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Cell cycle control and environmental response by second messengers in Caulobacter crescentus



Second messengers, c-di-GMP and (p)ppGpp, are vital regulatory molecules in bacteria, influencing cellular processes such as biofilm formation, transcription, virulence, quorum sensing, and proliferation. While c-di-GMP and (p)ppGpp are both synthesized from GTP molecules, they play antagonistic roles in regulating the cell cycle. In C. crescentus, c-di-GMP works as a major regulator of pole morphogenesis and cell development. It inhibits cell motility and promotes S-phase entry by inhibiting the activity of the master regulator, CtrA. Intracellular (p)ppGpp accumulates under starvation, which helps bacteria to survive under stressful conditions through regulating nucleotide levels and halting proliferation. (p)ppGpp responds to nitrogen levels through RelA-SpoT homolog enzymes, detecting glutamine concentration using a nitrogen phosphotransferase system (PTS Ntr). This work relates the guanine nucleotide-based second messenger regulatory network with the bacterial PTS Ntr system and investigates how bacteria respond to nutrient availability.


We propose a mathematical model for the dynamics of c-di-GMP and (p)ppGpp in C. crescentus and analyze how the guanine nucleotide-based second messenger system responds to certain environmental changes communicated through the PTS Ntr system. Our mathematical model consists of seven ODEs describing the dynamics of nucleotides and PTS Ntr enzymes. Our simulations are consistent with experimental observations and suggest, among other predictions, that SpoT can effectively decrease c-di-GMP levels in response to nitrogen starvation just as well as it increases (p)ppGpp levels. Thus, the activity of SpoT (or its homologues in other bacterial species) can likely influence the cell cycle by influencing both c-di-GMP and (p)ppGpp.


In this work, we integrate current knowledge and experimental observations from the literature to formulate a novel mathematical model. We analyze the model and demonstrate how the PTS Ntr system influences (p)ppGpp, c-di-GMP, GMP and GTP concentrations. While this model does not consider all aspects of PTS Ntr signaling, such as cross-talk with the carbon PTS system, here we present our first effort to develop a model of nutrient signaling in C. crescentus.


Caulobacter crescentus is an oligotrophic, Gram-negative α-proteobacterium, frequently found in freshwater environments. C. crescentus undergoes asymmetric cell division, yielding two distinct progeny cells (Fig. 1): a non-motile ‘stalked’ cell (st) immediately re-enters the cell cycle and initiates DNA replication, while a motile ‘swarmer’ cell (sw) explores its environment before differentiating into a stalked cell and re-entering the cell cycle [1]. The stalked cell is equipped with a holdfast to attach to solid surfaces in its environment, whereas the swarmer cell develops a flagellum to move around in search of a suitable nutrient environment. The asymmetric cell cycle affords C. crescentus a certain flexibility to cope with the vagaries of life in an oligotrophic, aquatic environment [2].

Fig. 1

The asymmetric cell cycle of C. crescentus. A stalked cell is non-motile with a holdfast. A swarmer cell is motile with pili and a flagellum. A swarmer cell transforms into a stalked cell before DNA replication commences. CtrA regulates cell cycle progression in time and space. CtrA is eliminated during the G1-to-S transition. The green intensity indicates increasing concentrations of CtrA during cell cycle progression. ClpXP, a protease specific for CtrA, shows up at the old pole of a cell to degrade CtrA. c-di-GMP cooperates with ClpXP for CtrA proteolysis

Since asymmetric cell division plays an essential role in survival for C. crescentus, understanding how the asymmetry is regulated provides insight into the life cycle of many bacteria with similar characteristics. Many proteins, genes, and other molecules involved in the asymmetric pattern have been reported [2, 3]. CtrA, a master regulator of the C. crescentus life cycle, regulates more than 100 genes involved in flagellum biogenesis, DNA replication, and cell division [4, 5]. As CtrA inhibits the initiation of DNA replication, active CtrA (the phosphorylated form) must be eliminated during the swarmer-to-stalked (G1-to-S) transition. There are two pathways to inactivate CtrA: proteolysis by ClpXP [6] and dephosphorylation by CckA [7].

In C. crescentus, the spatio-temporally regulated proteolysis of CtrA requires protease ClpXP and additional factors called adaptors [6, 8]. The adaptor complex consists of CpdR, RcdA, PopA, and a second messenger c-di-GMP (cdG) (Fig. 2). ClpXP primed by unphosphorylated CpdR localizes at the old pole (Fig. 1) and recruits the adaptor RcdA which directly interacts with PopA. PopA must be bound with cdG to adapt CtrA to the entire protease complex (Fig. 2), which means cdG is indispensable for CtrA proteolysis. In addition to regulating CtrA proteolysis, cdG also participates in CtrA dephosporylation through CckA [7]. CckA is a bifunctional enzyme, which can act as both a phosphatase and a kinase to regulate CtrA and CpdR. When cdG binds with CckA, CckA activity favors the phosphatase state over the kinase state. When cdG level peaks during the G1-to-S transition, the dephosphorylation of CtrA and CpdR is rapidly stimulated, which allows DNA replication to initiate [9]. In this way, cdG stimulates DNA replication by activating the dephosphorylation and degradation of CtrA (Fig. 2).

Fig. 2

c-di-GMP regulates DNA replication and cell motility through CtrA. (Left-hand side) cdG directly stimulates phosphatase activity of CckA, thereby dephosphorylating CtrA to allow the initiation of DNA replication. (Right-hand side) cdG is also required for CtrA proteolysis

While cdG stimulates the G1-to-S transition, alternative guanine-nucleotide based secondary messengers, guanosine tetraphosphate and guanosine pentaphosphate ((p)ppGpp), promote mobility and cell cycle arrest in C. crescentus. While the exact mechanisms are unknown, it is understood that (p)ppGpp indirectly promotes stablization of CtrA and degradation of DnaA, as well as interacting with RNA polymerase to influence global gene expression [10].

Additionally, cdG and (p)ppGpp control several key processes to help bacteria adjust to environmental cues, such as depletion of nutrients [10, 11]. There is evidence that bacteria accumulate (p)ppGpp in response to carbon and/or nitrogen limitation [10] by regulating RelA-SpoT homolog (RSH) enzymes. Furthermore, bacteria respond to the availability of carbon through cdG-regulated signaling processes [11]. However, the specific mechanisms by which stressful conditions affect cell cycle progression through the second messenger system and other key proteins in C. crescentus is not clear.

In this work, we combine cdG, (p)ppGpp, and GTP into one mathematical model to investigate the dynamics of these second messengers and how they respond to environmental changes through the PTS Ntr. Our model suggests that the concentration of cdG decreases dramatically following nitrogen deprivation in response to increased synthetase and decreased hydrolase activity of the bifunctional enzyme, SpoT. This observation suggests a novel mechanism by which C. crescentus may regulate its cell cycle in response to nitrogen availability. Our model also suggests that (p)ppGpp-associated stability of CtrA may be a result of reduced cdG activity due to depletion of GTP. The dynamics of PTS Ntr enzymes have not yet been measured experimentally, however our model predicts how they might behave under various levels of nitrogen availability. Intracellular glutamine, phosphoenolpyruvate (PEP), and pyruvate (Pyr) affect the phosphorylation state of PTS Ntr enzymes in our model, which suggests that a stringent response to nutrient availability by guanine nucleotide-based second messengers may be enforced through both glutamine level and the concentrations of PEP and pyruvate.


Diagram construction

Metabolism and characterization of c-di-GMP

The cellular concentration of cdG is regulated by its synthesis by diguanylate cyclases (DGCs) and its degradation by phosphodiesterases (PDEs) [12]. DGCs (like PleD and DgcB), whose activities reside in the highly conserved GGDEF domain, act as dimers to produce cdG from two GTP molecules [13]. cdG negatively regulates its own synthesis by allosterically binding with the I-site of DGCs to inhibit synthetase activity [12].

PDEs (such as PdeA and PdeB) cleave cdG to linear diguanylate (pGpG) or to GMP, based on the conserved EAL domain or HD-GYP domain, respectively [13]. As pGpG is eventually converted into GMP (Fig. 3), we ignore pGpG in the model and consider two molecules of GMP as the product of cdG degradation. In addition, the activity of some PDEs in C. crescentus is activated by binding GTP [14]. The initial velocity of hydrolysis by PDEs reaches V max/2 when the concentration of GTP is 4 μM. Because GTP concentration in bacteria is much higher than 4μM [1517], we assume PDEs are constantly saturated with GTP and do not include this interaction in our model.

Fig. 3

Schematic diagram of cdG metabolism. DGCs catalyze the synthesis of cdG. PDEs cleave cdG into pGpG, which is subsequently cleaved to two molecules of GMP

Metabolism and characterization of (p)ppGpp

(p)ppGpp accumulates in most bacteria under stressful conditions, such as nutrient starvation [10, 18]. In C. crescentus, (p)ppGpp delays the entry into S phase and the swarmer-to-stalked cell transition. This response gives C. crescentus an advantage in nutrient-deprived environments by maintaining its mobility to search for better environments and by delaying DNA replication to conserve energy [11]. C. crescentus utilizes the bifunctional enzyme SpoT, an RSH homologue, to catalyze the conversion between (GTP)GDP and (p)ppGpp [1820] (Figs. 4, 5).

Fig. 4

Metabolism of (p)ppGpp. SpoT, a bifunctional enzyme in C. crescentus, catalyzes both the synthesis and hydrolysis of (p)ppGpp

Fig. 5

Diagram of our second messenger model. Glutamine (Gln) acts as the nitrogen signal, which regulates the phosphorylation state of PTS Ntr enzymes. Solid black arrows represent conversion between molecular species. Solid purple lines indicate transfer of phosphoryl groups between species. Phosphoryl transfer is reversible. Dashed lines represent allosteric influences on reaction rates (an arrow-head represents activation and a bar-head represents inhibition). Dashed line 1 indicates product-inhibition based on cdG binding to the I-site of DGCs. Dashed line 2-1 indicates that phosphorylated NPr indirectly activates the synthase activity of SpoT, and dashed line 2-2 indicates that phosphorylated EIIA Ntr directly inhibits the hydrolase activity of SpoT

It has been reported that (p)ppGpp inhibits the synthesis of GMP and GDP through binding the corresponding synthetases, such as HPRT, GMK, and their homologues [21, 22]. The binding affinity of HPRT for pppGpp is Kd = 3.38 μM in E. coli, but only 0.24 μM in C. crescentus [22]. We ignored this inhibition (Fig. 5) because the HPRT homologue should be saturated with basal levels of (p)ppGpp in bacteria (10-50 μM [11, 22]).

Nitrogen phosphotransferase system

It has been well documented that (p)ppGpp responds to carbon and nitrogen deprivations [11, 19, 21]. While the specific mechanism underlying carbon starvation is not yet clear, the mechanism responsible for nitrogen starvation has been recently elucidated [10]. The accumulation of (p)ppGpp following nitrogen starvation is regulated by the nitrogen phosphotransferase system (PTSNtr) [10, 18].

The PTS Ntr consists of three components (EINtr,NPr,and EIIANtr) which form a phosphorylation cascade (Fig. 5). The first protein EI Ntr initiates the cascade through autophosphorylation using PEP as the phosphoryl donor. Then the phosphoryl group is transferred from EI Ntr to NPr and then to EIIA Ntr. This process is reversible, so three components exchange phosphate groups and reach a steady state. EIIA Ntr can transfer its phosphate group to other unknown molecules [23]. We assume that the rate of phosphoryl transfer from EIIA Ntr to these other molecules outside of the PTS Ntr is far slower than the transfer rate among PTS Ntr proteins and the exchange with PEP and pyruvate. Therefore, we do not include a terminal phosphate sink in our model of the PTS Ntr.

Glutamine binds to the conserved GAF domain of EI Ntr (Fig. 6) to prevent its autophosphorylation. Because glutamine works as a powerful nitrogen signal, enzymes involved in the PTS Ntr become highly phosphorylated under nitrogen starvation when the intracellular level of glutamine decreases rapidly [10]. The PTS Ntr influences cdG dynamics by its effects on SpoT activity. Bacterial two-hybrid assays and mutant experiments [18] indicate that phosphorylated EIIA Ntr directly interacts with SpoT to inhibit hydrolase activity, whereas phosphorylated NPr activates SpoT synthetase activity indirectly (Fig. 5). In this way, the PTS Ntr, which senses nitrogen availability through glutamine, subsequently regulates SpoT activity and (p)ppGpp levels.

Fig. 6

Schematic diagram of EI Ntr structure and phosphate transfer. The C-terminus of EI Ntr bears a PEP-binding domain (PBD) and the N-terminus is responsible for binding NPr (NBD). The red dashed arrows indicate the direction of phosphate transfer. The separate GAF domain senses nitrogen availability by binding glutamine, which inhibits phosphoryl group transferred from PEP to EI Ntr

Mathematical model

Based on the diagram in Fig. 5, the reactions of our model are as follows:

The activity of DGCs is subject to product inhibition through binding of cdG. As two cdG molecules bind allosterically to each DGC dimer, we assumed that cdG inhibition of DGC is a cooperative process. Thus we expressed the activity of [DGC] as a Hill function with a Hill exponent of 2 (Table 1, Eq. (1)). Unlike DGCs, PDEs act as monomers, which convert cdG to pGpG or GMP [13]. pGpG is subsequently converted into GMP [10]. We assumed this reaction is very fast and ignored the intermediate pGpG.

$$2\text{GTP} \stackrel{\text{DGCs}}{\longrightarrow} \text{c-di-GMP}\stackrel{\text{PDEs}}{\longrightarrow} 2 \text{GMP}. $$
Table 1 Equations of our mathematical model*

As GDP and GTP can be interconverted and their products, ppGpp and pppGpp, behave similarly [11, 19, 24], we lumped GDP and GTP into a single variable, ‘GTP’, and ppGpp and pppGpp are also condensed into one variable, (p)ppGpp. These ‘variables’ are interconverted by the synthetase and hydrolase activities of SpoT (SpoT sd and SpoT hd, respectively). To take the direct and indirect effects of NPr P and EIIA Ntr P into consideration, we define a variable, α (Table 1), as the synthetase:hydrolase ratio of SpoT [25].

The interconversion of GTP, GDP and GMP is described compactly in our mathematical model by the reversible reaction

PEP binds to the C-terminal domain of EI and donates a phosphoryl group to His-189 (Fig. 6). Then the phosphoryl group is transferred to the next two enzymes, NPr and EIIA Ntr, in sequence [26, 27]. Glutamine binds to an allosteric site of EI Ntr (the GAF domain) [28] and inhibits phosphoryl transfer to His-189 [10, 29]. The phosphorylation cascade is summarized by the following reactions:

where EI Ptot= EI P + EI PPyr and EI tot= EI + EIPEP. EIPEP and EI PPyr indicate EI bound with PEP and EI P bound with Pyr, respectively. k±i (i=1,2,3) are the rate constants of phosphorylation reactions, while \(\phantom {\dot {i}\!}k_{\text {b}_{\pm j}}\) (j=1,2) are the rate constants of binding reactions.

Here, we make several assumptions to describe PTS Ntr reactions effectively:

  1. (1)

    As PEP binding to EI is a rapid process [26, 30], we assumed that PEP and Pyr binding reactions are much faster than phosphorylation reactions (reaching quasi-steady state) [26]. Therefore, we converted the binding reactions into algebraic equations (Table 1, Eqs. (8, 9)).

  2. (2)

    We assumed that EI P and EI PPyr phosphorylate NPr at the same rate, but EI Pyr is unstable and immediately dissociates into EI and Pyr. Similarly, we assumed that EI and EI PEPcan be phosphorylated by NPr P, but EI PPEP is unstable and immediately dissociates into EI P and PEP.

  3. (3)

    Since there is limited experimental data for the kinetic rate constants of the nitrogen PTS, we utilized experiments on the carbon PTS system to estimate these rate constants in our model. The kinetics of the carbon and nitrogen PTSs are likely very similar as they are homologues [31, 32].

  4. (4)

    The total concentrations of EI Ntr, NPr and EIIA Ntr are assumed to be constants [33]. We estimated the total concentrations to be: [EI Ntr] T = 10 μM, [NPr] T = 30 μM, and [EIIA Ntr] T = 30 μM [3436].

The resulting mathematical model consists of seven ODEs and five algebraic equations (Table 1 and Additional file 1). Parameters are defined in Table 2. Whenever possible, we estimated parameters from experimental data. Initial conditions in Table 3 were estimated from the intracellular concentrations in bacteria. The maximum concentration of cdG in C. crescentus is around 0.28 μM [37]. The basal levels of (p)ppGpp and GTP in Gram-negative bacteria during normal conditions are around 50 μM and 1000 μM [15], respectively. The ratio of [(p)ppGpp] to [GTP] in C. crescentus varies from 0.15 to 1.9 under rich and limited nitrogen conditions [20, 38, 39]. We used these values to calibrate our model. The ODEs were solved in MATLAB with ode15s.

Table 2 Parameters
Table 3 Initial conditions

Simulations and results

Oscillations of DGCs and PDEs

Two well-known DGCs in C.crescentus are DgcB and PleD [37, 41]. During progression through the cell cycle, DgcB level stays constant, but the concentration and activity of PleD vary [41]. Hence, we model [DGC] as the sum of constant [DgcB] and variable [PleD]. Because experimental data on the fluctuation of active (phosphorylated) PleD over the course of the C. crescentus cell cycle is not available, we used total PleD flucutations as a substitute. Figure 7a shows immunoblot measurements (red dots) of total PleD, extracted by ImageJ from [41], and the corresponding curve fitted by MATLAB (R-square is 0.66). It appears that the second data point from Abel et al. [41] is inaccurate because PleD activity should peak around t=20, since cdG needs to be produced at a high level at this time to deplete active CtrA and initiate the G1-to-S transition. Assuming that the second experimental point is an error, we re-fit the total PleD without this point (Fig. 7b, R-square is 0.84). In agreement with our expectations, the fitted curve in Fig. 7b increases during G1-to-S transition and peaks around 30 min. The corresponding accuracy of curve fitting improves as well. Additionally, we borrowed the active PleD simulation of an as-yet unpublished model by Bronson Weston (Fig. 7c, magenta curve) which captures the dynamics of phosphorylation of PleD. Weston’s simulation of PleD P (Fig. 7c) shows a similar trend with the experimental data and re-fitted curve of total PleD (Fig. 7b,c), which serves to justify our methods for calibrating a curve for PleD activity. The different scaled levels between Weston’s simulation and experimental points are due to different normalization methods.

Fig. 7

Curve-fitting of PleD and PdeA data. a Original experimental data of total PleD [41] and a curve fitted to the data by MATLAB. Function is 0.1442 ×sin\(\left (\frac {\pi }{75}t+0.5037\right)\)+0.7384. b Refitted PleD curve after deleting the second data point. New function is 0.1834 ×sin\(\left (\frac {\pi }{75}t+0.5587\right)\)+0.7579. c Weston’s simulation (unpublished) of phosphorylated PleD and comparison with re-fitted curve and experimental data from B. d Experimental measurements of PdeA [43] and its fitted curve. Function is -0.3605 × sin\(\left (\frac {\pi }{75}t+0.1767\right)\)+0.361

While PdeA is the most active phosphodiesterase enzyme in C. crescentus [44], other PDEs, including PdeB, PdeC, and PdeD, have been identified in bacterial species B. subtilis, E. coli and L. monocytogenes [45]. Assuming there are other PDEs in C. crescentus as well, we represented total [PDE] in our model as the sum of [basal PDE] plus a variable [PdeA] estimated by the curve-fitting tool in MATLAB applied to quantitative PdeA measurements derived from Western blots of [46] using ImageJ. The PdeA points and the corresponding curve are shown in Fig. 7d with R-square being 0.77.

Oscillation of c-di-GMP over cell cycle in C. crescentus

We used experimental data of cdG concentration (peak point) [37] and bacterial nucleotide concentrations to estimate parameters that are not available in publications. Experimentally, cdG peaks at the swarmer-to-stalked transition (≈0.28μM) and then decreases until reaching the lowest value (<0.1μM) in the swarmer cell after cell division. Our simulation of cdG over time fits experimental data well and shows a stable oscillation through the cell cycle under nutrient-rich conditions (Fig. 8), in agreement with experimental data [37].

Fig. 8

c-di-GMP oscillates during the cell cycle. Blue dots indicate experimental data of c-di-GMP in a single C. crescentus wild-type cell during one cell cycle [37]. Only c-di-GMP of a swarmer cell is shown. Black line indicates the simulated c-di-GMP in a swarmer cell at Gln=10000 μM, PEP=300 μM, and Pyr=1500 μM

Comparison of simulated PTS Ntr to carbon-PTS experimental data

PTS and PTS Ntr have a lot in common. Enzymes of PTS Ntr (EINtr,NPr,and EIIANtr) are homologues of carbon-PTS enzymes (EI, HPr, and EIIA/B/C) [31]. They have similar structures and play parallel roles in nutrient uptake. In addition, these PTSs communicate with each other by phosphate exchange [28, 47]. PEP acts as the phosphoryl donor for both carbon and nitrogen PTSs. There are two significant differences between these systems [28]: (1) Enzymes II in PTS (juxtamembrane EIIB and transmembrane EIIC) assist in transmembrane transport of sugars [48] whereas PTS Ntr does not aid in sugar transport [32]. (2) PTS Ntr is regulated by glutamine levels as part of the nitrogen signaling pathway in prokaryotes, while PTS senses carbon sources in the environment through regulating transport and phosphorylation of carbohydrates like glucose [34, 49].

There is limited quantitative data for PTS Ntr in publications. Based on the similarities between PTS Ntr and PTS, we introduced some parameters obtained from PTS experiments to simulate PTS Ntr [27, 33] (Table 2). In order to calibrate the PTS Ntr model, we set [Gln] to 0 and compared simulations with carbon PTS experiments.

Kundig and Roseman [26, 50] measured how EI and HPr levels affect phosphorylation of PTS quantitatively (Table 4). We set our initial conditions to the experimental conditions of the paper, substituting [Npr] and [EINtr] for [Hpr] and [EI], respectively. As there is no information about pyruvate concentrations in their experiments, we estimated the [Pyr] based on one set of experimental data in Table 4. The Table indicates that our PTS Ntr simulations fit the experimental data well.

Table 4 Effect of EI and HPr (NPr) concentrations on phosphorylation of EI and HPr (NPr) in PTS system

Simulations under different nutrients conditions

Goodwin et al. [42] measured quantitatively how glutamine inhibits EI Ntr activity. In Table 5, we show model simulations under a range of glutamine levels. Lee et al. [51] showed that cellular glutamine in E. coli is very low under nitrogen-starvation and increases to more than 10000 μM when environmental ammonium is increased. Therefore, in our simulations, we used [Gln]=1 μM to represent limited nitrogen and [Gln]=10000 μM to describe abundant nitrogen.

Table 5 Simulations under different conditions

PEP, the phosphoryl donor of PTS Ntr, is an important indicator of carbon availability [52]. However, Osanai et al. [53] and Yuan et al. [54] showed that PEP and Pyr levels are stable under nitrogen shifts. Hogema et al. [55] measured intracellular PEP and Pyr in E. coli under different carbon conditions: cells were initially grown in minimal medium (ammonia with limited carbon) and had PEP and pyruvate concentrations of 2800 μM and [Pyr]=900 μM, respectively. After adding 10mM glucose to the medium (now ammonia with high carbon), PEP and pyruvate concentrations shifted to 300 μM and 1500 μM, respectively. In consideration of this experimental data, we set ‘[PEP]=300 μM, [Pyr]=1500 μM, [Gln]=10000 μM’ to represent ‘ammonia with high carbon’; and ‘[PEP]=300 μM, [Pyr]=1500 μM, [Gln]=1 μM’ to represent ‘nitrogen-starved’ condition. As cells require carbon and nitrogen to synthesize glutamine, we regard limited glutamine (proposed as 1000-2000 μM in Table 5) and ‘[PEP]=2800 μM and [Pyr]=900 μM’ as ‘ammonia with limited carbon’.

Table 5 summarizes the results of our simulations. cdG oscillations peak at 0.28 μM under ’ammonia with high carbon’, and peak at 0.02 μM under nitrogen depletion. These results suggest that depletion of nitrogen should result in cell cycle arrest, which is consistent with experimental observations [56]. In general, as glutamine concentrations decrease, cdG, GTP and GMP levels decrease while (p)ppGpp levels increase.

When we simulate conditions of ‘ammonia with limited carbon’, we find that cdG oscillations decrease in amplitude; however, concentrations are presumably not so low to induce cell cycle arrest. Thus, our results are consistent with the fact that C. crescentus continues to grow under such conditions [55]. Interestingly, our results suggest that (p)ppGpp levels should increase when decreasing carbon availability. Our results suggest that shifts in PEP and pyruvate concentrations due to limiting carbon availability will make the cell more sensitive to shifts in nitrogen. Table 5 suggests, that shifts in the direction of increased [PEP] and decreased [Pyr] favor increased activity in SpoT synthetase. Based on steady state analysis of ODEs in our model, phosphorylation of PTS Ntr proteins depends non-linearly on the [PEP]:[Pyr] ratio (Additional file 2). Increases in the ratio generally trend towards SpoT synthetase activity, while decreases trend toward hydrolase activity.

Our simulations show that the shift of c-di-GMP and (p)ppGpp levels in response to changes of nutrients is due to both a shift in internal glutamine concentration and an adjustment to the PEP and pyruvate levels (Table 5). Our model suggests that the PEP and Pyr levels regulating PTS Ntr is one potential pathway of (p)ppGpp response to carbon availability. Enzymes within the PTS Ntr system become highly phosphorylated under nitrogen starvation (Table 5), which is consistent with the existing qualitative analysis as well [10]. Additionally, our simulation fits the experimental observations (Table 6) well.

Table 6 Experimental information for concentrations and changes under starvation

Response to environmental change

Given the oligotrophic environments C. crescentus populates, we postulate that C. crescentus would have to respond rapidly to sudden shifts in nutrients in order to increase its fitness in these environments. Figure 9 shows how C. crescentus responds to environmental nitrogen-shifts in our simulation. The response time for starvation is within one cell replication cycle, which means C. crescentus can respond to nutrient deprivation quickly according to our model. Perhaps even more importantly, our model suggests that C. crescentus also recovers quite quickly to normal cell cycle oscillations when we reset glutamine to the starting value. A response within the time frame of one cell cycle would be a useful characteristic for C. crescentus to survive in oligotrophic environments.

Fig. 9

Response to nitrogen-shifts in our simulation. Blue line indicates simulated levels of cdG, GTP, and (p)ppGpp when [Gln]=10000 μM. Red line indicates simulated levels of these three molecules when glutamine changes to 100 μM at simulation time 600. Yellow line indicates the simulation when the glutamine recovers to 10000 μM. The end point of previous simulation is used to be the initial point of the following simulation at a different glutamine level


Progression through the cell cycle in C. crescentus requires precise coordination of metabolic and morphological events. The guanine nucleotide-based second messenger network, including cdG and (p)ppGpp, plays significant roles in regulating bacterial morphology and metabolism, such as controlling the activity of CtrA and adapting bacteria to environmental changes. In this study, we propose a mathematical model to simulate the guanine nucleotide-based second messenger network, and investigate how this network responds to nutrient shifts through PTS Ntr.

We calibrate our model using experimental data, and investigate two aspects influencing phosphorylation of PTS Ntr in simulations: 1) glutamine levels, which affects autophosphorylation of EI Ntr [10, 28]; and 2) PEP and Pyr levels, which influence the flux of phosphorus through the PTS Ntr system (Table 5, Additional file 2).

Simulations of nitrogen deprivation suggest that as (p)ppGpp accumulates in C. crescentus, GTP and cdG concentrations decrease significantly as a result of increasing SpoT synthetase activity. While it is suggested that (p)ppGpp stabilizes CtrA in C. crescentus [60], the exact mechanism is unknown. As cdG is essential for CtrA proteolysis, the stability of CtrA may increase due to diminished cdG concentration as a result of SpoT synthetase activity, rather than downstream effects of (p)ppGpp signaling. Thus, we propose that C. crescentus may respond to nitrogen starvation by stimulating the PTS Ntr system to induce SpoT synthetase activity, resulting in depletion of GTP and cdG levels to induce cell cycle arrest via stabilization of the chromosome replication inhibitor, CtrA.

Importantly, our results also suggest that changes to intracellular concentrations of PEP and pyruvate can have a significant impact on SpoT activity. We find that shifts in PEP and pyruvate concentrations in response to decreased sugar availability result in an increase in SpoT synthetase activity and an increase in sensitivity to shifts in glutamine concentration. Thus, two potential avenues to influence the PTS Ntr and SpoT are through adjusting PEP and pyruvate levels as well as glutamine.

Conclusions and future work

Our mathematical model of guanine nucleotide-based second messenger network in C. crescentus (Fig. 5) agrees with experimental observations compiled from the literature. Most previous research has focused separately on cdG [14, 37] dynamics or the PTS Ntr system [10, 42] in bacteria, but has never related the second messenger network with the PTS Ntr system in order to study environmental impacts.

In this work, the interactions within the guanine nucleotide-based second messenger network are converted into a set of differential and algebraic equations (Table 1) to simulate second messenger response to nutrient conditions. cdG and (p)ppGpp, which play significant roles in cell cycle regulation, are connected with PTS Ntr to explain the relationship between bacterial development and environmental changes.

The current model consists of seven ODEs and five algebraic equations, describing the synthesis, degradation, activation, inhibition, phosphorylation, dephosphorylation, binding, and release of physiological variables in C. crescentus. Our resulting simulations are in good agreement with experiments and our model makes several intriguing predictions, however there are still several exciting directions that we can take this model:

  1. (1)

    To better understand how nitrogen signaling influences the cell cycle of bacteria, we can combine this second messenger model with a detailed regulatory model of the C. crescentus cell cycle [61]. It will be interesting to see if a shift in cdG concentration due to changes in SpoT activity will be enough to induce cell cycle arrest, or if intervention by (p)ppGpp is also necessary.

  2. (2)

    [PEP] and [Pyr] are adjustable signals in our model rather than variables. In the future, we hope to expand our model to include [PEP] and [Pyr] as dynamical variables to provide more insight into cell responses of nitrogen signaling.

  3. (3)

    Carbohydrate PTS catalyzes the uptake of carbohydrates [49], and it communicates with PTS Ntr through transfers of phosphoryl groups [62]. Therefore, including carbohydrate PTS into our model will help to understand environmental responses for both carbon and nitrogen shifts.

Availability of data and materials

The datasets generated and analysed during the current study are available at



cyclic di-GMP, c-di-GMP


alarmones guanosine tetraphosphate and guanosine pentaphosphate


phosphotransferase system


RelA-SpoT homolog


diguanylate cyclases










nucleoside disphosphate kinases


  1. 1

    Shen X, Collier J, Dill D, Shapiro L, Horowitz M, McAdams HH. Architecture and inherent robustness of a bacterial cell-cycle control system. Proc Natl Acad Sci U S A. 2008; 105(32):11340–5.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  2. 2

    Sánchez-Osorio I, Hernández-Martínez CA, Martínez-Antonio A. Modeling asymmetric cell division in Caulobacter crescentus using a boolean logic approach In: Tassan JPandKubiak JZ, editor. Asymmetric Cell Division in Development, Differentiation and Cancer. Results and Problems in Cell Differentiation, vol. 61. Cham: Springer International Publishing: 2017. p. 1–21.

    Google Scholar 

  3. 3

    Jenal U. The role of proteolysis in the Caulobacter crescentus cell cycle and development. Res Microbiol. 2009; 160(9):687–95.

    CAS  PubMed  Article  Google Scholar 

  4. 4

    Laub MT, Chen SL, Shapiro L, McAdams HH. Genes directly controlled by CtrA, a master regulator of the Caulobacter cell cycle. Proc Natl Acad Sci U S A. 2002; 99(7):4632–7.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  5. 5

    Ryan KR, Judd EM, Shapiro L. The CtrA response regulator essential for Caulobacter crescentus cell-cycle progression requires a bipartite degradation signal for temporally controlled proteolysis. J Mol Biol. 2002; 324(3):443–55.

    CAS  PubMed  Article  Google Scholar 

  6. 6

    Smith SC, Joshi KK, Zik JJ, Trinh K, Kamajaya A, Chien P, Ryan KR. Cell cycle-dependent adaptor complex for ClpXP-mediated proteolysis directly integrates phosphorylation and second messenger signals. Proc Natl Acad Sci U S A. 2014; 111(39):14229–34.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  7. 7

    Lori C, Ozaki S, Steiner S, Boehm R, Abel S, Dubey BN, Schirmer T, Hiller S, Jenal U. Cyclic di-GMP acts as a cell cycle oscillator to drive chromosome replication. Nature. 2015; 523(7559):236–9.

    CAS  PubMed  Article  Google Scholar 

  8. 8

    Joshi KK, Bergé M, Radhakrishnan SK, Viollier PH, Chien P. An adaptor hierarchy regulates proteolysis during a bacterial cell cycle. Cell. 2015; 163(2):419–31.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  9. 9

    Chen YE, Tsokos CG, Biondi EG, Perchuk BS, Laub MT. Dynamics of two phosphorelays controlling cell cycle progression in Caulobacter crescentus. J Bacteriol. 2009; 191(24):7417–29.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  10. 10

    Hallez R, Delaby M, Sanselicio S, Viollier PH. Hit the right spots: cell cycle control by phosphorylated guanosines in alphaproteobacteria. Nat Rev Microbiol. 2017; 15(3):137–48.

    CAS  PubMed  Article  Google Scholar 

  11. 11

    Kalia D, Merey G, Nakayama S, Zheng Y, Zhou J, Luo Y, Guo M, Roembke BT, Sintim HO. Nucleotide, c-di-GMP, c-di-AMP, cGMP, cAMP, (p)ppGpp signaling in bacteria and implications in pathogenesis. Chem Soc Rev. 2013; 42(1):305–41.!divAbstract.

    CAS  PubMed  Article  Google Scholar 

  12. 12

    Jenal U, Malone J. Mechanisms of cyclic-di-GMP signaling in bacteria. Annu Rev Genet. 2006; 40:385–407.

    CAS  PubMed  Article  Google Scholar 

  13. 13

    Schirmer T, Jenal U. Structural and mechanistic determinants of c-di-GMP signalling. Nat Rev Microbiol. 2009; 7(10):724–35.

    CAS  PubMed  Article  Google Scholar 

  14. 14

    Christen M, Christen B, Folcher M, Schauerte A, Jenal U. Identification and characterization of a cyclic di-GMP-specific phosphodiesterase and its allosteric control by GTP. J Biol Chem. 2005; 280(35):30829–37.

    CAS  PubMed  Article  Google Scholar 

  15. 15

    Corrigan RM, Bellows LE, Wood A, Gründling A. ppgpp negatively impacts ribosome assembly affecting growth and antimicrobial tolerance in gram-positive bacteria. Proc Natl Acad Sci U S A. 2016; 113(12):1710–9.

    Article  CAS  Google Scholar 

  16. 16

    Jagath J, Rodnina M, Wintermeyer W. Conformational changes in the bacterial SRP receptor FtsY upon binding of guanine nucleotides and SRP. J Mol Biol. 2000; 295(4):745–53.

    CAS  PubMed  Article  Google Scholar 

  17. 17

    Ratnayake-Lecamwasam M, Serror P, Wong K, Sonenshein A. Bacillus subtilis CodY represses early-stationary-phase genes by sensing GTP levels. Genes Dev. 2001; 15:1093–103.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  18. 18

    Ronneau S, Petit K, De Bolle X, Hallez R. Phosphotransferase-dependent accumulation of (p)ppGpp in response to glutamine deprivation in Caulobacter crescentus. Nat Commun. 2016; 7:11423.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  19. 19

    Hauryliuk V, Atkinson GC, Murakami KS, Tenson T, Gerdes K. Recent functional insights into the role of (p)ppGpp in bacterial physiology. Nat Rev Microbiol. 2015; 13(5):298–309.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  20. 20

    Boutte C, Crosson S. The complex logic of stringent response regulation in Caulobacter crescentus: starvation signalling in an oligotrophic environment. Mol Microbiol. 2011; 80(3):695–714.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  21. 21

    Kriel A, Bittner AN, Kim SH, Liu K, Tehranchi AK, Zou WY, Rendon S, Chen R, Tu BP, Wang JD. Direct regulation of GTP homeostasis by (p)ppGpp: a critical component of viability and stress resistance. Mol Cell. 2012; 48(2):231–41.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  22. 22

    Anderson BW, Liu K, Wolak C, Dubiel K, She F, Satyshur KA, Keck JL, Wang JD. Evolution of (p)ppGpp-HPRT regulation through diversification of an allosteric oligomeric interaction. eLife. 2019; 8:47534.

    Article  Google Scholar 

  23. 23

    Pflüger-Grau K, Chavarría M, de Lorenzo V. The interplay of the EIIA Ntr component of the nitrogen-related phosphotransferase system (PTSNtr) of Pseudomonas putida with pyruvate dehydrogenase. Biochim Biophys Acta-General Subj. 2011; 1810(10):995–1005.

    Article  CAS  Google Scholar 

  24. 24

    Hogg T, Mechold U, Malke H, Cashel M, Hilgenfeld R. Conformational antagonism between opposing active sites in a bifunctional RelA/SpoT homolog modulates (p)ppGpp metabolism during the stringent response. Cell. 2004; 117(3):415.

    CAS  Article  Google Scholar 

  25. 25

    Santillán M. On the Use of the Hill Functions in Mathematical Models of Gene Regulatory Networks. Math Model Nat Phenom. 2008; 3(2):85–97.

    Article  Google Scholar 

  26. 26

    Karelina TA, Ma H, Goryanin I, Demin OV. EI of the phosphotransferase system of Escherichia coli: mathematical modeling approach to analysis of its kinetic properties. J Biophys. 2011; 2011:579402.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  27. 27

    Weigel N, Kukuruzinska MA, Nakazawa A, Waygood EB, Roseman S. Sugar transport by the bacterial phosphotransferase system. phosphoryl transfer reactions catalyzed by enzyme i of Salmonella typhimurium,. J Biol Chem. 1982; 257(23):14477–91.

    CAS  PubMed  PubMed Central  Google Scholar 

  28. 28

    Pflüger K, de Lorenzo V. Evidence of In Vivo cross talk between the nitrogen-related and fructose-related branches of the carbohydrate phosphotransferase system of pseudomonas putida. J Bacteriol. 2008; 190(9):3374–80.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  29. 29

    Ely B, Amarasinghe A, Bender RA. Ammonia Assimilation and Glutamate Formation in Caulobacter crescentus. J Bacteriol. 1978; 133(1):225–30.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  30. 30

    Patel HV, Vyas KA, Mattoo RL, Southworth M, Perler FB. Properties of the C-terinal domain of Enzyme I of the Escherichia coli phosphotransferase system. J Biol Chem. 2005; 281(26):17579–87.

    Article  CAS  Google Scholar 

  31. 31

    Houot L, Chang S, Pickering BS, Absalon C, Watnick PI. The phosphoenolpyruvate phosphotransferase system regulates Vibrio cholerae biofilm formation through multiple independent pathways. J Bacteriol. 2010; 192(12):3055–67.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  32. 32

    Li YZ, Wang D, Feng XY, Jiao J, Chen WX, Tian CF. Genetic analysis reveals the essential role of nitrogen phosphotransferase system components in Sinorhizobium fredii CCBAU 45436 symbioses with Soybean and Pigeonpea Plants. Appl Environ Microbiol. 2016; 82(4):1305–15.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  33. 33

    Wang J, Gilles ED, Lengeler JW, Jahreis K. Modeling of inducer exclusion and catabolite repression based on a pts-dependent sucrose and non-pts-dependent glycerol transport systems in Escherichia coli k-12 and its experimental verification. J Biotechnol. 2001; 92(2):133–58. Biochemical Engineering: Trends and Potentials.

    CAS  PubMed  Article  Google Scholar 

  34. 34

    Postma PW, Lengeler JW, Jacobson GR. Phosphoenolpyruvate: Carbohydrate Phosphotransferase System of Bacteria. Microbiol Rev. 1993; 57(3):543–94.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  35. 35

    Mattoo RL, Waygood EB. Determination of the levels of HPr and enzyme I of the phosphoenolpyruvate-sugar phosphotransferase system in Escherichia coli and Salmonella typhimurium. Can J Biochem Cell Biol. 1983; 61(1):29–37.

    CAS  PubMed  Article  Google Scholar 

  36. 36

    Scholte BJ, Schuitema AR, Postma PW. Isolation of III Glc of the phosphoenolpyruvate-dependent glucose phosphotransferase system of Salmonella typhimurium. J Bacteriol. 1981; 148(1):1257–264.

    Article  Google Scholar 

  37. 37

    Abel S, Bucher T, Nicollier M, Hug I, Kaever V, Wiesch PAZ, Jenal U. Bi-modal distribution of the second messenger c-di-GMP controls cell fate and asymmetry during the Caulobacter cell cycle. PLOS Genetics. 2013; 9(9):1003744.

    Article  CAS  Google Scholar 

  38. 38

    Benoist C, Guérin C, Noirot P, Dervyn E. Constitutive stringent response restores viability of Bacillus subtilis lacking structural maintenance of chromosome protein. PLOS One. 2015; 10(11):e0142308.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  39. 39

    Boutte C, Henry JT, Crosson S. ppGpp and polyphosphate modulate cell cycle progression in Caulobacter crescentus. J Bacteriol. 2012; 194(1):28–35.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  40. 40

    Povolotsky TL, Hengge R. ‘Life-style’ control networks in Escherichia coli: Signaling by the second messenger c-di-GMP. J Biotechnol. 2012; 160(1-2):10–16.

    CAS  PubMed  Article  Google Scholar 

  41. 41

    Abel S, Chien P, Wassmann P, Schirmer T, Kaever V, Laub MT, Baker TA, Jenal U. Regulatory cohesion of cell cycle and cell differentiation through interlinked phosphorylation and second messenger networks. Mol Cell. 2011; 43(4):550–60.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  42. 42

    Goodwin RA, Gage DJ. Biochemical characterization of a nitrogen-type phosphotransferase system reveals that enzyme EI Ntr integrates carbon and nitrogen signaling in Sinorhizobium meliloti. J Bacteriol. 2014; 196(10):1901–7.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  43. 43

    Joshi KK, Battle CM, Chien P. Polar localization hub protein PopZ restrains adaptor-dependent ClpXP proteolysis in Caulobacter crescentus. J Bacteriol. 2018; 200(20):e00221–18.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  44. 44

    Kharadi R, Castiblanco F, Waters M, Sundina W. Phosphodiesterase genes regulate amylovoran production, biofilm formation, and virulence in Erwinia amylovora. Appl Environ Microbiol. 2019; 85(1):02233–18.

    Google Scholar 

  45. 45

    Purcell EB, Tamayo R. Cyclic diguanylate signaling in Gram-positive bacteria. FEMS Microbiol Rev. 2016; 40(5):753–73.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  46. 46

    Abel S. Analysis of the c-di-GMP mediated cell fate determination in Caulobacter crescentus. PhD thesis, Universität Basel, Department of Biozentrum. 2009.

  47. 47

    Commichau FM, Forchhammer K, Stülke J. Regulatory links between carbon and nitrogen metabolism. Curr Opin Microbiol. 2006; 9(2):167–72. Cell Regulation / Edited by Werner Goebel and Stephen Lory.

    CAS  PubMed  Article  Google Scholar 

  48. 48

    Deutscher J, Aké F, Derkaoui M, Zébré A, Cao T, Bouraoui H, Kentache T, Mokhtari A, Milohanic E, Joyet P. The bacterial phosphoenolpyruvate: carbohydrate phosphotransferase system: regulation by protein phosphorylation and phosphorylation-dependent protein-protein interactions. Microbiol Mol Biol Rev. 2014; 78(2):231–56.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  49. 49

    Deutscher J, Francke C, Postma W. How phosphotransferase system-related protein phosphorylation regulates carbohydrate metabolism in bacteria. Microbiol Mol Biol Rev. 2006; 70(4):939–1031.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  50. 50

    Kundig W, Roseman S. Sugar transport. i. isolation of a phosphotransferase system from Escherichia coli,. J Biol Chem. 1971; 246(5):1393–406.

    CAS  PubMed  PubMed Central  Google Scholar 

  51. 51

    Lee C, Park Y, Kim M, Kim Y, Park S, Peterkofsky A, Seok Y. Reciprocal regulation of the autophosphorylation of Enzyme I Ntr by Glutamine and α-Ketoglutarate in Escherichia coli. Mol Microbio. 2013; 88(3):473–85.

    CAS  Article  Google Scholar 

  52. 52

    Brauer MJ, Yuan J, Bennett BD, Lu W, Kimball E, Botstein D, Rabinowitz JD. Conservation of the metabolomic response to starvation acroos two divergent microbes. PNAS. 2006; 103(51):19302–7.

    CAS  PubMed  Article  Google Scholar 

  53. 53

    Osanai T, Oikawa A, Shirai T, Kuwahara A, Lijima H, Tanaka K, Ikeuchi M, Kondo A, Saito K, Hirai MY. Capillary electrophoresis–mass spectrometry reveals the distribution of carbon metabolites during nitrogen starvation in Synechocystis sp. PCC 6803. Environ Microbiol. 2014; 16(2):512–24.

    CAS  PubMed  Article  Google Scholar 

  54. 54

    Yuan J, Doucette CD, Fowler WU, Feng XJ, Piazza M, Rabitz HA, Wingreen NS, Rabinowitz D. Metabolomics-driven quantitative analysis of ammonia assimilation in E.coli. Mol Sys Biol. 2009; 5(302):19302–7.

    Google Scholar 

  55. 55

    Hogema BM, Arents JC, Bader R, Eijkemans K, Yoshida H, Takahashi H, Alba H, Postma PW. Inducer exclusion in Escherichia coli by non-PTS substrates: the role of the PEP to pyruvate ratio in determining the phosphorylation state of enzyme IIA Glc. Mol Microbiol. 1998; 30(3):487–98.

    CAS  PubMed  Article  Google Scholar 

  56. 56

    Gorbatyuk B, Marczynski GT. Regulated degradation of chromosome replication proteins DnaA and CtrA in Caulobacter crescentus. Mol Microbiol. 2005; 55(4):1233–45.

    CAS  PubMed  Article  Google Scholar 

  57. 57

    Flärdh K, Axberg T, Albertson N, Kjelleberg S. Stringent control during carbon starvation of marine Vibrio Sp. Strain S14: molecular cloning, nucleotide sequence, and deletion of the relA gene. J Bacteriol. 1994; 176(19):5949–57.

    PubMed  PubMed Central  Article  Google Scholar 

  58. 58

    Bennett B, Kimball E, Gao M, Osterhout R, Van Dien S, Rabinowitz D. Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli. Nat Chem Biol. 2009; 5(8):593–9.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  59. 59

    Fischer M, Zimmerman TP, Short SA. A rapid method for the determination of Guanosine 5-triphosphate- 3-diphosphate by high-performance liquid chromatography. Anal Biochem. 1982; 121(1):135–9.

    CAS  PubMed  Article  Google Scholar 

  60. 60

    Gonzalez D, Collier J. Effects of (p)ppGpp on the progression of the cell cycle of Caulobacter crescentus. J Bacteriol. 2014; 196(14):2514–25.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  61. 61

    Li S, Brazhnik P, Sobral B, Tyson JJ. Temporal controls of the asymmetric cell division cycle in Caulobacter crescentus. PLOS Comput Biol. 2009; 5(8):e1000463.

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  62. 62

    Kremling A, Pflüger-Grau K, Chavarria M, Puchalka J, Santos V. Modeling and analysis of flux distributions in the two branches of the phosphotransferase system in Pseudomonas putida. BMC Syst Biol. 2012; 6(149):149.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

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This article has been published as part of BMC Bioinformatics Volume 21 Supplement 14, 2020: Selected original articles from the Sixth International Workshop on Computational Network Biology: Modeling, Analysis, and Control (CNB-MAC 2019): bioinformatics. The full contents of the supplement are available online at


This work was partially supported by the National Science Foundation (NSF) under awards CCF-1526666, MCB-1613741, and CCF-1909122. The funding sources played no role in the design of the study and collection, analysis, and interpretation of data and in writing the manuscript. Publication of this article is supported by NSF award CCF-1909122.

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BW conceptualized the project. CX and BW designed model equations and analyzed data. CX ran simulations, paramaterized the model, and wrote the first draft of the manuscript. CX, BW, and JT contributed to the text of the final draft of the manuscript. JT and YC provided biochemical expertise and computational technology, respectively. All author(s) read and approved the final manuscript.

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Correspondence to Yang Cao.

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Additional file 1

Calculations for ordinary differential equations.

Additional file 2

Phosphorylation of PTS Ntr is non-linearly dependent on the [PEP]:[Pyr] ratio in simulation.

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Xu, C., Weston, B.R., Tyson, J.J. et al. Cell cycle control and environmental response by second messengers in Caulobacter crescentus. BMC Bioinformatics 21, 408 (2020).

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  • c-di-GMP
  • (p)ppGpp
  • Caulobacter crescentus
  • Nitrogen starvation
  • Cell cycle