Tuberculosis and Mefloquine

Mycobacterial infection and more specifically tuberculosis, represents one of the major epidemiological challenges of the world. Much improvement in drug development can be obtained with a better understanding of the physiology and metabolism of the causing agents of the disease [8]. Mycobacterium tuberculosis is a highly adaptable bacterium that causes tuberculosis. Although several anti-tuberculosis compounds, both first- and second-line, are available to kill the bacterium, its ability to rapidly mutate requires new compounds to be actively researched [9]. It has been shown that mefloquine, an anti-malarial compound, is bactericidal against Mycobacterium avium and Mycobacterium tuberculosis, and no resistant mutants could be obtained from in vitro screening [6]. It is therefore possible that a new anti-tuberculosis compound may be derived from mefloquine as more research on its properties and mechanism of action, such as the present work, come to light.

Proteomics Data

Bacterial cultures were essentially performed as described in [10, 11]. Bacteria: Mycobacterium tuberculosis H37Rv was used in the studies (American Type Culture Collection, Manassas, Virginia 20110, USA). Bacteria were cultured in Middlebrook 7H10 agar supplemented with albumin, dextrose and catalase. Proteomic Analysis: M. tuberculosis (100 ml in 500 ml flask) with a cell density of 1 × 10⁸ cells/ml was grown for 7 days in Middlebrook 7H9 broth supplemented with ADC. DMSO (carrier/solvent) or 8 mcg/ml of mefloquine (Sigma Co, St Louis, MO) dissolved in DMSO. Cultures were then harvested by centrifugation at 3,000 r.p.m. for 10 minutes at time intervals of 6h, 2 and 4 days. Cell pellets were washed 3 times in saline/tween (0.8% w/v NaCl/ 0.05 v/v Tween 80) solution. The pellets were resuspended in bacterial cell lysis buffer (Sigma) containing 80 mcl of protease inhibitor cocktail. Bacterial cells were lysed by bead beating 3x (speed of 8 per 2 min) using a mini BeadBeater and kept on ice for an additional number of minutes between sessions.

Samples were then centrifuged at 15,000 rpm at 4°C for 20 min, and the soluble fraction was transferred to a new tube and stored at −20°C. Soluble proteins samples were run on a 12% NuPage Bis Tris gel and processed through in-gel trypsin digestion (Promega MAX surfactant trypsin enhancer) for mass spectrometry. Mass spectrometry was performed on a termo Scientific LTQ-FT-MS Ultra System (Kalamazoo, MI) and the analysis was made using Scaffold 4 software (Proteome Software, Corvallis, OR). In Scaffold, the minimum characteristics for protein identification confidence were set as 99% for protein threshold, minimum number of peptides equal to 2 and peptide threshold of 95%. Quantitative value (normalized total spectra) were used for subsequent analysis. Scaffold viewer is freely available for download from the Proteome Software website [12]. Proteomic analysis was repeated two times and mean values of each experimental condition and time point were used for subsequent FBA calculations. Data is available as supporting information S1 Dataset. Table 1 shows these measurements for a sample of the most highly expressed proteins at each time point. Proteins are identified by their respective locus tag for the H37Rv strain [13]. In this paper, the locus tag for the H37Rv strain for each protein is followed by the respective UniProt entry acession number in parentheses the first time the protein is mentioned. In the following section we briefly review the FBA technique and explain in detail the proposed method for defining a proteomics-based objective function.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Fold change for top over expressed proteins per time point.

https://doi.org/10.1371/journal.pone.0134014.t001

Flux Balance Analysis

The core procedure of the flux balance technique has been thoroughly described elsewhere [14, 15]. It is a linear optimization method for studying metabolism based solely on stoichiometric knowledge of the organism’s network of biochemical reactions without relying on knowledge of enzyme kinetics. By constructing an in silico model of the metabolic network and defining a suitable metabolic objective function, FBA then identifies an optimal metabolic phenotype as a vector of fluxes for each reaction present in the model. A large genome-scale in silico network of the Mycobacterium tuberculosis has already been constructed and is presented in [16]. The in silico reconstruction of this GSMN (Genome-Scale Metabolic Network) comprises 856 metabolic reactions involving metabolites with 726 specific enzymes catalyzing associated reactions. The model is available in the SBML (Systems Biology Markup Language) and CSV formats in S1 File. The SBML format can be used in several standalone packages with parsers for the format (such as JyMet explained below), while the CSV format is usually more flexible for inclusion in text processing pipelines and simple scripts written in languages yet without specific SBML parsers.

Several methods have already been presented that incorporate experimental data onto FBA methods to achieve metabolic predictions that better characterize the different environmental and experimental conditions [4, 17]. Data is usually incorporated in the form of hard or soft constraints, and when both transcriptomics and proteomics data are used, it is to solve for inconsistencies between measurements of transcriptional and translational activities [18]. To the best of our knowledge, experimental data has not been used in the specification of the objective function. In this work we propose the use of proteomics to determine the FBA objective function. In this study we are attempting to estimate the complete metabolic state of the bacterial cell using an in silico model. Although it is clear that quantitative enzyme information by itself (without using e.g. metabolomics, signalling proteins, pathway knowledge, RNA expression, etc.), when used in a in silico model to improve results of an optimization procedure cannot produce a complete picture of the metabolism under drug exposure, it is our conjecture that it can produce a better characterization of the metabolism in situations where the assumption of an objective function for optimal growth (maximization of biomass) can not be made.

Simulation scripts for all the FBA calculations used in this paper were written in the R programming language and are available in the supplementary data file S1 File. For solving the flux balance analysis optimization problems we used a freely available wrapper on the GLPK (GNU Linear Programming Kit) called SurreyFBA. The program is freeware and available for download from (http://sysbio3.fhms.surrey.ac.uk/). Its main features have been presented in [19]. The program can be used as a CLI (command-line interface) program, which is more suitable for inclusion in the R scripts used in our simulations, but also as a GUI (graphical user interface) using the JyMet frontend, that is included with SurreyFBA. The SurreyFBA program accepts in silico metabolic models in both SBML format and simpler CSV text files, and both these models are also included as supplementary information S1 File. Alternatively, several other packages are also available for performing similar calculations [20].

Defining the Objective Function from Proteomics Data

In this section we describe our proposed objective function. We explain how proteomics data can be used to determine an objective function for FBA in cases where the organism is under drug-induced stress, and thus optimal growth should not be assumed as the metabolic goal of the cell. We propose to define the objective to be a linear combination of fluxes as in [2, 21]. However, the weights associated to the different fluxes are determined in a different manner. The objective function is the linear combination (1) where v = [v₁, v₂, …, v_N] is the flux vector, and c is the vector of coefficients of the linear combination. The dimension N of both vectors is equal to the number of reactions (i.e. metabolic fluxes) in the model. In the case of biomass maximization, vector c is an all-zero vector except for a one (1.0) in the position corresponding to the biomass reaction: (2) where v_bio is the corresponding flux for biomass in the model. In our method we propose to use the same linear combination of fluxes for the objective function, but instead of maximizing the biomass flux, we calculate the coefficients c_k from proteomics data.

We first define a vector p containing the quantitative values of protein levels obtained with the proteomics experiment (cf. Materials and Methods) for one experimental condition and time point. Vector p is of length K and given by: (3) where each element p_k corresponds to a value representing the level of protein k in the sample. While proteomics experiments are very precise and reliable (as opposed to microarray experiments, where the signal-to-noise ratio is much lower), the number K of identified proteins is only a subset of the whole proteome of the cell, a difficulty stemming from two facts; (1) the method performs identification by comparison of peptide fragments against a database, so that only previously identified proteins are accounted for and (2) not all proteins may be susceptible to the cleavage procedure.

Moreover, since some proteins may not appear in a specific sample (e.g. protein A may be present in sample 6h control but not in sample day 1 mefloquine), we set the levels of all proteins absent from a sample to zero. It is also important to note that while the proteome experiment quantifies both enzymes and signaling proteins, vector p contains only the subset of proteins with enzymatic activity and that are present in the in silico model. Although this leaves a number of important regulatory proteins not accounted for, we propose to include regulatory information in a subsequent analysis.

As a second step, vector p is normalized by its maximum value to yield a vector of relative protein levels : (4) where is also of dimension K. This normalized vector will be used in the expressions from the GSMN-TB model that combine enzyme actions, as we explain shortly. It is important to note that each value is associated with one enzyme.

Following the normalization procedure we identify which reactions in the metabolic model are catalyzed by the enzymes represented in . The values of the elements of are then used to determine the values of the coefficients c_k for our proposed objective. In the simplest case where each enzyme catalyzes one reaction, we set the corresponding coefficient c_k of each reaction to the respective value of the catalyzing enzyme. For all the other fluxes, i.e. those not present in , the respective coefficients are set to zero since these represent proteins not observed in the proteomics experiment.

More complex situations arise when one reaction is catalyzed not by a single enzyme, but by the combined action of a set of enzymes. In such situations, the determination of the coefficients c_k of the objective function depends on the relationship between enzymes and metabolic reactions. Therefore, it is important to understand how enzymes and reactions are related in the metabolic model, and how this information is used in the definition of the proposed objective function. In the GSMN-TB model, metabolic reactions that are catalyzed by a set of enzymes are associated with a boolean expression that combines the action of all enzymes needed for catalysis of the reaction. These expressions were manually curated by the authors of the GSMN-TB model and more details and references can be found in [16]. As an example, let us check model reaction R022 (myo-inositol synthesis). For this reaction the catalytic proteins are combined in the following boolean expression: (5) where the operators ∨ and ∧ represent the boolean operators OR and AND respectively. The proteins in this expression are the two transferases Rv2612c (IGY178), Rv1822 (I6X2EA) and the synthase Rv0046c (I6X8D3), all involved in inositol synthesis [22].

In these cases, to obtain the coefficients for the fluxes that will be used in the objective function, it is first necessary to substitute the proteomics data in into the corresponding boolean expressions (similar to Eq (5)). The mathematical operation for the boolean OR results in the maximum of the terms, while the AND operation results in the minimum of the two terms, in a similar fashion as done in [2]. The resulting values from the boolean expressions are used as the final values for the elements in c of coefficients for the objective function. We note that vector c will have a number of non-zero elements that is usually different from K, unless we have the very specific situation mentioned before where each reaction is catalyzed by a distinct enzyme. Moreover, we will usually have K (the number of proteins available in the proteomics experiment) larger than the number of non-zero elements in c (reactions catalyzed by these enzymes), although it is possible that in some situations the number of reactions in the objective function is greater than the number of enzymes, for example when the same enzyme (or combination of enzymes) catalyzes several reactions in the model.

As is clear from the objective function Eq (1), each weight c_k multiplies the corresponding metabolic flux v_k. As an example, suppose we identify three proteins 1, 2 and 3 with levels p₁ = 1.0, p₂ = 2.0 and p₃ = 3.0 in a given sample. The corresponding normalized vector is obtained using Eq (4) and is equal to . For the sake of this example, we assume that these three proteins catalyze three reactions R023, R042 and R128 in the GSMN model. We assume further that protein 1 catalyzes reaction v₂₃, protein 2 catalyzes reaction v₄₂ and an AND combination of proteins 1 and 3 catalyze reaction v₁₂₈. The objective function to be maximized by FBA is then defined to be: (6) where the vector of weights is given by c = [1/3;2/3;1/3], since the AND expression is calculated using the minimum of the two values in .

We note that by using data from different time points it is possible to define different objective functions for different time points, something that it is not possible when either the more common objective biomass yield or any other time-independent objective function is used. In this work we assume that our proteomics data for the control group should not be significantly different even for different time points, thus we use an average value of these data to perform FBA for the control condition. Our proposed methodology focus on defining an objective function by using proteomics data. Therefore, our FBA constraints are unaltered and are the same as the ones used with the regular FBA procedure. This way, when we present results of comparisons between our method and the E-flux method, we are comparing two variants of the plain FBA procedure modified by the introduction of proteomics data: one method (E-flux) uses proteomics data to redefine flux constraints and a biomass objective function, while the method proposed here uses proteomics data to define the objective function and unconstrained internal fluxes (as in the regular FBA method).

In this study we have performed comparisons of the proposed methodology with the alternative method E-flux [2]. This method was originally devised to use transcriptomics data to adjust FBA constraints using a “pipe capacity” analogy. Since the E-flux method can also be used with proteomics data, we run FBA using our proposed methodology and the E-flux method with the same set of data and compare the results obtained. We first simulated both methods and the regular FBA procedure using only biomass maximization without any experimental data. Biomass was constrained to the same value as the regular FBA procedure for comparison. We analyzed the results comparing the number of reactions in the model that carried zero flux in the optimal vector and are catalyzed by essential enzymes needed for growth as presented by [7]. Here we restrict our analysis to the control experimental condition, where we assume that the objective of the organism is optimal growth, represented by maximization of biomass production. It is expected that in a situation where the organism is not under any biological stress we would end up with a small number of these essential reactions (i.e. metabolic reactions catalyzed by essential enzymes).

As a validation step, we performed comparison of prediction error between our proposed method and the E-flux method for a control condition and treatment conditions in different time points. We perform FBA for both methods using randomly chosen subsets of our proteomics data and the remaining subset of proteins to evaluate the prediction of the model in terms of enzyme abundances. This cross-validation step was performed as follows: For one specific time point and experimental condition the set of proteomics data was randomly split in two groups using a 80/20 rule, i.e. 80% of the proteins were used to defined the objective function in our proposed method and to define normalized constraints for the E-flux method, while 20% of the proteins were used as a validation set to compare fluxes and enzyme abundances. This procedure was repeated 16 times with different random splits. The enzymes in the validation set were evaluated in the boolean expressions and the resulting values were used for comparison with the corresponding fluxes obtained with FBA. Normalized squared prediction error was used to evaluate prediction accuracy of the two methods. In doing so, we normalized the error by the number of reactions in the validation set, as without normalization different splits would result in a different number of reactions depending on the boolean expressions evaluated. The validation procedure was repeated and results obtained in different realizations are in agreement. In order to obtain some insight into the metabolic behavior for alternative optima, we perform a final step of flux variability analysis, again comparing both methods. Our results are presented and discussed in the next section.

Proposed Methodology and E-flux

First we compare the results of FBA for the biomass objective function and the objective function defined using quantitative proteomics data from the control condition only. We must check whether using a proteomics objective function instead of the more common biomass goal, still produces sound flux results. One possible way is to observe the number of reactions carrying zero flux that are considered essential, and where by an essential reaction we mean a metabolic reaction catalyzed by enzymes considered essential for growth according to Sassetti et al. [7]. In the following we term these zero-flux reactions catalyzed by essential enzymes (ZFER) and use the number of these reactions as a first metric of quality of FBA results. We assume that reactions catalyzed by enzymes essential for growth should present flux value different from zero. In Table 2 we present the number of ZFERs after performing three FBA simulations in a control condition (where biomass yield, i.e. optimal growth, is assumed in the absence of any biological stress): biomass objective function, proteomics objective function, E-flux method with proteomics constraints. We note that the flux configuration using standard FBA without any proteomics data produces 100 ZFERs. Using our proposed objective reduces the number of ZFERs to 66, likely improving FBA results, since we have a significantly smaller number of fluxes which are catalyzed by essential enzymes that are equal to zero. Using proteomics data to determine flux constraints, as in [2], the number of ZFERs increases to 103. Therefore, we note that the proposed methodology of using proteomics data to define an objective function even in a control condition still produces good results, and with less reactions catalyzed by essential enzymes carrying zero flux. In Table 2 we also present the percentage of essential reactions in the model, since this is different from the number of essential enzymes, because of the combined action of enzymes defined by the boolean expressions explained in the previous section. Although the proportion is very significative, it is interesting to note that in general this issue is not often addressed in articles that study metabolism with FBA (e.g. [1]). The resulting smaller number of reactions with zero flux when utilizing the proteomics objective function may be indicative of extra information brought into the optimization problem by the proteomics data. We note that of all the reactions still remaining with zero flux with the new objective function, most were also observed with the biomass objective, showing that the proteomics objective does not induce different reactions to zero, but only lowers the number of these when compared to biomass maximization, therefore adding knowledge to the problem.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Number of reactions catalyzed by essential enzymes according to [7] carrying zero flux.

https://doi.org/10.1371/journal.pone.0134014.t002

It is important to discuss further the need for a biomass constraint. In the GSMN, the biomass reaction is a convenience equation defined as a weighted linear combination of macromolecule precursors such as DNA, RNA, protein, other small molecules, essential cell wall components, etc. The biomass reaction used in our simulations with the GSMN-TB in silico model is the following: where the numerical weights represent the stoichiometric coefficients for each metabolite. We note that mols of several components are needed to obtain one mol of biomass along with 47 ADP and orthophosphate molecules resulting from the hydrolysis of the ATP molecules. The calculations for determination of this biomass reaction are not the focus of the present work and may be found in detail in [16]. It is based on manual curation of literature and reflects the knowledge about the actual composition of cells of Mycobacterium tuberculosis. The names of metabolites in this stoichiometric equation follow the nomenclature of convenience used in the GSMN model and can be found in the additional data file 6 from [16]. Here, PE (L-1-phosphatidyl-ethanolamine), TAGbio (triacylglycerol), PIMs (phosphatidylinositol mannosides), LAM (lipoarabinomannan), MAPC (mycolic-acid-arabinogalactan-peptidoglycan complex), P-L-GLX (poly-L-glutamate-glutamine), CL (cardiolipin), LM (lipomannan), PI (phosphate).

Since the biomass function above is an external convenience transport reaction in the model, when we modify the objective function from biomass to the one defined in terms of the proteomics data (which affect mainly intracellular reactions which are precursors of the components in the biomass equation), the consumption and production of biomass components will no longer be maximized, and the resulting optimal flux vector will be different from the one obtained when we assume biomass maximization. Moreover, since the proteomics objective function may produce a metabolic state with biomass flux zero even under the control, it is important to constrain the biomass equation to a minimum value so that conclusions are not off-target. In the above comparison we constrained biomass yield to the same value obtained with regular FBA when maximizing a biomass objective.

It is important to note though, that our goal is not to use proteomics-defined objective functions as a replacement for biomass maximization, but rather for situations of drug stress. As a source of validation however, it is reasonable to expect that, by using control data to define the objective function, the metabolic functioning of the cell should be similar. That is why we performed comparisons for the control condition as well as for the treatment condition.

After having compared essential reactions, we compared our proposed methodology with the E-flux method in terms of prediction error. To this end we performed several runs of FBA with a subset of the proteomics data and validated the results with the remaining subset, as explained in the previous section. Results for mean squared error of prediction are presented in Table 3. These are the mean results of 16 runs of the simulation. In this table we observe that the mean squared error of prediction for the validation group of proteins is lower for the proposed method in all time points. We performed a t-test on the difference of the errors for the two methods and report in the last row the p-values for a significance level of 95% and 15 degrees of freedom. We observe that even for higher p-values, the error difference is consistently lower in the case of using the proposed methodology for all conditions. In Fig 1 we present a boxplot of the errors obtained in each of the 16 folds of the validation procedure for both methods. We observe that in some situations (specific splits of the proteomics set) it is possible to have a lower error for the E-flux method, but in the mean the proposed methodology is consistently better.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 3. Comparison of the MSEP for the proposed method and the E-flux method.

https://doi.org/10.1371/journal.pone.0134014.t003

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Mean squared error of prediction for the proposed method and the E-flux method for three experimental conditions.

The use of proteomics data to define objective functions in FBA yields lower predicion errors.

https://doi.org/10.1371/journal.pone.0134014.g001

In constraint-based optimization it may be possible that optimal solutions are not unique. Alternative optima represent situations where the metabolic system reaches the same optimal objective function value using a different set of reactions, which is possible due to redundancies inherent to the metabolic network. Therefore, we next use flux variability analysis (FVA) [23] with our proposed method and E-flux to analyze the impact of possible alternative optima. In this paper we choose to evaluate the presence of alternative optimal solutions using the technique of FVA that has been successfully used to obtain insights on alternative optima and is also readily available for simulation with SurreyFBA. Another possibility is the use of the MILP method to enumerate all the possible non-unique optimal solutions. This approach however, in the case of genome-scale metabolic networks, may be computationally intractable due to the exponentially growing number of extreme points that may exist [23, 24]. FVA basically determines the range of variability for each flux in the network due to the presence of alternative optima, so it allows us to study some important features of the behavior of the system due to its redundant network.

Alternative optima are responsible for the situation where different uses of the underlying network of metabolic reactions correspond to the same cellular function [24]. By defining the optimization problem as the maximization of a subset of internal reaction fluxes instead of biomass, it may be expected that the variability in fluxes would be reduced. Since the biomass function is itself a linear combination of several internal fluxes, it could be the case that more redundancy is present in its maximization in contrast to maximizing a set of internal fluxes themselves. This is what is observed with our FVA simulations. In Table 4 we show that by using proteomics to define the objective function indeed results in a lower number of reaction fluxes with high flux variability. For this table we consider reactions with high flux variability those for which the flux range (i.e. maximum flux value minus minimum flux value produced by FVA) is larger than 0.05. This result is interesting since it shows that by using an objective that maximizes specific fluxes according to observed proteomics, redundancy in the network plays a less prominent role than with biomass maximization. We see that with our proposed objective, the goal of the cell is more focused, since a significantly smaller number of reactions allow large magnitude variability in their fluxes in all experimental conditions studied.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 4. Number of reactions with large flux variability for the proposed proteomics objective function and the E-flux method.

https://doi.org/10.1371/journal.pone.0134014.t004

We also observed, for each experimental condition, the flux variability in reactions catalyzed by essential enzymes according to the essentiality criterion in [7]. It is interesting to observe that with the proteomics objective function most of the essential reactions present zero variability. We have verified a variability reduction in all FVA simulations when using the proposed objective function defined by proteomics data. This is a good indication that the incorporation of protein data in the objective function, instead of only using it to determine constraints, represents a promising approach to help discern biologically relevant metabolic flux configurations with the aid of experimental information. In general, we observe that the number of alternative optima is reduced using our proposed objective.

The FVA simulations reveal that, besides reducing the number of reactions that show large variability, using the proteomics objective function also reduces the magnitudes of these variabilities when compared to using the biomass function. Fig 2 shows the logarithm of the mean values of the range of variability in all experimental conditions for our proposed methodology and the E-flux method. From these results we see that the proposed objective function indeed helps in reducing the magnitude of variability, therefore producing an optimal flux vector that is less affected by the presence of possible alternative optima. In all experimental conditions the FVA ranges for the E-flux method are larger than with our proposed methodology.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Comparison of flux variability between the proposed method and the E-flux method for all experimental conditions (individual replicates).

The use of proteomics data to define objective functions in FBA yields lower mean flux variability due to alternative optimal solutions.

https://doi.org/10.1371/journal.pone.0134014.g002

The obtained results indicate that there are clear advantages to use objective functions defined by experimental proteomics data, mainly in situations of cellular stress (e.g. antibiotics exposure), where biomass maximization may not be the best assumed objective. We believe that more research in this direction is required to further evaluate this new and promising approach to FBA.

Metabolic Fluxes and Pathways

The metabolic model comprises 856 reactions for which an optimal flux is obtained with FBA. When we modify the objective function from biomass to one defined by proteomics data, out of 856 reactions, a small number (10%) of the reactions in the control condition present significant change in their optimal flux value (i.e. 76 reactions). It is important to note that by using an objective function defined in terms of proteomics data, as mentioned above, implicitly assumes that metabolic fluxes are mainly regulated by enzyme concentrations, disregarding the fact that their activity may also be regulated by metabolite concentrations or other signalling proteins. Nonetheless, it is a useful option whenever none of these extra data is used.

The intracellular fluxes that most greatly varied from one objective function to the other are part of metabolic pathways related to carbon source (glucose) degradation and energy production, as can be seen in the plot for the region with lower indices (in the GSMN-TB model most reactions belonging to pathways of energy transduction such as glycolysis, citrate cycle, energy metabolism have low indexes). Other two reactions with fluxes that varied significantly are R134, R363, due to the presence of high levels of protein katG—Rv1908c (P9WIE5), for peroxidase-catalase activity, in the control condition. All reaction names and formulae are available in [16] in the additional data file 4.

Many proteins present both enzymatic as well as signal transduction roles in the cell, but in FBA only the enzymes are taken into account. It is therefore possible, that some proteins having high levels in the proteome for roles other than enzymatic activity, will produce spurious results in FBA. One important factor that may cause difficulties when using proteomics data to define the objective function is that enzyme activity is not simply a function of enzyme levels, but is also regulated by metabolite concentrations and other regulation mechanisms. This is actually a fact that can help with the understanding of metabolic regulation. If a proteomics-defined objective function is not close to the one obtained when biomass is maximized, it is possible that the main differences are largely due to lack of information on metabolite concentrations and enzyme regulation. As an example, the high levels of katG observed in proteomics may not translate into high enzymatic activity due to the presence of inhibitor molecules or other regulator proteins that are not being accounted for in the simple FBA optimization.

The incorporation of transcription factors [25] and regulatory information onto FBA is not new [26] and it has been shown to improve the results [4]. It is therefore possible that by incorporating regulatory information we may eliminate some of the sources of noise corrupting the FBA predictions. A straightforward approach to add regulatory constraints onto FBA has been presented, for example, in [27]. The method uses knowledge of the transcriptional network of the organism with a set of simple boolean expressions that enables the analysis of metabolic fluxes further constrained by gene regulation.

Lastly, two other facts may also cause interference in the FBA results. First, the limited number of proteins that a proteomics experiment can identify compared to the complete proteome of a cell. Further, the in silico metabolic model itself (GSMN-TB) is not complete and many blanks are left in those parts of the metabolic network that are either not known, not implemented in the model, are presently not associated with specific enzymes or even have annotation inconsistencies. These factors, together with the lack of signalling information, may account for the major differences observed when proteomics is used to define an objective function.

After having compared the metabolic flux results in the control condition, we now turn to compare the changes in metabolic configuration using only objective functions defined in terms of proteomics data for both control and drug conditions. We observe the resulting fold-change differences in metabolic fluxes between the two conditions. We limit the comparison to fluxes presenting fold-change larger than 2 or smaller than 0.5. We discuss the significance of the obtained fluxes by comparison with biological knowledge on the behavior of the bacterium when exposed to mefloquine, as presented in [6].

The fold-change in flux is presented for each time point in Fig 3. A large number of reactions in the model are not active (i.e. have zero flux) in either condition, so these were set to a fold-change value of one.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Comparison of fold-change.

Logarithm of fold change of metabolic flux for mefloquine to control condition.

https://doi.org/10.1371/journal.pone.0134014.g003

According to Table II in [6], upon exposure to mefloquine genes Rv0904c (I6WZQ9), Rv3411c (I6X784) and Rv3515c (I6YCB1) show large fold-change values. None of these three genes are present in our proteomics data. However, the pathways in which these enzymes participate are correctly identified by FBA. For example, large metabolic fold-change is observed in reactions R156, R163 and R495, all pertaining to pathways for lipid biosynthesis, like the FAS1, where Rv0904c is the gene encoding the catalyzing enzyme. We note that these are predicted by FBA only on day 2 and day 4, but not on the 6 hours time point. Gene Rv3411c, encoding an enzyme participating in the pathway for nucleotide (purine) biosynthesis, although not available in proteomics, catalyzes a reaction in a pathway that is correctly predicted by FBA (in time point 6 hrs) to have larger fluxes upon mefloquine exposure. A similar conclusion can be drawn for the protein encoded by the gene Rv3515c. These results indicate that FBA can correctly predict reactions in pathways that have been shown to be more active upon mefloquine exposure.

FBA results also show a large increase in biotin synthesis (R425,R426), which is a precursor molecule in the FAS1 system [21] of lipid biosynthesis and mycolic acid production. This molecule is used in the beginning of the pathway, and it is just sensible that the fluxes of its production would be predicted to be high in earlier time points. Another pathway with several reactions showing increased fold-change are reactions for cell wall synthesis, namely peptidoglycan biosynthesis (R712-R714). It is interesting to note that these reactions are not present in the first time point of 6 hrs, but only in time points day 2 and day 4.

By using a proteomics-defined objective function for FBA allowed us to obtain a metabolic flux configuration on a per-time point basis, something that is not possible with maximization of biomass or any other function that is not time-dependent. We have observed this advantage with the biotin reactions discussed above. As another example, we observe that reaction R003, in the pathway for glycerol metabolism, presents flux changes over time. In the 6 hour sample this flux has fold-change 0.2, changing to 0.5 in day 2 and back to 0.2 in day 4. It is interesting to note that the genes coding for the enzymes that catalyze this reaction, Rv2249c (I6X3P8) and Rv3302c (I6Y352) are not in the proteomics data, so that the flux is driven indirectly by the expression of other enzymes in the model.

Another reaction with dynamic behavior is observed for reaction R069 in pyruvate metabolism. The enzyme catalyzing this reaction is encoded by Rv1127c (O06579), which is not in the proteomics data, however flux through it increases over 100 fold from time point 6hr to time point day 2.

In terms of metabolic pathways, pathways that consistently present large fold-change are degradation of branched-chain amino acids such as valine and isoleucine, of which several reactions are present in the top reactions in all three time points. In the case of studying metabolism to identify metabolic pathways used for survival one should observe the later time points, when bacteria are closer to death. In these time points, large fold-change are observed in pathways for propanoate metabolism (reactions R080), threonine biosynthesis (reactions R227, R231, R891), biotin biosynthesis (reactions R425, R427, R925), peptidoglycan (cell wall) biosynthesis (R712, R714).

We have included a list of metabolic reactions in the in silico model that presented the largest fold-change values from the control condition to the mefloquine condition in time points 6 hours, day 2 and day 4, respectively as S1 Table, S2 Table and S3 Table. Each file contains the reactions obtained at each time point. These files can be generated automatically using the available R code, also available as S1 File.