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1.  Kinetic modelling of phospholipid synthesis in Plasmodium knowlesi unravels crucial steps and relative importance of multiple pathways 
BMC Systems Biology  2013;7:123.
Background
Plasmodium is the causal parasite of malaria, infectious disease responsible for the death of up to one million people each year. Glycerophospholipid and consequently membrane biosynthesis are essential for the survival of the parasite and are targeted by a new class of antimalarial drugs developed in our lab. In order to understand the highly redundant phospholipid synthethic pathways and eventual mechanism of resistance to various drugs, an organism specific kinetic model of these metabolic pathways need to be developed in Plasmodium species.
Results
Fluxomic data were used to build a quantitative kinetic model of glycerophospholipid pathways in Plasmodium knowlesi. In vitro incorporation dynamics of phospholipids unravels multiple synthetic pathways. A detailed metabolic network with values of the kinetic parameters (maximum rates and Michaelis constants) has been built. In order to obtain a global search in the parameter space, we have designed a hybrid, discrete and continuous, optimization method. Discrete parameters were used to sample the cone of admissible fluxes, whereas the continuous Michaelis and maximum rates constants were obtained by local minimization of an objective function.The model was used to predict the distribution of fluxes within the network of various metabolic precursors.
The quantitative analysis was used to understand eventual links between different pathways. The major source of phosphatidylcholine (PC) is the CDP-choline Kennedy pathway.
In silico knock-out experiments showed comparable importance of phosphoethanolamine-N-methyltransferase (PMT) and phosphatidylethanolamine-N-methyltransferase (PEMT) for PC synthesis.
The flux values indicate that, major part of serine derived phosphatidylethanolamine (PE) is formed via serine decarboxylation, whereas major part of phosphatidylserine (PS) is formed by base-exchange reactions.
Sensitivity analysis of CDP-choline pathway shows that the carrier-mediated choline entry into the parasite and the phosphocholine cytidylyltransferase reaction have the largest sensitivity coefficients in this pathway, but does not distinguish a reaction as an unique rate-limiting step.
Conclusion
We provide a fully parametrized kinetic model for the multiple phospholipid synthetic pathways in P. knowlesi. This model has been used to clarify the relative importance of the various reactions in these metabolic pathways. Future work extensions of this modelling strategy will serve to elucidate the regulatory mechanisms governing the development of Plasmodium during its blood stages, as well as the mechanisms of action of drugs on membrane biosynthetic pathways and eventual mechanisms of resistance.
doi:10.1186/1752-0509-7-123
PMCID: PMC3829661  PMID: 24209716
Malaria; Phospholipid metabolism; Plasmodium knowlesi; Mathematical model; Fluxomics; Hybrid optimization
2.  Metabolomics-driven quantitative analysis of ammonia assimilation in E. coli 
Despite extensive study of individual enzymes and their organization into pathways, the means by which enzyme networks control metabolite concentrations and fluxes in cells remains incompletely understood. Here, we examine the integrated regulation of central nitrogen metabolism in Escherichia coli through metabolomics and ordinary-differential-equation-based modeling. Metabolome changes triggered by modulating extracellular ammonium centered around two key intermediates in nitrogen assimilation, α-ketoglutarate and glutamine. Many other compounds retained concentration homeostasis, indicating isolation of concentration changes within a subset of the metabolome closely linked to the nutrient perturbation. In contrast to the view that saturated enzymes are insensitive to substrate concentration, competition for the active sites of saturated enzymes was found to be a key determinant of enzyme fluxes. Combined with covalent modification reactions controlling glutamine synthetase activity, such active-site competition was sufficient to explain and predict the complex dynamic response patterns of central nitrogen metabolites.
doi:10.1038/msb.2009.60
PMCID: PMC2736657  PMID: 19690571
active-site competition; flux regulation; HPLC-MS; metabolic dynamics; predictive model
3.  Mechanistic analysis of multi-omics datasets to generate kinetic parameters for constraint-based metabolic models 
BMC Bioinformatics  2013;14:32.
Background
Constraint-based modeling uses mass balances, flux capacity, and reaction directionality constraints to predict fluxes through metabolism. Although transcriptional regulation and thermodynamic constraints have been integrated into constraint-based modeling, kinetic rate laws have not been extensively used.
Results
In this study, an in vivo kinetic parameter estimation problem was formulated and solved using multi-omic data sets for Escherichia coli. To narrow the confidence intervals for kinetic parameters, a series of kinetic model simplifications were made, resulting in fewer kinetic parameters than the full kinetic model. These new parameter values are able to account for flux and concentration data from 20 different experimental conditions used in our training dataset. Concentration estimates from the simplified kinetic model were within one standard deviation for 92.7% of the 790 experimental measurements in the training set. Gibbs free energy changes of reaction were calculated to identify reactions that were often operating close to or far from equilibrium. In addition, enzymes whose activities were positively or negatively influenced by metabolite concentrations were also identified. The kinetic model was then used to calculate the maximum and minimum possible flux values for individual reactions from independent metabolite and enzyme concentration data that were not used to estimate parameter values. Incorporating these kinetically-derived flux limits into the constraint-based metabolic model improved predictions for uptake and secretion rates and intracellular fluxes in constraint-based models of central metabolism.
Conclusions
This study has produced a method for in vivo kinetic parameter estimation and identified strategies and outcomes of kinetic model simplification. We also have illustrated how kinetic constraints can be used to improve constraint-based model predictions for intracellular fluxes and biomass yield and identify potential metabolic limitations through the integrated analysis of multi-omics datasets.
doi:10.1186/1471-2105-14-32
PMCID: PMC3571921  PMID: 23360254
Metabolic engineering; Kinetics; Central metabolism; Constraint-based; FBA
4.  Mathematical Modelling of Polyamine Metabolism in Bloodstream-Form Trypanosoma brucei: An Application to Drug Target Identification 
PLoS ONE  2013;8(1):e53734.
We present the first computational kinetic model of polyamine metabolism in bloodstream-form Trypanosoma brucei, the causative agent of human African trypanosomiasis. We systematically extracted the polyamine pathway from the complete metabolic network while still maintaining the predictive capability of the pathway. The kinetic model is constructed on the basis of information gleaned from the experimental biology literature and defined as a set of ordinary differential equations. We applied Michaelis-Menten kinetics featuring regulatory factors to describe enzymatic activities that are well defined. Uncharacterised enzyme kinetics were approximated and justified with available physiological properties of the system. Optimisation-based dynamic simulations were performed to train the model with experimental data and inconsistent predictions prompted an iterative procedure of model refinement. Good agreement between simulation results and measured data reported in various experimental conditions shows that the model has good applicability in spite of there being gaps in the required data. With this kinetic model, the relative importance of the individual pathway enzymes was assessed. We observed that, at low-to-moderate levels of inhibition, enzymes catalysing reactions of de novo AdoMet (MAT) and ornithine production (OrnPt) have more efficient inhibitory effect on total trypanothione content in comparison to other enzymes in the pathway. In our model, prozyme and TSHSyn (the production catalyst of total trypanothione) were also found to exhibit potent control on total trypanothione content but only when they were strongly inhibited. Different chemotherapeutic strategies against T. brucei were investigated using this model and interruption of polyamine synthesis via joint inhibition of MAT or OrnPt together with other polyamine enzymes was identified as an optimal therapeutic strategy.
doi:10.1371/journal.pone.0053734
PMCID: PMC3553166  PMID: 23372667
5.  Bringing metabolic networks to life: integration of kinetic, metabolic, and proteomic data 
Background
Translating a known metabolic network into a dynamic model requires reasonable guesses of all enzyme parameters. In Bayesian parameter estimation, model parameters are described by a posterior probability distribution, which scores the potential parameter sets, showing how well each of them agrees with the data and with the prior assumptions made.
Results
We compute posterior distributions of kinetic parameters within a Bayesian framework, based on integration of kinetic, thermodynamic, metabolic, and proteomic data. The structure of the metabolic system (i.e., stoichiometries and enzyme regulation) needs to be known, and the reactions are modelled by convenience kinetics with thermodynamically independent parameters. The parameter posterior is computed in two separate steps: a first posterior summarises the available data on enzyme kinetic parameters; an improved second posterior is obtained by integrating metabolic fluxes, concentrations, and enzyme concentrations for one or more steady states. The data can be heterogenous, incomplete, and uncertain, and the posterior is approximated by a multivariate log-normal distribution. We apply the method to a model of the threonine synthesis pathway: the integration of metabolic data has little effect on the marginal posterior distributions of individual model parameters. Nevertheless, it leads to strong correlations between the parameters in the joint posterior distribution, which greatly improve the model predictions by the following Monte-Carlo simulations.
Conclusion
We present a standardised method to translate metabolic networks into dynamic models. To determine the model parameters, evidence from various experimental data is combined and weighted using Bayesian parameter estimation. The resulting posterior parameter distribution describes a statistical ensemble of parameter sets; the parameter variances and correlations can account for missing knowledge, measurement uncertainties, or biological variability. The posterior distribution can be used to sample model instances and to obtain probabilistic statements about the model's dynamic behaviour.
doi:10.1186/1742-4682-3-42
PMCID: PMC1781439  PMID: 17173670
6.  Thermal robustness of signaling in bacterial chemotaxis 
Cell  2011;145(2):312-321.
Summary
Temperature is a global factor that affects the performance of all intracellular networks. Robustness against temperature variations is thus expected to be an essential network property, particularly in organisms without inherent temperature control. Here we combine experimental analyses with computer modeling to investigate thermal robustness of signaling in chemotaxis of Escherichia coli, a relatively simple and well-established model for systems biology. We show that steady-state and kinetic pathway parameters that are essential for chemotactic performance are indeed temperature-compensated in the entire physiological range. Thermal robustness of steady-state pathway output is ensured at several levels by mutual compensation of temperature effects on activities of individual pathway components. Moreover, the effect of temperature on adaptation kinetics is counterbalanced by pre-programmed temperature dependence of enzyme synthesis and stability to achieve nearly optimal performance at the growth temperature. Similar compensatory mechanisms are expected to ensure thermal robustness in other systems.
doi:10.1016/j.cell.2011.03.013
PMCID: PMC3098529  PMID: 21496648
7.  An in silico platform for the design of heterologous pathways in nonnative metabolite production 
BMC Bioinformatics  2012;13:93.
Background
Microorganisms are used as cell factories to produce valuable compounds in pharmaceuticals, biofuels, and other industrial processes. Incorporating heterologous metabolic pathways into well-characterized hosts is a major strategy for obtaining these target metabolites and improving productivity. However, selecting appropriate heterologous metabolic pathways for a host microorganism remains difficult owing to the complexity of metabolic networks. Hence, metabolic network design could benefit greatly from the availability of an in silico platform for heterologous pathway searching.
Results
We developed an algorithm for finding feasible heterologous pathways by which nonnative target metabolites are produced by host microorganisms, using Escherichia coli, Corynebacterium glutamicum, and Saccharomyces cerevisiae as templates. Using this algorithm, we screened heterologous pathways for the production of all possible nonnative target metabolites contained within databases. We then assessed the feasibility of the target productions using flux balance analysis, by which we could identify target metabolites associated with maximum cellular growth rate.
Conclusions
This in silico platform, designed for targeted searching of heterologous metabolic reactions, provides essential information for cell factory improvement.
doi:10.1186/1471-2105-13-93
PMCID: PMC3506926  PMID: 22578364
8.  Using in silico models to simulate dual perturbation experiments: procedure development and interpretation of outcomes 
BMC Systems Biology  2009;3:44.
Background
A growing number of realistic in silico models of metabolic functions are being formulated and can serve as 'dry lab' platforms to prototype and simulate experiments before they are performed. For example, dual perturbation experiments that vary both genetic and environmental parameters can readily be simulated in silico. Genetic and environmental perturbations were applied to a cell-scale model of the human erythrocyte and subsequently investigated.
Results
The resulting steady state fluxes and concentrations, as well as dynamic responses to the perturbations were analyzed, yielding two important conclusions: 1) that transporters are informative about the internal states (fluxes and concentrations) of a cell and, 2) that genetic variations can disrupt the natural sequence of dynamic interactions between network components. The former arises from adjustments in energy and redox states, while the latter is a result of shifting time scales in aggregate pool formation of metabolites. These two concepts are illustrated for glucose-6 phosphate dehydrogenase (G6PD) and pyruvate kinase (PK) in the human red blood cell.
Conclusion
Dual perturbation experiments in silico are much more informative for the characterization of functional states than single perturbations. Predictions from an experimentally validated cellular model of metabolism indicate that the measurement of cofactor precursor transport rates can inform the internal state of the cell when the external demands are altered or a causal genetic variation is introduced. Finally, genetic mutations that alter the clinical phenotype may also disrupt the 'natural' time scale hierarchy of interactions in the network.
doi:10.1186/1752-0509-3-44
PMCID: PMC2689188  PMID: 19405968
9.  Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tuberculosis, and its application to assessment of drug targets 
Background
Targeting persistent tubercule bacilli has become an important challenge in the development of anti-tuberculous drugs. As the glyoxylate bypass is essential for persistent bacilli, interference with it holds the potential for designing new antibacterial drugs. We have developed kinetic models of the tricarboxylic acid cycle and glyoxylate bypass in Escherichia coli and Mycobacterium tuberculosis, and studied the effects of inhibition of various enzymes in the M. tuberculosis model.
Results
We used E. coli to validate the pathway-modeling protocol and showed that changes in metabolic flux can be estimated from gene expression data. The M. tuberculosis model reproduced the observation that deletion of one of the two isocitrate lyase genes has little effect on bacterial growth in macrophages, but deletion of both genes leads to the elimination of the bacilli from the lungs. It also substantiated the inhibition of isocitrate lyases by 3-nitropropionate. On the basis of our simulation studies, we propose that: (i) fractional inactivation of both isocitrate dehydrogenase 1 and isocitrate dehydrogenase 2 is required for a flux through the glyoxylate bypass in persistent mycobacteria; and (ii) increasing the amount of active isocitrate dehydrogenases can stop the flux through the glyoxylate bypass, so the kinase that inactivates isocitrate dehydrogenase 1 and/or the proposed inactivator of isocitrate dehydrogenase 2 is a potential target for drugs against persistent mycobacteria. In addition, competitive inhibition of isocitrate lyases along with a reduction in the inactivation of isocitrate dehydrogenases appears to be a feasible strategy for targeting persistent mycobacteria.
Conclusion
We used kinetic modeling of biochemical pathways to assess various potential anti-tuberculous drug targets that interfere with the glyoxylate bypass flux, and indicated the type of inhibition needed to eliminate the pathogen. The advantage of such an approach to the assessment of drug targets is that it facilitates the study of systemic effect(s) of the modulation of the target enzyme(s) in the cellular environment.
doi:10.1186/1742-4682-3-27
PMCID: PMC1563452  PMID: 16887020
10.  Genome-Scale Metabolic Model of Helicobacter pylori 26695 
Journal of Bacteriology  2002;184(16):4582-4593.
A genome-scale metabolic model of Helicobacter pylori 26695 was constructed from genome sequence annotation, biochemical, and physiological data. This represents an in silico model largely derived from genomic information for an organism for which there is substantially less biochemical information available relative to previously modeled organisms such as Escherichia coli. The reconstructed metabolic network contains 388 enzymatic and transport reactions and accounts for 291 open reading frames. Within the paradigm of constraint-based modeling, extreme-pathway analysis and flux balance analysis were used to explore the metabolic capabilities of the in silico model. General network properties were analyzed and compared to similar results previously generated for Haemophilus influenzae. A minimal medium required by the model to generate required biomass constituents was calculated, indicating the requirement of eight amino acids, six of which correspond to essential human amino acids. In addition a list of potential substrates capable of fulfilling the bulk carbon requirements of H. pylori were identified. A deletion study was performed wherein reactions and associated genes in central metabolism were deleted and their effects were simulated under a variety of substrate availability conditions, yielding a number of reactions that are deemed essential. Deletion results were compared to recently published in vitro essentiality determinations for 17 genes. The in silico model accurately predicted 10 of 17 deletion cases, with partial support for additional cases. Collectively, the results presented herein suggest an effective strategy of combining in silico modeling with experimental technologies to enhance biological discovery for less characterized organisms and their genomes.
doi:10.1128/JB.184.16.4582-4593.2002
PMCID: PMC135230  PMID: 12142428
11.  Kinetics of Phosphomevalonate Kinase from Saccharomyces cerevisiae 
PLoS ONE  2014;9(1):e87112.
The mevalonate-based isoprenoid biosynthetic pathway is responsible for producing cholesterol in humans and is used commercially to produce drugs, chemicals, and fuels. Heterologous expression of this pathway in Escherichia coli has enabled high-level production of the antimalarial drug artemisinin and the proposed biofuel bisabolane. Understanding the kinetics of the enzymes in the biosynthetic pathway is critical to optimize the pathway for high flux. We have characterized the kinetic parameters of phosphomevalonate kinase (PMK, EC 2.7.4.2) from Saccharomyces cerevisiae, a previously unstudied enzyme. An E. coli codon-optimized version of the S. cerevisiae gene was cloned into pET-52b+, then the C-terminal 6X His-tagged protein was expressed in E. coli BL21(DE3) and purified on a Ni2+ column. The KM of the ATP binding site was determined to be 98.3 µM at 30°C, the optimal growth temperature for S. cerevisiae, and 74.3 µM at 37°C, the optimal growth temperature for E. coli. The KM of the mevalonate-5-phosphate binding site was determined to be 885 µM at 30°C and 880 µM at 37°C. The Vmax was determined to be 4.51 µmol/min/mg enzyme at 30°C and 5.33 µmol/min/mg enzyme at 37°C. PMK is Mg2+ dependent, with maximal activity achieved at concentrations of 10 mM or greater. Maximum activity was observed at pH = 7.2. PMK was not found to be substrate inhibited, nor feedback inhibited by FPP at concentrations up to 10 µM FPP.
doi:10.1371/journal.pone.0087112
PMCID: PMC3903622  PMID: 24475236
12.  Metabolic flux balance analysis and the in silico analysis of Escherichia coli K-12 gene deletions 
BMC Bioinformatics  2000;1:1.
Background
Genome sequencing and bioinformatics are producing detailed lists of the molecular components contained in many prokaryotic organisms. From this 'parts catalogue' of a microbial cell, in silico representations of integrated metabolic functions can be constructed and analyzed using flux balance analysis (FBA). FBA is particularly well-suited to study metabolic networks based on genomic, biochemical, and strain specific information.
Results
Herein, we have utilized FBA to interpret and analyze the metabolic capabilities of Escherichia coli. We have computationally mapped the metabolic capabilities of E. coli using FBA and examined the optimal utilization of the E. coli metabolic pathways as a function of environmental variables. We have used an in silico analysis to identify seven gene products of central metabolism (glycolysis, pentose phosphate pathway, TCA cycle, electron transport system) essential for aerobic growth of E. coli on glucose minimal media, and 15 gene products essential for anaerobic growth on glucose minimal media. The in silico tpi-, zwf, and pta- mutant strains were examined in more detail by mapping the capabilities of these in silico isogenic strains.
Conclusions
We found that computational models of E. coli metabolism based on physicochemical constraints can be used to interpret mutant behavior. These in silica results lead to a further understanding of the complex genotype-phenotype relation.
Supplementary information:
doi:10.1186/1471-2105-1-1
PMCID: PMC29061  PMID: 11001586
13.  Flux Balance Analysis of Ammonia Assimilation Network in E. coli Predicts Preferred Regulation Point 
PLoS ONE  2011;6(1):e16362.
Nitrogen assimilation is a critical biological process for the synthesis of biomolecules in Escherichia coli. The central ammonium assimilation network in E. coli converts carbon skeleton α-ketoglutarate and ammonium into glutamate and glutamine, which further serve as nitrogen donors for nitrogen metabolism in the cell. This reaction network involves three enzymes: glutamate dehydrogenase (GDH), glutamine synthetase (GS) and glutamate synthase (GOGAT). In minimal media, E. coli tries to maintain an optimal growth rate by regulating the activity of the enzymes to match the availability of the external ammonia. The molecular mechanism and the strategy of the regulation in this network have been the research topics for many investigators. In this paper, we develop a flux balance model for the nitrogen metabolism, taking into account of the cellular composition and biosynthetic requirements for nitrogen. The model agrees well with known experimental results. Specifically, it reproduces all the 15N isotope labeling experiments in the wild type and the two mutant (ΔGDH and ΔGOGAT) strains of E. coli. Furthermore, the predicted catalytic activities of GDH, GS and GOGAT in different ammonium concentrations and growth rates for the wild type, ΔGDH and ΔGOGAT strains agree well with the enzyme concentrations obtained from western blots. Based on this flux balance model, we show that GS is the preferred regulation point among the three enzymes in the nitrogen assimilation network. Our analysis reveals the pattern of regulation in this central and highly regulated network, thus providing insights into the regulation strategy adopted by the bacteria. Our model and methods may also be useful in future investigations in this and other networks.
doi:10.1371/journal.pone.0016362
PMCID: PMC3026816  PMID: 21283535
14.  Identification of Genome-Scale Metabolic Network Models Using Experimentally Measured Flux Profiles 
PLoS Computational Biology  2006;2(7):e72.
Genome-scale metabolic network models can be reconstructed for well-characterized organisms using genomic annotation and literature information. However, there are many instances in which model predictions of metabolic fluxes are not entirely consistent with experimental data, indicating that the reactions in the model do not match the active reactions in the in vivo system. We introduce a method for determining the active reactions in a genome-scale metabolic network based on a limited number of experimentally measured fluxes. This method, called optimal metabolic network identification (OMNI), allows efficient identification of the set of reactions that results in the best agreement between in silico predicted and experimentally measured flux distributions. We applied the method to intracellular flux data for evolved Escherichia coli mutant strains with lower than predicted growth rates in order to identify reactions that act as flux bottlenecks in these strains. The expression of the genes corresponding to these bottleneck reactions was often found to be downregulated in the evolved strains relative to the wild-type strain. We also demonstrate the ability of the OMNI method to diagnose problems in E. coli strains engineered for metabolite overproduction that have not reached their predicted production potential. The OMNI method applied to flux data for evolved strains can be used to provide insights into mechanisms that limit the ability of microbial strains to evolve towards their predicted optimal growth phenotypes. When applied to industrial production strains, the OMNI method can also be used to suggest metabolic engineering strategies to improve byproduct secretion. In addition to these applications, the method should prove to be useful in general for reconstructing metabolic networks of ill-characterized microbial organisms based on limited amounts of experimental data.
Synopsis
One of the major uses of in silico models in biology is to identify discrepancies between model predictions and experimental data and use these discrepancies to drive discovery of novel biological mechanisms. However, models only allow for identification of the discrepancies; they do not necessarily provide any assistance in discovering what are the missing or incorrect functionalities in the model that cause these discrepancies. Herrgård et al. describe a new in silico method, optimal metabolic network identification, or OMNI, that performs this discovery process in an efficient and systematic manner for genome-scale metabolic networks. Given a preliminary metabolic network model and experimentally determined metabolic flux data, OMNI finds the changes that need to be made to the model so that its predictions match the experimental data as well as possible. Herrgård et al. apply the method to identify metabolic bottlenecks in experimentally evolved Escherichia coli strains and to diagnose problems in strains designed through metabolic engineering strategies to overproduce specific desirable byproducts. The OMNI method can also be adapted to number of other settings, including identification of novel biochemical pathways in ill-characterized organisms based on limited amounts of experimental data.
doi:10.1371/journal.pcbi.0020072
PMCID: PMC1487183  PMID: 16839195
15.  Identification of Genome-Scale Metabolic Network Models Using Experimentally Measured Flux Profiles 
PLoS Computational Biology  2006;2(7):e72.
Genome-scale metabolic network models can be reconstructed for well-characterized organisms using genomic annotation and literature information. However, there are many instances in which model predictions of metabolic fluxes are not entirely consistent with experimental data, indicating that the reactions in the model do not match the active reactions in the in vivo system. We introduce a method for determining the active reactions in a genome-scale metabolic network based on a limited number of experimentally measured fluxes. This method, called optimal metabolic network identification (OMNI), allows efficient identification of the set of reactions that results in the best agreement between in silico predicted and experimentally measured flux distributions. We applied the method to intracellular flux data for evolved Escherichia coli mutant strains with lower than predicted growth rates in order to identify reactions that act as flux bottlenecks in these strains. The expression of the genes corresponding to these bottleneck reactions was often found to be downregulated in the evolved strains relative to the wild-type strain. We also demonstrate the ability of the OMNI method to diagnose problems in E. coli strains engineered for metabolite overproduction that have not reached their predicted production potential. The OMNI method applied to flux data for evolved strains can be used to provide insights into mechanisms that limit the ability of microbial strains to evolve towards their predicted optimal growth phenotypes. When applied to industrial production strains, the OMNI method can also be used to suggest metabolic engineering strategies to improve byproduct secretion. In addition to these applications, the method should prove to be useful in general for reconstructing metabolic networks of ill-characterized microbial organisms based on limited amounts of experimental data.
Synopsis
One of the major uses of in silico models in biology is to identify discrepancies between model predictions and experimental data and use these discrepancies to drive discovery of novel biological mechanisms. However, models only allow for identification of the discrepancies; they do not necessarily provide any assistance in discovering what are the missing or incorrect functionalities in the model that cause these discrepancies. Herrgård et al. describe a new in silico method, optimal metabolic network identification, or OMNI, that performs this discovery process in an efficient and systematic manner for genome-scale metabolic networks. Given a preliminary metabolic network model and experimentally determined metabolic flux data, OMNI finds the changes that need to be made to the model so that its predictions match the experimental data as well as possible. Herrgård et al. apply the method to identify metabolic bottlenecks in experimentally evolved Escherichia coli strains and to diagnose problems in strains designed through metabolic engineering strategies to overproduce specific desirable byproducts. The OMNI method can also be adapted to number of other settings, including identification of novel biochemical pathways in ill-characterized organisms based on limited amounts of experimental data.
doi:10.1371/journal.pcbi.0020072
PMCID: PMC1487183  PMID: 16839195
16.  Development of a kinetic metabolic model: application to Catharanthus roseus hairy root 
A kinetic metabolic model describing Catharanthus roseus hairy root growth and nutrition was developed. The metabolic network includes glycolysis, pentose-phosphate pathway, TCA cycle and the catabolic reactions leading to cell building blocks such as amino acids, organic acids, organic phosphates, lipids and structural hexoses. The central primary metabolic network was taken at pseudo-steady state and metabolic flux analysis technique allowed reducing from 31 metabolic fluxes to 20 independent pathways. Hairy root specific growth rate was described as a function of intracellular concentration in cell building blocks. Intracellular transport and accumulation kinetics for major nutrients were included. The model uses intracellular nutrients as well as energy shuttles to describe metabolic regulation. Model calibration was performed using experimental data obtained from batch and medium exchange liquid cultures of C. roseus hairy root using a minimal medium in Petri dish. The model is efficient in estimating the growth rate.
doi:10.1007/s00449-005-0034-z
PMCID: PMC1705518  PMID: 16453114
Metabolic model; Plant cells; Kinetic model; Metabolic regulation; Cell nutrition
17.  Dynamics and Design Principles of a Basic Regulatory Architecture Controlling Metabolic Pathways 
PLoS Biology  2008;6(6):e146.
The dynamic features of a genetic network's response to environmental fluctuations represent essential functional specifications and thus may constrain the possible choices of network architecture and kinetic parameters. To explore the connection between dynamics and network design, we have analyzed a general regulatory architecture that is commonly found in many metabolic pathways. Such architecture is characterized by a dual control mechanism, with end product feedback inhibition and transcriptional regulation mediated by an intermediate metabolite. As a case study, we measured with high temporal resolution the induction profiles of the enzymes in the leucine biosynthetic pathway in response to leucine depletion, using an automated system for monitoring protein expression levels in single cells. All the genes in the pathway are known to be coregulated by the same transcription factors, but we observed drastically different dynamic responses for enzymes upstream and immediately downstream of the key control point—the intermediate metabolite α-isopropylmalate (αIPM), which couples metabolic activity to transcriptional regulation. Analysis based on genetic perturbations suggests that the observed dynamics are due to differential regulation by the leucine branch-specific transcription factor Leu3, and that the downstream enzymes are strictly controlled and highly expressed only when αIPM is available. These observations allow us to build a simplified mathematical model that accounts for the observed dynamics and can correctly predict the pathway's response to new perturbations. Our model also suggests that transient dynamics and steady state can be separately tuned and that the high induction levels of the downstream enzymes are necessary for fast leucine recovery. It is likely that principles emerging from this work can reveal how gene regulation has evolved to optimize performance in other metabolic pathways with similar architecture.
Author Summary
Single-cell organisms must constantly adjust their gene expression programs to survive in a changing environment. Interactions between different molecules form a regulatory network to mediate these changes. While the network connections are often known, figuring out how the network responds dynamically by looking at a static picture of its structure presents a significant challenge. Measuring the response at a finer time scales could reveal the link between the network's function and its structure. The architecture of the system we studied in this work—the leucine biosynthesis pathway in yeast—is shared by other metabolic pathways: a metabolic intermediate binds to a transcription factor to activate the pathway genes, creating an intricate feedback structure that links metabolism with gene expression. We measured protein abundance at high temporal resolution for genes in this pathway in response to leucine depletion and studied the effects of various genetic perturbations on gene expression dynamics. Our measurements and theoretical modeling show that only the genes immediately downstream from the intermediate are highly regulated by the metabolite, a feature that is essential to fast recovery from leucine depletion. Since the architecture we studied is common, we believe that our work may lead to general principles governing the dynamics of gene expression in other metabolic pathways.
A quantitative, high-temporal resolution study of gene induction in a metabolic pathway reveals an intricate connection between the regulatory architecture and the dynamic response of the system, pointing to possible principles underlying the design of these pathways.
doi:10.1371/journal.pbio.0060146
PMCID: PMC2429954  PMID: 18563967
18.  Impact of Global Transcriptional Regulation by ArcA, ArcB, Cra, Crp, Cya, Fnr, and Mlc on Glucose Catabolism in Escherichia coli†  
Journal of Bacteriology  2005;187(9):3171-3179.
Even though transcriptional regulation plays a key role in establishing the metabolic network, the extent to which it actually controls the in vivo distribution of metabolic fluxes through different pathways is essentially unknown. Based on metabolism-wide quantification of intracellular fluxes, we systematically elucidated the relevance of global transcriptional regulation by ArcA, ArcB, Cra, Crp, Cya, Fnr, and Mlc for aerobic glucose catabolism in batch cultures of Escherichia coli. Knockouts of ArcB, Cra, Fnr, and Mlc were phenotypically silent, while deletion of the catabolite repression regulators Crp and Cya resulted in a pronounced slow-growth phenotype but had only a nonspecific effect on the actual flux distribution. Knockout of ArcA-dependent redox regulation, however, increased the aerobic tricarboxylic acid (TCA) cycle activity by over 60%. Like aerobic conditions, anaerobic derepression of TCA cycle enzymes in an ArcA mutant significantly increased the in vivo TCA flux when nitrate was present as an electron acceptor. The in vivo and in vitro data demonstrate that ArcA-dependent transcriptional regulation directly or indirectly controls TCA cycle flux in both aerobic and anaerobic glucose batch cultures of E. coli. This control goes well beyond the previously known ArcA-dependent regulation of the TCA cycle during microaerobiosis.
doi:10.1128/JB.187.9.3171-3179.2005
PMCID: PMC1082841  PMID: 15838044
19.  Robustness portraits of diverse biological networks conserved despite order-of-magnitude parameter uncertainty 
Bioinformatics  2011;27(20):2888-2894.
Motivation: Biological networks are robust to a wide variety of internal and external perturbations, yet fragile or sensitive to a small minority of perturbations. Due to this rare sensitivity of networks to certain perturbations, it is unclear how precisely biochemical parameters must be experimentally measured in order to accurately predict network function.
Results: Here, we examined a model of cardiac β-adrenergic signaling and found that its robustness portrait, a global measure of steady-state network function, was well conserved even when all parameters were rounded to their nearest 1–2 orders of magnitude. In contrast, β-adrenergic network kinetics were more sensitive to parameter precision. This analysis was then extended to 10 additional networks, including Escherichia coli chemotaxis, stem cell differentiation and cytokine signaling, of which nine exhibited conserved robustness portraits despite the order-of-magnitude approximation of their biochemical parameters. Thus, both fragile and robust aspects of diverse biological networks are largely shaped by network topology and can be predicted despite order-of-magnitude uncertainty in biochemical parameters. These findings suggest an iterative strategy where order-of-magnitude models are used to prioritize experiments toward the fragile network elements that require precise measurements, efficiently driving model revision.
Contact: jsaucerman@virginia.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btr496
PMCID: PMC3187657  PMID: 21880701
20.  Determining Host Metabolic Limitations on Viral Replication via Integrated Modeling and Experimental Perturbation 
PLoS Computational Biology  2012;8(10):e1002746.
Viral replication relies on host metabolic machinery and precursors to produce large numbers of progeny - often very rapidly. A fundamental example is the infection of Escherichia coli by bacteriophage T7. The resource draw imposed by viral replication represents a significant and complex perturbation to the extensive and interconnected network of host metabolic pathways. To better understand this system, we have integrated a set of structured ordinary differential equations quantifying T7 replication and an E. coli flux balance analysis metabolic model. Further, we present here an integrated simulation algorithm enforcing mutual constraint by the models across the entire duration of phage replication. This method enables quantitative dynamic prediction of virion production given only specification of host nutritional environment, and predictions compare favorably to experimental measurements of phage replication in multiple environments. The level of detail of our computational predictions facilitates exploration of the dynamic changes in host metabolic fluxes that result from viral resource consumption, as well as analysis of the limiting processes dictating maximum viral progeny production. For example, although it is commonly assumed that viral infection dynamics are predominantly limited by the amount of protein synthesis machinery in the host, our results suggest that in many cases metabolic limitation is at least as strict. Taken together, these results emphasize the importance of considering viral infections in the context of host metabolism.
Author Summary
Viral infection is a serious problem with relatively few known solutions. Much of the complexity of viral infection is contributed by the host's own resources that the virus commandeers. Viruses lack the machinery and precursors required to replicate, and thus may be considered metabolic products of their host. Our goal is a systems-level understanding of host-viral metabolic interaction via computational tools and quantitative dynamic measurements. Here we present an integrated model of T7 phage viral replication and host E. coli metabolism that predicts phage production changes across media conditions and provides insight into the underlying limiting factors in T7 replication. The model simulations, supported by our experimental measurements, highlight the role of host metabolism in determining the dynamics of viral infection.
doi:10.1371/journal.pcbi.1002746
PMCID: PMC3475664  PMID: 23093930
21.  Metabolic Control Analysis of Glycerol Synthesis in Saccharomyces cerevisiae 
Glycerol, a major by-product of ethanol fermentation by Saccharomyces cerevisiae, is of significant importance to the wine, beer, and ethanol production industries. To gain a clearer understanding of and to quantify the extent to which parameters of the pathway affect glycerol flux in S. cerevisiae, a kinetic model of the glycerol synthesis pathway has been constructed. Kinetic parameters were collected from published values. Maximal enzyme activities and intracellular effector concentrations were determined experimentally. The model was validated by comparing experimental results on the rate of glycerol production to the rate calculated by the model. Values calculated by the model agreed well with those measured in independent experiments. The model also mimics the changes in the rate of glycerol synthesis at different phases of growth. Metabolic control analysis values calculated by the model indicate that the NAD+-dependent glycerol 3-phosphate dehydrogenase-catalyzed reaction has a flux control coefficient (Cv1J) of approximately 0.85 and exercises the majority of the control of flux through the pathway. Response coefficients of parameter metabolites indicate that flux through the pathway is most responsive to dihydroxyacetone phosphate concentration (RDHAPJ = 0.48 to 0.69), followed by ATP concentration (RATPJ = −0.21 to −0.50). Interestingly, the pathway responds weakly to NADH concentration (RNADHJ = 0.03 to 0.08). The model indicates that the best strategy to increase flux through the pathway is not to increase enzyme activity, substrate concentration, or coenzyme concentration alone but to increase all of these parameters in conjunction with each other.
doi:10.1128/AEM.68.9.4448-4456.2002
PMCID: PMC124078  PMID: 12200299
22.  Systematic Construction of Kinetic Models from Genome-Scale Metabolic Networks 
PLoS ONE  2013;8(11):e79195.
The quantitative effects of environmental and genetic perturbations on metabolism can be studied in silico using kinetic models. We present a strategy for large-scale model construction based on a logical layering of data such as reaction fluxes, metabolite concentrations, and kinetic constants. The resulting models contain realistic standard rate laws and plausible parameters, adhere to the laws of thermodynamics, and reproduce a predefined steady state. These features have not been simultaneously achieved by previous workflows. We demonstrate the advantages and limitations of the workflow by translating the yeast consensus metabolic network into a kinetic model. Despite crudely selected data, the model shows realistic control behaviour, a stable dynamic, and realistic response to perturbations in extracellular glucose concentrations. The paper concludes by outlining how new data can continuously be fed into the workflow and how iterative model building can assist in directing experiments.
doi:10.1371/journal.pone.0079195
PMCID: PMC3852239  PMID: 24324546
23.  Mutational Analysis of UMP Kinase from Escherichia coli 
Journal of Bacteriology  1998;180(3):473-477.
UMP kinase from Escherichia coli is one of the four regulatory enzymes involved in the de novo biosynthetic pathway of pyrimidine nucleotides. This homohexamer, with no counterpart in eukarya, might serve as a target for new antibacterial drugs. Although the bacterial enzyme does not show sequence similarity with any other known nucleoside monophosphate kinase, two segments between amino acids 35 to 78 and 145 to 194 exhibit 28% identity with phosphoglycerate kinase and 30% identity with aspartokinase, respectively. Based on these similarities, a number of residues of E. coli UMP kinase were selected for site-directed mutagenesis experiments. Biochemical, kinetic, and spectroscopic analysis of the modified proteins identified residues essential for catalysis (Asp146), binding of UMP (Asp174), and interaction with the allosteric effectors, GTP and UTP (Arg62 and Asp77).
PMCID: PMC106910  PMID: 9457846
24.  Biochemical Competition Makes Fatty-Acid β-Oxidation Vulnerable to Substrate Overload 
PLoS Computational Biology  2013;9(8):e1003186.
Fatty-acid metabolism plays a key role in acquired and inborn metabolic diseases. To obtain insight into the network dynamics of fatty-acid β-oxidation, we constructed a detailed computational model of the pathway and subjected it to a fat overload condition. The model contains reversible and saturable enzyme-kinetic equations and experimentally determined parameters for rat-liver enzymes. It was validated by adding palmitoyl CoA or palmitoyl carnitine to isolated rat-liver mitochondria: without refitting of measured parameters, the model correctly predicted the β-oxidation flux as well as the time profiles of most acyl-carnitine concentrations. Subsequently, we simulated the condition of obesity by increasing the palmitoyl-CoA concentration. At a high concentration of palmitoyl CoA the β-oxidation became overloaded: the flux dropped and metabolites accumulated. This behavior originated from the competition between acyl CoAs of different chain lengths for a set of acyl-CoA dehydrogenases with overlapping substrate specificity. This effectively induced competitive feedforward inhibition and thereby led to accumulation of CoA-ester intermediates and depletion of free CoA (CoASH). The mitochondrial [NAD+]/[NADH] ratio modulated the sensitivity to substrate overload, revealing a tight interplay between regulation of β-oxidation and mitochondrial respiration.
Author Summary
Lipid metabolism plays an important role in the development of metabolic syndrome, a major risk factor for cardiovascular disease and diabetes. Furthermore, inborn errors in lipid oxidation cause rare, but severe diseases in children. To obtain more insight into the response of lipid oxidation to dietary and medical interventions, we constructed a computational model. The model correctly simulated the rate of lipid oxidation and the time courses of most acyl carnitines. The latter are used as diagnostic markers in blood. Subsequently, we subjected the model to an increased supply of lipids, as often happens in obese people. We discovered that the lipid-oxidation machinery easily becomes overloaded, very much like a highway during rush hours: the more cars enter the road, the slower they proceed and the more they clog the road. Analogously, an overload of lipids slowed down the lipid oxidation and led to an accumulation of intermediate metabolites in the pathway. Potential protection mechanisms of cells consist of restricted entry of lipids into the oxidation pathway or efficient downstream processing of reaction products. In future research we will use the model to test dietary or medical interventions in silico and thereby guide the development of new treatment and prevention strategies.
doi:10.1371/journal.pcbi.1003186
PMCID: PMC3744394  PMID: 23966849
25.  Relationships between kinetic constants and the amino acid composition of enzymes from the yeast Saccharomyces cerevisiae glycolysis pathway 
The kinetic models of metabolic pathways represent a system of biochemical reactions in terms of metabolic fluxes and enzyme kinetics. Therefore, the apparent differences of metabolic fluxes might reflect distinctive kinetic characteristics, as well as sequence-dependent properties of the employed enzymes. This study aims to examine possible linkages between kinetic constants and the amino acid (AA) composition (AAC) for enzymes from the yeast Saccharomyces cerevisiae glycolytic pathway. The values of Michaelis-Menten constant (KM), turnover number (kcat), and specificity constant (ksp = kcat/KM) were taken from BRENDA (15, 17, and 16 values, respectively) and protein sequences of nine enzymes (HXK, GADH, PGK, PGM, ENO, PK, PDC, TIM, and PYC) from UniProtKB. The AAC and sequence properties were computed by ExPASy/ProtParam tool and data processed by conventional methods of multivariate statistics. Multiple linear regressions were found between the log-values of kcat (3 models, 85.74% < Radj.2 <94.11%, p < 0.00001), KM (1 model, Radj.2 = 96.70%, p < 0.00001), ksp (3 models, 96.15% < Radj.2 < 96.50%, p < 0.00001), and the sets of AA frequencies (four to six for each model) selected from enzyme sequences while assessing the potential multicollinearity between variables. It was also found that the selection of independent variables in multiple regression models may reflect certain advantages for definite AA physicochemical and structural propensities, which could affect the properties of sequences. The results support the view on the actual interdependence of catalytic, binding, and structural residues to ensure the efficiency of biocatalysts, since the kinetic constants of the yeast enzymes appear as closely related to the overall AAC of sequences.
doi:10.1186/1687-4153-2012-11
PMCID: PMC3494524  PMID: 22867018
Michaelis-Menten constant; Turnover number; Specificity constant; Glycolytic enzymes; Sequence-dependent properties; Multivariate relationships

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