in the signalingnetwork as the production of MprA brings about further MprA synthesis. The mprAB operon has a basal level ofgene expression independent of the operation of the positive feedback loop. Once the mprAB operon is activated,MprA-P regulates the transcription of the alternate sigma factor gene sigE , which in turn controls the transcriptionof rel . We construct a mathematical model to study the dynamics of the above signaling pathway. The new featureincluded in the model takes into account the possibility that the production of stress-induced proteins like MprAand MprB slows down cell growth. This effectively generates a positive feedback loop as explained in Refs. [32, 34].Figure 2(a) shows the mean amount of GFP fluorescence in the total mycobacterial population as measured in aflow cytometry experiment ( mprA promoter fused with gfp ) versus time. Figure 2(a) shows the specific growth rateof the cell population versus time. The inset shows the experimental growth curve for the mycobacterial population.The growth was monitored by recording the absorbance values at 600 nm spectrophotometrically (see Methods).The specific growth rate at time t is given by N ( t ) dN ( t ) dt where N ( t ) is the number of mycobacterial cells at time t . Nutrient depletion limits growth and proliferation and culminates in the activation of stress response genes. Itappears that in many cases rapid growth and stress response are mutually exclusive so that the production of a3 To t a l M ea n x G F P Time (h)
20 30 40 50 60-0.050.000.050.100.150.200.250.300.350.40 O . D . Time (h) MprA
Figure 2. Growth retardation due to protein synthesis. (a) Mean amount of GFP fluorescence in the caseof mprA promoter fused with gfp and (b) specific growth rate µ of mycobacterial population versus time in hours(h).stress response protein gives rise to a slower growth rate [36]. The balance between the expressions of growth-related and stress-induced genes determines the cellular phenotype with respect to growth rate and stress response.Persister cells in both E. coli [9, 10] and mycobacteria [21, 22] have slow growth rates. In the case of
M. smegmatis ,we have already established that the slower growing persister subpopulation has a higher level of Rel, the initiatorof stringent response, as compared to the normal subpopulation [19]. The new addition to our mathematicalmodel [19] involves nonlinear protein decay rates arising from cell growth retardation due to protein synthesis. Webriefly discuss the possible origins of the nonlinearity and its mathematical form [32, 34]. The temporal rate ofchange of protein concentration is a balance between two terms: rate of synthesis and rate of decay. The decay rateconstant ( γ eff ) has two components: the dilution rate due to cell growth ( µ ) and the natural decay rate constant( γ ), i.e., γ eff = µ + γ where µ is the specific growth rate. In many cases, the expression of a protein results in cellgrowth retardation [32, 34]. The general form of the specific growth rate in such cases is given by µ = φ θx (1)where x denotes the protein concentration and φ, θ are appropriate parameters. In Ref. [32], the expression for µ (Eq. (1)) is arrived at in the following manner. The Monod model [37] takes into account the effect of resource ornutrient limitation on the growth of bacterial cell population. The rate of change in the number of bacterial cells is dNdt = µN (2)where the specific growth rate µ is given by µ = µ max sk + s (3)In (3), s is the nutrient concentration and k the half saturation constant for the specific nutrient. When s = k ,the specific growth rate attains its half maximal value ( µ max is the maximum value of specific growth rate). Themetabolic burden of protein synthesis affecting the growth rate is modeled by reducing the nutrient amount s by ǫ ,i.e., µ = µ max ks (1 − ǫ ) (4)The magnitude of ǫ is assumed to be small and proportional to the protein concentration x . Following theprocedure outlined in the Supplementary Information of [32], namely, applying Taylor’s expansion to (4) andputting ǫ = λx ( λ is a constant), one obtains the expression in Eq. (1) with φ = µ max ss + k and θ = kλs + k . Thus,the decay rate of proteins has the form − γ eff x = − ( γ + µ ) x where µ is given by Eq. (1). There are alternativeexplanations for the origin of the nonlinear decay term, e.g., the synthesis of a protein may retard cell growth if itis toxic to the cell [33]. In the case of mycobacteria, there is some experimental evidence of cell growth retardationbrought about by protein synthesis. The response regulator MprA has an essential role in the stringent response4 x GFP
Figure 3. Specific growth rate µ versus GFP fluorescence intensity x GF P fitted with an expressionsimilar to that given in Eq. (1).
The values of µ GF Pmax and θ GF P are µ GF Pmax = 0 .
94 and θ GF P = 0 . mprA insertion mutant resulted in reduced persistence in a murine model but the growth of the mutant was proved to besignificantly higher than that observed in the cases of the wild-type species [38, 39].Our experimental data (Figure 3) provide further support to the hypothesis that MprA synthesis leads to reducedspecific growth rate. The data points represent GFP fluorescence intensity with gfp fused to the mprA promoter.The GFP acts as a reporter of the mprA promoter activity culminating in MprA (also MprB) synthesis. The datapoints shown in Figure 3 are those that correspond to the growth period of 16-23 hours in Figure 2.The data points are fitted by an expression similar to that in Eq. (1) with µ GF Pmax = 0 .
94 and θ GF P = 0 . Bimodal Expression of mprA , sigE and rel in M. smegmatis
In the earlier study [19], we investigated the dynamics of rel transcription in individual cells of
M. smegmatis grown in nutrient medium up to the stationary phase, with nutrient depletion serving as the source of stress. Weemployed flow cytometry to monitor the dynamics of green fluorescent protein (GFP) expression in
M. smegmatis harboring the rel promoter fused to gfp as a function of time. The experimental signature of bistaility lies inthe coexistence of two subpopulations. We now extend the study to investigate the dynamics of mprA and sigE transcription in individual
M. smegmatis cells in separate flow cytometry experiments. Figures 4(a) and (b) showthe time course of mprA -GFP and sigE -GFP expressions respectively as monitored by flow cytometry. In both thecases, the distribution of GFP-expressing cells is bimodal indicating the existence of two distinct subpopulations.In each case, the cells initially belong to the subpopulation with low GFP expression. The fraction of cells withhigh GFP expression increases as a function of time. The two subpopulations with low and high GFP expression5 igure 4. Time course of (a) mprA-gfp and (b) sigE-gfp expression.
M. smegmatis harboring theappropriate promoter construct was grown for different periods of time (indicated in hours (h)) and the specificpromoter-driven expression of GFP was monitored by flow cytometry. With time, there is a gradual transitionfrom the L to the H subpopulation.are designated as L and H subpopulations respectively. In the stationary phase, the majority of the cells belong tothe H subpopulation. The presence of two distinct subpopulations confirms the theoretical prediction of bistability.We analysed the experimental data shown in Figure 4 and found that at any time point the distribution P ( x, t )of GFP levels in a population of cells is a sum of two overlapping and time-independent distributions, one Gaussian( P ( x )) and the other lognormal ( P ( x )), i.e., P ( x, t ) = C ( t ) P ( x ) + C ( t ) P ( x ) (5)The coefficients C i ’s (i=1, 2) depend on time whereas P ( x ) and P ( x ) are time-independent. The general formsof P ( x ) and P ( x ) are, P ( x ) = exp ( − ( x − x w ) ) w p π (6) P ( x ) = exp ( − ( lnx − x w ) ) x w √ π (7)Figures S2(a) and (b) in Additional File 1 illustrate the typical forms of the Gaussian and lognormal dis-tributions. The Gaussian distribution has a symmetric form whereas the lognormal distribution is asymmetricand long-tailed. Figure 5 shows the experimental data for cell count versus GFP fluorescence intensity at se-lected time points in the cases when gfp is fused with mprA and sigE promoters in separate experiments. Thedotted curves represent the individual terms in the r.h.s. of Eq. (5) and the solid curve denotes the linear com-bination P ( x, t ). The different parameters of P ( x ) and P ( x ) have the values x = 97 . . , w =103 . . , x = 5 . . , w = 0 . . gfp is fused with mprA ( sigE ). The ratioof the coefficients, C ( t ) /C ( t ), has the value listed by the side of each figure. Figure S3 displays a similar analysisof the experimental data when gfp is fused to the rel promoter.In the earlier study [19], the total cell population was divided into L and H subpopulations depending on whetherthe measured GFP fluorescence intensity was less or greater than a threshold intensity. In the present study, wehave obtained approximate analytic expressions for the distributions of GFP fluorescence intensity in the L and Hsubpopulations. The two distributions, Gaussian and lognormal, have overlaps in a range of fluorescence intensityvalues (Figure 5 and Figure S3 in Additional File 1). We next used the binning algorithm developed by Chang etal. [42] to partition the cells of the total population into two overlapping distributions, one Gaussian (Eq. (6)) and6 (cid:13) 100(cid:13) 200(cid:13) 300(cid:13) 400(cid:13) 500(cid:13)0(cid:13)100(cid:13)200(cid:13)300(cid:13)400(cid:13)500(cid:13) C e ll C oun t (cid:13) (cid:13)mprA 4hrs(cid:13) c(cid:13) /c(cid:13) = 40.93(cid:13) (cid:13)SigE 4hrs(cid:13) c(cid:13) /c(cid:13) = 10.82(cid:13) C e ll C oun t (cid:13) (cid:13)mprA 16hrs(cid:13) c(cid:13) /c(cid:13) = 3.294(cid:13) (cid:13)SigE 16hrs(cid:13) c(cid:13) /c(cid:13) = 3.157(cid:13) C e ll C oun t (cid:13) (cid:13)mprA 22hrs(cid:13) c(cid:13) /c(cid:13) = 0.676(cid:13) (cid:13)SigE 22hrs(cid:13) c(cid:13) /c(cid:13) = 0.721(cid:13) GFP Fluorescence Intensity(cid:13) C e ll C oun t (cid:13) (cid:13)mprA 48hrs(cid:13) c(cid:13) /c(cid:13) = 0.163(cid:13) GFP Fluorescence Intensity(cid:13) (cid:13)SigE 48hrs(cid:13) c(cid:13) /c(cid:13) = 0.105(cid:13)
Figure 5. Fitting of data with two distributions.
Experimental data for cell count versus GFP fluorescenceintensity at selected time points when gfp is fused with mprA and sigE promoters respectively. The solid curverepresents P ( x, t ) in equation (5) and the dotted curves are the individual terms on the r.h.s.7he other lognormal (Eq. (7)). At time t, let N(t) be the total number of cells. For each cell, the data x j for thefluorescence intensity is used to calculate the ratios, g ( x j ) = P ( x j ) P ( x j ) + P ( x j ) , g ( x j ) = P ( x j ) P ( x j ) + P ( x j ) (8)where P ( x ) and P ( x ) are the distributions in Eqs. (6) and (7). A random number r is generated and the cell j is assigned to the L subpopulation if 0 ≤ r < g ( x j ) , the cell belongs to the H subpopulation otherwise. Oncethe total population is partitioned into the L and H subpopulations, one can calculate the following quantities: ω i ( t ) = N i ( t ) N ( t ) ( i = 1 , µ i ( t ) = X x ji ( t ) /N i ( t ) (9) σ i ( t ) = X ( x ji ( t ) − µ i ( t )) / ( N i ( t ) − i = 1 , ω i ( t ) is the fraction of cells in the i th subpopula-tion at time t, µ i ( t ) is the mean fluorescence intensity for the i th subpopulation and σ i ( t ) the associated variance.Figure 6 shows the results of the data analysis. Figure 6(a) shows the plots of mean GFP fluorescence level forthe L subpopulation (basal level) versus time in the three cases of gfp fused with the promoters of mprA , sigE and rel respectively. Figure 6(b) displays the data for the fractions of cells, ω ( t ) , versus time in the three casesand Figure 6(c) shows the transition rate versus time along with the coefficients of variation CV (CV= standarddeviation/mean) of the protein levels in the L subpopulation versus time.Figure S4 (Additional File 1) shows the plots of mean GFP fluorescence level for the total population versus timein the three cases of gfp fused with the promoters of mprA , sigE and rel respectively. As in the case of the basallevel versus time data (Figure 6(a)), the plots are sigmoidal in nature. We solved the differential equations of thetheoretical model described in Additional File 1 and obtained the concentrations of MprA, MprB, SigE, MprA-P,MprB-P and GFP versus time. Some of these plots are shown in Figure S5 (Additional File 1) and reproduce thesigmoidal nature of the experimental plots. We note that the sigmoidal nature of the curves is obtained only whenthe non-linear nature of the degradation rate is taken into account.As we have already discussed, the distribution of GFP levels in the mycobacterial cell population is a linearcombination of two invariant distributions, one Gaussian and the other lognormal, with only the coefficients in thelinear combination dependent on time. Friedman et al. [43] have developed an analytical framework of stochasticgene expression and shown that the steady state distribution of protein levels is given by the gamma distribution.The theory was later extended to include the cases of transcriptional autoregulation as well as noise propagation in asimple genetic network. While experimental support for gamma distribution has been obtained earlier [44], a recentexhaustive study [45] of the E. coli proteome and transcriptome with single-molecule sensitivity in single cells hasestablished that the distributions of almost all the protein levels out of the 1018 proteins investigated, are well fittedby the gamma distribution in the steady state. The gamma distribution was found to give a better fit than thelognormal distribution for proteins with low expression levels and almost similar fits for proteins with high expressionlevels. We analysed our GFP expression data to compare the fits using lognormal and gamma distributions. For allthe three sets of data ( gfp fused with the promoters of mprA , sigE and rel ), the lognormal and gamma distributiongive similar fits at the different time points. Figure S6 (Additional File 1) shows a comparison of the fits for thecase of gfp-mprA . The lognormal appears to give a somewhat better fit than the gamma distribution, specially atthe tail ends. Hysteresis in gfp expression
Some bistable systems exhibit hysteresis, i.e., the response of the system is history-dependent. In the earlier study,experimental evidence of hysteresis was obtained with gfp fused to the promoter of rel . The experimental procedurefollowed for the observation of hysteresis is as follows. In PPK-KO, the ppk1 knockout mutant, the ppk1 gene wasintroduced under the control of the tet promoter. We grew PPK-KO carrying the tetracycline-inducible ppk1 and rel-gfp plasmid in medium with increasing concentration of tetracycline (inducer). For each inducer concentration,the distribution of cells expressing gfp was analysed by flow cytometry in the stationary phase (steady state) andthe mean GFP level was measured. A similar set of experiments was carried out for decreasing concentrationsof tetracycline. In the present study, hysteresis experiments in the manner described above were carried out inthe two cases of gfp fused to mprA and sigE promoters respectively. Figure 7 shows the hysteresis data (mean8 (cid:13) 10(cid:13) 20(cid:13) 30(cid:13) 40(cid:13) 50(cid:13) 60(cid:13)90(cid:13)100(cid:13)110(cid:13)120(cid:13)130(cid:13)140(cid:13)150(cid:13) B a s a l Le v e l M ean (cid:13) Time (h)(cid:13)
MprA(cid:13) w (cid:13) (cid:13) Time (h)(cid:13)
MprA(cid:13) C V , L s ubpopu l a t i on (cid:13) Time (h)(cid:13) T r an s i t i on R a t e (cid:13) Time (h)(cid:13) B a s a l Le v e l M ean (cid:13) SigE(cid:13)
Time (h)(cid:13) w (cid:13) (cid:13) SigE(cid:13) T r an s i t i on R a t e (cid:13) C V , L s ubpopu l a t i on (cid:13) Time (h)(cid:13) (a)(cid:13) B a s a l Le v e l M ean (cid:13) Time (h)(cid:13)
Rel(cid:13) (b)(cid:13) w (cid:13) (cid:13) Time (h)(cid:13) Rel(cid:13) C V , L s ubpopu l a t i on (cid:13) T r an s i t i on R a t e (cid:13) Time (h)(cid:13) (c)(cid:13)
Figure 6. Analysis of the time course of gfp expression. (a) Mean protein level in L subpopulation (basallevel) versus time in hours in the three cases of gfp fused with mprA, sigE and rel promoters respectively. (b)Fraction of cells ω (t) in the H subpopulation versus time in hours in the three cases. (c) Transition rate from theL to the H subpopulation and the CV of the protein levels in the L subpopulation versus time in hours in thethree cases. The experimental data are analysed using binning algorithm to obtain the plots (a), (b) and (c).9 (cid:13) 5(cid:13) 10(cid:13) 15(cid:13) 20(cid:13) 25(cid:13)0(cid:13)20(cid:13)40(cid:13)60(cid:13)80(cid:13)100(cid:13)120(cid:13) Inducer Concentration (nM)(cid:13) M ean G F P F l uo r e sc en c e (cid:13) (a) M ean G F P F l uo r e sc en c e (cid:13) Inducer Concentration (nM)(cid:13) (b)
Figure 7. Hysteresis in gfp expression . The gene gfp is fused with (a) mprA and (b) sigE promoter. Filledtriangles and squares represent the experimental data of mean GFP fluorescence with increasing and decreasingconcentrations of tetracycline inducer respectively.GFP fluorescence versus inducer concentration) in the two cases for increasing (branch going up) and decreasing(branch going down) inducer concentrations. The existence of two distinct branches is a confirmation of hysteresisin agreement with theoretical predictions (Figures S1 A-C). Figure 8 shows the GFP distributions in the stationaryphase for two sets of experiments with different histories, one in which the inducer concentration is increased fromlow to a specific value (indicated as “Low” in black) and the other in which the same inducer concentration isreached by decreasing the inducer concentration from a high value (indicated as “High” in red). The distributionsshow that two regions of monostability are separated by a region of bistability. In the cases of monostability, thedistributions with different histories more or less coincide. In the region of bistability, the distributions are distinctindicating a persistent memory of initial conditions.
Discussion
The development of persistence in microbial populations subjected to stress has been investigated extensively inmicroorganisms like
E. coli and mycobacteria [9, 10, 21, 22, 28, 29]. In an earlier study [19], we demonstrated theroles of positive feedback and gene expression noise in generating phenotypic heterogeneity in a population of
M.smegmatis subjected to nutrient depletion. The heterogeneity was in terms of two distinct subpopulations designatedas L and H subpopulations. The subpopulations corresponded to persister and non-persister cell populations withthe stringent response being initiated in the former. In the present study, we have undertaken a comprehensivesingle cell analysis of the expression activity of the three key molecular players in the stringent response pathway,namely, MprA, SigE and Rel. This has been done by fusing gfp to the respective genes in separate experimentsand monitoring the GFP levels in a population of cells via flow cytometry. The distribution has been found to bebimodal in each case.In our earlier study [19], with only the positive autoregulation of the mprAB operon taken into account, bista-bility was obtained in a parameter regime with restricted experimental relevance. The inclusion of the effectivepositive feedback loop due to growth retardation by protein synthesis gives rise to a considerably more extendedregion of bistability in parameter space. The persister cells with high stringent response regulator levels are knownto have slow growth rates [21,22,28,29]. This is consistent with the view that stress response diverts resources fromgrowth to stress-related functions resulting in the slow growth of stress-resistant cells [36]. Figures 2 and 3 provideexperimental evidence that the mean intensity of GFP fluorescence monitoring mprA-gfp expression increases withtime while the specific growth rate µ of the M. smegmatis population decreases in the same time interval. Thereciprocal relationship between the two quantities is represented by an expression similar to that in Eq. (1). Sinceour knowledge of the detailed genetic circuitry involved in the stringent response is limited, we have not attemptedto develop a model to explain the origin of cell growth retardation due to protein synthesis. Further experiments(e.g., sorting of the mycobacterial cell population into two subpopulations) are needed to provide conclusive evi-dence that increased protein synthesis retards cell growth. The stringent response pathway involving MprA and10 igure 8. Hysteresis via GFP distributions.
The distributions in the stationary phase with two differenthistories (see text) when gfp is fused with (a) mprA and (b) sigE promoter. The specific inducer concentrationsare mentioned with each plot.MprB is initiated when the mycobacterial population is subjected to stresses like nutrient depletion. There isnow experimental evidence of complex transcriptional, translational, and posttranslational regulation of SigE inmycobacteria [46–49]. A double positive feedback loop arises due to the activation of transcription initiation of sigE by MprA-P and the activation of the transcription of the mprAB operon by the SigE-RNAP complex. Post-translational regulation of SigE is mediated by RseA, an anti-sigma factor. Barik et al. [49] have identified a novelpositive feedback involving SigE and RseA which becomes functional under surface stress. More experiments needto be carried out to obtain insight on the intricate control mechanisms at work when mycobacteria are subjectedto stresses like nutrient deprivation. This will lead to a better understanding of the major contributory factorstowards the generation of phenotypic heterogeneity in mycobacterial populations subjected to stress.
Conclusions
In the present study, we have characterised quantatively the single cell promoter activity of three key genes in thestringent response pathway of the mycobacterial population
M. smegmatis . Under nutrient depletion, a “responsiveswitching” occurs from the L to the H subpopulation with low and high expression levels respectively. A compre-hensive analysis of the flow cytometry data demonstrates the coexistence of two subpopulations with overlappingprotein distributions. We have further established that the GFP distribution at any time point is a linear super-position of a Gaussian and a lognormal distribution. The coefficients in the linear combination depend on timewhereas the component distributions are time-invariant. The Gaussian and lognormal distributions describe thedistribution of protein levels in the L and H subpopulations respectively. The two distributions overlap in a rangeof GFP fluorescence intensity values. We also find that the experimental data for the H subpopulation can be fittedvery well by the gamma distribution though the lognormal distribution gives a slightly better fit. In the case ofskewed positive data sets, the two distributions are often interchangeable [50]. An analytical framework similarto that in Ref. [43] is, however, yet to be developed for the mycobacterial stringent response pathway studied inthe paper. The major components in the pathway are the two-component system mprAB and multiple positivefeedback loops. The two-component system is known to promote robust input-output relations [51] and persistenceof gene expression states [52] which may partly explain the good fitting of the experimental data by well-knowndistributions. Further quantitative measurements combined with appropriate stochastic modeling are needed tocharacterise the experimentally observed subpopulations more uniquely. We used the binning algorithm developed11n [42] to partition the experimental cell population into the L and H subpopulations. This enabled us to computequantities like the mean protein level in the L subpopulation, the fraction of cells in the H subpopulation and theCV of GFP levels in the L subpopulation as a function of time. The picture that emerges from the analysis ofexperimental data is that of bistability, i.e., the coexistence of two distinct subpopulations and stochastic transitionsbetween the subpopulations resulting in the time evolution of the fraction of cells in the H subpopulation. As pointedout in the earlier study [19], the rate of transition to the H subpopulation and the CV of the L subpopulation levelsattain their maximum values around the same time point (Figure 5(c)) indicating the role of gene expression noisein bringing about the transition from the L to the H subpopulation. We have not attempted to develop theoreticalmodels describing the time evolution of the relative weights, ω i ’s ( i = 1 , Methods
Strains
M. smegmatis mc
155 was grown routinely in Middle Brook (MB) 7H9 broth (BD Biosciences) medium supple-mented with 2% glucose and 0.05% Tween 80.
Construction of plasmids for fluorescence measurements
The mprAB promoter was amplified from the genomic DNA of
M. smegmatis using the sense and antisense primers,5’-AA
GGTACC
GCGCAACACCACAAAAAGCG-3’ and 5’-TA
GGATCC
AGTTTTGACTCACTATCTGAG-3’respectively and cloned into the promoter-less replicative gfp vector pFPV27 between the KpnI and BamHI sites(in bold). The sigE and rel promoters fused to gfp have been described earlier [19, 31]. The resulting plasmidswere electroporated into
M. smegmatis mc
155 for further study. For the study of hysteresis, expression of ppk1 under a tetracycline-inducible promoter in an
M. smegmatis strain inactivated in the ppk1 gene (PPK-KO), hasbeen described earlier [19].
FACS analysis
M. smegmatis cells expressing different promoters fused to GFP were grown in medium supplemented with kanamycin(25 µg/ml ) and analysed at different points of time on a FACS Caliber (BD Biosciences) flow cytometer as describedearlier [19]. Briefly, cells were washed, resuspended in PBS and fluorescence intensity of 20,000 events was measured.The data was analyzed using Cell Quest Pro (BD Biosciences) and WINMIDI software. The flow cytometry datais represented in histogram plots where the x-axis is a measure of fluorescence intensity and the y-axis representsthe number of events.
Measurement of growth rate
M. smegmatis expressing promoter- gfp fusion constructs were grown in Middle Brook (MB) 7H9 broth supplementedwith glucose and Tween 80, and kanamycin (25 µg/ml ). Growth at different time points was measured by recordingabsorbance values at 600 nm (a value of 1 OD is equal to 10 cells or 200 µg dry weight of cells). A growth curvewas generated by plotting absorbance values against time (inset of Figure 2). The specific growth rate µ (Eq. (2))at different time points is determined by taking derivatives of the growth curve at the different time points (Figure2). Authors contributions
IB, JB and MK conceptualised, supervised and coordinated the study. KS, JB and MK carried out the experiments.SG, BG and IB developed the theoretical model, performed the data analysis and interpreted the data. IB draftedthe manuscript. All authors read and approved of the final version.12 cknowledgements
IB, JB and MK thank M. Thattai for some useful discussions. This work was supported in part by a grant fromthe Department of Biotechnology, Government of India to MK. SG is supported by CSIR, India, under Grant No.09/015(0361)/2009-EMR-I. 13 eferences
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Mathematial model
The reaction scheme describing the processes shown in Figure 1 is given by B + B k ⇋ k B − B k −→ B + B (10) A + B k ⇋ k A − B k −→ A + B (11) A + B k ⇋ k A − B k −→ A + B (12) G AB + A k a ⇋ k d G ∗ AB β −→ A + B (13) G AB + A s −→ A + B (14)In the equations, A ( A ) represents the phosphorylated (unphosphorylated) form of MprA and B ( B ) denotesthe phosphorylated (unphosphorylated) form of MprB. The inactive and active states of the mprAB operon arerepresented by G AB and G AB * respectively. In the inactive state, MprA and MprB proteins are synthesized ata basal rate s and in the active state protein production occurs at an enhanced rate β . Eq. (1) describes theautophosphorylation reaction of MprB with the poly P chain serving as a source of phosphate groups. Eq. (2)describes the transfer of the phosphate group from the phosphorylated MprB to MprA. Eq. (3) corresponds todephosphorylation of phosphorylated MprA by unphosphorylated MprB which thus acts as a phosphatase (inthe earlier study [1], phosphorylated MprB was assumed to act as a phosphatase which is not consistent withexperimental evidence). Eqs. (4) and (5) describe activation of the mprAB operon by phosphorylated MprA andbasal expression of the operon respectively. Refs. [2–4] provide experimental justification for the reaction schemeshown in Eqs. (1)-(5). Using standard mass action kinetics, we write down the rate equations for the concentrationof each of the key molecular species participating in the biochemical events. The equations are: d [ A ] dt = k [ A − B ] − k [ A ][ B ] + k [ A − B ] − γ [ A ] − φ [ A ]1 + θ [ A ] (15) d [ A ] dt = s + β [ A ] /k A ] /k + k [ A − B ] − k [ A ][ B ] + k [ A − B ] − γ [ A ] − φ [ A ]1 + θ [ A ] (16) d [ B ] dt = k [ B − B ] − k [ A ][ B ] + k [ A − B ] − γ [ B ] − φ [ B ]1 + θ [ B ] (17) d [ B ] dt = s + β [ A ] /k A ] /k + k [ B − B ] − k [ B ] + k [ A − B ] − k [ A ][ B ]+( k + k )[ A − B ] − γ [ B ] − φ [ B ]1 + θ [ B ] (18) d [ B − B ] dt = − k [ B − B ] + k [ B ] − k [ B − B ] (19) d [ A − B ] dt = k [ A ][ B ] − k [ A − B ] − k [ A − B ] (20) d [ A − B ] dt = k [ A ][ B ] − ( k + k )[ A − B ] (21)17 [ SigE ] dt = s + β [ A ] /k ′ A ] /k ′ − δ [ SigE ] (22) d [ GF P ] dt = s + β [ SigE ] /k ′′ SigE ] /k ′′ − δ [ GF P ] (23)Eq. (13) represents SigE synthesis due to transcriptional activation of the sigE gene by phosphorylated MprA-P.Eq. (14) describes GFP production due to the activation of the rel promoter by SigE. The rate constants γ , γ , δ and δ are the degradation rate constants. The last terms in Eqs. (6)-(9) represent the nonlinear decay rates thegenesis of which is explained in the main text (see Eq. 4) [5]. Eqs. (6)-(14) correspond to the case where gfp is fusedto the rel promoter. In the other cases when gfp is fused to the mprA or sigE promoter, appropriate modificationsin the set of equations are required.The steady state solution of Eqs. (6)-(14) is obtained by setting all the rates of change to be zero. In the caseof bistability, there are three steady state solutions, two stable and one unstable [6–8]. In the steady state, one hasto solve the following set of coupled nonlinear algebraic equations: α [ A ][ B ] − α [ A ][ B ] − γ [ A ] − φ [ A ]1 + θ [ A ] = 0 (24) s + β [ A ] /k A ] /k − α [ A ][ B ] + α [ A ][ B ] − γ [ A ] − φ [ A ]1 + θ [ A ] = 0 (25) α [ B ] − α [ A ][ B ] − γ [ B ] − φ [ B ]1 + θ [ B ] = 0 (26) s + β [ A ] /k A ] /k − α [ B ] + α [ A ][ B ] − γ [ B ] − φ [ B ]1 + θ [ B ] = 0 (27) s + β [ A ] /k ′ A ] /k ′ − δ [ SigE ] = 0 (28) s + β [ SigE ] /k ′′ SigE ] /k ′′ − δ [ GF P ] = 0 (29)where, α = k k k + k , α = k k k + k , α = k k k + k , k = k d k a (30)The solutions of Eqs. (15)-(20) are obtained with the help of Mathematica. Figures S1 A-C show the steadystate solutions generated by varying the parameter α (associated with the autophosphorylation of MprB). Theparameters have values: α = 2 . , α = 2 . , γ = 0 . , s = 0 . , β = 4 , k = 1 , γ = 1 , φ = 0 . , θ = 1 , θ = 10 , s =0 . , β = 4 , k ′ = 10 , δ = 1 , s = 0 . , β = 4 , k ′′ = 2 , δ = 0 . α (Eq. (21)) includes the rate constant k , a varyinginducer concentration is equivalent to varying the parameter α . There is some experimental evidence that MprA-Pregulates the expression of the mprAB operon in the form of dimers [9]. Inclusion of this feature in our modelmakes the bistable behaviour more prominent. 18 eferences
1. Sureka K, Ghosh B, Dasgupta A, Basu J, Kundu M and Bose I (2008) Positive feedback and noise activatethe stringent response regulator Rel in mycobacteria. PLoS ONE 3: e 17712. Sureka K, Dey S, Datta P, Singh AK, Dasgupta A, et al. (2007) Polyphosphate kinase is involved in stress-induced mprAB-sigE-rel signaling in mycobacteria. Mol Microbiol 65: 261-276.3. Zahrt TC, Wozniak C, Jones D, Trevett A (2003) Functional analysis of the Mycobacterium tuberculosisMprAB two-component signal transduction system. Infect Immun 71: 6962-6870.4. Ferrell JE Jr. (2002) Self-perpetuating states in signal transduction: positive feedback, double-negative feed-back and bistability. Curr. Opin. Cell Biol. 14: 140-148.5. Tan C, Marguet P and You L (2009) Emergent bistability by a growth-modulating positive feedback circuit.Nat. Chem. Biol. 5 : 842-8486. Ferrell JE Jr. (2002) Self-perpetuating states in signal transduction: positive feedback, double-negative feed-back and bistability. Curr. Opin. Cell Biol. 14: 140-148.7. Veening J-W, Smits WK and Kuipers OP (2008) Bistability, epigenetics and bet-hedging in bacteria. Annu.Rev. Microbiol. 62: 193-2108. Pomerening JR (2008) Uncovering mechanisms of bistability in biological systems. Curr. Opin. Biotechnol.19:381-8.9. He H, Zahrt TC (2005) Identification and characterization of a regulatory sequence recognized by Mycobac-terium tuberculosis persistence regulator MprA. J Bacteriol 187: 202-212.19 .20 0.25 0.30 0.35 0.40 0.45 0.500.00.51.01.52.0 autophosphorylation rate C on c o f M p r A C on c o f S i g C on c o f R e l Figure S1:
Bistability and hysteresis in the deterministic model. Steady state concentrations of MprA, SigE andRel versus the parameter α (Eq. (21)). Figure S2: (a) Gaussian and (b) lognormal distributions which describe the distribution of GFP leads in the Land H subpopulations respectively.
Figure S3:
Experimental data for cell count versus GFP fluorescence intensity at selected time points when gfp isfused with rel promoter. The solid curve represents P ( x, t ) in Eq. (5) and the dotted curves are the individual termson the r.h.s. The different parameters of P ( x ) and P ( x ) have the values x = 157 . , w = 150 . , x =6 . , w = 0 . gfp is fused with rel . 20 (cid:13) 10(cid:13) 20(cid:13) 30(cid:13) 40(cid:13) 50(cid:13) 60(cid:13)100(cid:13)150(cid:13)200(cid:13)250(cid:13)300(cid:13)350(cid:13) (a)(cid:13) MprA(cid:13)Time (h)(cid:13) T o t a l M ean (cid:13) (b)(cid:13) SigE(cid:13)Time (h)(cid:13) T o t a l M ean (cid:13) (c)(cid:13) Rel(cid:13)Time (h)(cid:13) T o t a l M ean (cid:13) Figure S4:
Mean GFP fluorescence level for the total population versus time in the three cases of gfp fused withthe promoters of (a) mprA , (b) sigE and (c) rel . C on c o f M p r A C on c o f S i g E C on c o f R e l Figure S5:
Concentrations of MprA, SigE and GFP (in arbitrary units) versus time. The values of the concentra-tions are obtained by solving Eqs. (6)-(14) in Text S1. 21 igure S6:
Comparison of fits of experimental data for cell count versus GFP fluorescence intensity at selectedtime points when gfp is fused with mprA promoter, with lognormal (Eq. (7)) and gamma distributions. The gammadistribution has the form P ( x ) = x a − exp ( − xb ) b a Γ( a ) , where the parameters a and b have the values a = 33 . , b = 11 . aa