In this work, a dynamic metabolic model for CHO cells was further developed, calibrated and challenged using datasets obtained under four different culture conditions, including two batch and two fed-batch cultures comparing two different culture media. The recombinant CHO-DXB11 cell line producing the EG2-hFc monoclonal antibody was studied. Quantification of extracellular substrates and metabolites concentration, viable cell density, monoclonal antibody concentration and intracellular concentration of metabolite intermediates of glycolysis, pentose-phosphate and TCA cycle, as well as of energetic nucleotides, were obtained for model calibration. Results suggest that a single model structure with a single set of kinetic parameter values is efficient at simulating viable cell behavior in all cases under study, estimating the time course of measured and non-measured intracellular and extracellular metabolites. Model simulations also allowed performing dynamic metabolic flux analysis, showing that the culture media and the fed-batch strategies tested had little impact on flux distribution. This work thus paves the way to an  Serum-frategies ,4 and forategies ,6. The irategies , medium rategies  or from rategies . Those ain silico platform [Metabolic flux analysis (MFA) and flux balance analysis (FBA) studies have been conducted on CHO cells ,13,14,15platform ,21,22.Provost and Bastin  and Gao 5 cells mL-1 in a 2-L Labfors 4 bioreactor . Cultures were performed at 37°C and. dissolved oxygen was maintained at 50% of air saturation by surface aeration. pH control at pH 7 was performed by feeding CO2 in surface aeration and NaOH (1 M) addition was used when CO2 reached a concentration lower than 0.5% of the gas feed. Agitation (pitched-blade impeller) speed was set at 60 RPM at inoculation and was then gradually increased up to 120 RPM to follow the cells oxygen demand, from reaching a maximal O2 concentration of the total gas flow rate of 100%. Cultures were performed until cell viability decreased below 50%. Samples were taken daily for cell counting and cell viability determination, as well as for glucose concentration in the media. In fed-batch cultures, nutrients addition was performed daily to avoid limitations, based on the extracellular glucose concentration, maintaining the concentration above 10 mM. The remaining sample was then centrifuged at 100 g and the supernatant was frozen (-80°C) and kept for further analysis of media composition. Cell extractions, for the quantification of intracellular metabolites, were performed as described in Ghorbaniadgdam et al. [6 cells were collected and washed 2 times with cold PBS, and then extracted in three steps with cold methanol, while vortexed with 0.2 g of sand , sonicated in ice bath for 5 min and then centrifuged at 21000 g between each steps. Respiration assays were performed daily from 48 h, by closing the bioreactor inlet gas flow rate and decreasing the agitation speed (30 RPM), which allows to minimize the O2 transfer while maintaining an homogeneous cell suspension, until the dissolved oxygen level reach 35% of air saturation.Four different CHO cell cultures were performed to calibrate the model. The CHO-DXB11 cell line, producing a chimeric heavy chain monoclonal antibody (EG2-hFc) , has beem et al. . BrieflyTwo different culture media were tested, the Biogro-CHO  without glucose and glutamine (see below for concentrations) and the PowerCHO-2  without glutamine (see below for concentration). The Biogro-CHO medium was supplemented with 25 mM and 10 mM glucose , and with 4 mM and 2.4 mM glutamine , for batch and fed-batch cultures respectively. The PowerCHO-2 medium was supplemented with 6.5 mM glutamine and 1 mL Anti-Clumping Agent per liter of culture medium . Two fed-batch strategies were defined based on the two culture media specific composition. Previous work with the same cell line aiming at identifying limiting nutrients in both Biogro-CHO and PowerCHO-2 media (data not shown) suggested that neither glucose nor amino acids are the substrates limiting cell growth; the individual effects of each compound were evaluated from a fractional experimental plan. Based on those results, with glucose and glutamine being the fastest consumed substrates, medium feed for Biogro-CHO fed-batch cultures was composed of regular medium at 13X glucose (130 mM) and 8X glutamine (25 mM) concentrations (i.e. below solubility limits). The fed-batch culture performed with the PowerCHO-2 medium was fed with a 2.5X concentrated PowerCHO-2 medium (100 mM glucose and 16 mM glutamine). That strategy allowed avoiding early nutritional limitation for the measured components. For both culture media, a fed-batch with daily feeding and a control batch culture were performed in parallel. Samples for all analysis were taken daily, except for the batch culture with the Biogro-CHO, for which the samples were taken every 12 h to better monitor the culture dynamics, since this culture duration showed being shorter than the others.Viable cell concentration was determined by cell counting using a hemocytometer and trypan blue  exclusion method. Extracellular concentrations for glucose, lactate, glutamine and glutamate were analyzed using a YSI 2700 SELECT Biochemistry Analyzer . Ammonia concentration was measured with the Ammonia Assay Kit . Amino acids concentration were determined using a Agilent 1290 HPLC system  as described in Ghorbaniadgdam et al. [-1 of Bovine Serum Albumin (BSA)  incubated for 1 h. The wells were washed and filled with either standard or the sample diluted 1000 to 16000 times in a PBS-BSA solution and incubated for 1 h. The wells were then washed and incubated 1 h with peroxidase conjugated Anti-Human IgG . The reaction was revealed with 3,3',5,5'-Tetramethylbenzidine , stopped after 20 min using 2 M H2SO4 and the absorbance measured at 450 nm with a Victor 3V multilabel reader .Monoclonal antibody concentration was determined by enzyme-linked immunosorbent assay (ELISA). A Costar 96-well plate  was first incubated overnight with Fc specific Anti-Human IgG  diluted to 1/30000 in phosphate saline buffer (PBS). The wells were washed with PBS solution containing 0.2% Tween 20 . The remaining sites were then blocked using a solution of PBS containing 0.3 g LVASTA and VAlaTA), serine conversion to pyruvate (VSDHH), as well as amino acids conversion to alpha ketoglutarate and succinate in distinct reactions (VAAtoSUC and VHISARGTA respectively). The biochemical reactions stoichiometry was preserved from the previous model. Metabolite pool consumption for cell growth was that proposed in Sheik et al. [-1 for the cell proteins in biomass and of a conversion factor of 3.15*10−4 gDW 10−6 cells. For simplification purposes, the assumption was made that all the lipids within the biomass were derived from citrate, and the nucleotides precursors were issued from ribulose-5-phosphate and glycogen from glucose-6-phosphate. Amino acids consumption for mAb synthesis was calculated from the average IgG1 sequence proposed in Quek et al. [The mathematical model presented in this work is based on a previous model developed for other two CHO cell lines ,30,33, ak et al.  for cellk et al. . ATP conk et al. . Also, aVHK), phosphoglucose isomerase (VPGI) and reverse lactate dehydrogenase (VrLDH), by glucose-6-phosphate, phosphoenolpyruvate and pyruvate, respectively. The AMP-to-ATP ratio activates phosphofructokinase (VPFK), lactate dehydrogenase (VLDH) and VHK, while fructose-6-phosphate activates pyruvate kinase (VPK). The reactions involving an inhibition mechanism were described according to the mathematical formulation of a non-competitive inhibition  is also inhibited by glutamine to account for the switch from alanine production to alanine consumption when glutamine level is low, as observed in our experimental data. Reverse reactions are also modeled for glutamine synthetase (VGlnT), glutamate dehydrogenase (VGLDH), lactate dehydrogenase (VLDH), glutamate transport (VGluT) and adenylate kinase (VAK), but not for VASTA because there was no evidence from our measurements of a net production of extracellular aspartate, but only a net consumption.In the present work,  lactate ,39, and  alanine ,41. The VPFK . Before proceeding with the calibration step of the model, the parameters were analysed in order to identify and only optimize the value of the most sensitive ones. The Morris Screening method was used for determining the ranking of the global sensitivity of each parameters, an approach previously applied to a similar dynamic model ,44. Thiss follow :EEi(p)=The elementary effect was calculated 35 times for each parameter using a step Δ of 2/3 and the boundaries were set to ±25% of the initial guess. The outputs were the function evaluation at the experimental sampling times for the selected 32 outputs chosen for optimization , the optimization step was performed with the following objective function, the parameter vector p representing the 20 most sensitive parameters:n,t(p) is the nth model output evaluated at the tth experimental time, yexp is the experimental data and σ is the standard deviation of the experimental measurement. Those three steps were repeated in the same order until optimisation results yielded realistic  parameter values with sufficiently narrow confidence intervals and minimal residual error. At each iteration, the initial guesses were changed and the parameters to be optimized were selected according to the sensibility analysis results. The results presented in this work correspond to the final step of this process, which correspond to the minimal residual error attained.The initial guess for all parameters were those from previous work . The Kmn) to improve the optimization process by allowing similar weight to each parameter. The lower bounds for all parameters were set to 0. Finally, flux values and the 95% confidence interval for each optimized parameter were calculated using the MATLAB built-in functions nlparci and nlpredci as well as the Jacobian matrix from the lsqcurvefit function. When available, initial conditions were taken from experimental data or from [Experimental data from 24 h after inoculation to when the cell viability decreased under 95% were considered, and the molecular species used for optimization are the same as for sensitivity analysis. The parameter values were also normalized to their specific order of magnitude  were the same in each case. The goal was to evaluate the appropriateness of dividing the model in 2 culture phases.6 cells mL-1 and 69 mg mAb L-1 for the fed-batch culture, and 8.2x106 cells mL-1 and 67 mg mAb L-1 for the batch culture) than the cultures using Biogro-CHO . High non-limiting glucose condition  were identified as the most sensitive and were kept for the parameter optimization subsequent steps. The number of parameters was restrained to the most sensitive ones in order to increase the accuracy and the efficiency of the optimization process.Vmax) and 4 are affinity constants (Km), and the remaining parameters are inhibition (2) and activation constants (3). Growth (Vmaxgrowth), glutamine metabolism (VmaxGlnT), glycolysis  and energetic metabolism  were among sensitive parameters. Interestingly, the pathways with sensitive Vmax parameters are among the ones previously identified as sensitive but for other CHO cell lines [Km, 3 are associated to cell energetics with KmNADH and KmATP, respectively involved in NADH and ATP consumption, and KmADP/ATP, which affects seven energy-producing reactions. Within the regulation constants, the sensitivity of KmG6P is explained by the fact that glucose-6-phosphate level directly controls the glycolytic influx from a retro-inhibition term, with KdG6P also being a sensitive constant. The value of KmG6P has a direct impact on the glucose-6-phosphate level, which in return affects greatly the glycolytic flux. Finally, sensitivity of KdNH4growth may be linked to high NH4 concentration accumulating in the media and thus expected to limit cell growth. The fact that 3 of those sensitive regulation constants, along with the VrmaxAKand VfmaxAK, are closely linked to the AMP-to-ATP ratio highlights the crucial role of this regulation pathway on glycolysis. Moreover, the AMP-to-ATP ratio is an efficient regulator of cell metabolism, since it varies faster than the ADP-to-ATP ratio [Of the 20 sensitive parameters, 11 are maximal rate constants  lower in PowerCHO-2, while lower KmNADH and higher Vmaxresp for the PowerCHO-2 could reveal a higher respiration rate for this medium. The absence of difference between batch and fed-batch cultures is in agreement with another dynamic model describing hybridoma metabolism [Vmax for the conversion of glutamate to proline and for the conversion of asparagine to asparatate being different. The overall performance of the model in the present work suggests that a unique model can be used to adequately simulate different fed-batch strategies on different culture media with a unique set of parameter values, which was not the case when analysing different mAb recombinant CHO clones [The model was first calibrated using all four sets of the experimental data obtained in this work, as described in the Material and Methods section. The resulting model was then used to produce simulations of experimental data Figs –S3 Figs.tabolism . In thatO clones . MoreoveO clones  that a mKmG6P is slightly lower after 72 h (2.6*10−8 mmol.10-6cells versus 2.9*10−8 mmol.10-6cells), which could indicate the limitation of glucose-6-phosphate depletion, and the value of KaAMP is higher (0.11 versus 0.09), which may reveal a decrease of glycolytic activity and lactate production at the mid-exponential phase. Overall, although simulation error can be lower when changing the value of these two parameters, the structure of the model also shows that it is possible to describe the whole culture behaviour from inoculation to the decline phase with a unique set of parameter values. While some discrepancies between experimental and simulated data for some species can still be observed, this model is, to the best of our knowledge, the only capable to simulate intracellular and extracellular concentrations for batch and fed-batch cultures. It thus represents a first step in the development of a predictable in-silico platform of cell behaviour. Moreover, since the model does not describe cell viability, and considering that the metabolomic data remain reliable at high cell viability, it was decided to limit the further evaluation of the model to the data sets with cell viability level of 95% and above. The decline phase is thus not described nor simulated, limiting the scope of the model to the exponential and early plateau phase.Moving further challenging the model structure performance, we have evaluated the benefit of dividing the model to describe two distinct but successive phases: before (< 72 h) and after (> 72 h) mid-exponential growth phase. This time point approximates the moment where growth and other major fluxes start declining. Although a fully dynamic model that includes pathway regulation, such as in this work, is thought being able to cope with cell behaviour variation with time, the aim was to evaluate the effect on model simulations accuracy. The idea of dividing the culture into two ,24,49, tTherefore, a unique model structure with a unique set of parameter values has been used to simulate each culture Figs –4. The sVAlaTA flux in the latter stages of the culture, since the pyruvate concentration stays constant in the simulations compared to experimental data. Also, in the model, the VAlaTA reverse reaction is inhibited by extracellular glutamine, while the shift seems closely related to glutamine depletion, suggesting that the chosen descriptive mechanism might not be optimal. Moreover, the uptake rate for some amino acids seems to be overestimated  was similar to that for lactate consumption (VLDH) rate (~ 2x10-4 mmol.10-6cells.h-1 after 48 h), a value range that is consistent with literature with [-4 mmol glucose.10-6 cells.h-1 and [-4 mmol lactate.10-6 cells.h-1 at exponential phase [−5 mmol.10-6cells.h-1 that is close to a value of 2.71x10-5 reported by Templeton et al. [-5 mmol.10-6cells.h-1) has been reported by Ahn & Antoniewicz [-6mmol.10-6cells.h-1 at 48 h) is similar to values reported at exponential phase with 1.8±0.2 mmol.10-6cells.h-1 [-6 cells.h-1 [The model, which showed being efficient at describing cell behaviour for the four culture conditions assessed, was then used as an r fluxes  at all tr fluxes  Tables a.h-1 and x10-4 mmoal phase ,17,50. Toniewicz  at exponells.h-1  and at eVGlnT) is significantly lower for the batch culture using Biogro-CHO than for the fed-batch culture using PowerCHO-2. Ammonia production rate (VGLDH+VGlnT+VSDHH+VASN+VHISARGTA) seems lower for Biogro-CHO compared to PowerCHO-2, although the difference is only significant when comparing the batch mode with that medium to other cultures. This result was expected since Biogro-CHO medium contains significantly less glutamine at inoculation (and after 48 h), thus limiting VGlnT and indirectly ammonia production.There are very few differences in the flux levels for the first 72 h of the culture when the four cases are compared. At 48 h, the glutamine consumption rate , and for the net ATP production rate (VPGK + VPK + VAKGDH + VPC + VGlnT + 2*2.5*Vresp). In the case of VHK and VLDH, the only significant difference after 96 h is observed between the batch culture using Biogro-CHO and the other cultures, a result that may be due to faster glucose depletion in the former case. However, both the glutamine consumption rate and the ammonia production rate show maintaining their activity levels in the two fed-batch cultures. This result indicates that the feed strategy was able to maintain glutamine metabolism towards the TCA cycle and to limit glutamine depletion. Unlike glutaminolysis, glycolysis is not maintained at the same activity level in fed-batch cultures even if glucose was not limiting. This could be due to the inhibition effect of lactate and alanine on phosphofructokinase  and lactate production rates. The pentose phosphate pathway global activity  are significantly lower than the ones for PowerCHO-2 . Since VPDH activity relies on the intracellular concentration of pyruvate and on the NAD/NADH ratio in our model, it may be affected indirectly by the culture medium composition in the latter culture stages from extracellular metabolites concentration. However, further investigations are required to clearly elucidate the cause behind this difference of behaviour.Although all metabolic fluxes show a decreasing trend whatever the culture conditions from 48–96 h, significant differences of behaviour raised in the latter culture stages comparing flux levels among cultures. This flux decrease was noticeable for glucose consumption VHK, , lactateVG6PDH, , howeverVPDH)-to-glycolytic flux (VPK) and the VPDH contribution to the TCA cycle both suddenly increase until the end of the culture  who also used a dynamic model for hybridoma cells to compare culture modes showing a similar flux distribution for both modes. However, other work performing a MFA study on NSO cells  showed aVPDH) enzyme, while another fraction of the glycolytic flux is directed toward alanine production (VAlaTA) (~10%) and pyruvate carboxylase (VPC) (less than 5%). The inefficient use of glucose for ATP production is a well-known characteristic of CHO cells [The CHO cells under study exhibit an inefficient glucose metabolism with more than 75% of glycolysis resulting in lactate production, which leads to lactate accumulation an thus growth inhibition (< 58.5 mM lactate ). AroundHO cells , convertVPDH enzyme, the TCA cycle is largely fed from amino acids metabolism (VAlaTA+VGLDH+5*VAAtoSUC), indeed accounting for 60±1 to 62±1% after 48 h depending on the culture, compared to only 22±1% for the pyruvate dehydrogenase. The major contribution of glutamine and asparagine to TCA feeding in CHO cells was reported previously [VGLDH) was negligible; most of the glutamate integrating the TCA cycle via alanine transferase (VAlaTA). Unlike VGLDH, VAlaTA pathway does not produce directly ammonia, a metabolite known to inhibit cell growth and viability as well as recombinant proteins glycosylation pattern [VGlnT, of asparagine to aspartate via VASN, which can be further transformed to glutamate via aspartate transferase, both produce ammonia as a by-product. While the cells manage to maintain an efficient amino acids metabolism in regards to ammonia secretion, the use of amino acids to fuel the TCA cycle still produces undesired metabolites compared to the use of glycolysis. In our case for fed-batch culture, the inhibition term of growth equation in regards to lactate went from 0.99 initially to 0.89 using Biogro-CHO, and from 0.99 initially to 0.86 using PowerCHO-2. Concerning ammonia, however, its inhibition term in the growth equation changed from 0.957 in both fed-batch cultures initially to 0.372 for the fed-batch culture using Biogro-CHO, and 0.278 for the fed-batch culture using PowerCHO-2 after 120 h. The accumulation of ammonia, more than the accumulation of lactate, may explain the slow growth observed in the latter stages in both fed-batch cultures, and the absence of improvement of the mAb final titer compared to the batch cultures regardless of the culture medium used. Moreover, the inhibition factor linking growth rate to ammonia concentration was previously identified as a sensitive parameter . To the best of our knowledge, it is the first time a metabolic model that includes such a wide array of intracellular concentrations is used to compare culture media and fed-batch strategies for CHO cells. Given its flexible dynamic structure, while the model is cell line-specific, our results suggest that it is not culture medium-specific. In addition to the concentration profiles, given the dynamic nature of the model, we performed a dynamic metabolic flux analysis from model simulation that was in agreement with literature. Model simulations suggest that the cell line used in this study (CHO-DXB11) has a robust metabolism, showing little changes in terms of flux distribution throughout nearly all of the exponential and plateau phase. That metabolism was maintained regardless the medium or the culture mode for most of the culture duration. The fed-batch mode showed stabilizing cell metabolism for an extended period of time. However, sustained amino acids metabolism in fed-batch cultures led to important ammonia accumulation, which may have limited growth while resulting, however, in higher mAb production. We thus believe such model can be further used as an S1 FigSame conditions and symbols than in (TIF)Click here for additional data file.S2 FigSame conditions and symbols than in (TIF)Click here for additional data file.S3 FigSame conditions and symbols than in (TIF)Click here for additional data file.S1 Table-3mmol.10-6 cells and 9.17x10-3 mmol.mg-1 respectively.All units are in millimole. Conversion factors for biomass and mAb are 2.93x10(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 TableParameter values for all parameters, including non-optimized parameters, and the boundary of their confidence interval (95%), when it applied. All the data available was used for parameter estimation (four cultures).(DOCX)Click here for additional data file.S5 TableParameter values and confidence intervals (95%) for the same conditions than in (DOCX)Click here for additional data file.S6 TableParameter values and confidence intervals (95%) for the same conditions than in (DOCX)Click here for additional data file.S7 Table-6cells.h-1) and their confidence intervals at 48 h and 96 h for the same conditions than in Metabolic fluxes Click here for additional data file.S8 Table-6cells.h-1) and their confidence intervals at 48 h and 96 h for the same conditions than in Metabolic fluxes Click here for additional data file.S9 Table-6cells.h-1) and their confidence intervals at 48 h and 96 h for the same conditions than in Metabolic ratios Click here for additional data file.


Escherichia coli lipid A biosynthesis, drawing parameters from the experimental literature. This model accounts for biosynthesis regulation, which occurs through regulated degradation of the LpxC and WaaA  enzymes. The LpxC degradation signal appears to arise from the lipid A disaccharide concentration, which we deduced from prior results, model results, and new LpxK overexpression results. The model agrees reasonably well with many experimental findings, including the lipid A production rate, the behaviors of mutants with defective LpxA enzymes, correlations between LpxC half-lives and cell generation times, and the effects of LpxK overexpression on LpxC concentrations. Its predictions also differ from some experimental results, which suggest modifications to the current understanding of the lipid A pathway, such as the possibility that LpxD can replace LpxA and that there may be metabolic channeling between LpxH and LpxB. The model shows that WaaA regulation may serve to regulate the lipid A production rate when the 3-deoxy-D-manno-oct-2-ulosonic acid (KDO) concentration is low and/or to control the number of KDO residues that get attached to lipid A. Computation of flux control coefficients showed that LpxC is the rate-limiting enzyme if pathway regulation is ignored, but that LpxK is the rate-limiting enzyme if pathway regulation is present, as it is in real cells. Control also shifts to other enzymes if the pathway substrate concentrations are not in excess. Based on these results, we suggest that LpxK may be a much better drug target than LpxC, which has been pursued most often.Lipid A is a highly conserved component of lipopolysaccharide (LPS), itself a major component of the outer membrane of Gram-negative bacteria. Lipid A is essential to cells and elicits a strong immune response from humans and other animals. We developed a quantitative model of the nine enzyme-catalyzed steps of  Escherichia coli cells, covering about 75% of the cell surface area ,2],3],[3]2],2],,5],,[5],2],,2],.Lipopolysaccharide (LPS) is a glycolipid that forms the major component of the outer leaflet of the outer membrane of most Gram-negative bacteria. It occurs with roughly 1 million copies in ,5]5]. The lipid A, or endotoxin component  . These KDO residues connect to several additional sugar residues, and sometimes also to phosphate, pyrophosphorylethanolamine, or phosphorylcholine residues, which together form the core oligosaccharide . This core then connects to the O-antigen, which is a long polysaccharide that varies widely between different bacterial species and different strains within each species . Of these three components, the lipid A moiety is of particular interest because it is the only component that is essential for cell viability and is highly conserved . These also make its biosynthetic pathway an attractive target for new antibiotics ,9],10],[10]9],9],.LPS comprises three components: lipid A, core oligosaccharide, and O-antigen omponent  includes,2],5],,[5],2],,2],. However, it has received remarkably little quantitative analysis, which is essential for testing the internal consistency of models and for investigating pathway regulation mechanisms. In one modeling study, Kenanov et al.  investigated the elementary flux modes  for the biosynthesis of all E. coli lipids. They found close agreement between the predicted and experimental viability of knock-out mutants. This supported the lipid biosynthesis pathway architecture that they used, which is also the one that is commonly accepted and that which we assume in this work. In other modeling work, we recently simulated the chemical kinetics of the first two steps of lipid A biosynthesis . We found that the second enzyme (LpxC) has sufficient catalytic activity to overcome the first enzyme’s unfavourable equilibrium constant. We are not aware of any other computational models of lipid A biosynthesis.The lipid A biosynthesis pathway architecture, shown in E. coli because E. coli has been the subject of most lipid A research. However, the lipid A biosynthesis pathway is well conserved across Gram-negative bacteria , so our model may be applicable to other Gram-negative bacteria as well. We used published parameters where possible and estimated others as required. Our model can reproduce the observed lipid A production rate and agrees reasonably well with results from several lipid A biosynthesis experiments. These include data that correlated LpxC half lives and cell generation times , and our own experiments on LpxK overexpression. Our model also disagrees with several experimental results. These disagreements highlight potentially interesting biological behaviour such as metabolic channeling and additional sources of pathway regulation.Here, we build on the prior experimental and modeling work to present a quantitative model of the central steps of lipid A biosynthesis. This model is specific to . This level of detail was determined to be adequate because preliminary simulations using spatial stochastic simulations (with Smoldyn ) and non-spatial stochastic simulations (with StochKit ) yielded essentially identical results. The COPASI files are available as supplementary information and will be submitted to the BioModels database.Simulations were performed with non-spatial deterministic methods using the COPASI software E. coli K-12 strain AG1 , supE44, relA1) containing a plasmid (pCA24N)  bearing E. coli LpxK-GFP gene fusion (to the C-terminus) was obtained from the National BioResource Project (NIG) Japan. Cells were grown at 30°C in LB media  containing 20 μg/ml of chloramphenicol and when required, protein expression was induced using IPTG .An ,20]20]. Briefly, an overnight culture was inoculated into fresh LB containing different concentrations of IPTG at an OD600 of 0.05 and grown to mid log phase (OD600 = 0.5). The respective cultures were normalized to the same OD600 of 0.5. 3 ml of normalized culture was centrifuged at 13,000 rpm for 1 min and the cell pellets re-suspended in 100 μl of 2x Laemmli sample buffer . The samples were heated for 10 min prior to centrifugation for 5 min. The supernatants were collected for Western blot analysis.Cell extracts were prepared as described previously 20 μl of each sample were loaded onto a 10% SDS-polyacrylamide gel. Following electrophoresis, proteins were transferred to a PVDF membrane using the Bio-Rad Trans-Blot Turbo system. An LpxC antiserum generated in rabbit (a generous gift from Prof. Franz Narberhaus) and a secondary anti-rabbit peroxidase-linked antibody  were used for immunodetection at dilutions of 1:20000 and 1:10000 respectively. Blots were developed using the ECL chemiluminiscent reagents (Bio-Rad) and the signals detected using the ChemiDoc MP system (Bio-Rad).E. coli lipid A biosynthesis proceeds through nine enzyme-catalyzed steps, which are sometimes referred to as the Raetz pathway ,7]7]  and β-hydroxymyristoyl-ACP substrates. Both substrates are consumed in other metabolic pathways as well in vitro, suggesting that the reaction products are not committed to proceed on through the lipid A pathway but may instead revert back into the pathway substrates. The product is then deacetylated by LpxC (EC 3.5.1.108) in an essentially irreversible reaction, making this the first committed pathway step ,28],,. For this and other reasons, LpxC is likely to be a primary biosynthesis control point  (and is a prime drug target), as discussed below. The third pathway enzyme, LpxD (EC 2.3.1.191), incorporates a second hydroxymyristate moiety onto the lipid A precursor ,32]32]. LpxD is similar to LpxA in that they are acyltransferases, and consume the same β-hydroxymyristoyl-ACP substrate . Both LpxD reaction products inhibit the LpxD reaction, acting as either competitive or non-competitive inhibitors against each substrate . We simplified this by only including non-competitive inhibition by UDP-2,3-bis(β-hydroxymyristoyl)-D-glucosamine. Ignoring inhibition by ACP had minimal effect on our results because we fixed its concentration.The first three steps of the lipid A pathway occur in the cytoplasm. First, LpxA (EC 2.3.1.129) acylates UDP-GlcNAc with β-hydroxymyristoyl-ACP. This reaction has an unfavourable equilibrium constant of 0.01  and LpxB (EC 2.4.1.182) . LpxH cleaves most of the UDP moiety to leave just a single phosphate on the remaining lipid portion, which is called lipid X. Feedback regulation has not been proposed before for LpxH but proved necessary for our model to achieve steady-state behaviour, as described below. Then, LpxB combines lipid X with the preceding lipid metabolite, UDP-2,3-bis(β-hydroxymyristoyl)-D-glucosamine, to form lipid A disaccharide .The fourth and fifth lipid A biosynthesis steps are catalyzed by the peripheral membrane proteins LpxH (EC 3.6.1.54) A,36]36]. Remarkably, Lipid IVA has been reported to be an endotoxin agonist in mouse cells and an endotoxin antagonist in human cells . Next, WaaA  sequentially transfers two KDO sugar residues to lipid IVA to produce KDO2-lipid IVA,39],,40]; in the latter case, the reaction produces “alternate lipid A”, which we define as having more than 2 KDO sugar residues. In addition, the WaaA reaction has been shown to be reversible, based on the finding that in vitro combinations of the reaction products , and KDO2-lipid IVA) led to detectible concentrations of the KDO-lipid IVA intermediate . However, the authors only observed trace quantities of lipid IVA even after prolonged incubations, thus, the forward reaction is likely to be strongly thermodynamically favourable, and in which case, the in vivo back-reaction rate is probably negligible. For this reason, our model treats WaaA catalysis as being irreversible. Finally, the “late acyltransferases,” LpxL (EC 2.3.1.-)  and LpxM (EC 2.3.1.-) ,43]43], incorporate lauroyl and myristoyl chains to the KDO2-lipid IVA, thus giving the final KDO2-lipid A product six acyl chains. Cells are still viable without LpxM, or without LpxL and with overexpressed LpxM . In cold-adapted E. coli, the LpxL function is replaced by LpxP (EC 2.3.1.-), which incorporates a palmitoleate instead of the laurate, presumably as a way of adjusting membrane fluidity .The remaining four steps of lipid A biosynthesis are catalyzed by integral membrane enzymes. LpxK (EC 2.7.1.130) is a kinase that phosphorylates lipid A disaccharide to produce lipid IV2-lipid A is joined to core oligosaccharide and then flipped from the inner leaflet of the inner membrane to the outer leaflet of the inner membrane by MsbA (EC 3.6.3.39), an ABC transporter ,46]46]. Next, several enzymes add the O-antigen to form LPS, and then transport the LPS on to the outer leaflet of the outer membrane .After synthesis, KDO,48],,52]. FtsH is an essential protein due to its role in regulating LpxC ,53]53]. Lipid A biosynthesis regulation is less well established than is the synthetic pathway, so we describe these aspects of our model in more detail.Lipid A synthesis is regulated, at least in part, through controlled degradation of LpxC LpxC, and FtsH*WaaA, respectively). This assumption of substrate-specific FtsH activation is supported by several findings: (i) FtsH degradation of RpoH and λ CII is substrate-specific, accomplished through separate adapter proteins ,54]54], (ii) neither increased nor decreased FtsH degradation of LpxC have a significant effect on the intracellular concentration of RpoH  or the activity of WaaA , and (iii) LpxC is degraded more slowly at higher temperatures whereas WaaA is degraded more rapidly at higher temperatures ,50]50]. Substrate-specific activation of FtsH for LpxC may occur through YciM acting as an LpxC adapter protein .We assume that FtsH can reversibly convert between an inactive state, an active state for degrading LpxC, and a different active state for degrading WaaA -D-glucosamine, lipid X, and lipid A disaccharide. Of these, UDP-2,3-bis(β-hydroxymyristoyl)-D-glucosamine was already regulated by product inhibition, which makes its concentration a poor indicator of pathway flux and hence a poor candidate. Preliminary simulations that represented FtsH knock-out mutants, and hence did not include FtsH regulation, exhibited lipid A disaccharide accumulation . Unless specified otherwise, we assumed a 30 minute (1800 s) doubling time, which is the experimental value in rich media , 61]61]. For the most part, we did not account for protein synthesis, protein degradation, or cell volume growth during a cell generation. These approximations are legitimate because metabolic enzyme concentrations for constitutive enzymes likely remain constant over the course of the cell cycle. We modeled the interactions of individual substrates and enzymes for a single , 22], , , 25]25], so their relative concentrations are controlled by factors outside our simulation. We kept their levels constant at 2 million molecules (5 mM) throughout most simulations, which led to substrate saturation conditions. Additionally, we fixed the ACP level to 1024 molecules, based on proteomic results .We investigated lipid A metabolism with either excess or limiting concentrations of the UDP-GlcNAc, β-hydroxymyristoyl-ACP, and CMP-KDO substrates. The stoichiometric ratios of these substrates to lipid A are 2:1, 4:1, and 2:1, respectively, due to consumption of multiple copies and/or lipid dimerization by LpxB. The first two of these substrates are also precursors for other biosynthetic pathways E. coli cytosolic fractions . Several of these are integral membrane proteins, so their experimental protein counts are likely to be lower limits for their true counts in a cell. We used the same proteomic data source for the copy number of LpxM , another integral membrane protein, but then increased the count 20-fold as described below. We calculated LpxC, LpxH, and LpxB protein counts from protein purification data 33]63][63]33][6[63]33]71]. However, it was legitimate here because our model includes regulatory feedbacks that extend over most of the pathway length. These are alternative ways to enable models attain steady-state, and in fact are typically more effective than reversible reactions . Also, most of the lipid A reactions are likely to be nearly irreversible, due to either favourable energetics or much more abundant substrates than products .We modeled all pathway reactions using single-substrate or bi-substrate Michaelis-Menten mechanisms. We ignored reaction reversibility in most cases. This can lead to misleading results in metabolic models because it ignores feedback effects that arise from product inhibition and hence can prevent models from attaining a steady-state kcat is the enzyme catalytic rate constant, and Km is the Michaelis constant. Most of these kcat and Km values have been published using data from in vitro experiments (i) The specific activity of LpxK in crude E. coli membrane extract was estimated to be 22 nmol/min/mg in a plasmid-containing strain but 7-fold lower in wild type . There are about 432 LpxK molecules per cell and E. coli membranes include about 580,000 individual proteins , so the LpxK purity in crude membrane is about 0.074%. Thus, the pure wild-type specific activity is about 4 μmol/min/mg, from which kcat is about 2.1 s-1. We estimated that the LpxK Km value is 40 μM from a figure presented by Ray and Raetz . Although Km estimations from crude samples are prone to inaccuracies when the substrate can be catalyzed by other enzymes in the lysates, there is no evidence of such competition for the LpxK substrate. (ii) We estimated the LpxM catalytic rate constant, kcat, as 0.6 s-1 from the specific activity of the enzyme in crude lysates , much as we did for LpxK. We estimated the LpxM Km value from data shown in et al. . To do so, we simulated Clementz et al.’s experiment using COPASI , with the same enzyme and substrate concentrations that they used (0.1 μg/mL and 25 μM for protein and KDO2-lipid IVA respectively in a 20 μL reaction mixture), from which we identified the Km value that corresponded to their figure results at a time of 30 minutes. (iii) We treated the MsbA catalyzed translocation of KDO2-lipid A across the inner membrane as another Michaelis-Menten process, setting its Km value to 0.021 mM and its kcat value to 166 s-1, based on data shown in .We used single-substrate Michaelis-Menten kinetics for the LpxC, LpxK, LpxL, LpxM, and MsbA steps. Here, the metabolite flux iseriments , althougKi is the inhibition constant and the other parameters are the same as in . This implies that the pure enzyme specific activity is about 105 μmol/min/mg, which is combined with the LpxH molecular weight of 26.8 kDa , to yield its kcat as about 47 s-1. The estimation of our Ki value is discussed below.We used single-substrate Michaelis-Menten kinetics with inhibition for the LpxH enzyme. In this case, the metabolite flux is2-lipid A steps. Treating the forward and reverse LpxA reactions as independent irreversible reactions is legitimate in non-spatial models, such as ours, because doing so does not introduce any new approximations . Most bi-substrate enzymatic reactions follow either a sequential or ping-pong mechanism . In the sequential mechanism, the enzyme forms a ternary complex with both substrates before catalyzing the reaction. In the ping-pong mechanism, the enzyme binds one substrate, forms one product, and then binds the second substrate and forms the second product. The only bi-substrate reactions in the lipid A pathway that have been investigated in sufficient detail to determine mechanisms are the steps catalyzed by LpxA  and LpxD , both of which were found to follow the sequential mechanism. Lacking further experimental evidence, we assumed sequential mechanisms for the other bi-substrate reactions in the lipid A pathway as well. The sequential mechanism metabolite flux is1] and [S2] are the two substrate concentrations, with respective Michaelis-Menten constants Km1 and Km2. We needed to estimate these parameters in some cases. (i) The LpxA kinetic parameters were determined previously for the forward reaction , 76]76], but not for the reverse reaction. Thus, we assumed the same Km values for the reverse reaction as for the forward reaction , based upon the likelihood that the enzyme binding affinities are not substantially affected by the acyl group transfer. However, we set the reverse reaction kcat value to 100 times that of the forward reaction to account for the reaction’s unfavourable equilibrium constant of approximately 0.01 . (ii) We estimated the LpxB kcat value by starting from the specific activity of LpxB purified to near homogeneity , much as we did for LpxH, which resulted in a kcat value of 129 s-1. (iii) The WaaA specificity for KDO2-lipid A is 8.7 fold lower than for lipid IVA. To account for this, we reduced the kcat value for the former reaction by 8.7 fold while keeping other reaction constants the same.We used bi-substrate Michaelis-Menten kinetics for the forward LpxA, reverse LpxA, LpxB, and WaaA catalysis of KDOFinally, we used bi-substrate Michaelis-Menten kinetics with inhibition for the LpxD and WaaA steps. Assuming the sequential mechanism again, which was shown to be the correct mechanism for LpxD, the metabolite flux iskcat value as 16.7 s-1 from the specific activity of the purified protein . We computed the inhibition constant from results by Belunis and Raetz  which showed that 100 μM of lipid A inhibited the WaaA reaction by 24.1% in vitro. Their experimental conditions involved purified enzyme and substrates, thus excluding the possibility of FtsH playing a role in the inhibition. Whilst assuming a non-competitive inhibition . Together, these processes combine to give the net production rate for each of these proteins aset al which showed that LpxC in wild-type E. coli can have a half-life of 120 minutes under nutrient and temperature conditions that lead to rapid growth. We assumed that the long LpxC half-life arose because FtsH was essentially inactive under these conditions. This implies that the uncatalyzed LpxC degradation has a half-life of about 120 minutes and kdegrade is about 9.62×10–5 s-1. Separately, it has been shown that cells with inhibited FtsH activity, using a temperature sensitive mutant, exhibit 4-fold elevated LpxC concentrations , thus increasing LpxC counts from about 385 molecules to about 1540 molecules. Combining this molecule count with the kdegrade value and the assumption that [FtsH*LpxC] equaled zero in this mutant, enables ktranslate value of about 0.148 molec./s. Next, combining the kdegrade, ktranslate, and the wild-type LpxC count of 385 molecules enables kFtsH[FtsH*LpxC] is 2.89×10–4 s-1. We cannot solve for kFtsH by itself from the available information, but estimate its value below.To determine the production and degradation parameters for LpxC, we started with results presented in Schäkermann , from which we computed that kdegrade is about 1.8×10–4 s-1. Next, the half-life of WaaA in wild-type cells under optimal growth conditions is about 10 minutes . This gives the combined degradation rate constant, kdegrade + kFtsH[FtsH*WaaA], as approximately 1.15×10–3 s-1, implying that the catalyzed degradation rate constant is about 9.8×10–4 s-1. Combining the total degradation rate with the wild-type WaaA abundance of 153 molecules per cell gives the protein translation rate, ktranslate, as 0.176 molecules/s.We computed the WaaA synthesis and degradation parameters similarly. First, a mutant without FtsH maintained about 72% of its WaaA concentration after 30 minutes . We did not account for FtsH sequestration through activation for other degradation targets, such as RpoH or misfolded proteins. We modeled FtsH activation and inactivation with mass action kinetics, meaning that we treated net FtsH activation towards a specific substrate according to2-lipid A for the WaaA substrate), and [FtsH] represents the concentration of inactive FtsH. The first term on the right hand side represents the activation rate and the second represents the inactivation rate.Our model treats FtsH activation in a substrate-specific manner, but with the constraint that the total FtsH count per cell is conserved at 579 molecules kactive, kinactive, and kFtsH. However, the available experimental data only enabled us to quantify the product kFtsH[FtsH*], for each substrate, with values given above. Thus, the system is underdetermined, with multiple possible combinations of parameters values that are each equally good at agreeing with the available data. We addressed this by making a few assumptions. First, we assumed that during growth on rich media, 10% of the total FtsH is activated for degradation of LpxC, 10% is activated for degradation of WaaA, and 80% is inactive . This is intuitively sensible because it assumes a reasonably large reservoir of inactive FtsH to allow for strong regulatory control and other proteolysis tasks. Combining this assumption with the prior values for the kFtsH[FtsH*] products yield kFtsH of 2.0 mM-1s-1 for LpxC and kFtsH of 6.8 mM-1s-1 for WaaA. Secondly, we assumed that both kinactive values equal 0.1 s-1. This gives the active states a 10 s lifetime, which is fast enough to enable rapid control. We then solved for kactive from the steady-state version of kactive is 0.14 mM-1s-1 for LpxC and 32.3 mM-1s-1 for WaaA. Note that the assumptions made here do not affect the model’s steady-state condition at all, making them necessary for running simulations but irrelevant to the results that we present below.The FtsH proteolysis rate, for either LpxC or WaaA, depends on three parameters, Our initial model, defined using literature parameter values where available and our best estimates elsewhere, exhibited a lipid A production rate that was much too low. Also, several internal metabolite concentrations accumulated to very high levels. We addressed these problems with two model adjustments.E. coli cells actually produce per generation. This did not change even if we removed FtsH degradation of LpxC and WaaA and all negative feedbacks. We found that this slow production rate arose from LpxM acting as a bottleneck in the pathway, as seen by its substrate increasing linearly over time, rather than stabilizing at a steady-state level. This may indicate that cells have more than the 186 LpxM proteins that proteomic research on the cell cytoplasm indicated , which would not be surprising because LpxM is an integral membrane protein. Alternatively, it may be that other enzymes acylate LpxM’s substrate in parallel to LpxM; in particular, LpxL and LpxP can catalyze essentially the same lipid A synthesis reaction , . Assuming the former explanation, we increased the LpxM molecule count 20 fold, from 186 to 3720. This removed substrate accumulation upstream of LpxM and caused the model to produce lipid A at about 1 million molecules per generation.Our initial model simulations only produced about 20% of the 1 million lipid A molecules that in vivo. We found that the accumulation arose because LpxH rapidly diverted UDP-2,3-bis(β-hydroxymyristoyl)-D-glucosamine towards lipid X, while LpxB only consumed lipid X in a 1:1 ratio with UDP-2,3-bis(β-hydroxymyristoyl)-D-glucosamine. For this reason, we assumed that LpxH is regulated through product inhibition, as described above. The experimental lipid X count was reproduced when we set Ki to 0.2 μM; however, this value is unusually small and it created a bottleneck in the pathway, which we observed as accumulation of the LpxC product and decreased lipid A production . Thus, we decided to decrease LpxH inhibition by increasing Ki. As mentioned above, mutants with inactive FtsH exhibit 4-fold increased LpxC concentrations ; they were also shown to produce 32% more lipid A . We decided to set the LpxH inhibition constant so that our model would reproduce this result, which turned out to be a Ki value of 0.015 mM. This value was large enough that it did not cause the LpxC product to accumulate in wild-type cells. However, the LpxC product still accumulated in cells without FtsH due to the higher metabolite flux through the LpxC step and the lack of product inhibition at this step. This Ki value caused the steady-state lipid X concentration to be about 22,000 molecules, in either wild-type or FtsH mutant cells, which is much larger than the 2000 that were observed experimentally . We found that this difference cannot be eliminated simply by adjusting enzyme kinetic parameters without creating large metabolite accumulations, which suggests that this region of the biosynthesis pathway includes dynamics that are not in our model. For example, the difference could arise from metabolic channeling between the LpxH and LpxB enzymes.Our initial simulations also resulted in high lipid X concentrations, which rose over the course of several cell generations and stabilized at about 400,000 copies. In contrast, 2000 copies were observed  showed that cells that have defective LpxA copies, which have at least 150-fold lower LpxA specific activities, have 5- to 10-fold increased LpxC concentrations and an LPS content that is reduced by approximately 30% (their strain SM101 at 30°C). We modeled this perturbation by decreasing the LpxA kcat value by 150 fold, to 0.048 s-1. Our simulation resulted in a 3.9 fold increase in LpxC levels, in reasonably close agreement with experiment. This is essentially the maximum LpxC increase that our model can produce under any condition, arising from our assumption that cells with completely inactive FtsH exhibit 4-fold higher LpxC concentrations . However, our model only produced 24,000 lipid A molecules per generation, rather than the 1.1 million molecules that it produces with our standard parameters  on E. coli, meaning the lowest drug concentration required to inhibit visible growth, is between 0.20 and 0.25 μg/ml , 20]20]. Barb et al. showed that CHIR-090 acts by inhibiting LpxC through the two-step mechanism . They reported the reaction kinetics parameters as k4/k3 = 4 nM, k5 = 1.9 min-1, and k6 = 0.18 min-1. They did not report separate parameters for k3 and k4, but their results only becomes logical if this complexation reaction comes to equilibrium reasonably quickly. Thus, we assume here that k4 = 0.1 s-1, from which we compute that k3 = 25000 mM-1s-1. We added this mechanism to our model to see if it would exhibit the same inhibitory effect. Firstly, we noticed that fixing the free inhibitor concentration to a constant value does not affect the steady-state biosynthesis pathway at all. This seems reasonable because the LpxC count is not fixed in our model, but arises from the LpxC translation and degradation rates, which the inhibitor does not affect . On the other hand, the inhibitor induces a very strong transient effect. . From the data shown in in vitro inhibition constant of CHIR-090, Ki*, which is 0.5 nM . Taking the in vivo MIC as 0.25 μg/ml, and using the CHIR-090 molecular weight of 437.4 g/mol, shows that the MIC is 570 nM of extracellular CHIR-090. Combining this with the intracellular MIC suggests that the intracellular CHIR-090 concentration is about 1000 fold lower than the extracellular concentration.CHIR-090 is a powerful antibiotic that controls et al.  showed that faster growing cells, such as those grown in rich media and/or at higher temperatures, stabilize LpxC more rapidly than slowly growing cells. We simulated these experiments as a way of validating our model. We only considered Schäkermann et al.’s results for rich medium because all of our model parameters were estimated from experiments performed with rich medium. For each LpxC half-life value from Table 2 of Schäkermann et al. , we used LpxC that would produce it . They also found that overexpressing LpxC with 0.01% arabinose resulted in a protein half-life of about 11 minutes .Führer . The 0.1% arabinose induction experiment is harder to match because this resulted in 1.7 fold more LPS, whereas LpxC overexpression could not produce more than 1.36 fold more lipid A in our model due to LpxD acting as a bottleneck. A possible explanation for this difference is that Führer et al. found that LpxC overexpression led to longer cell generation times , in addition to the effects mentioned above. Thus, it may be that cells produce lipid A only 36% faster than normal, but they take twice as long to divide, leading to 1.7 fold more LPS in cells. Together, these results show that our model agrees qualitatively with Führer et al.’s LpxC overexpression experiments, and it could agree quantitatively as well, but this cannot be assessed currently with the available experimental data.We simulated arabinose induction by increasing our model’s LpxC translation rate constant and observing its effect on the lipid A production rate and LpxC half-life . As in t observed that E. coli grown on minimal medium had a 150 minute generation time. Replicating this in our model was straightforward. As above, we used the assumption that a cell generation is the time that the model takes to produce 1 million lipid A molecules. Our model reproduces the 150 minute generation time when any one substrate limits the lipid A production rate, with 16,000 UDP-GlcNAc molecules, or 43 β-hydroxymyristoyl-ACP molecules, or 510 CMP-KDO molecules. It also reproduces the 150 minute generation time when all three substrates are partially limiting, with 80,000 UDP-GlcNAc, 210 β-hydroxymyristoyl-ACP, and 2400 CMP-KDO molecules (about 5 times the prior numbers). Thus, substrate limitation does increase generation times in the model, as expected.It is well known that organisms grow more slowly when nutrients are limited. For example, Taniguchi et al.  in that the low substrate concentrations in the model led to decreased lipid A disaccharide counts, which caused slower LpxC degradation, whereas Schäkermann et al. showed that substrate limitation leads to faster LpxC degradation. They found that growth in minimal medium leads to an LpxC half-life of about 10 minutes . This appears to occur because substrate limiting conditions lead to increased (p)ppGpp alarmone concentrations, which increase FtsH expression . Our model could agree with these data as well, but only if the total FtsH count was increased roughly 25-fold, to about 14,000 molecules . This modified model exhibited a 10 minute LpxC half-life and a 160 minute generation time, in close agreement with results presented in Schäkermann et al. The cost of achieving this agreement was that the high FtsH concentration led to fast WaaA degradation, which made WaaA catalysis of CMP-KDO the rate-limiting step as observed by the fact that lipid IVA accumulated rapidly. The large FtsH expression increase and the lipid IVA accumulation suggest that our model is incorrect for substrate limiting conditions. In particular, achieving the combination of rapid LpxC degradation and relatively low lipid A disaccharide concentrations, without increasing the FtsH concentration 25-fold, requires additional LpxC degradation regulation.However, these results disagree with those of Schäkermann et al. As mentioned above, a preliminary model that did not include FtsH feedback regulation exhibited lipid A disaccharide accumulation , which l, 81]81], we defined flux control coefficients asi represents one of the 10 pathway enzymes, J represents the biosynthesis rate of lipid A at the outer membrane, and Ei represents the count of enzyme i. We quantified flux control coefficients by starting the model at steady-state, varying an enzyme count by 5%, and observing the effect on the lipid A production rate. When we set the three pathway substrates to saturating concentrations and used the “open-loop” case, in which we removed negative feedback through FtsH but kept the wild-type enzyme counts from ,55]55]. However, the “closed-loop” case, in which we replaced the feedbacks through FtsH and thus returned to a better model for the wild-type pathway, showed no sensitivity to LpxC concentration perturbations . Finally, limiting KDO-CMP shifted control to WaaA in the open-loop case, and to MsbA in the closed-loop case. These results show that control of pathway flux is typically localized to relatively few enzymes, but ones which depend on the substrate concentrations.Yet different enzymes controlled pathway flux when we reduced substrate concentrations. For each substrate, we set its concentration to the value that led to about 0.5 million lipid A molecules produced per generation and then computed flux control coefficients for each enzyme. Limiting UDP-GlcNAc shifted control to LpxA. This contrasts the view that LpxA does not affect pathway flux, simply because it is reversible and has an unfavorable equilibrium constant Next, we investigated the sensitivity of lipid A biosynthesis on enzyme counts for the case of large perturbations, assuming saturating substrate concentrations. For each enzyme, we determined what fraction of the wild-type count  would le leads to the obvious question of why it is regulated in addition to LpxC. From our sensitivity analysis, one answer may be that WaaA regulation is used to control pathway flux when the CMP-KDO concentration is limiting  Our initial model produced lipid A at 20% of the observed rate and exhibited LpxM substrate accumulation, which suggest that LpxM is actually present at a much higher concentration than was measured with proteomic methods . (ii) High modeled levels of lipid X suggest that the LpxH kinetics are regulated by product inhibition, and also that LpxH and LpxB may form a complex that performs metabolic channeling. (iii) The model exhibited 4-fold increased LpxC when LpxA was made defective, instead of the observed 5–10 increase ; this may arise from experimental differences, or due to unmodeled aspects of LpxC regulation, such as transcription regulation. (iv) The model exhibited a 98% reduction in the lipid A synthesis rate when LpxA was defective, instead of the 30% that was observed experimentally , which suggests the presence of alternate metabolic routes around LpxA, such as by LpxD. (v) The model underestimated cell generation times when LpxC had a very long half-live , which suggest that the growth rates of fast growing cells are not limited by the lipid A production rate. (vi) The model could exhibit the experimentally observed LpxC half-life and cell generation time when substrates were limited , but only when the total FtsH concentration was increased 25-fold; this suggests that there are additional mechanisms that regulate LpxC degradation. None of these speculations are proven by the model. Instead, they are possible solutions to situations in which the experiments that we drew on to create the model do not agree with experiments that were used to test the model. They provide hypotheses for further experimental investigation.Quantitative disagreements between our model and experiments are particularly useful because they show which model assumptions are likely to be incorrect. These errors then enable new insights about the true system behaviour. In particular: , which might make cells unable to counteract its inhibition. Additionally, when we accounted for feedback regulation, we found that the lipid A production rate is particularly sensitive to the LpxK concentration Click here for additional data file.S2 FileParameters are same as in S1 with the inclusion of (CPS)Click here for additional data file.