Modular architecture of the glucose PTS and mathematical modeling
We present a biochemical map of the E. coli
glucose PTS () and developed a dynamic model from this map (Supplementary Tables S1 and S2
; see also Materials and methods) by using CADLIVE (Kurata et al, 2005
). Details of the graphical notation are described elsewhere (Kurata et al, 2003
). Generally, it is of great importance to increase the sugar uptake rate for enhanced substance production. We aimed at increasing the glucose uptake rate. To assign a particular function to each gene in terms of an enhanced uptake rate, the biochemical map of the glucose PTS was decomposed into functional modules () and flux modules () analogous to an engineering control systems block diagram (Kurata et al, 2006
). Specifically, if we define the phosphotransfer cascade of IICBGlc
), HPr (ptsH
), and EI (ptsI
) as the plant to be controlled, then the entity that drives this plant is the signal from the accelerator actuator. The phosphorylation signal of IIAGlc
-P is sensed by the FB sensor module and sent to the computer module that consists of adenylate cyclase (CYA), cyclic AMP (cAMP), and cAMP receptor protein (CRP), while it is also transmitted to the signal transduction pathways to enhance other carbon transport systems. The complex of IIAGlc
-P:CYA, which is formed in the FB sensor module, produces the cAMP signal in the computer module, resulting in the formation of CRP:cAMP. CRP:cAMP is the output of the computer module, which modulates the accelerator and brake actuator modules. The accelerator actuator module comprises the synthesis process of the IICBGlc
, HPr, and EI proteins, supplying these PTS proteins to the plant module; the brake actuator module of the Making Large Colonies Protein (Mlc) suppresses the synthesis of the same PTS proteins.
Superimposed on these functional modules, we identify two major flux modules, the accelerator flux module and the brake flux module. Although our description of these fluxes is qualitative, the components of the fluxes can be easily identified in . First, we identified the accelerator flux module where the signal of the IIAGlc-P increase goes through the FB sensor, computer, accelerator actuator, and plant modules to induce the synthesis of IICBGlc, HPr, and EI (). Second, we identified the brake flux module where the signal of the IIAGlc-P increase goes through the FB sensor, computer, brake actuator, accelerator actuator, and plant modules, which regulates the PTS component synthesis by suppressing the accelerator actuator.
We provide an example of the signal processing under glucose depletion conditions. Since the phosphorous of IIAGlc-P is not transferred to glucose, the IIAGlc-P concentration immediately increases. The sensor module then assesses an increase in the signal molecule, transmitting its information to the computer module. The computer module calculates the output signal necessary for an adequate control action, which is transmitted simultaneously to the accelerator actuator module and the brake actuator module. The phosphotransfer activity in the plant module is determined by the balance between the accelerator and brake actuator modules.
The mathematical equations can be connected to the functional modules for the full model (Supplementary Table S1
). In this model, Equations (1.1–1.8) in Supplementary Table S1
describe the plant module, which corresponds to the phosphotransfer reactions in the PTS. Equations (2.1–2.3) in Supplementary Table S1
describe the FB sensor module, which senses the extracellular glucose concentration. The computer module corresponds to Equations (3.1–3.13), which contains transcription and translation of the crp
genes and cAMP production. The brake actuator module corresponds to Equations (4.1–4.13), which describes the role of the Mlc protein. Equations (5.1–5.26) show the accelerator actuator module, which contains the transcription and translation reactions of the ptsG
, and crr
To demonstrate how the mathematical model reproduces the dynamic behaviors of the glucose PTS with respect to glucose, we simulated the model as shown in . These dynamic behaviors were very consistent with the experimental data. As shown in , the concentration of IIAGlc-P rapidly increased just after glucose depletion, while that of IIAGlc decreased. Since phosphorus is not transferred to glucose due to its depletion, the phosphorylated proteins accumulate in the plant module. As shown in , the concentration of cAMP greatly increased in response to glucose depletion and gradually decreased after the peak, then reached a steady-state. The accumulated IIAGlc-P protein, which is assumed to be the signal for adenylate cyclase activation, binds to adenylate cyclase in the FB sensor module, thereby enhancing the synthesis of cAMP. As shown in , the concentration of the complex of Mlc and promoter 1 for the ptsG gene increased in response to glucose depletion, which resulted from the decrease in the IICBGlc concentration. Consequently, the complex of Mlc and promoter 1 of the ptsG gene suppresses the gene expression of the ptsG gene. In the same manner, ptsH and ptsI gene expression was suppressed by the complex of Mlc and promoter 0 of the ptsH and ptsI genes. If the concentration of IICBGlc is high, IICBGlc captures Mlc to prevent Mlc from binding to promoter 1 of the ptsG gene, which permits transcription to proceed. As shown in , the expression of the ptsG, ptsH, and ptsI genes diminished in response to glucose depletion. This suppression was caused mainly by the brake actuator module. Actually, since the effect of the brake actuator module is greater than that of the accelerator actuator module in the absence of glucose, the synthesized Mlc protein suppresses the transcription of the ptsG, ptsH, and ptsI genes. The phosphotransfer activity decreases in the plant module, thereby decreasing glucose uptake. In the PTS, to solve the problem of glucose depletion, the signal of glucose depletion, the accumulated IIAGlc-P, is transferred to the signal transduction pathways to enhance other carbon transport systems.
Figure 3 Simulated time course for molecular concentrations in response to glucose depletion in the PTS. The extracellular glucose concentration was changed from 0.2 M to 0.2 nM at 510 min. (A) Time evolution for IIAGlc protein in the phosphate relay cascade. (more ...)
Validation of the mathematical model by experimental data
To further validate the mathematical model, we compared the simulated results with experimental data that were not used for the mathematical modeling, as shown in . Such comparison of the simulated results with experimental data demonstrated that the dynamic behavior of the mathematical model was consistent with that of the experimental data.
Figure 4 Validation of the mathematical model. (A) The intracellular cAMP concentration and CRP:cAMP complex concentration were simulated with respect to the extracellular glucose concentration. The black line and red line show the cAMP concentration and the CRP:cAMP (more ...)
As shown in , the dynamic model reproduced the experimental behavior that the concentration of intracellular cAMP and CRP:cAMP varied with the extracellular glucose concentration in a dose-dependent manner (Notley-McRobb et al, 1997
). The cAMP concentration in glucose-abundant medium was lower than that in glucose-deficient medium. As shown in , the IIAGlc
protein was dephosphorylated at a high extracellular glucose concentration and the phosphorylation status of IIAGlc
protein was responsible for the extracellular concentration (Hogema et al, 1998
). These simulated results were consistent with the experimental data. Zeppenfeld et al (2000)
measured the ptsG
promoter activity in wild type and an mlc
knockout strain (mlc−
) using a lacZ
fusion in minimum medium with glucose and glycerol. In wild-type cells, the ptsG
promoter activity in glucose medium was higher than that in glycerol medium, which may result from the de-repression of Mlc. In both glycerol and glucose medium, the ptsG
promoter activity in an mlc−
knockout strain was higher than that in wild-type cells. As shown in , the expression of the ptsG
gene was successfully reproduced by the simulation, where the glucose dose dependency for ptsG
gene expression was observed both in wild type and an mlc
knockout mutant and the gene expression level in the mlc−
mutant was higher than that in wild-type cells regardless of the extracellular glucose concentration.
Extraction of critical genes for enhanced glucose uptake
The functional and flux module decomposition of the PTS model () readily provides a rational strategy for enhanced glucose uptake. The mlc and crp genes of the transcription regulation factors affect the expression of multiple genes. The mlc gene is responsible for the brake actuator, thus mlc knockout is expected to enhance the synthesis of the PTS proteins. The crp gene belongs to the computer module for the accelerator actuator, and thus overexpression of the crp gene has a potential to enhance the synthesis of the PTS proteins. Since the ptsG, ptsH, ptsI, and crr genes are the catalysts for the phosphorylation cascade in the plant module, it is reasonable to increase their expression for enhanced glucose uptake rates. It is critical for enhanced glucose uptake to increase the PTS proteins in the plant module (the ptsG, ptsH, ptsI, and crr genes), to delete the brake actuator module (the mlc gene), or to enhance the accelerator actuator module through the computer module (the crp gene). Regarding the crp gene manipulation it is necessary to consider the quantitative balance between the accelerator and brake flux modules, because CRP:cAMP not only enhances the accelerator actuator but also the brake actuator.
Simulation and perturbation analysis of the rationally designed PTS
To further explore target genes critically responsible for enhancing glucose uptake, we performed perturbation analysis with regard to crp
, and crr
gene expression, as shown in , where the specific glucose uptake rates were simulated with respect to a 10-fold change in the copy number of these genes. When the concentration of a target gene was varied by 10-fold from the default condition (wild type), the ratio of the specific glucose uptake rate for a mathematical mutant to that for the wild type was simulated. The ratio of the phosphoenolpyruvate (PEP) concentration to the pyruvate (Pyr) concentration ([PEP]/[Pyr]) was set to 1 and each concentration was set to 1 mM (Chassagnole et al, 2002
). We calculated the effect of the mlc
gene disruption and crp
gene amplification (crp+
) on the specific glucose uptake rate. The ptsI
gene amplification showed the most enhanced specific glucose uptake rate for all the strains: wild type, the mlc
knockout mutant, and the crp
-overexpressing mutant. An mlc
knockout mutant that overexpressed the crp
genes was predicted to enhance the specific glucose uptake rate by the greatest degree. Since the ratio of the intracellular PEP to the Pyr concentration affected the specific glucose uptake rate by the PTS (Hogema et al, 1998
), we simulated the ptsI
amplification effect on an enhanced specific glucose uptake rate using various values of the ratio of [PEP]/[Pyr], by changing each molecule concentration from 0.1 to 10 mM and confirmed that ptsI
amplification was always effective in enhancing the glucose uptake (data not shown). Based on this result, the subsequent simulations were performed with 1:1 ratio at 1 mM of PEP and Pyr concentration.
Prediction of changes in the specific glucose uptake rate for mathematical mutants
To analyze the mechanism of how the glucose uptake rate is increased by ptsI
gene amplification, the PTS component concentrations were simulated with respect to a change in the ptsI
gene dose, as shown in . Since the specific glucose uptake rate is defined as the rate of the phosphotransfer reaction from phosphorylated IICBGlc
to glucose per cell, that is, the production rate of glucose-6-phosphate (G6P), the glucose uptake rate is closely related to that for the phosphorylated status of IICBGlc
protein. As shown in , the concentrations of phosphorylated proteins increased with an increase in the concentration of the ptsI
gene. This simulated result suggests that the increase in the PTS flux is caused by an increase in the EI protein concentration. In the simulation, the phosphorylated IIAGlc
protein becomes abundant when the ptsI
gene is 10-fold amplified compared with the default condition. The phosphorylation status of the IIAGlc
protein is known to depend on extracellular sugars and most of the IIAGlc
proteins are unphosphorylated when glucose is used in the medium. The phosphorylation of the IIAGlc
protein is suggested to be the signal for increasing the activity of adenylate cyclase that converts ATP into cAMP (Hogema et al, 1998
). As shown in , the specific glucose uptake rate and the intracellular cAMP and CRP:cAMP complex concentrations increased with an increase in the EI concentration. The increase in the CRP:cAMP concentration activates the transcription of the ptsG
gene and pts
operon, subsequently increasing the specific glucose uptake rate.
Figure 5 Effects of ptsI gene amplification on the PTS components in the dynamic simulation. The ptsI gene concentration in a cell was changed within a range from 2.43 pM to 54.3 nM. The default concentration was 0.24 nM (one gene per a cell), as shown by the (more ...)
Out of the ptsG
, and ptsI
genes, the ptsI
gene was selected for detailed analysis because its amplification enhanced the specific glucose uptake rate most strongly. In addition, some background information supports this selection. The ptsI
gene encodes the EI protein, which catalyzes the phosphate transfer reaction from PEP to the EI protein. This reaction is suggested to be a rate-limiting step for glucose uptake in the PTS (Weigel et al, 1982
; Patel et al, 2006
), and the enhanced EI protein concentration is expected to lead to an increase in the glucose PTS flux. The transcriptional attenuation of ptsH
occurs and the amount of ptsI
transcripts is suggested to be one-tenth of that of the ptsH
transcripts (De Reuse and Danchin, 1988
). Supposedly, the attenuation of the ptsI
transcript is one of the intrinsic points governing the glucose PTS flux. Therefore, the ptsI
gene was a reasonable choice among the enzymes of the phosphorylation cascade in the plant module.
Experimental validation of rationally designed cells
The mlc knockout mutant that overexpresses both the crp and ptsI genes was predicted to enhance the specific glucose uptake rate most strongly. To evaluate the validity of the presented strategy, we carried out biological experiments. Since CRP is one of the global regulators whose functions are not fully clear, unexpected effects may be caused by crp gene amplification. Thus, we excluded crp-overexpressing mutants.
First, we investigated the effect of ptsI gene amplification. The simulation results suggest that more than 10 copies of the ptsI gene are required for the enhancement of specific glucose uptake; thus, a high-copy number plasmid was used for ptsI gene expression. The enhancement of EI protein expression was confirmed by SDS–polyacrylamide gel electrophoresis (data not shown). To test our prediction on the ptsI-amplified strain, MG1655/pUC118-ptsI, and a control strain, MG1655/pUC118, were cultivated in 20 ml of M9 glucose medium in a shaking incubator for 18 h. Growth, glucose uptake, specific glucose uptake, and extracellular cAMP concentration were measured (). Regardless of the similar growth of both strains, the specific glucose uptake rate of the ptsI-amplified strain was significantly higher than that of the control strain. These experimental findings supported the prediction that an increased EI protein concentration enhances the specific glucose uptake rate under normal cell growth conditions.
Experimental results of growth, glucose uptake, specific glucose uptake, and cAMP concentration in growing cells
Second, we compared the specific glucose uptake rate between the ptsI
-overexpressing strain and a control, using non-growing cells in minimum medium without thiamine required for JM109 growth (). The specific glucose uptake rate of the ptsI
-amplified strain, JM109/pUC118-ptsI
, was higher than that of the control strain, JM109/pUC118. The observed growth (ΔOD600
) was less than 0.6 in both strains. Mainly, the incorporated glucose was converted into acetic acid or other organic acids (data not shown). This result indicates that the ptsI
gene amplification enhances the specific glucose uptake rate. This is also supported by previous kinetic studies that the EI protein concentration is critical for increasing the phosphate flux in the PTS (Weigel et al, 1982
; Patel et al, 2006
Figure 6 Comparison of the specific glucose uptake between wild type and the ptsI-overexpressing mutant. The glucose uptake and cell growth of JM109/pUC118-ptsI (circle) and JM109/pUC118 (square) were measured under non-growing conditions. Three replicate experiments (more ...)
Third, we examined the effect of how ptsI gene amplification in the mlc knockout mutant derived from MG1655 (MG1655M) enhances the specific glucose uptake rate. The ptsI amplification strain, MG1655M/pUC118-ptsI, and a control strain, MG1655M/pUC118, were cultured in 20 ml of M9 glucose medium in a shaking incubator for 18 h. We compared the specific glucose uptake among the four strains (). The MG1655M/pUC118-ptsI strain showed the highest specific glucose uptake even though it had the lowest growth. The next highest was the MG1655/pUC118-ptsI strain. The predictions for specific glucose uptake rates were validated by the experiments (), demonstrating that amplification of the ptsI gene increases the specific glucose uptake rate and further enhances it in an mlc knockout mutant.
Discrepancies between simulation and experiment
In the simulation, the intracellular cAMP concentration in the ptsI
-amplified strain was higher than that in wild type, but this was not consistent with the experimental data, as shown in . We measured the cAMP concentration in the medium. The cAMP concentration in the ptsI
gene amplification strain was lower than that in the control strain. In vivo
, the ATP level may decrease or adenylate cyclase may not be activated by the ptsI
gene amplification. Thus, we investigated the discrepancy in cAMP concentration. Inada et al (1996)
showed that the dephosphorylation activity for the phosphorylated IIAGlc
protein was observed when E. coli
was cultured with glucose. Recently, not only the phosphorylated IIAGlc
protein but also other factors have been reported to be involved in the activation of adenylate cyclase (Park et al, 2006
). These mechanisms may explain the reason why the cAMP concentration shows the discrepancy between the mathematical and biological models.
Subsequently, we improved the glucose PTS model that the activation of adenylate cyclase does not occur in the presence of glucose and simulated the model as shown in . Q
 in Equation (3.4) was set to zero when glucose was present in the medium (Supplementary Table S1
). In the improved model the cAMP concentration hardly decreased (data not shown), which was more consistent with experimental data than the previous model (). Furthermore, the model improvement solved another discrepancy regarding the relationship between glucose uptake rates and the IICBGlc
enhancement experiment. The glucose uptake rate was suggested to be increased by IICBGlc
enhancement (Rohwer et al, 2000
), while the glucose uptake rate was simulated to decrease with an increase in the copy number of the ptsG
gene (). By model improvement, ptsG
gene amplification increased the glucose uptake, which was consistent with the experimental result ().
Prediction of changes in the specific glucose uptake rates in the improved dynamic model that excludes adenylate cyclase activation by IIAGlc-P
The simulation of the improved model suggests that the effect of the phosphorylated IIAGlc-activated adenylate cyclase is very limited in the presence of glucose; in other words, unknown factors other than the phosphorylated IIAGlc play an important role in controlling the computer module.
Severe growth suppression
The specific glucose uptake rate was suppressed by Mlc in the wild type, while it was retained in an mlc−
knockout mutant. Mlc is reported to suppress the expression of the ptsG
gene and the pts
operon (Plumbridge, 1998
; Kim et al, 1999
; Tanaka et al, 1999
), thereby governing glucose uptake. As the dynamic simulation predicted, the mlc
knockout enhanced the specific glucose uptake rate through synthesis of the PTS components, but our experimental results showed unexpected severe growth suppression with the combination of mlc
gene deletion with ptsI
It is known that the excess accumulation of G6P inhibits cellular growth in E. coli
(Kadner et al, 1992
). The growth suppression in MG1655M/pUC118-ptsI
may be caused by the excess accumulation of sugar phosphate due to the rapid glucose uptake (). Recently, small RNAs in E. coli
have been shown to respond to an intracellular sugar concentration and the transcripts of the ptsG
gene are degraded by RNaseE (Morita et al, 2003
). We speculate that E. coli
has some unknown severe control systems for the pool size of sugar phosphate and no activation of adenylate cyclase in glucose medium can be due to such control systems. A further refined and extended model including G6P metabolism will clarify the control mechanism of glucose uptake.
Power of computer-aided rational design
We have presented a general strategy for the rational design of biochemical networks for an engineering purpose. The strategy consists of constructing a biochemical network, dynamic simulation, module-based analysis, perturbation analysis, and experimental validation. CAD supports construction of a biochemical network map, building its dynamic model, and system analysis. Module-based analysis decomposes a biochemical network map into hierarchical modules, functional and flux modules, in a manner analogous to control engineering architectures. If an engineering purpose is determined, functional modules are readily determined and an engineering function is assigned to each module. This facilitates rational design of a genetic manipulation responsible for achieving the purpose and an intuitive understanding of how the biochemical network of interest can be improved or modified. Perturbation analysis further explores critical genes responsible for achieving the engineering purpose.
Using CADLIVE we performed mathematical modeling, simulation, and system analysis to make a strategy of how the glucose PTS can be genetically engineered for enhanced glucose uptake. We found the critical factors responsible for an enhanced specific glucose uptake rate, for example, ptsI amplification and mlc knockout. Mathematical simulation and subsequent perturbation analysis predicted that the combination of amplification of ptsI and deletion of mlc would enhance the specific glucose uptake rate. Finally, experimental data validated this prediction.
Rational design of a robust system
Rational design requires an understanding of the mechanism of how a biochemical network provides a robust property to a target performance, or identifying the genes that show fragility of the performance to their genetic change. Manipulation for a particular flux module has a great potential to change the network performance of interest, for example, deletion of a negative FB loop or enhancement of a positive FB loop readily alters the cellular performance. In the glucose PTS, the brake actuator flux module has a negative FB loop. An increase in ptsI gene expression enhances phosphorylation of the PTS proteins (), IIAGlc-P:CYA binding, CRP:cAMP synthesis, and Mlc production in turn, thereby suppressing ptsI gene expression. By contrast, the accelerator actuator flux module has a positive FB loop. An increase in ptsI gene expression enhances phosphorylation of the PTS proteins, IIAGlc-P:CYA binding, and CRP:cAMP synthesis in turn, which further enhances ptsI gene expression. Genetic manipulation for such a negative or positive FB loop shows a great potential to enhance the specific glucose uptake or activation of the PTS proteins. Knockout of the mlc gene is reasonable for ptsI gene overexpression, because it removes the negative FB loop that suppresses EI protein expression. Perturbation analysis in both the mathematical model and biological experiment support this design strategy.
In the improved model, positive and negative FBs were cancelled by disabling the function that IIAGlc-P:CYA synthesizes cAMP, where the glucose PTS system forms a more straight forward network. The brake flux module without the negative FB shows less suppression of PTS proteins with respect to EI or HPr overexpression, and the accelerator flux module without the positive FB weakens the expression of them. Actually, the specific glucose rate would be determined through the quantitative balance between the brake and accelerator modules. In the improved model, the decrease in the specific glucose uptake rate for ptsI or ptsH overexpression for wild type and an mlc knockout mutant ( and ) would be due to deletion of the positive FB loop, while the increased uptake rates for other mutants would be caused by removal of the negative FB loop. It is of critical importance for rational design to understand the quantitative mechanism of how a flux module provides robustness to genetic changes.
Toward a perfect design
The simulation results did not necessarily explain the experimental results. As mentioned above, there was a discrepancy in the change in the cAMP concentration between the mathematical and experimental models. The combination of ptsI
amplification and mlc
deficiency was predicted to be a better strategy for enhanced specific glucose uptake, but it led to severe growth inhibition. From the mathematical simulation of specific glucose uptake, the ptsI
gene-overexpressing strain was predicted to have a ratio of 3.87 compared with control, but experimentally at best a ratio of 1.2 (0.018/0.015) was observed ( and ). Likewise, the ratio for the mlc−
background was 5.70, but experimentally 1.7 (0.026/0.015) ( and ). These differences seem to be due to the insufficient model size or lack of various FB regulations of enzyme and gene expressions that provide robustness to genetic modifications in the actual cells. In addition the other proteins, mannose PTS and non-PTS transporter, GalP, which are involved in permeation of glucose (Curtis and Epstein, 1975
; Hernandez-Montalvo et al, 2003
), may affect the experimental results.
The PEP/Pyr ratio is determined as a result of many enzymatic reactions including glycolysis, pentose-phosphate pathway, and anaplerotic pathways. Since growth is the output of complex interactions of a variety of molecules, it is still hard to accurately predict cell growth at the molecular interaction level. A large and complex model would be necessary that includes various regulations of enzyme and gene expressions in the glycolysis, pentose-phosphate pathway, TCA cycle, and anaplerotic pathway. An extended model is expected to clearly describe the experimental results.
If some discrepancies are found between the mathematical and experimental models, we need to feed this information back into model improvement. Ideally we should iterate the process consisting of mathematical analysis and experimental validation until prediction agrees with experimental results completely. This iteration cycle is key to the rational design of biochemical systems.
In conclusion, a computer-aided rational design approach was successfully applied to microbe engineering or breeding and verified by biological experiments. This methodology will lead to rapid development for not only applied biology that designs biochemical networks within a cell, but also fundamental research that reveals the mechanism of how biochemical networks generate particular cellular functions.