Abstract
Background
Constraintbased flux analysis of metabolic network model quantifies the reaction flux distribution to characterize the state of cellular metabolism. However, metabolites are key players in the metabolic network and the current reactioncentric approach may not account for the effect of metabolite perturbation on the cellular physiology due to the inherent limitation in model formulation. Thus, it would be practical to incorporate the metabolite states into the model for the analysis of the network.
Results
Presented herein is a metabolitecentric approach of analyzing the metabolic network by including the turnover rate of metabolite, known as fluxsum, as key descriptive variable within the model formulation. By doing so, the effect of varying metabolite fluxsum on physiological change can be simulated by resorting to mixed integer linear programming. From the results, we could classify various metabolite types based on the fluxsum profile. Using the iAF1260 in silico metabolic model of Escherichia coli, we demonstrated that this novel concept complements the conventional reactioncentric analysis.
Conclusions
Metabolite fluxsum analysis elucidates the roles of metabolites in the network. In addition, this metabolite perturbation analysis identifies the key metabolites, implicating practical application which is achievable through metabolite fluxsum manipulation in the areas of biotechnology and biomedical research.
Background
Cellular metabolism is more often than not represented and analysed based on a stoichiometric modelling framework under the stationary assumption of the metabolic network [1]. Such stationary approaches, e.g. flux balance analysis (FBA), circumvent issues related to kinetic modeling, including the lack of experimental data and the need for estimation of kinetic parameters, and provide useful information about the characteristics of the system as evident in various nonlinear dynamic analysis techniques [2]. Furthermore, the assumption of metabolic steadystate is usually valid since the intracellular dynamics are typically much faster than extracellular dynamics [1] and metabolite concentrations generally equilibrate in a much shorter time (in seconds) compared to the timescale of genetic regulation (in minutes) [35]. Consequently, the constraintbased reconstruction and analysis (COBRA) approach provides an elegant method of characterizing and predicting cellular phenotype and metabolic states through the application of FBA which solves a linear optimization problem by assuming some form of cellular objective as the performance criterion [68].
Metabolites and biochemical reactions in the metabolic network can be graphically represented by nodes and edges connecting the nodes respectively. Based on this graphical representation, it is obvious that there can be two approaches in the analysis of the network, focusing on the flow of materials through either the nodes (metabolitecentric approach) or edges (reactioncentric approach). Typical FBA can be conducted based on a reactioncentric approach where constraints were introduced to restrict the range of reaction flux values so as to define a feasible solution space [9]. This analysis is intrinsically reactioncentric since reaction fluxes are the key description variables in the model formulation [10]. Previous studies involving the application of FBA mostly dealt with gene or reaction knockouts [1113] and manipulation of reaction rates [14], which examined the phenotypic morphology resulting from the alteration of reaction fluxes. These reactioncentric approaches, especially in [14], provided us with a quantitative understanding of the reaction essentiality in a metabolic network.
On the other hand, the metabolitecentric approach towards addressing metabolite essentiality was, to date, only attempted by a handful of studies [1517] which mostly presented qualitative effects of removing metabolites from the network. Only [16] demonstrated the use of a quantitative measure of metabolite essentiality known as the "fluxsum" which indicates the turnover rate of a particular metabolite. Recognizing the fact that metabolites play important roles in shaping the metabolic network [18], we propose a methodology for the quantitative analysis of metabolite essentiality that can overcome the limitations of the previous formulation and extend the scope of analysis. As the constraintbased modeling, we incorporated metabolite fluxsum constraints with the reaction flux constraints in the mathematical formulation so as to investigate the effect of varying metabolite fluxsum on cellular metabolism and phenotypic change. The efficacy and usefulness of this metabolitecentric approach was demonstrated by applying it to the E. coli system using i AF1260 in silico metabolic model [19].
Methodology
Defining the fluxsum
The constraintbased analysis of the metabolic network evaluates the steadystate flux distribution which satisfies the flux balance condition: for any internal/intermediate metabolites i, where S_{ij }refers to the stoichiometric coefficient of metabolite i participating in reaction j and v_{j}, the flux of reaction j. At pseudosteadystate, there is no accumulation of intermediate metabolites but the absolute rate of metabolite consumption or production can be nonzero. Therefore, we can define a new descriptive variable of "fluxsum" to represent the turnover rate of a metabolite by summing up all the incoming or outgoing fluxes around the metabolite [16]. This definition clearly indicates that the unit of fluxsum is equivalent to that of the reaction flux (i.e. mmol/gDCWhr). Hence, we let Φ_{i }denote the fluxsum of metabolite i and its mathematical form is given by . This variable can be further constrained to explore phenotypic changes under perturbed conditions such as attenuation or intensification in the metabolic network.
Fluxsum constraint with binary variables
The nonlinear fluxsum term within the mathematical formulation was originally recast into a series of linear constraints based on the mathematical relationship (a  b)^{2 }≤ (a + b)^{2 }which leads to a  b ≤ a + b only under the condition that a ≥ 0 and b ≥ 0 [16,20]. By introducing two positive variables a_{j }and b_{j}, they let S_{ij}v_{j }= a_{j } b_{j }for metabolite i. Thus, the constraint effectively ensured that the fluxsum of metabolite i, Φ_{i}, is less than or equal to the value of C. Since this method enables us to specify "≤" constraints on fluxsums, it sufficed the analysis of fluxsum attenuation. However, this technique is inadequate for the implementation of fluxsum intensification, which requires "≥" constraints. In order to overcome the limitation, we reformulate fluxsum constraints as follows: Similarly, we let the rate of consumption/production of metabolite i due to reaction j be expressed in terms of two positive variables: , where and . Thus the fluxsum of metabolite i can be expressed as . We observed that if and only if either or , or simply . Then, the fluxsum of metabolite i is given by when either or . This condition can be satisfied by introducing indicators or binary variables: and , and the constraints ; ; and . Note that big M is some finitely large number that should at least be larger than the largest possible reaction flux observed experimentally. The rationale for using big M instead of infinity is that the product of zero and infinity is undefined. This formulation of fluxsum circumvents the "bad" nonlinear constraint [20].
Fluxsum analysis
In order to conduct fluxsum attenuation and intensification analyses, we need reference values representing the base case and the range of feasible fluxsum values. The collection of fluxsum values corresponding to the unperturbed system or base case would be referred to as the basal fluxsum distribution that can be calculated from the flux distribution as a result of FBA. The minimum fluxsum value of any metabolite is set as zero since Φ_{i }≥ 0 while the maximum fluxsum can be evaluated using the new mathematical formulation that is elaborated below. Based on these reference values, we can attenuate or intensify each metabolite's fluxsum by gradually decreasing or increasing the fluxsum value from the basal value to zero or the maximum value, respectively. In summary, the entire process of fluxsum analysis is carried out in 3 steps:
Step 1: Evaluate basal fluxsum distribution.
Step 2: Evaluate fluxsum maxima of individual metabolites.
Step 3: Manipulate fluxsum by attenuation and intensification.
The mathematical details for every step of the procedure are described as follows:
Step 1: Evaluate basal fluxsum distribution
The basal fluxsum distribution can be evaluated based on the "wildtype" flux distribution which is determined by solving the following FBA formulation under the unperturbed or normal condition:
In this study, we assumed the cellular objective to be biomass formation (or cell growth), v_{biomass}. The preceding formulation allowed the input of experimental observations by specifying the values of α_{j}, β_{j}, λ_{i }and μ_{i}. In the case where upper and lower bounds of fluxes are unavailable, the flux capacities can be set as α_{j }= 0, β_{j }= +inf for irreversible reactions and α_{j }= inf, β_{j }= +inf for reversible reactions. Similarly, for metabolite uptake or secretion constraints on exchange fluxes (v_{EX_i}), we can set λ_{i }= 0, μ_{i }= +inf for metabolites that are secreted only; λ_{i }= inf, μ_{i }= 0 for metabolites that are consumed only; and λ_{i }= inf, μ_{i }= +inf for metabolites that can enter and leave the system freely.
After solving (P1), the basal fluxsum value of any metabolite i is calculated using the formula , indicating the summation of all incoming or outgoing fluxes around metabolite i under the normal condition.
Step 2: Evaluate fluxsum maxima of individual metabolites
The fluxsum maxima of metabolites can be calculated by solving the following mixedinteger optimization (MIP) problem:
We let denote the maximum fluxsum value of (P2) for metabolite i.
Step 3: Manipulate fluxsum by attenuation or intensification
With the reformulation of fluxsum constraints we fix the fluxsum of any metabolite at a particular value and evaluate the corresponding metabolic state. In order to ensure feasibility, the basal fluxsum can be considered as the starting point, followed by examining the effects of decreasing and increasing metabolite fluxsums through fluxsum attenuation and intensification analysis, respectively. The mathematical formulation for this analysis is given as follow:
By solving this MIP problem, we can obtain the biomass production values for different levels of fluxsum attenuation or intensification. Note that either (C1) or (C2) is implemented depending on whether the problem is fluxsum attenuation or intensification respectively. The parameters k_{att }and k_{int }control the levels of fluxsum attenuation and intensification respectively. Initially, setting k_{att }= 1 or k_{int }= 0 constrains the fluxsum at the basal level. Subsequently, we can attenuate or intensify the fluxsum by decreasing k_{att }or increasing k_{int }until k_{att }= 0 or k_{int }= 1, where the fluxsum would reach zero or the maximum value, respectively. The decrement and increment of k_{att }and k_{int }can be in steps of 0.1 so that they only take on values from the set {0, 0.1, 0.2 ... 1.0}.
Application
In silico model settings
The genomescale in silico E. coli model iAF1260 was employed to demonstrate the efficacy and applicability of the current fluxsum approach. The model was made up of 1668 metabolites (951 cytoplasmic and 418 periplasmic intermediates and 299 external metabolites) and 2382 reactions including the biomass reaction, thus making up a 1668 by 2382 stoichiometric matrix [18]. In the current model, the metabolites are compartmentalized. Hence, we distinguish same metabolites in different compartments using suffixes [c], [p] and [e] for cytosol, periplasm and extracellular matrix respectively. For example H_{2}O [c], H_{2}O [p] and H_{2}O [e] indicate water found in three different compartments. The cellular objective was assumed to be the maximization of biomass production. The reaction reversibility constraints were set as given by [19]. The nongrowth associated maintenance energy is maintained at 8.39 mmol ATP/(gDCWhr) while the maximum glucose and oxygen uptake rates were assumed as 10 mmol/(gDCWhr) and 20 mmol/(gDCWhr) respectively to simulate the aerobic growth condition of Escherichia coli in glucose minimal medium. All these settings were based on previous observation for glucose and oxygen uptake rates and experimentally determined ATP requirement for maintenance [6,19,21]. The GAMS IDE software version 22.4 was used to solve all the mathematical programming problems in this study.
Basal fluxsum
We generated a basal metabolite fluxsum distribution (Figure 1) for the iAF1260 model by solving (P1), resulting in 4.20 and 23.9 for average (μ_{FS}) and standard deviation (sd) of the fluxsum values respectively. About 70% of the metabolites have zero fluxsum in the base case while metabolites with high () and ultrahigh (
Figure 1. Basal fluxsum distribution. Metabolites with ultrahigh basal fluxsum values were cofactors like ATP, ADP and H^{+}. It was also observed that a large number of metabolites (i.e. 795 or 58.1%) were not utilized and many of them were found to be blocked metabolites.
Figure 2. Basal fluxsum vs degree of participation. Most of the 17 metabolic cofactors with high fluxsum were highly connected and participated in proportionally as many basal active reactions, except for periplasmic hydrogen ions (red marker). The Rsquare value for the linear relationship was 0.912 without considering the outlier (red marker). The 17 metabolites are ADP [c], ATP [c], CO_{2 }[c], H_{2}O [c], H^{+ }[c], NAD [c], NADH [c], PI [c], Q_{8 }[c], Q_{8}H_{2 }[c], CO_{2 }[p], H_{2}O [p], H^{+ }[p], O_{2 }[p], CO_{2 }[e], H_{2}O [e] and O_{2 }[e]. Only ADP [c], ATP [c], H_{2}O [c], H^{+ }[c], H^{+ }[p] and PI [c] have ultrahigh fluxsum.
Fluxsum maxima
Interestingly, the evaluation of fluxsum maxima, obtained from solving (P2), allowed us to identify different types of metabolites. Firstly, we found blocked metabolites with maximum fluxsum equal to zero. The consumption and production of these metabolites were blocked due to reaction pathway deadends (Figure 3). The blocked metabolite is analogous to the blocked reaction reported by [23]. Thus, similarly we can define unconditionally blocked metabolites as metabolites with zero maximum fluxsum even when all of the exchange fluxes were completely unconstrained. Removing all the reactions associated with unconditionally blocked metabolites can reduce the size of the stoichiometric matrix without affecting the simulation results. For the iAF1260 model, it was observed that 442 and 189 intermediate metabolites were conditionally and unconditionally blocked, respectively, under the aerobic glucose minimal medium condition.
Figure 3. Deadends and blocked metabolites. In a simple system involving metabolites A, B, C, D, E and F, metabolites D and E are pathway deadends. Reactions B → C, B → E and C → D are blocked reactions since metabolites D and E are neither consumed nor secreted. Consequently, metabolites C, D and E are blocked metabolites.
Secondly, we identified 75 cyclic metabolites involved in internal cycles, also known as Type III pathways [24], in the iAF1260 model. Cyclic metabolites have maximum fluxsums equal to infinity regardless of any substrate uptake constraint imposed on the system since any rate of production of such metabolites can be balanced by the same rate of consumption within the cycle. Therefore, the determination of fluxsum maxima provides an alternative method for identifying Type III pathways.
Lastly, we identified 55 fully utilized metabolites with nonzero maximum fluxsum which are equal to their basal fluxsum values. As the cell strives for maximal growth, these metabolites are turned over at their full capacity. On the other hand, 797 partially utilized metabolites are not turned over at their full capacity during maximum cell growth, thus their fluxsums can be further intensified. This phenomenon is further examined in a later section. Note that some partially utilized metabolites may be basal inactive.
Fluxsum attenuation analysis
In the iAF1260 model, 394 out of 1369 intermediate metabolites had a nonzero basal fluxsum and were amenable for fluxsum attenuation analysis. Thus, we solved (P3) with constraint (C1) for these 394 basal active metabolites, thereby giving rise to the fluxsum attenuation profile (Figure 4). From the profile, we identified 342 essential and 52 nonessential metabolites as those with zero and nonzero biomass production, respectively, at full fluxsum attenuation. Of the essential metabolites, some were involved in amino acid biosynthesis: tetrahydrodipicolinate, L,L2,6diaminopimelate and meso2,6diaminopimelate, and these metabolites were in fact associated with the essential genes reported by [25]. Thus, essential metabolites can be associated with lethal reactions and the removal of any of such metabolites or reactions leads to no cell growth. Hence, they signify critical points of fragility in the metabolic network. Interestingly, 86.8% of the basal active metabolites were essential metabolites while only 68.5% of the basal active reactions were lethal. The observed higher level of reaction redundancy would be attributable to the presence of redundant pathways that connect essential metabolites. This also elucidated that a metabolite associated with a lethal reaction would inevitably be essential while a reaction involving essential metabolite(s) might not necessarily be lethal.
Figure 4. Fluxsum attenuation profile. The horizontal axis corresponds to the value of k_{att}. The vertical axis corresponds to the biomass production normalized with respect to the basal biomass production. Profiles of essential metabolites intersect the origin and each could be classified as either type "AE", "BE" or "CE", with the suffix "E" indicating that the metabolite is essential.
The fluxsum attenuation profile (Figure 4) reproduced the general profiles of type "A", "B" and "C" essential metabolites as reported by [16]. In this study, we labeled the metabolites as type "AE", "BE" and "CE" with the suffix "E" indicating that the metabolites were essential. It is not surprising to observe type "AE" profile (304 out of 342 essential metabolites) since all constraints are linear and biomass production is expected to vary linearly with the synthesis of some metabolites. Interestingly, the type "CE" profile (6 out of 342 essential metabolites) showed a more rapid drop than type "AE" when the fluxsum was attenuated and these metabolites were found to be involved in providing the ATP requirement for nongrowth associated maintenance (NGAM). The fluxsum threshold, below which biomass production is impossible, corresponds to the ATP requirement for NGAM. The amount of fluxsum in addition to this threshold value is then associated with biomass production. Thus, the threshold fluxsums of type "CE" metabolites allow us to calculate the distribution of the resources between growth and NGAM requirements. The peculiar shape of type "BE" profile (32 out of 342 essential metabolites) was attributed to the existence of alternate optimal solutions [26] where a small reduction of fluxsum can be compensated by other "equivalent" fluxes. When the fluxsums of these metabolites were further attenuated, there would be no "equivalent" compensation for synthesizing the essential biomass components. Thus the biomass production rate would drop below the optimal value and hit zero eventually.
It was also observed that some metabolites exhibited a profile that seemed to be a hybrid between type "AE" and "BE". This can be due to the traversing of the optimal solution across linear edges of the solution space with different gradients as the attenuation of the fluxsum reduced the solution space. These gradients of the edges in the solution space can be interpreted as the sensitivity of biomass production to the alteration of fluxsum. A simple reaction network is used to illustrate how the hybrid profile is generated (Figure 5).
Figure 5. A sample network containing a hybrid metabolite. The cellular objective of the sample network (A) was to maximize Z and the system could be formulated as a linear programming problem (B). We attenuate the fluxsum of metabolite M1, which is also equal to x_{1}, and examine the effects on the objective Z. When x_{1 }was attenuated by decreasing the value of C, the maximum value of Z decreased as the objective function (red line) traversed the edges of the solution space (shaded region) in the direction shown by the blue arrow. As the objective function passes x_{1 }= 1, the "rate" of decrease of Z changes due to the difference in gradients of the edges.
Fluxsum intensification analysis
In fluxsum intensification analysis, we examined how the increase of metabolite fluxsum affects the cell growth. 442 blocked, 75 cyclic and 55 fully utilized metabolites were omitted for this analysis due to infeasibility. Thus the fluxsum intensification analysis was only carried out for the remaining 797 partially utilized metabolites.
By solving (P3) with constraint (C2), we generated the fluxsum intensification profile (Figure 6). Then we classified the metabolites in a similar fashion as in fluxsum attenuation analysis. We defined competitive metabolites as the fluxsum intensification analogues for essential metabolites in the fluxsum attenuation case. Then, we classify competitive metabolites as type "AC", "BC" and "CC" based on the shape of the intensification profile (Figure 6), with the suffix "C" meaning competitive. Competitive metabolites compete for the same resources required for the biomass production. Thus, their complete fluxsum intensification resulted in zero cell growth. On the other hand, uncompetitive metabolites are probably cofactors in biomass production or some intermediates involved in alternate pathways for the production of biomass components, thus allowing the cell to grow even at 100% fluxsum intensification (Figure 7). In the iAF1260 model, we found 785 competitive metabolites and 12 uncompetitive metabolites.
Figure 6. Fluxsum intensification profile. The horizontal axis corresponds to the value of k_{int}. The vertical axis corresponds to the biomass production normalized with respect to the basal biomass production. Metabolites with profile that intersected the point (1, 0) were competitive metabolites which could be classified as either "AC", "BC" or "CC" with the suffix "C" indicating that it is competitive and the other metabolites are considered uncompetitive.
Figure 7. Fluxsum intensification of competitive and uncompetitive metabolites. In the base case, the maximum biomass production can be achieved due to optimal distribution of carbon fluxes to all the biomass components. If we intensify the fluxsum of any of the competitive metabolites (red nodes), the metabolite would compete for the limited resources and perturb the optimal distribution of carbon fluxes, resulting in reduced biomass production. On the other hand, intensifying the fluxsums of uncompetitive metabolites (blue nodes) does not perturb the optimal carbon flux distribution while the fluxsum of fully utilized metabolites (orange nodes) cannot be intensified. It is obvious that all metabolites contributing to biomass production shown in the figure are both essential and competitive.
Discussion
Fluxsum attenuation and intensification
When the E. coli system was perturbed by attenuating and intensifying the metabolite fluxsums, we could observe various types of metabolites and classified them according to the profile shape (see Figure 8; refer to Additional file 1 for the full list of metabolites in each category). In order to understand the rationale of this classification, we further examined the biological relevance of such fluxsum attenuation and intensification. As the cell strives to maximize its growth, it fully utilizes its resources and distributes them optimally to synthesize the essential cellular components. This optimum distribution was determined by FBA of the unperturbed case. Based on the result, fluxsum attenuation of essential metabolites forces the cell to utilize less of its resources, leading to slower production of cellular components and subsequent slower growth. On the other hand, intensifying the fluxsum of competitive metabolites causes the suboptimal distribution of resources which also results in the slower cell growth. Thus intensifying the fluxsum of a competitive metabolite may attenuate the fluxsum of other essential metabolites.
Additional file 1. List of different types of metabolites identified in this study. Metabolites are abbreviated in a similar fashion as in Feist et al. (2007).
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Figure 8. Summary of metabolite classification. The numbers of metabolites in each category is shown in brackets. The abbreviations "E" and "NE" denote essential and nonessential metabolites respectively. "AC","BC", "CC" and "AE", "BE", "CE" refer to the types of metabolites identified in fluxsum intensification and attenuation analyses respectively.
From a network topological perspective, essential metabolites are found along the pathways synthesizing essential cellular components while competitive metabolites are from the pathways parallel to these essential ones, sharing at least one common metabolite precursor so that they can compete for the same resources. Competitive metabolites can also be essential if there are parallel essential pathways sharing common precursors such as 12 metabolites reported in [27]. The combination of fluxsum attenuation and intensification analyses allows us to identify 253 of such essential and competitive metabolites. Interestingly, these metabolites generally exhibited type "AC" profile during fluxsum intensification (Figure 9), indicating that the intensification of any essential metabolite in parallel pathways is very detrimental to the cell growth.
Figure 9. Composite profile of essential and competitive metabolites. This profile is considered a "composite" profile because different regions of xaxis represents different variables: negative values on the xaxis correspond to the value of (k_{att } 1) while the positive values correspond to the value of k_{int}. When the xaxis is equal to zero, the fluxsum is at basal value where there is no attenuation or intensification.
Application of metabolite classification
The classification of metabolites based on fluxsum analysis, summarized in Figure 8, allows us to consider various practical applications. For example, in antipathogen study, researchers would be interested in developing strategies to identify targets which inhibit the growth of pathogens. In this sense, types "AE" and "CE" metabolites, identified through fluxsum analysis, serve as promising targets since the attenuation of their fluxsum may lead to the significant reduction in the cell growth. Similarly, types "AC" and "CC" metabolites can also be potential regulators affecting pathogenic growth through their fluxsum intensification. We also observed that fully utilized metabolites, except for periplasmic oxygen and cytosolic isopentenyl diphosphate, are fully coupled with the cell growth, thus indicating that these metabolites are perfectly correlated with the cell growth from the metabolite point of view. Note that the concept of flux coupling was discussed in [23]. Consequently, these metabolites can be considered as potential indicators for the cell viability as well as good metabolic engineering targets for controlling cell growth. As another application, the identification of blocked metabolites can be useful for improving the process of metabolic network reconstruction. During automated reconstruction, it is common to have gaps in the draft metabolic network which would result in the failure to predict experimentally observed cellular phenotypes and thus it is required to consider a systematic way to fill these gaps [28]. The first step in the gapfilling process is to identify the location of these gaps in the metabolic network. Through fluxsum analysis, we can identify metabolites which are in vivo essential and in silico blocked. Then appropriate metabolic reactions can be introduced into the incomplete metabolic network model, thus bridging the gap between these metabolites and the other in silico active metabolites.
Biotechnological application of fluxsum analysis
In this study, we demonstrated the effects of changing metabolite fluxsums on the cell growth in E. coli. In a similar vein, we can also analyze the effects of metabolite fluxsums on the production of desired biomolecules for the biotechnological application. Here, we carried out fluxsum attenuation and intensification analyses, thereby identifying potential metabolite targets to be manipulated so as to increase anaerobic succinate production in E. coli (see Additional file 2). Surprisingly, we found that pyruvate is the only candidate for fluxsum attenuation leading to the enhanced production of succinate. This result was previously validated in an experiment whereby knocking out the genes of pyruvate producing and assimilating enzymes increased succinate production in E. coli [29]. In addition, we also identified fluxsum intensification targets, such as glyoxylate, 2phosphoglycerate and 3phosphoglycerate, which were also reported as effective targets for increasing succinate production (see Additional file 2).
Additional file 2. Demonstration of fluxsum analysis for increasing succinate production in Escherichia coli.
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Conclusions
This paper presents a novel method for analyzing the metabolic network using a metabolitecentric approach within the context of constraintbased flux analysis. We utilized fluxsum constraints to understand the role of metabolites and apply this knowledge to generate testable hypotheses about the relationship between target metabolites and physiological changes, indicating the potential application of the metabolitecentric approach to biomedical research. Fluxsum analysis was also shown to be useful in the biotechnological application for improving the production of desired metabolite such as succinate in E. coli. In summary, the fluxsum analysis methodology can be considered as a useful technique providing better understanding of the cellular metabolism and alternative perspectives on how to engineer the system.
Authors' contributions
BKSC and DL developed the modeling approach. BKSC did the computational simulations and drafted the manuscript. DL revised the manuscript. All authors read and approved the final manuscript.
Acknowledgements
The work was supported by the Academic Research Fund (R279000258112) from the National University of Singapore. We thank the reviewers for the constructive comments which helped to improve the quality of the manuscript.
References

Llaneras F, Pico J: Stoichiometric modelling of cell metabolism.
J Biosci Bioeng 2008, 105:111. PubMed Abstract  Publisher Full Text

Strogatz SH: Nonlinear dynamics and Chaos: with applications to physics, biology, chemistry, and engineering. Reading, Mass.: AddisonWesley Pub; 1994.

Segre D, Vitkup D, Church GM: Analysis of optimality in natural and perturbed metabolic networks.
Proc Natl Acad Sci USA 2002, 99:1511215117. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Heinrich R, Schuster S: The regulation of cellular systems. New York: Chapman & Hall; 1996.

Fell D: Understanding the control of metabolism. London: Portland Press; 1997.

Varma A, Palsson BO: Stoichiometric flux balance models quantitatively predict growth and metabolic byproduct secretion in wildtype Escherichia coli W3110.
Appl Environ Microbiol 1994, 60:37243731. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Becker SA, Palsson BO: Contextspecific metabolic networks are consistent with experiments.
PLoS Comput Biol 2008, 4:e1000082. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Raman K, Chandra N: Flux balance analysis of biological systems: applications and challenges.
Brief Bioinform 2009, 10:435449. PubMed Abstract  Publisher Full Text

Price ND, Reed JL, Palsson BO: Genomescale models of microbial cells: evaluating the consequences of constraints.
Nat Rev Microbiol 2004, 2:886897. PubMed Abstract  Publisher Full Text

Oberhardt MA, Chavali AK, Papin JA: Flux balance analysis: interrogating genomescale metabolic networks.
Methods Mol Biol 2009, 500:6180. PubMed Abstract  Publisher Full Text

Burgard AP, Pharkya P, Maranas CD: Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization.
Biotechnol Bioeng 2003, 84:647657. PubMed Abstract  Publisher Full Text

Motter AE, Gulbahce N, Almaas E, Barabasi AL: Predicting synthetic rescues in metabolic networks.
Mol Syst Biol 2008, 4:168. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Thiele I, Vo TD, Price ND, Palsson BO: Expanded metabolic reconstruction of Helicobacter pylori (iIT341 GSM/GPR): an in silico genomescale characterization of single and doubledeletion mutants.
J Bacteriol 2005, 187:58185830. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Pharkya P, Maranas CD: An optimization framework for identifying reaction activation/inhibition or elimination candidates for overproduction in microbial systems.
Metab Eng 2006, 8:113. PubMed Abstract  Publisher Full Text

Imielinski M, Belta C, Halasz A, Rubin H: Investigating metabolite essentiality through genomescale analysis of Escherichia coli production capabilities.
Bioinformatics 2005, 21:20082016. PubMed Abstract  Publisher Full Text

Kim PJ, Lee DY, Kim TY, Lee KH, Jeong H, Lee SY, Park S: Metabolite essentiality elucidates robustness of Escherichia coli metabolism.
Proc Natl Acad Sci USA 2007, 104:1363813642. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Kim TY, Kim HU, Lee SY: Metabolitecentric approaches for the discovery of antibacterials using genomescale metabolic networks.
Metab Eng 2009, in press. PubMed Abstract  Publisher Full Text

Schmidt S, Sunyaev S, Bork P, Dandekar T: Metabolites: a helping hand for pathway evolution?
Trends Biochem Sci 2003, 28:336341. PubMed Abstract  Publisher Full Text

Feist AM, Henry CS, Reed JL, Krummenacker M, Joyce AR, Karp PD, Broadbelt LJ, Hatzimanikatis V, Palsson BO: A genomescale metabolic reconstruction for Escherichia coli K12 MG1655 that accounts for 1260 ORFs and thermodynamic information.
Mol Syst Biol 2007, 3:121. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Drud AS: CONOPT. [http://www.gams.com/dd/docs/solvers/allsolvers.pdf] webcite

Varma A, Boesch BW, Palsson BO: Stoichiometric interpretation of Escherichia coli glucose catabolism under various oxygenation rates.
Appl Environ Microbiol 1993, 59:24652473. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Ma HW, Zeng AP: The connectivity structure, giant strong component and centrality of metabolic networks.
Bioinformatics 2003, 19:14231430. PubMed Abstract  Publisher Full Text

Burgard AP, Nikolaev EV, Schilling CH, Maranas CD: Flux coupling analysis of genomescale metabolic network reconstructions.
Genome Res 2004, 14:301312. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Schilling CH, Letscher D, Palsson BO: Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathwayoriented perspective.
J Theor Biol 2000, 203:229248. PubMed Abstract  Publisher Full Text

Gerdes SY, Scholle MD, Campbell JW, Balazsi G, Ravasz E, Daugherty MD, Somera AL, Kyrpides NC, Anderson I, Gelfand MS, et al.: Experimental determination and system level analysis of essential genes in Escherichia coli MG1655.
J Bacteriol 2003, 185:56735684. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Mahadevan R, Schilling CH: The effects of alternate optimal solutions in constraintbased genomescale metabolic models.
Metab Eng 2003, 5:264276. PubMed Abstract  Publisher Full Text

Neidhardt FC, Ingraham JL, Schaechter M: Physiology of the bacterial cell: a molecular approach. Sunderland, Mass.: Sinauer Associates; 1990.

Satish Kumar V, Dasika MS, Maranas CD: Optimization based automated curation of metabolic reconstructions.
BMC Bioinformatics 2007, 8:212. PubMed Abstract  BioMed Central Full Text  PubMed Central Full Text

Lee SJ, Lee DY, Kim TY, Kim BH, Lee J, Lee SY: Metabolic engineering of Escherichia coli for enhanced production of succinic acid, based on genome comparison and in silico gene knockout simulation.
Appl Environ Microbiol 2005, 71:78807887. PubMed Abstract  Publisher Full Text  PubMed Central Full Text