Quorum sensing (QS) is an important determinant of bacterial phenotype. Many cell functions are regulated by intricate and multimodal QS signal transduction processes. The LuxS/AI‐2 QS system is highly conserved among Eubacteria and AI‐2 is reported as a ‘universal’ signal molecule. To understand the hierarchical organization of AI‐2 circuitry, a comprehensive approach incorporating stochastic simulations was developed. We investigated the synthesis, uptake, and regulation of AI‐2, developed testable hypotheses, and made several discoveries: (1) the mRNA transcript and protein levels of AI‐2 synthases, Pfs and LuxS, do not contribute to the dramatically increased level of AI‐2 found when cells are grown in the presence of glucose; (2) a concomitant increase in metabolic flux through this synthesis pathway in the presence of glucose only partially accounts for this difference. We predict that ‘high‐flux’ alternative pathways or additional biological steps are involved in AI‐2 synthesis; and (3) experimental results validate this hypothesis. This work demonstrates the utility of linking cell physiology with systems‐based stochastic models that can be assembled de novo with partial knowledge of biochemical pathways.
Bacteria can communicate by releasing and detecting small chemical signal molecules in a process termed ‘quorum sensing’. This confers the ability of single‐celled bacteria to coordinate their behavior as a multicellular unit (Miller and Bassler, 2001; Withers et al, 2001). There are several quorum‐sensing systems differentiated by the mode of signal transduction (e.g., freely diffusible signals, cell‐surface receptor‐mediated phosphorelay systems, and post‐translationally modified peptide signals). The luxS‐derived autoinducer, AI‐2, is of great interest owing to its cross‐species and pro/eukaryotic connectivity (Xavier and Bassler, 2003; Vendeville et al, 2005). Elucidating the intricacies of AI‐2‐mediated regulation and the mechanisms associated with AI‐2 synthesis and transport will play an important role in deciphering the behavior of luxS‐containing bacteria in various environments.
In Escherichia coli cultures, the presence of glucose enhances AI‐2 production substantially (Wang et al, 2005a). In order to elucidate the possible mechanisms underpinning this phenomenon, we simulated the appearance and disappearance of AI‐2 in extracellular fluids using a stochastic Petri net (SPN) model, based on the algorithms of Gillespie (1977). This approach has been proven successful in modeling several biological systems (Arkin et al, 1998; Matsuno et al, 2000). An SPN model (Figure 2) was built from the known AI‐2 biosynthesis pathways and the partially elucidated AI‐2 uptake processes of E. coli (Wang et al, 2005a, 2005b)
A base model was constructed for growth in LB medium, wherein an AI‐2 synthesis rate was optimized to match our experimental data. Specifically, a piecewise constant optimization was carried out using an identically constructed ODE model with median output quantities for state variables. Our decision to optimize the AI‐2 synthesis rate was based on our experimental observations that AI‐2 synthase LuxS and Pfs transcript levels are high during exponential growth and that the transcription of the AI‐2 uptake transporter is not initiated until late exponential phase (Wang et al, 2005a, 2005b). Hence, synthesis is regulated first, followed by uptake. The simulation results were in good agreement with experimental data.
The stimulation of AI‐2 owing to the presence of glucose was then investigated. Experimental results revealed an increase in luxS mRNA in the presence of glucose and an overall decrease in time as the cells entered the stationary phase. A similar time course was found for pfs mRNA, although there was no apparent difference due to glucose. Corresponding simulation results showed that an increase in luxS transcript levels does not appreciably enhance AI‐2 formation.
The network was then perturbed by overexpression of luxS and pfs, wherein expression vectors for His‐LuxS and His‐Pfs were introduced into W3110 cells, respectively. The cells were induced by IPTG in growth media both with and without glucose. LuxS and Pfs protein levels increased by more than 200‐fold compared to controls. Surprisingly, AI‐2 production increased only 16%. Hence, the dramatic increase in enzyme only marginally enhanced AI‐2 production. Simulations were remarkably consistent with experimental results.
In the presence of glucose, luxS and pfs overexpression resulted in a two‐fold increase in AI‐2. As a more than 200‐fold increase in LuxS and Pfs alone does not appreciably increase AI‐2, we surmised that the carbon fluxes through these metabolic pathways acted in tandem with the increased enzyme level. Based on previous research (Holms, 1996; Oh and Liao, 2000), a 50% flux increase in carbon flux could be expected when cells are grown in the presence of glucose. To interrogate a flux‐based hypothesis, the overexpression of luxS and pfs was simulated with increased carbon flux. The results showed enhanced AI‐2, but not at levels that would corroborate experimental observations.
We based further computational experiments on the work of Almaas et al (2004), who suggested that high‐flux reactions experience noticeable flux changes whereas low‐flux reactions are minimally affected. Specifically, we suspected that the reaction from 4,5‐dihydroxy‐2,3‐pentanedione (DPD) (the immediate product of LuxS) to AI‐2 is a high‐flux reaction for AI‐2 formation. That is, we were interested in whether DPD level could be increased substantially or that an alternative, currently undiscovered, pathway to DPD or AI‐2 could be involved. In the first case, increased reaction rate could be obtained by increased reactant concentration. Both models were tested. As DPD is reportedly highly reactive, we concluded that it is unlikely that a two‐ to three‐fold higher level of DPD could exist in cells grown in glucose. We investigated the possibility of alternative sources for AI‐2 formation, or the potential that there may be additional biological steps in the pathway that are altered directly or indirectly by glucose (Figure 7C). The detection of AI‐2 in reactions of adenosine with cell extracts from luxS and pfs null mutants confirmed that cells can indeed create AI‐2 from alternative pathways.
A dramatic increase in extracellular activity of quorum sensing signal molecule, autoinducer‐2 (AI‐2), is noted when E. coli cells are grown in the presence of glucose. Our stochastic model of the AI‐2 genetic circuit predicted that this phenomenon was largely independent of the mRNA and protein levels of the two terminal AI‐2 synthases, Pfs and LuxS. Perturbation experiments with overexpressed Pfs and LuxS, confirmed this finding.
It is well known that the metabolic flux through the activated methyl cycle is enhanced in the presence of glucose. A 50% simulated increase in this flux did not quantitatively account for the observed increases in AI‐2. Correspondingly, we have predicted that either ‘high‐flux’ alternative pathways or additional biological steps are involved in AI‐2 synthesis. We have experimentally validated this hypothesis by demonstrating the conversion of adenosine to AI‐2 in extracts of both luxS and pfs mutant cells.
This work demonstrates the combined use of experiments together with systems‐based stochastic models can lead to the new insight on biochemical mechanisms, genetic regulation, and the dynamics of even partially elucidated biochemical pathways.
Bacteria utilize an intricate communication system for sensing and interpretation of environmental cues that has recently been shown to mediate coordinated population‐based behavior. This process, termed ‘quorum sensing’ (QS), involves the production, the release and detection of small chemical signal molecules, called autoinducers. Conceptually, a threshold stimulatory concentration of autoinducer is achieved, then a signal transduction cascade is initiated that ultimately results in a change of the ‘collective’ behavior of the organism (Nealson et al, 1970; Fuqua and Greenberg, 1998; Miller and Bassler, 2001). QS has been found to be a regulator of cellular processes such as bioluminescence production (Bassler et al, 1994; Miller and Bassler, 2001), virulence gene expression (Zhu et al, 2002), biofilm formation (Balestrino et al, 2005; Yoshida et al, 2005), cell division, motility, metabolism, and recombinant protein production (DeLisa et al, 2001a, 2001b; Sperandio et al, 2002). Indeed, QS is an integral component of global gene regulatory networks (Withers et al, 2001), and has been suggested to be ‘a language for bacteria’, mediating social engagements between prokaryotes and eukaryotes (Sperandio et al, 2003; Williams et al, 2004; Vendeville et al, 2005).
There are several types of QS systems, including (1) an acylated homoserine lactone (AI‐1) system used by a variety of Gram‐negative bacteria (Fuqua et al, 2001), (2) a post‐translationally modified peptide signaling system of Gram‐positive species (Sturme et al, 2002), and (3) a system mediated by a highly conserved autoinducer synthase, LuxS, which appears among a variety of Gram‐negative and Gram‐positive bacterial species (Surette et al, 1999; Federle and Bassler, 2003; Sperandio et al, 2003; Xavier and Bassler, 2003). Because of its cross‐species and even pro–eukaryotic connectivity, the luxS‐mediated system has been the topic of intense research. The most well‐studied luxS‐derived autoinducer, AI‐2, is a product of the activated intracellular methyl cycle, and the flux of metabolites through this cycle affects the rate of its formation (Posnick and Samson, 1999; Winzer et al, 2003). Indeed, the production rate of AI‐2 has been shown to be linearly proportional to cell growth rate (DeLisa et al, 2001a). Alternatively, its level in batch cultures in the extracellular medium appears to be modulated by a sophisticated autoregulated energy‐dependent mechanism, suggesting an important cellular function (Xavier and Bassler, 2005). Understanding the intricacies of AI‐2‐mediated regulation and the mechanisms by which AI‐2 influences transcription and/or cellular phenotype will naturally play a role in deciphering the behaviors of these luxS‐containing bacteria in various environments.
Large‐scale system biology platforms for transcriptomics, proteomics, and metabolomics enable transient experimental mapping of biological systems; however, the conceptual framework of these genetic systems cannot be fully developed without computational or simulation approaches. That is, the mathematical models serve to integrate experimental data as well as facilitate hypotheses that can be tested, and serve to provide valuable insights into the general principles of biological system organization (Westerhoff and Palsson, 2004).
In this work, a stochastic model based on the algorithms of Gillespie (1977) was used to simulate the AI‐2 circuit of Escherichia coli K12. Specifically, a stochastic Petri net (SPN) model, a mathematical approach succinctly reviewed by Goss and Peccoud (1998) and successfully used for modeling several biological systems (Arkin et al, 1998; Matsuno et al, 2000; Srivastava et al, 2001), was developed for the appearance and disappearance of AI‐2 in extracellular fluids of laboratory batch cultures of E. coli. This stochastic approach can accommodate large and discrete transitions in its reacting species (Gillespie, 1977; McAdams and Arkin, 1997), and favorably contrasts the deterministic approach, which assumes that the time evolution of a chemically reacting system is continuous. That is, for biological systems, such as genetic regulatory networks with species at very low concentrations (or number) and slow reaction rates, random fluctuations can exist owing to inherent stochastic events. These, in turn, can yield significant variability in system behavior, particularly when modeled stochastically (McAdams and Arkin, 1999; Smolen et al, 2000; Gibson and Mjolsness, 2001; Mettetal et al, 2006).
Our particular interest was the apparent stimulation of AI‐2 due to the presence of glucose, as its presence appears to interfere with QS signaling in E. coli. Based on initial simulation and experimental results in LB medium, we investigated several experimental and computational hypotheses related to redistribution of metabolic flux within the AI‐2 biosynthesis pathway. The results suggest the existence of an alternative glucose‐regulated pathway for autoinducer AI‐2 synthesis. We subsequently discovered the conversion of nucleic acid precursor, adenosine, to AI‐2 via a pathway other than the well‐known Pfs–LuxS pathway. That is, upon interrogating our model simulations and the enzymatic synthesis of AI‐2 in vitro (Schauder et al, 2001; Miller et al, 2004), we discovered the existence of an alternative pathway for its synthesis, which is shown here. Other attributes of this SPN approach to investigate bacterial QS are revealed: (1) the stochastic approach formally enables estimation of variance for the simulated concentrations, which can be compared to experimental data, (2) the simulated genetic circuit can be assembled from ‘subcircuits’ as the complexity and interconnectivity with the rest of metabolism is established, (3) inferences from the literature concerning metabolic flux and other events such as transcription, translation, and biomolecular assembly formation can be tested, and perhaps most importantly, (4) this approach enables a computational framework that allows one to postulate mechanisms and concepts that can ultimately be tested using bacterial genetics.
AI‐2 biosynthesis and uptake pathways in E. coli (Figure 1) have been partially elucidated (Schauder et al, 2001; Xavier and Bassler, 2005): AI‐2 is derived from S‐adenosylmethionine (SAM), a major methyl donor in metabolic processes. SAM transfers a methyl group to methyl acceptors by methyltransferases, such as CheR (Yi and Weis, 2002), yielding S‐adenosylhomocysteine (SAH). SAH is hydrolyzed to S‐ribosylhomocysteine (SRH) by a nucleosidase, Pfs, with a concomitant release of adenine. LuxS cleaves the thioether linkage of SRH and yields homocysteine and 4,5‐dihydroxy‐2,3‐pentanedione (DPD). It has been reported that AI‐2 results from the autocyclization of DPD in at least two additional reactions (Chen et al, 2002; Miller et al, 2004; Semmelhack et al, 2005). SAM, together with diamine and putrescine, is also decarboxylated to form a major triamine, spermidine. This triamine plays an important role in proliferation and differentiation of E. coli (Cohen, 1998). This reaction also releases a toxic by‐product 5′‐thiomethyladenosine (MTA), which is then acted upon by Pfs, yielding adenine and 5′‐thiomethylribose (MTR). MTR is reportedly excreted to the medium in E. coli (Schroeder et al, 1973). The export mechanisms of AI‐2 are unknown. Extracellular AI‐2 is transported into the cell by an ABC transporter, Lsr (Taga et al, 2003; Wang et al, 2005a). Its uptake was recently shown to be glucose dependent (Wang et al, 2005a). The role of AI‐2 beyond regulating its uptake remains unresolved in E. coli K12, although many targets have been proposed (DeLisa et al, 2001a, 2001b).
An SPN model (Figure 2) was constructed for the AI‐2 biosynthesis and uptake pathways (Figure 1). The SPN circuit includes both SAM utilization branches, because Pfs acts on both SAH and MTA, which may enable pathway competition.
Experiments with wild‐type E. coli have demonstrated that extracellular AI‐2 accumulates in the exponential phase and then is rapidly depleted at the onset of the stationary phase (Surette and Bassler, 1998). Extracellular AI‐2 level is presumed to be a function of synthesis and uptake (Taga et al, 2003; Winzer et al, 2003; Wang et al, 2005a). Our observations, which are consistent with these hypotheses, are that AI‐2 is stable in spent culture media devoid of cells (data not shown), so that intrinsic instability of AI‐2 is negligible. Thus, for simplicity, we partitioned our SPN so that AI‐2 accumulation and uptake are two independent processes. Hence, a quorum signal ‘switch’ was included to control the AI‐2 synthesis and uptake transition. Three input gates (Trans_thresh, Excret_thresh, Phos_thresh) together with a growth rate indicator were used to control the switching process (Figure 2). The instantaneous specific growth rate, which was calculated from experimental data, was used to determine the stage of cell growth and to ‘open’ specific input gates.
All initial markings and their appropriate references are listed in Table I. For all species, one token represents a single molecule and this was taken as 1 nM concentration (Arkin et al, 1998). Similarly, all rate constants and their original sources are listed in Table II. Most of these rate constants were collected from literature data of earlier studies (Draper, 1996; Kushner, 1996; Records Jr et al, 1996), such as rates of transcription, translation, and metabolic enzyme activity. LuxS and pfs transcription rates were derived from a typical transcription rate (Records Jr et al, 1996) modified by our transcriptional promoter probe data (see Supplementary Figure 1), whereas their mRNA degradation rates were determined from previous reports (Kushner, 1996) together with our NIH image quantified Northern blotting data (see Supplementary Figure 2). These deterministic rate constants were transformed into stochastic constants based on the relationship between mRNA synthesis, degradation, and the cell volume (detailed information is provided in Supplementary information and Supplementary Figure 3).
A base model was constructed for growth in LB medium wherein an AI‐2 synthesis rate was found to match our AI‐2 data. To be specific, a piecewise constant optimization routine was carried out using an identically constructed ODE model with median output quantities for state variables. The AI‐2 uptake rate was based on AI‐2 uptake experiments in luxS mutant strains MDAI2 and LW3 (Li et al, 2004), together with lsr transcription rate results (Wang et al, 2005a). AI‐2 excretion and AI‐2 phosphorylation rates were based on intracellular AI‐2 experiments, indicating that intracellular AI‐2 was insignificant as compared to extracellular levels (data not shown).
ODE parameter optimization was executed using a Matlab® optimization toolbox (http://www.mathworks.com/access/helpdesk/help/toolbox/optim/optim.shtml). AI‐2 circuit simulations were run using Mobius on a laptop PC, kindly provided by Dr William Sanders (Center for Reliable and High Performance Computing at the University of Illinois at Urbana‐Champaign: http://www.mobius.uiuc.edu/). As our simulations monitor constituents in a single cell, each simulation was terminated at a cell's doubling. For example, during the exponential phase, doubling time was 35 min, the simulation was terminated at 35 min, and constituents’ levels were divided by two and set as initial markers for the subsequent run.
AI‐2 production in LB medium is partially influenced by Pfs and LuxS
AI‐2 activity exists in LB medium of cells grown without glucose, although at a much lower level than with glucose (Wang et al, 2005a). Simulations were performed on the AI‐2 circuit for cells cultured in LB medium without glucose. During these simulations and because there exist solid literature data on most remaining constants, the AI‐2 synthesis rate (ksyn) was optimized by minimizing the variance between the simulated results and corresponding experimental data. Hence, the optimized synthesis rate, which enables good agreement with experimental data, is a piecewise constant that increases with time (‘LB_sim’ in Figure 3A and Table III). That the reaction rate increased with time is an interesting result that will be discussed later. Our decision to optimize the AI‐2 synthesis rate as opposed to uptake rate was based on our experimental observations that luxS and pfs transcript levels are high during exponential growth and that lsr transcription is not initiated until late exponential phase (Wang et al, 2005a, 2005b). Hence, synthesis is regulated first, followed by uptake.
It has also been reported that glucose can stimulate AI‐2 synthesis. In Wang et al (2005a), we demonstrated that the rates of luxS transcription were increased owing to the presence of glucose and this increase was mediated by the cAMP–CRP complex. In Figure 3 and Table IV, we show the luxS, pfs, and speED mRNA levels, detected by both Northern blot and qRT–PCR, in cells grown with and without glucose. Interestingly, the Northern data suggest a two‐ to seven‐fold increase in luxS mRNA in glucose‐grown cells, whereas the qRT–PCR data track the transcription rate data obtained previously (∼1.5‐ to 2‐fold increase; Wang et al, 2005a). Because of the apparent variability in mRNA data based on the two measurement techniques, the rates of luxS and pfs transcription were calculated twice, corresponding to both data sets (Table IV) and both sets of simulation results indicated only a 10% increase in calculated AI‐2 (Figure 3A, only ‘Enz_sim’ is shown here for the Northern data). Importantly, irrespective of the mRNA quantities, the experimentally observed AI‐2 levels were three‐fold higher than that predicted by SPN. Not seen in these simulations are the estimated variances calculated by the stochastic model. In particular, the AI‐2 variance was less than 5% of the mean throughout the simulation period. The most widely varied constituents were indeed the levels of luxS and pfs mRNA (∼16%), as indicated in Figure 3C, which roughly correspond to the standard errors associated with the Northern blot measurements.
These results suggest that changes in the levels of these key enzymes do lead to the stimulation of AI‐2 production, but at levels much less than that needed to rectify simulation with experimental results from cultures containing glucose.
In order to test this enzyme dependence further, the AI‐2 circuit was experimentally perturbed by luxS and pfs overexpression. IPTG‐inducible expression vectors for the production of LuxS and Pfs were introduced into W3110 cells, which, in turn, were grown in the presence and absence of glucose. First, in the absence of glucose and consistent with Figure 3, luxS overexpression resulted in only a small AI‐2 increase (about 16%) relative to the control (plasmid without luxS insertion) (Figure 4A). Interestingly, pfs overexpression resulted in no clear trend and no appreciable difference relative to the control (plasmid without pfs insertion) (Figure 4A). In order to mimic the effects of luxS and pfs overexpression on the AI‐2 SPN, their transcription rates were increased 200‐fold. This is a much more severe test of the reaction network's dependence on LuxS and Pfs expression than the simulations above (Figure 3). The resultant LuxS and Pfs protein levels were calculated to be around 200‐ to 300‐fold higher than that of wild‐type cells in the mid‐exponential phase (Figure 4D). Although not shown, the levels of these enzymes in the wild‐type cells did not change significantly with time (i.e., they roughly correspond to transcript levels in Figure 3C). The corresponding calculated AI‐2 levels were raised by less than 10% (Figure 4C). These simulation results corroborate the experimental findings that luxS and pfs overexpression only minimally influences AI‐2 production in LB medium without glucose.
In Figure 5A, cells overproducing each of the synthases in the presence of glucose exhibited significantly higher levels of AI‐2. In the case of LuxS, the increase was more immediate than with Pfs. The levels of LuxS and Pfs in these overproducing cells were estimated to be 200‐fold greater than that of uninduced controls (quantified results in Figure 5D). By increasing luxS mRNA (owing to the presence of glucose) in the network, and performing similar luxS or pfs overexpression simulations as stated in LB medium, we saw only similarly increased AI‐2 levels (less than 10%, data not shown).
Taken together, these simulations have demonstrated that the expression level of LuxS and Pfs enzymes cannot notably enhance AI‐2 production. However, experiments have clearly demonstrated that overexpression of LuxS and Pfs can effectively increase AI‐2 production when glucose is present. This discrepancy suggests that the increase in AI‐2 production due to the presence of glucose may result from factors other than LuxS and Pfs, in ways that have yet to be revealed. This is partially explored by examining carbon flux through the biosynthesis pathways.
Glucose provides enhanced flux through the LuxS synthesis pathway
Based on the work of Holms (1996) on flux analysis of E. coli grown with different carbon sources and the work of Oh and Liao (2000), the presence of glucose and varied carbon sources can significantly enhance the flux through central metabolic pathways. According to their data, a 50% increase in the flux of material through the AI‐2 circuit due to the presence of glucose is reasonable. Hence, we carried out several ‘what if’ simulations, whereby metabolic fluxes other than the AI‐2 synthesis rate from DPD and its uptake were upregulated 50% as compared to that without glucose. In the first set of simulations (GlcFlx_sim; Figure 5C), the two‐fold increase of luxS mRNA due to glucose was included, but without overexpression of luxS and pfs. The calculated AI‐2 increased 35% over that without glucose. The addition of luxS and pfs overexpression to the case of increased metabolic flux only marginally increased AI‐2 levels (LuxS_sim, Pfs_sim in Figure 5C).
In Figure 5A, cells overproducing each of the synthases in the presence of glucose exhibited significantly higher levels of AI‐2. In the case of LuxS, the ∼2‐fold increase was more immediate than that with Pfs. In Figure 5B, the level of LuxS and Pfs in these overproducing cells was estimated to be 200‐fold greater than that of the uninduced controls (quantified results are depicted in Figure 5D). Simulations with glucose present (i.e., higher initial luxS mRNA) predict that overexpression of both luxS and pfs enhances AI‐2 production over the LB SPN calculations, but by less than or near two‐fold (Figures 5C and 4C). Interestingly, the simulated levels of LuxS was higher than that without glucose (Figures 5D and 4D). It is again noteworthy that the LuxS and Pfs protein levels were within the variances calculated by the SPN. Also, experimental observations indicated a more immediate response in the case of LuxS overexpression, yet there was no distinct difference in calculated AI‐2 even though the calculated LuxS level appeared to increase more quickly than Pfs. We note that in experiments, the peak AI‐2 levels were similar in both overexpression cases (∼800 normalized activity units; Figure 5A), and roughly 1.5‐fold higher than the +glucose case without enzyme overexpression (Figure 5A). That the SPN captured the relative increase in AI‐2 (∼1.5‐ to 2‐fold) due to the enzyme overexpression in the presence of glucose was both interesting and noteworthy, but our simulations still missed the overall enhancement resulting from glucose itself. Most importantly, an approximately 250‐ to 500‐fold increase in each enzyme resulted in only a maximum two‐fold increase in AI‐2.
Trends in all of the above simulations are consistent with our experimental results and a previous report that flux increases stimulate AI‐2 production (Posnick and Samson, 1999). Because the simulated AI‐2 levels remained much lower than the experimental data, we hypothesized that the rate of AI‐2 synthesis from DPD was itself a function of glucose, with an as yet to be determined functional form. This has varied ramifications, as will be discussed.
In order to set up further simulation experiments, we performed a piecewise linear optimization analysis to ‘find’ the AI‐2 synthesis rate constant (ksynGlc) that best matched the experimental data with glucose present. As our simulation rate constants are most grounded in events associated with transcription, translation, and flux in the enzyme‐mediated reactions, we optimized the AI‐2 synthesis rate under the condition of 50% increased metabolic flux. In Figure 6, the corresponding best‐fit simulation results for the glucose case are, as expected, in close agreement with the data (Figure 6, Glc_sim1). The experimental results and the previous GlcFlx_sim from Figure 5C are also included. In Table III, the corresponding synthesis rates for the conversion of DPD to AI‐2 increased ∼10‐fold over the previous case during the period of maximum AI‐2 increase (2–3 h). The maximum difference between calculated results and measurements was less than 15%.
A second simulation was run, in which the ‘optimized’ AI‐2 synthesis rate was run without enhanced metabolic flux (Figure 6, Glc_sim2). This tests whether the influence of glucose on the well‐studied synthesis pathway is the potential problem in our SPN circuit. The results are again significantly different from the experiments, reinforcing the suspicion that our model construction from DPD to AI‐2 is flawed. That is, the net result of these simulations demonstrated that increases in ‘upstream’ metabolic flux stimulate AI‐2 production, but that the apparent non‐enzymatic conversion of DPD to AI‐2 may be the basis for discrepancy. One explanation is that there are alternative pathways other than those well documented (as shown in Figure 1) for AI‐2 synthesis. These may be induced and/or undergo a dramatic flux increase due to the presence of glucose.
Alternatively, when cells enter the stationary phase, AI‐2 uptake takes place. As stated above, the AI‐2 uptake rate was determined in the initial model based on LB medium (Li et al, 2004). However, in the presence of glucose (0.8% glucose in LB), AI‐2 uptake was observed to be slower as compared to that without glucose, owing to the CRP‐mediated repression of glucose on AI‐2 uptake (Taga et al, 2003; Wang et al, 2005a). A reduced uptake rate would increase the extracellular AI‐2 level. Although not noted earlier, a revised AI‐2 uptake rate (reduced by more than 40%) was used in the above simulations representing glucose addition (Table III). However, when the AI‐2 uptake rate constant was lowered 10‐fold to reflect nearly complete repression of uptake, there was no depletion of AI‐2 level in the supernatant (not shown here). This is inconsistent with the experimental results, which clearly demonstrated AI‐2 uptake, even in cells devoid of the active lsr uptake transporter (Wang et al, 2005a). A further modification is envisioned wherein uptake and synthesis are coordinated so that cessation of synthesis ends after AI‐2 uptake begins. Our experimental evidence with lsrK knockouts however demonstrates that AI‐2 synthesis indeed ends at switch times or conditions as indicated, and AI‐2 levels remain the same during the stationary phase (Wang et al, 2005a). If there were still AI‐2 synthesis under the condition without any uptake, we would see a continually increased AI‐2 activity.
Is conversion of 4,5‐dihydroxy‐2, 3‐pentanedione a high‐flux reaction?
We were interested in the report of Almaas et al (2004), which suggests that the biochemical activity of metabolism is dominated by a few high‐flux backbone reactions embedded in a network of mostly small‐flux reactions. They reported that only high‐flux reactions go through noticeable flux changes, whereas low‐flux reactions undergo small shifts. Based on this, we speculated that there may be hidden high‐flux reactions among the AI‐2 synthesis pathways. As stated above and confirmed by experiment and simulation, the increase in transcription and/or translation of luxS and pfs cannot enhance AI‐2 production significantly. Further, a dramatic increase, more than 200‐fold, in upstream precursor, SAM, only stimulated an approximate 60% AI‐2 increase (Posnick and Samson, 1999).
This turned our attention to post‐LuxS processing (the correct cyclization of DPD; Miller et al, 2004), which is reported to be a result of mass action kinetics as opposed to an enzyme‐ or chaperone‐mediated event. We wonder whether this conversion, putatively in the cell cytoplasm, could proceed without any biological assistance. After many efforts including our own, biologically produced AI‐2 has never been isolated without further biological assistance such as binding to a cognate receptor (Chen et al, 2002; Meijler et al, 2004; Miller et al, 2004; Semmelhack et al, 2004, 2005). Similarly, pure DPD has also not been reported, instead ‘pure’ DPD is a mixture of DPD together with its two anomers at their low concentration (Meijler et al, 2004). The mechanism by which AI‐2 is formed from its precursor, DPD, remains enigmatic in E. coli. Hence, we predicted that the reaction from DPD to AI‐2 potentially serves as a hidden high‐flux reaction in the AI‐2 QS network.
During our ‘fit’ simulations, the AI‐2 synthesis rate increased significantly with the growth of cells. This rate constant represents the net reaction rate from DPD to AI‐2; our results clearly indicated that the reaction from DPD to AI‐2 has a strong impact on AI‐2 level. Furthermore, mechanistically, DPD is putatively the principal molecule from which all bacterial AI‐2 is derived (Miller et al, 2004; De Keersmaecker et al, 2005; Semmelhack et al, 2005). Because of the apparent impact of this reaction on AI‐2 level, we performed additional simulations (Figure 7) to differentiate potential mechanisms that contribute to this pathway. First, we intentionally reduced the AI‐2 synthesis rate constant, k′synGlc, to gauge its importance on AI‐2 formation from DPD in the case of glucose‐mediated flux increases and Pfs/LuxS synthase mRNA changes (DPD_sim1; Figure 7A). This reduced synthesis rate was ∼3‐fold lower than the ‘optimized’ AI‐2 synthesis rate (ksynGlc) in the earlier glucose simulations (Glc_sim1, Glc_sim2 in Figure 6), but was maintained ∼3‐fold higher than the initial simulations (e.g., GlcFlx_sim in Figure 5). The resultant AI‐2 level was much lower than that from our observations, as expected. This case represents a logical extension of our experimental findings, and is included to represent an intermediate level of enhanced reaction (Figure 7A and Table V).
Second, ‘DPD_sim2’ was carried out by maintaining an ∼20% higher DPD concentration than the previous cases, but with the same AI‐2 synthesis rate constant k′synGlc as in DPD_sim1. In Mobius, this is accomplished by redefining the input function of DPD tokens, so that upon transition or ‘firing’, the number of DPD tokens was not reduced by one and was instead unchanged. This case represents a situation where other reactions produce DPD from as yet unidentified pathways (indicated by a side entry reaction in DPD_sim2 of Figure 7C). The simulated results were in good agreement with our experimental data.
Third, ‘DPD_sim3’ (same as Glc_sim1 in Figure 6) was performed under the original DPD configuration with the ‘optimized’ synthesis rate constant, ksynGlc. This simulation represents the situation where the rate constant from DPD to AI‐2 was increased 40‐fold over time (indicated by the thick arrow in Figure 7C). As noted above, the simulations fit the data well.
The AI‐2 synthesis rates for all three simulations are listed in Table V. The DPD levels (relative to the initial tokens) under these three different conditions are depicted in Figure 7B along with the base LB case. An initial rapid transient was observed in which the +glucose cases reached a significantly higher level. The ∼3‐fold increase in AI‐2 synthesis rate constant (k′synGlc) coupled with an artificially increased DPD level (DPD_sim2) resulted in a close fit with the experimental data. An additional 3‐fold increase in the AI‐2 synthesis rate constant, ksynGlc, coupled with the original DPD conditions also resulted in a good fit of the experimental data (DPD_sim3).
Readily apparent from these simulations is that AI‐2 production can be made to match experiments either by elevating the intracellular DPD level or by increasing the AI‐2 synthesis rate constant from DPD. Our simulations are consistent with either an alternative source of DPD or an enhanced reaction rate from DPD, both of which served to explain the increased AI‐2 level in the presence of glucose.
In total, our simulations suggest that in order to accurately simulate the AI‐2 level in the extracellular medium, the reaction from DPD to AI‐2 must increase in time, and in the presence of glucose, must increase an additional 10‐fold beyond the base case. Or alternatively, the reaction rate must increase ∼3‐fold in concert with a significantly increased level of intracellular DPD. All of these scenarios suggest that the reaction from DPD may be a high flux reaction that varies significantly in rate.
Experiments demonstrating existence of alternative AI‐2 synthesis pathways
In order to probe this hypothesis experimentally, we turned to the substrates and by‐products of this two‐enzyme AI‐2 synthesis system. In particular, we considered the potentially broad substrate specificity of Pfs (it participates in both reaction pathways; Figure 1). We incubated soluble cell extracts and imidazole‐eluted enzyme fractions of NC13 (a pfs null mutant) and DH5α (a luxS frameshift mutant) with and without the overexpression of His‐Pfs and His‐LuxS, respectively, with adenosine. Then, we assayed for BB170‐responsive autoinducer AI‐2 activity (Figure 8). Interestingly, all reactions of soluble cell extracts incubated with adenosine were found to induce BB170 cells to produce luminescence, irrespective of the absence of His‐Pfs or His‐LuxS. Further, imidazole‐eluted fractions of Co2+ resin‐immobilized His‐Pfs or His‐LuxS induced no or negligible amounts of luminescence when reacted with adenosine (positive controls with SAH showed significant AI‐2 production). Reaction of soluble cell extracts with Co2+‐immobilized enzymes but without adenosine induced negligible luminescence and, moreover, adenosine itself showed no independent autoinducer activity on BB170 cells (data not shown). HPLC analysis revealed no reaction of adenosine with either purified Pfs or LuxS (data not shown).
Because AI‐2 activity is made from cell extracts in the absence of Pfs in one case and LuxS in the other, and because the purified enzyme fractions yield no autoinducer from adenosine, we conclude that adenosine is not a substrate for either enzyme. Instead, other enzymes or precursors in soluble cell extracts are likely responsible for converting adenosine to a BB170‐responsive autoinducer.
In further studies of in vitro AI‐2 synthesis, we found that LuxS could act on SAH directly, producing AI‐2 activity (Hashimoto et al, in preparation). This was not revealed in vivo, as conditioned medium from pfs null mutants was devoid of AI‐2. Nevertheless, several preparations of LuxS were shown to convert SAH to AI‐2 activity. We note that eukaryotes convert SAH to adenosine and homocysteine via SAH hydrolase in one step. Although the products of LuxS‐mediated SAH degradation do not include adenosine, the potential for enzymatic cross‐reactivity with SAH was an interesting finding. Thus, we speculated that E. coli may convert adenosine to AI‐2 via a non‐LuxS pathway. Interestingly, an alternative pathway for DPD and AI‐2 formation was found in tomato, where DPD was formed from d‐ribulose‐5‐phosphate spontaneously. d‐Ribulose‐5‐phosphate was synthesized from d‐ribose‐5‐phosphate and the enzyme is responsible for this conversion is ribose‐5‐phosphate isomerase (Hamada et al, 2003; Hauck et al, 2003). In a related work, LuxS‐independent AI‐2 formation was reported from a sugar phosphate, ribulose‐5‐phosphate, which exhibited stronger induction of the AI‐2‐specific reporter strain than a spontaneously formed product 4‐hydroxy‐5‐methyl‐furanone from DPD (Hofmann, 1998; Tavender et al, 2004). In E. coli, adenosine can be salvaged to ribose‐1‐phosphate through pentose phosphate metabolism, whereas ribose‐1‐phosphate can be converted to ribose‐5‐phosphate by phosphopentomutase, then ribose‐5‐phosphate can be isomerized to ribulose‐5‐phosphate (Sorensen and Hove‐Jensen, 1996). The existence of AI‐2 from reaction of adenosine with cellular extracts from either luxS or pfs mutant may then be the result of a series of reactions of adenosine salvation through ribose metabolism. The reconstruction of this pathway in vitro is currently underway.
These experimental findings demonstrate that alternative pathways for autoinducer AI‐2 formation exist, and our simulation results suggest that their rates are dependent on glucose. It is uncertain whether all these alternative pathways are related to DPD, whose autocyclization is putatively responsible for AI‐2 formation (Schauder et al, 2001; Chen et al, 2002; Miller et al, 2004). We favor the existence of DPD‐related alternative pathways for AI‐2 formation because (1) chemically synthesized DPD was shown to be a strong inducer of AI‐2 activity (Meijler et al, 2004; De Keersmaecker et al, 2005) and (2) all the identified autoinducers were shown to be derived from DPD (Miller et al, 2004; Semmelhack et al, 2005). In summary, these reports indicate that alternative pathways to AI‐2 other than those well documented exist, among which ribose sugar phosphates may be involved. We suggest that the dramatic AI‐2 increase in the presence of glucose may be attributed to the prevalence of sugar phosphates in cells grown with glucose or to other ill‐defined pathways in E. coli.
An SPN model was employed to simulate AI‐2 QS circuit in E. coli. Simulation results were in good agreement with experimental data, particularly for the case of cells grown in LB media without glucose. The appearance and disappearance of AI‐2 in the growth medium was directly calculated based on the known biochemical pathways. The mRNA levels of two important AI‐2 synthases (Pfs and LuxS) were accurately depicted. Moreover, the SPN model predicted both the relative increase in the synthase level as well as the relative insensitivity of AI‐2 due to this perturbation. It is also noteworthy that the variances calculated by the SPN were similar to the experimental errors associated with several of our measurements (e.g., mRNA levels, LuxS, Pfs levels). By representing this network in the Mobius simulation environment, one can with relative ease add additional structure and complexity, in order to generate testable hypotheses regarding the predicted outcomes.
As an example, we speculated that increased metabolic flux from the addition of glucose to the growth media would be required to enhance AI‐2 production (additional synthases would be insufficient). This was validated by the simulation results, where a 50% increase in flux resulted in ∼35% AI‐2 production (Figure 6). More importantly, our simulations led to a hypothesis that a significant increase in AI‐2 production from cells grown with glucose may have resulted from unrevealed alternative pathways involving compounds such as sugar phosphates or other unknown regulators modulating the flux to AI‐2 (Sperandio et al, 2003; Tavender et al, 2004). In separate experimental tests using cell extracts, we confirmed that adenosine can be converted to AI‐2 from both pfs and luxS mutants, demonstrating for the first time a biological route to AI‐2 from adenosine. It is likely, however, that this particular pathway is masked in vivo, as the addition of adenosine to wild‐type cells does not stimulate AI‐2 production (not shown). Our results would suggest that the presence of glucose instead alters the relative flux between these pathways.
We also showed that the level of DPD plays an important role in AI‐2 formation. This is consistent with recent reports indicating that DPD is the core molecule for AI‐2 formation (Meijler et al, 2004; Semmelhack et al, 2004, 2005). Our simulations showed that AI‐2 production can be effectively influenced by modulating the flux from DPD to AI‐2, which can be achieved by increasing the concentration of DPD or by enhancing the AI‐2 synthesis rate constant. However, we note that DPD is reportedly highly reactive and unstable (Winzer et al, 2002; Meijler et al, 2004). Therefore, we believe that it is unrealistic that a cell can maintain a high DPD level without chaperones or other compartmentalization moieties for enabling stimulated AI‐2 synthesis. It has been demonstrated in vitro that AI‐2 can be derived from DPD and its two ring‐closed equilibrium anomers without enzyme catalysis, suggesting that the species specificity is derived at the level of the cognate receptor (Meijler et al, 2004; Semmelhack et al, 2004, 2005). In the absence of a DPD‐specific efflux transporter, it is likely that DPD undergoes intramolecular nucleophilic attack by the hydroxyl group on the carbonyl carbon in vivo, producing five‐membered cyclic furanose anomers. These two anomers go through mutarotation, like other cyclic sugar anomers, and the equilibrium between these two anomers can be shifted owing to addition of the boric acid, which can stimulate the production of Vibrio harveyi AI‐2 anomer and repress the release of the Salmonella typhimurium AI‐2 anomer (Miller et al, 2004).
Early in the 1960s, Pigman and Isbell (1968) reported that ring‐closure reactions from unstable acyclic chain forms are extremely rapid, with reaction rate constants as high as 102 per minute. They also noted that the maximum mutarotation rate between the two cyclic anomers is only about 10−2 per minute. At the same time, they noted that if there are no factors other than water to facilitate anomer mutarotation, the reaction rate is very slow, of the order 10−3 per minute (Isbell and Pigman, 1969). They further pointed out that this slow mutarotation rate can be increased by factors such as acids or bases. Therefore, we speculated that the ring‐closure reaction (from DPD to cyclic AI‐2 precursors) is a fast reaction, whereas the mutarotation rate of different cyclic AI‐2 anomers is the slow step for forming specific quorum‐sensing AI‐2 signal. Our initial AI‐2 synthesis rate was based on a slow sugar cyclic anomers’ mutarotation rate under water's catalysis, which is in the range of the reported literature data. During the simulations with glucose, we increased the initial AI‐2 synthesis rate to match experimental data. However, according to the current knowledge of the AI‐2 synthesis process, the conversion of DPD to AI‐2 is determined exclusively by mass action kinetics at a presumably constant temperature, pressure, pH, etc. Hence, it is infeasible that the AI‐2 reaction rate from DPD, as described here, will increase so dramatically unless the concentration of DPD within the cell increases concomitantly, which is seemingly also infeasible.
In order to rectify these discrepancies, it is logical that other enzyme‐ or chaperone‐mediated activities interact with the DPD → AI‐2 reaction or other pathways lead to a substantial (∼2 to 3‐fold) increase in flux to DPD within the cell. Hauck et al (2003) already demonstrated the existence of an alternative pathway to AI‐2 and Tavender et al (2004) showed that ribulose‐5‐phosphate can strongly induce the bioluminescence of AI‐2‐specific response reporter). Adenosine can be shunted to ribulose‐5‐phosphate through pentose phosphate metabolism; therefore, we suspect that ribose sugar phosphates may be possible candidates for conversion to AI‐2. Independently, we measured transcript levels of the enzymes involved in the oxidative pentose phosphate pathway (catalyzing reactions from glucose‐6‐phosphate to ribulose‐5‐phosphate) and they were observed to increase about 1.4‐ to 2.1‐fold owing to the presence of glucose (in DNA microarray experiments not shown here; Wang et al, in preparation). Increased activity of these enzymes may yield more ribulose‐5‐phosphate, a putative precursor for AI‐2 (Hauck et al, 2003; Tavender et al, 2004).
It is particularly noteworthy that there are two different structures of AI‐2 reported from the same precursor, DPD (Chen et al, 2002; Miller et al, 2004), in two different biological systems. If there is more than one reaction for producing or consuming one metabolite, it is more likely that one reaction dominates (Almaas et al, 2004). Based on this theory, one autoinducer structure should be favored. Bassler and co‐workers (Miller et al, 2004)have already demonstrated this by showing that the AI‐2 structure in V. harveyi is distinct from that in S. typhimurium, where boric acid can shift the direction/equilibrium of these two different structure signal molecules. It is not unreasonable to suggest that under different biological contexts (microbe, microenvironment, etc.), the pathways for the formation of AI‐2 are different. This is corroborated by our calculations demonstrating that the AI‐2 synthesis rates in the absence and presence of glucose are different and change over time. One might even expect that the resultant AI‐2 structure varies as growth condition changes. Analogously, we have already demonstrated that genes affected by luxS mutation vary with growth condition, such as cell density or glucose addition (Wang et al, 2005b).
Questions such as these arise, and can be put into an experimental context, upon the examination of model simulations relative to experimental observations. The use of SPN in Mobius environment makes the implementation of a model easier than using other programming languages; there is no need to write specific code for each model. This makes it easy to replicate, modify, or extend a particular model (Goss and Peccoud, 1998), so that a large system can be decomposed into several small systems, which can then be reconstituted into more complex systems of larger scale. Indeed, our current model was originally comprised of an AI‐2 synthesis model only. This makes it possible to achieve an integrated understanding of the hierarchical nature of quorum signaling regulatory cascades. For different layers of genetic pathways, from available biological information, we can construct models as we did in this study, then modify and integrate them for a global model based on experimental validation.
Materials and methods
Plasmid, bacterial strains, and culture conditions
pTrcHisC (Invitrogen) was used for construction of pTrcHis‐pfs and pTrcHis‐luxS. Detailed methods for plasmid construction are outlined elsewhere (Hashimoto et al, in preparation). These plasmids were subsequently transformed into the strains DH5α and NC13: DH5α carrying pTrcHis‐pfs and NC13 carrying pTrcHis‐luxS, for overexpressing Pfs and LuxS, respectively. Glucose, biotin (Cadieux et al, 2002), and IPTG, when present, were added at 0.8%, 10 ng/ml, and 1 mM, respectively. Bacterial strains and plasmids used in this paper are summarized in Table VI.
AI‐2 activity assay
E. coli cell‐free culture supernatants were tested for the presence of AI‐2 using the V. harveyi reporter strain BB170 (Surette and Bassler, 1998). Briefly, 20 μl of AI‐2 cell‐free supernatant was mixed with 180 μl of BB170 suspension, which was prepared by 5000‐fold dilution of a 16‐h overnight culture in AB medium. A 20 μl portion of growth medium (AB and LB medium) was added to 180 μl BB170 suspension as negative control. All the cultures were grown at 30°C and 225 r.p.m. (New Brunswick Scientific); bioluminescence was measured hourly. Fold activation was calculated by bioluminescence from experimental samples divided by that of the negative controls, and then normalized by cell optical density.
RNA preparation and Northern blot analysis
Overnight cultures grown in LB were diluted 100‐fold into fresh LB and grown to mid‐exponential phase, then diluted again into LB or LB with glucose at OD600 near 0.03. Cultures were then incubated at 30°C with shaking at 250 r.p.m. Total RNA was isolated and diluted on an OD equivalent basis from culture volumes equivalent to 1 ml at an OD600 of 1.0 using a Qiagen RNeasy mini kit (Qiagen, Valencia, CA). Same amount of RNA was loaded on a 1% formaldehyde agarose gel and then transferred to a positively charged nylon membrane. A digoxygenin DNA labeling and detection kit (Boehringer Mannheim) was used for labeling DNA probes and detection according to the manufacturer's instructions. For probe construction, the following oligonucleotides were used: luxS1
5′‐CTAGATGTGCAGTTCCTGCAA‐3′ and luxS2
5′‐ATGCCGTTAGATAGCTTC‐3′ for a luxS‐specific probe; pfs1
5′‐AATCGGGCTTATCGCGAGTAAA‐3′ and pfs2
5′‐GCAAGTTTCTGCACCAGTGACTC‐3′ for a pfs‐specific probe; speD1
5′‐GCGCGACGGTTATATTATATC‐3′ and speD2
5′‐CGCTAATCAATGGTTACGATATCGGA‐3′ for a speD‐specific probe. Northern results were repeated in triplicate and quantified using NIH ImageJ software.
cDNA was synthesized from total RNA with random hexamers using the SuperScript™ III First‐Strand Synthesis System for RT–PCR (Invitrogen) according to the manufacturer's instructions. Primers were designed and purchased from Integrated DNA Technologies (Coralville, IA). Regular PCR was used to check the uniqueness of the primers before using the cDNA for quantification PCR. Real‐time RT–PCR was performed in 50 μl of reaction mixture containing the Platinum SYBR Green qPCR Supermix UDG (Invitrogen), 0.2 μM of primers, and cDNA (50°C, 2 min; 95°C, 2 min; 95°C, 15 s, 40 cycles; 60°C, 1 min). The reaction and detection of dye‐labeled PCR products were performed with an Applied Biosystems 7300 Real‐time PCR System (Applied Biosystems). 16S rRNA was used as the endogenous control and primers are listed in Table VII. Samples obtained from the 3 h time points of the LB with 0.8% glucose cultures were used to normalize data.
Culture volumes equivalent to 2 ml at an OD600 of 1.0 were withdrawn at the growth of 6 h time point and spun down at 12 000 r.p.m. for 5 min in a microcentrifuge. The cell pellets were resuspended and lysed in 300 μl BugBuster protein extraction reagent (Novagen) under room temperature for 30 min and then spun down at 12 000 r.p.m. for 10 min. The soluble cell extract was 1:1 (v/v) mixed with sodium dodecyl sulfate (SDS) sampling buffer (12.5% 0.5 M Tris–HCl (pH 6.8), 10% glycerol, 2% SDS, 5% β‐mercaptoethanol, 0.0025% bromophenol blue), heated at 100oC for 5 min, and vortexed. Samples were loaded onto a 15% SDS–polyacrylamide gel for electrophoresis. Proteins were visualized by staining with Coomassie blue and quantified after developing linearized standard curves with purified proteins.
We thank BL Bassler, H Aiba, R Kolter, A Hochschild, LI Rothfield, and M Berlyn for generously providing strains and plasmids used in the study. We are very grateful to Daniel Mitchell and Stephen Ramsey for the wonderful discussions and suggestions about SBML. We are grateful J March for the proofreading. This work was supported by the National Science Foundation (grants BES‐0124401 and BES‐0222687).
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