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How to integrate transcriptomics data with kinetic metabolic models?

How to integrate transcriptomics data with kinetic metabolic models?


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I have created a convenience kinetics model. Now, I want to integrate the transcriptomics data with my convenience kinetics model for altering/weighing the kinetic parameter values. I have read some publications related to this work but can't get a satisfactory idea of how to do it properly.

Details

I've got a pancreatic model for the study on type 2 diabetic patients. It has a few compartments and the reaction pathways; the species are metabolites. All the reactions are convenience kinetics based. Enzyme is a constant factor, so its production and regulation is not considered. From my model, I'll get the Vm values for all the reactions and then I'm supposed to get the Vm (Vmax of Michaelis-Menten kinetics) values for the type 2 diabetic patients by somehow integrating the transcriptomics data with it. I was asked to use the fold change values but I couldn't find any relevant publication on this topic (my PI has suggested me these but hasn't worked in this area before).

Any leads or references will be highly appreciated.


You can call convenience kinetics rate laws as approximate rate laws or you might have heard about "modular rate laws", they are more or less the same. We use this approximate rate law approach in cases where we don't have the experimental data for all the true rate law parameters.


I am assuming that in your model, the reactants and products (species) are metabolites and each reaction denotes conversion of one metabolite to another.

From transcriptomics, you will get the relative expression levels of different genes. When you have two samples from different conditions you can calculate the differential expression.

A model can be as complex as you can make it but we can start with simple assumptions. As you said, enzymes are assumed to be constant with respect to metabolites and are not dynamically changing. I also guess that you are not considering genes other than enzymes to be affecting the metabolic reactions (you might actually want to consider the solute transporters). Also, you are assuming Michaelis-Menten kinetics for all reactions.

In that case your Vmax (i.e. maximum rate of a reaction) would be kcat × E0 where kcat is the turnover number and E0 is the total amount of enzyme.

E0 can be approximated using the transcriptomics data. However, transcriptomics data is relative and not absolute. If you need absolute quantification, you must have at least one reference whose absolute mRNA copy number is known. Another issue is that the ratio of protein and mRNA expression would not be the same for all genes and it is basically the amount of active protein you need to know. So proteomics would be one step closer.

When you are comparing two conditions, you can use the differential expression (fold change values) to adjust the parameters between the two conditions. For e.g. if you know that phosphofructokinase is 2 fold downregulated in diabetes (compared to healthy case) then you can reduce the Vmax of the corresponding reaction by 2 fold in your diabetes model. However, it all would make sense only if the parameters of your "healthy" model are reasonably close to the biological reality.

Moreover, you still need to know kcat. It cannot be obtained from high throughput studies. You may have to either make some guesses or check out papers/databases. Also, your rate is not always Vmax. To estimate the dynamic rate you must know KM too (when the substrate is in excess you can ignore KM). BRENDA may have some information about these constants for different enzymes.

At a very crude level, you can remove the reactions whose corresponding enzymes have zero expression.


These are some articles on integration of transcriptomics data with FBA (not kinetic models):

Machado and Herrgård actually claim that integration of transcriptomics data does not improve their model predictions:

Also, it is observed that for many conditions, the predictions obtained by simple flux balance analysis using growth maximization and parsimony criteria are as good or better than those obtained using methods that incorporate transcriptomic data.


Integration of lipidomics and transcriptomics data towards a systems biology model of sphingolipid metabolism

Sphingolipids play important roles in cell structure and function as well as in the pathophysiology of many diseases. Many of the intermediates of sphingolipid biosynthesis are highly bioactive and sometimes have antagonistic activities, for example, ceramide promotes apoptosis whereas sphingosine-1-phosphate can inhibit apoptosis and induce cell growth therefore, quantification of the metabolites and modeling of the sphingolipid network is imperative for an understanding of sphingolipid biology.

Results

In this direction, the LIPID MAPS Consortium is developing methods to quantitate the sphingolipid metabolites in mammalian cells and is investigating their application to studies of the activation of the RAW264.7 macrophage cell by a chemically defined endotoxin, Kdo2-Lipid A. Herein, we describe a model for the C16-branch of sphingolipid metabolism (i.e., for ceramides with palmitate as the N-acyl-linked fatty acid, which is selected because it is a major subspecies for all categories of complex sphingolipids in RAW264.7 cells) integrating lipidomics and transcriptomics data and using a two-step matrix-based approach to estimate the rate constants from experimental data. The rate constants obtained from the first step are further refined using generalized constrained nonlinear optimization. The resulting model fits the experimental data for all species. The robustness of the model is validated through parametric sensitivity analysis.

Conclusions

A quantitative model of the sphigolipid pathway is developed by integrating metabolomics and transcriptomics data with legacy knowledge. The model could be used to design experimental studies of how genetic and pharmacological perturbations alter the flux through this important lipid biosynthetic pathway.


Introduction

Ribosomes are the workplaces of protein biosynthesis, and defects in the pathway of ribosome biogenesis have an effect on many cellular processes, like metabolism, which critically depend on enzymatic proteins. While metabolism is known to affect ribosome function via the target of rapamycin (TOR) signalling pathway, little is known about how defects in ribosome biogenesis feed back on metabolism 1 . The Arabidopsis thaliana REIL proteins are involved in the late cytosolic steps of 60S ribosome subunit maturation and are required for growth under low temperature 2 . The reil1-1 reil2-1 double mutant is deficient for both REIL paralogs and, unlike Arabidopsis Col-0 wild type, does not resume growth after cold shift, even to moderate 10 (^) C chilling conditions. This experimental system is ideally suited to investigate the cytosolic ribosome biogenesis defect at the metabolic level, since both wild type and mutant show growth arrest during the early hibernation phase (less than seven days after cold shift) followed by differential growth in the later stages. Therefore, mechanistic insights in the impact of defects of the mutant’s ribosome biogenesis on metabolism may become apparent early after cold shift, during hibernation phase.

One possibility to investigate the feedback of ribosome biogenesis defects on metabolism is the characterization of reaction fluxes. Metabolic fluxes depend, in part, on the metabolite pools 3 . They also depend on the enzymatic setup of a cell, which is in turn governed by gene regulatory and signalling networks that affect protein activity 4 . However, determination of metabolic fluxes is a tedious and labour-intensive task 5,6,7 . A targeted analysis that predicts relevant fluxes for hypothesis generation based on integration of available high-throughput data sets from systems biology studies may streamline the planning of such time-consuming experimental flux studies.

In this regard, constraint-based approaches have proved as a valuable tool for hypotheses generation regarding flux distributions and their differential behaviour. For instance, the simplest of these approaches, flux balance analysis (FBA), can predict steady-state fluxes in bacteria at exponential growth 8 . In general, metabolic fluxes of a system are predicted under the assumption that this system operates in steady-state and optimizes an objective (e.g. biomass yield). If feasible, the resulting mathematical approach often results in a non-unique flux distribution. To this end, constraints defined through integration of high-throughput data can reduce the solution space of feasible flux distributions 9,10,11 . Such approaches have been shown to result in a more accurate prediction which is closer to the actual physiological state 12 . Despite the availability of methods that integrate high-throughput data, their full potential has yet to be realized 13 .

Of particular interest are approaches which allow integration of relative metabolite levels, since these datasets are easier to obtain in contrast to absolute metabolite concentrations used in thermodynamic flux balance analysis 14 as well as approaches that use time-series data (e.g. TREM-Flux 15 , uFBA 16 , and dFBA 17 ). iReMet-flux 18 is the only constraint-based approach to date that can integrate relative metabolite levels to investigate differential flux behaviour between two scenarios. It relies on a mass-action-like description of reaction rates (i.e. flux). In contrast to uFBA, iReMet-Flux does not require data on absolute quantification of metabolite levels and therefore allows for a broader application due to the availability of relative metabolomics data. In contrast to TREM-Flux, it does not assume a linear scaling with the change of metabolite levels between two time points. In addition, iReMet-Flux differs from a recent approach in which the relative metabolomics data are integrated on a qualitative level (i.e. increases or decreases) 14 . Similar to the objective on which MOMA is based 19 , iReMet-flux minimizes the flux differences between two scenarios, but does not rely on pre-calculated flux distributions for a reference scenario. Additionally, iReMet-flux allows for the integration of relative enzyme levels either by direct usage of quantitative or qualitative proteomics data, or via gene expression ratio that can serve as a proxy 10,20,21 . However, if employed to time-series data, it does not account for the magnitude of possible flux changes between time steps. To address this problem, we extended iReMet-flux to account for temporal changes, while keeping the possibility of multi-level high-throughput data integration.

Here, we aimed to develop a novel constraint-based approach, termed TC-iReMet2, that facilitates the integration of relative metabolite and transcript levels while accounting for temporal change of physiological parameters. We used TC-iReMet2 to investigate differential flux behaviour of A. thaliana Col-0 wild type and reil1-1 reil2-1 double mutant plants before and after cold shift. Finally, we provided directly testable hypotheses about the impact of REIL-mediated deficiency in ribosome biogenesis on metabolism.


Results

Formulation of TC-iReMet2

We propose Time Course Integration of Relative Metabolite and Transcript levels (TC-iReMet2) that estimates fluxes based on the integration of time-course data on relative metabolite and transcript levels. The key feature of TC-iReMet2 is that it accounts for the possible magnitude of flux changes between time points and thus could provide a more accurate explanation of flux rerouting over time. We show that TC-iReMet2 can be applied to study flux redistributions in pathways in a large-scale metabolic network of A. thaliana. Unlike genome-scale metabolic networks 22 , we refer to large-scale models as those reconstructed following a bottom-up approach 23 .

Similar to other constraint-based approaches, TC-iReMet2 uses a stoichiometric matrix S of the considered metabolic model. The rows of the stoichiometric matrix correspond to metabolites, and columns stand for reactions. The integer entries denote the molarity of a product (positive entry) or a substrate (negative entry) in a reaction, ensuring mass and charge conservation. In the following, we assume that the investigated metabolic network contains P reactions and n metabolites, and that its functioning is compared between two experimental scenarios, denoted by A and B (e.g. mutant and wild type) over to time points t + 1 and t. Furthermore, we denote by p 1 the number of irreversible reactions and by p - p 1 the number of reversible reactions.

Under mass action kinetics, a flux through an irreversible reaction i, 1 ≤ p 1 ≤ p 1 , can be formally described by v i = k i E i ∏ j = 1 n ( x j ) | S ji | , where x j denotes the concentration of metabolite j, S ji denotes the stoichiometric coefficient with which a metabolite j enters a reaction i as a substrate, E i denotes the enzyme concentration and k i denotes the reaction specific rate constant. Note that this expression can be written equally for scenario A: v i A = k i A E i A ∏ j = 1 n ( x j A ) | S ji | and scenario B: v i B = k i B E i B ∏ j = 1 n ( x j B ) | S ji | , where the rate constant k i is the only unchanged parameter ( k i A = k i B ) - as it summarizes the key property of the same enzyme. Therefore, the relationship of a single flux between two scenarios can be written as:

To simplify the notation, we will refer to the ratio of metabolite levels of j as r j = x j A x j B and the ratio of enzyme levels catalyzing reaction i as q i = E i A E i B . This allows us to rewrite the ratio of flux rates of reaction i as v i A v i B = q i ∏ j = 1 n ( r j ) | S ji | or equivalently v i A = [ q i ∏ j = 1 n ( r j ) | S ji | ] v i B .

Determining the entirety of metabolite and enzyme concentrations is not possible with the existing technologies 24 , 25 . For metabolite ratios, only a small portion of the metabolome, and hence metabolite ratios, can be quantified. To account for the case that a metabolite ratio cannot be measured, general upper and lower boundaries for metabolite ratios are introduced. If the ratio of metabolite j is experimentally quantified, it is indicated by χ ( r j ) = 1 and otherwise by χ ( r j ) = 0 .

In the absence of enzyme ratios, we use the Gene Protein Reaction (GPR) rules of metabolic models to approximate enzyme ratios using transcriptomic data. The GPR roles are defined by a set of Boolean expressions that describe which genes encode an enzyme. For example, gene products encoding for isoenzymes or isoforms are linked by an OR operator. Conversely, protein subunits that must be present simultaneously to form an active enzyme are linked by an AND operator. In case of an enzyme encoded by one gene, the enzyme concentration is approximated by its expression value. For each reaction that is catalyzed by a complex requiring multiple genes, the enzyme concentration is set to the minimum expression value of gene products connected by the AND operator. For the OR operator, the sum of expression values for the respective genes is used. These rules were applied to each reaction in both scenarios, fractioned and assigned as the corresponding enzyme ratio. Therefore, an enzyme ratio is represented by a ratio of gene expression levels following the GPR rules. Equivalently to metabolite ratios, if a GPR rule for reaction i is defined, it is indicated by H ( q i ) = 1 and for reactions without a defined GPR rule, by H ( q i ) = 0 .

In this setup, we only consider constraints for irreversible reactions, since more than 80% of reactions that are assumed to follow mass�tion-like kinetics (this excludes artificial and transport reactions) are irreversible in the analyzed model of A. thaliana. This has been verified by performing flux variability analysis at a fixed flux through the biomass reaction, to specify that 80% of reactions operate in only one direction 18 . A ratio constraint for reaction i is included if not only the enzyme ratio, but also at least one of the substrate ratios corresponding to that reaction is available. For metabolites or enzymes whose ratios could not be determined we use the extremal values found at that specific time point. Let F(i) denote the set of substrates of reaction i. Additionally, let the set of irreversible reactions with at least one experimentally quantified metabolite ratio and approximated enzyme ratio be denoted by I = < i | ∑ j ∈ F ( i ) χ ( r j ) > 0 & H ( q i ) > 0 >. A measured metabolite ratio for j and transcript ratio of i are indicated by r ^ j min ≤ r ^ j ≤ r ^ j max and q ^ i min ≤ q ^ i ≤ q ^ i max , respectively. The bounds are defined as multiples of the standard deviation for the ratio. Cofactors were treated as unmeasured metabolites and for them the lower and upper bounds are m i n m : m ∈ < ℓ | χ ( r ℓ ) = 1 >r ^ m min and m a x m : m ∈ < ℓ | χ ( r ℓ ) = 1 >r ^ m max , respectively. Equivalently we can write m i n m : m ∈ < η | H ( q η ) = 1 >q ^ m min and m a x m : m ∈ < η | H ( q η ) = 1 >q ^ m max for unmeasured transcript ratios. Furthermore, to account for enzymes that are substrate saturated and in turn would lead to infeasibilities due to metabolite ratio constraints, slack variables ε i were introduced to relax the strict ratio constraints. To minimize these relaxations a weighting of the summed slack variables of ϵ = 0.01 was used. Hence, a ratio constraint was formulated as follows:

Similarly, a ratio constraint for the biomass reaction can be formulated. To this end, a time-point specific biomass fraction, denoted by ϰ t + 1 , can be calculated. First, the maximum biomass yield, denoted by opt, is calculated for both scenarios via FBA. A biomass fraction ϰ t + 1 between both scenarios is then determined by using proxies for biomass (for a detailed description see Methods - Parameterizing the objection and of TC-iReMet2 and estimating fractions of biomass yield). We fix the biomass reaction of scenario B to its respective value derived from FBA. In contrast, biomass flux in scenario A is fixed to a fraction ϰ t + 1 of its optimal yield. Lower and upper bounds are specified as deviations, denoted by δ , of the calculated fraction. Therefore, biomass fluxes for both scenarios can be constrained as follows:

Furthermore, we assume that: (i) the metabolic network to operate in quasi-steady state at every time point. Hence, S v A = S v B = 0 , where v A and v B denote the flux distributions of scenarios A and B respectively. (ii) the biological system aims to maintain an optimal state given by the enzymatic setup. This assumption is captured by making sure that the flux distributions between the two scenarios at a given time point t + 1 are as close as possible, i.e. | | ( v t + 1 B - v t + 1 A ) | | 2 2 . (iii) the physiological state at time t + 1 depends on the physiological state at time t. We model this assumption by accounting for the magnitude of possible physiological changes by assuring that the difference of flux distributions between time points is as small as possible, i.e. | | ( v t + 1 B - v t B ) | | 2 2 , | | ( v t + 1 A - v t A ) | | 2 2 , respectively. This magnitude obviously depends on the difference between time points, where the magnitude of possible flux changes increases with time. To this end, we introduce weighting factors to minimize the difference of flux distributions between scenarios at the current time point, weighted by α , as well as for differences between prior time points for scenario A, weighted by β , and scenario B, weighted by γ .

In summary, the TC-iReMet2 approach is cast as a quadratic program (QP) as follows:

Application of TC-iReMet2 to data from the reil1-1 reil2-1 A. thaliana mutant

We employed TC-iReMet2 to gain insights into the metabolic effects of the ribosome biogenesis defect that is caused by A. thaliana REIL deficiency. To this end, we compared predicted flux differences between Col-0 wild type and reil1-1 reil2-1 double mutant with deficiency in cytosolic 60S ribosome biogenesis. The REIL proteins are required for growth when plants are shifted to cold ( < 10   ∘ C ) conditions, but not at optimal temperature ( ≃ 20   ∘ C ) 2 . The reil1-1 reil2-1 double mutant and wild type differ only slightly in size when grown at 20  ∘ C . Young developing leaves of the mutants showed an acute tip and two basal serrations instead of the typical rounded leaves of the Col-0 wild type, and were similar to the pointed leaves phenotype of cytosolic ribosome mutants 26 – 28 . However, the pointed-leaf phenotype of the reil1-1 reil2-1 double mutant was no longer apparent after transfer to soil and at developmental stages < 1.10 29 that were analyzed in this study. When shifted to 10  ∘ C (cold), both the mutant and the wild type stopped growing. Following seven days in the cold, the wild type resumed growth, while the mutant remained strongly growth-inhibited (Fig.  1 , Supplementary Table  S1 ). The mutant survived at least four weeks after cold shift and maintained cellular integrity as was determined by electrolyte leakage assays of rosette leaves 30 . Growth parameters of wild type and reil1-1 reil2-1 were determined as proxies of relative biomass accumulation at day 0, day 1, days 7 and 21 after cold shift using morphometric data (see Methods – parameterizing the objective function). Along with the morphometric data, the relative changes of metabolite pools and transcripts were profiled 30 (see "Methods" section for details).

Morphometric analyses of reil1-1 reil2-1 and wild type after shift from optimized (20  ∘ C) to low temperatures (10  ∘ C). Reil1-1 reil2-1 double mutants and A. thaliana Col-0 wild type plants were shifted at developmental stage 1.10 29 . Week-0 plants were grown at 20  ∘ C and assayed before the temperature shift. Rosette diameter, (A) leaf area, (B), (mean +/− standard deviation n = 3� plants), for original data and definitions of morphometric parameters refer to Schmidt et al. 2013 2 . The R coefficients represent the Pearson correlation between mutant and wild type with respect to the Diameter (A) (P-value = 2 . 91 - 11 ) and Leaf area (B) (P-value = 1 . 53 - 5 ).

The experimental setup and the availability of transcriptomics data and data on relative metabolite levels allowed the application of TC-iReMet2 29 , 31 to quantify the nominal and relative differences in metabolic fluxes of the wild type and the mutant (Supplementary Fig.  S1 ). We refer to nominal changes as the sum of predicted flux differences, defined as the absolute value of difference between wild type and mutant flux, over all analyzed time points. The nominal changes may provide a skewed picture about the differences, particularly since the differences in fluxes between reactions in a given flux distribution differ in several orders of magnitude 20 . As a result, differences between fluxes that are anyhow small will be dominated by the differences between fluxes that take larger values. To remedy this issue, we also calculated the relative changes, defined as the sum of normalized flux differences over all analyzed time points, where the flux differences between wild type and mutant were normalized to their respective absolute maximum value over all time points. To apply TC-iReMet2 we used a bottom-up assembled model of A. thaliana, ArabidopsisCore 23 . This model consists of 549 reactions, of which 229 are transport reactions and artificial reactions representing growth (biomass) and non-growth-associated maintenance functions (NGAM 22 ).

Sum of predicted flux differences

The overall flux distance of wild type compared to mutant across all predicted reactions differed before cold shift, with the wild type having a higher overall flux (Fig.  2 A). This prediction was consistent with the slight growth advantage of the wild type at the optimized growth temperature (Fig. ​ (Fig.1). 1 ). The difference of fluxes between consecutive time points remained approximately constant during the common hibernation phase, up to day 7. When the wild type resumed growth in the cold, the overall predicted flux differences increased approximately 3-fold. When considering the sum of flux changes per time step for wild type (Supplementary Fig.  S2 ) and mutant (Supplementary Fig. S3), we find similar changes for the wild type and the mutant at the steps from 0 days to 1 day and 1 day to 7 days, with an increase in the change from day 7 to day 21 (Fig.  2 B). However, we observe that the changes between day 7 and 21 are considerably larger in the wild type in comparison to the mutant, in line with the resumed growth of the former in the cold. In the following, we identify the reactions and pathways which contribute most to these observed differences.

Changes in predicted sum of Fluxes. Shown are the optimal values of the Euclidean distance (displayed on y-axis) at each corresponding time point or time step (displayed on x-axis). Distances were visualized by plotting the Euclidean distance value above each bar. (A) Displayed are the sums of flux difference between wild type and mutant at each corresponding time point. (B) Displayed are the sums of flux differences between wild type fluxes and mutant fluxes between each two time consecutive points.

Analysis of differential reactions

We next considered the flux differences for each reaction in the metabolic model. Additionally, we investigated reactions displaying large changes in flux differences at early time points, as the most interesting to understand the changes in the metabolic network functionality in response to the cold shift.

K-means clustering of reaction behaviour

We focussed on differential behaviour of all reactions between mutant and wild type, excluding transport reactions and artificial reactions to avoid bias due to lack of gene association for these reactions. To this end, we applied K-means clustering to group reactions (Supplementary Table  S2 ) with similar relative flux changes, where the number of clusters was determined by the silhouette index (Supplementary Fig.  S4 ). As a result, we identified K = 7 clusters of reactions (Fig.  3 ), with a maximum silhouette index value of 0.78, based on the relative flux changes (Fig.  3 A). For comparison, we also consider the K-mean clustering of the nominal flux changes (Fig. ​ (Fig.3B). 3 B). To provide an intuitive description of clusters as well as reaction behaviour over time, we introduce a three-character pattern consisting of Up (U), Down (D) and No changes (N) if the respective relative flux differences increased, decreased or stayed the same between two time points. Using this classification method we found 17 from the 27 possible patterns displayed by 320 reactions. A total of 111 reactions were classified by the most common pattern ’UUU’ making up roughly 35% of all observed patterns.

Overview of K-means clustering based on relative changes in reaction fluxes. K-means with Euclidean distance was used to identify seven clusters (C) of reactions (excluding transporters and artificial reactions). (A) Shows flux difference values normalized to the absolute maximum difference of each reaction for each time point. Corresponding nominal flux differences are shown in (B).

Overall, we mainly identified conserved flux differences in the first three time points with a shift in flux difference at day 21. This behaviour can be observed in the three biggest clusters. Cluster 5 consisted of 164 reactions, which exhibit an increase of relative flux changes (UUU). In contrast, cluster 2, consisting of 46 reactions, exhibited mainly decrease of relative flux changes (DDD). This inverse behaviour is best captured by the function of RuBisCO as it exhibits strong flux changes for its carboxylation function (cluster 5) and oxygenation function (cluster 2). Reactions in cluster 3 mainly exhibited no changes (NNN). Similarly, cluster 6 summarizes reactions that exhibit constant positive flux change over all time points. The remaining clusters 1, 4 and 7 group reactions that exhibit an inverse shift in behaviour at day 21.

If we consider the top 10 reactions (Supplementary Table  S3 ) with respect to relative and nominal changes directly after cold shift, we find H-serine dehydrogenase (HSerDHNADP_h (UDU), HSerDHNAD_h(DUD)), isocitrate dehydrogenase (iCitDHNADP_m (DDD), iCitDHNAD_m(UUD)) as well as 6-phosphogluconic dehydrogenase (6PGDHNAD_h(DUD)), glutamate dehydrogenase (GluDH1NADP_m(DUD)) and glutamate synthetase (GluSNAD_h(UDD)) conserved among both measures. All these reactions are redox reactions. Additionally, 6-phosphogluconic dehydrogenase (6PGDHNADP_h(UDU)), glutamate dehydrogenase (GluDH2NAD_m(DUD)) and glutamate synthetase (GluSNAD_h(UDD)) can only be found in the top 10 reactions of nominal changes. Conversely, malate dehydrogenase (MalDH2NADP_c(UNN)), fructose-biphosphate aldolase (SBPA_h(UDD)) and sedoheptulose-biphosphatase (SBPase_h(UDD)) can only be found in the top 10 reactions of relative changes.

Pathways enriched in reactions with highly altered fluxes across time points

Metabolic reactions do not function in isolation, so analysis and interpretation of the prediction is best carried out in terms of pathways. To identify the pathways that are changed over time, we used the metabolic pathways as defined by the underlying A. thaliana model 23 (for definitions of pathway membership refer to Arnold et al. 2014 23 (Supplementary Table  S4 ). We inspected and considered as relevant those pathways that were enriched with reactions displaying large predicted flux differences between wild type and mutant (Fig. ​ (Fig.4). 4 ). A reaction was defined to exhibit large changes, if its absolute sum of flux changes across all time points was above the median of considered reactions present in the model (excluding transport and artificial reactions, as specified above). To identify pathways enriched with such reactions we used the Fishers exact test with significance threshold P considering multiple hypotheses correction following the Benjamini–Hochberg procedure (Supplementary Table  S5 ). Considering nominal changes, we found five pathways to be enriched for reactions with large changes. These pathways, ordered by decreasing P-value, with p < 0.01, include: the Calvin�nson-Cycle (CBC), photorespiration, gluconeogenesis, leucine synthesis, and in addition with < 0.05 , glycolysis. Considering relative instead of nominal changes, we found pathways with p < 0.01 to include the Calvin�nson cycle, glycolysis, gluconeogenesis, and in addition with p < 0.05 , photorespiration.

Pathways enriched in reactions with highly altered fluxes. Displayed are pathways significantly ( P < = 0.05 ) enriched in regulated reactions based on (A) relative and (B) nominal differences. They are descending ordered according to their respective P-value. Size of the dots corresponds to the count of reactions present in the pathway. Bar size represents the negative logarithm of the P-value (x-axis).

Flux sampling analysis with quadratic constraints

We examined how specific these findings are by sampling the solution space given in optimal solution for each considered time point. As a sufficiently large enough sample size gives information about range of fluxes as well as their probability, it gives the means to explore for alternative solutions and so for the uniqueness of the solution. In this case for each considered time point the proposed approach (see Methods - Flux sampling for TC-iReMet2) did not find a solution after 1000 trials. Therefore, this analysis indicates that the findings are specific, in the sense that alternative optima are unlikely, and significant as there are no other possible flux distributions in optimal solution.


Conclusions

Understanding the metabolic response of a biological system exposed to different environmental stimuli is of great importance for obtaining insights in the contribution of individual system components and pathways to the physiology of the system. While gene expression data only provide putative insights into the physiological response of a system, metabolomics data and the corresponding flux profiles reflect the ultimate physiological response. Here we propose an optimization-based approach, TREM-Flux, which can be used to integrate time-resolved transcriptomics and quantitative metabolomics data and to predict the corresponding flux. Application of TREM-Flux in a genome-scale model reconstruction pinpoints the metabolic functions involved in the time-resolved metabolic response, as illustrated in the case of rapamycin treatment in C. reinhardtii.

Our findings point out the added value of considering metabolite levels in genome-scale models by obtaining more accurate predictions of the active physiological state. The predicted flux distributions can be used to determine differences in particular metabolic functions between control and treatment under different growth conditions. The integration of additional data, such as enzyme activities and protein levels, could further reduce the solution space in future analysis. To this end, experiments will have to be carefully planned to account for differences in time scales on which cellular processes take place with sampling at high enough resolution to allow better insights into the changes of the levels of molecular components. Although the present study relies on data and a genome-scale model from green algae, we believe that any other organisms could be analogously interrogated if data sets and network reconstructions of similar quality are available.


Integrating –omics data into genome-scale metabolic network models: principles and challenges

Charlotte Ramon, Mattia G. Gollub, Jörg Stelling Integrating –omics data into genome-scale metabolic network models: principles and challenges. Essays Biochem 26 October 2018 62 (4): 563–574. doi: https://doi.org/10.1042/EBC20180011

At genome scale, it is not yet possible to devise detailed kinetic models for metabolism because data on the in vivo biochemistry are too sparse. Predictive large-scale models for metabolism most commonly use the constraint-based framework, in which network structures constrain possible metabolic phenotypes at steady state. However, these models commonly leave many possibilities open, making them less predictive than desired. With increasingly available –omics data, it is appealing to increase the predictive power of constraint-based models (CBMs) through data integration. Many corresponding methods have been developed, but data integration is still a challenge and existing methods perform less well than expected. Here, we review main approaches for the integration of different types of –omics data into CBMs focussing on the methods’ assumptions and limitations. We argue that key assumptions – often derived from single-enzyme kinetics – do not generally apply in the context of networks, thereby explaining current limitations. Emerging methods bridging CBMs and biochemical kinetics may allow for –omics data integration in a common framework to provide more accurate predictions.


Correlation-based integration

One of the simplest ways to explore multi-omics data in an integrative way is to explicitly set out to look for correlative links between the data sets. Correlations have frequently been used to examine the associations between transcriptomic data and metabolomics measurements. There are many ways to assess the correlation of two sets of measurements, the most common of these being Pearson’s and Spearman’s correlation for parametric and non-parametric data, respectively.

Naively, one expects metabolites to correlate with those genes with which they have associations however, this is not always the case. While on the one hand, Urbanczyk-Wochniak found more than double the number of significantly correlated metabolite–transcript pairs than would be expected by chance in potato tubers [ 17 ], and Fendt et al . [ 18 ] quantified transcripts, proteins and metabolites in yeast and other species on perturbations (for instance single enzyme modulations) and showed an inverse relationship between the log fold change of a metabolite and the log fold change of the protein or transcript catalyzing the reaction. They also found a great deal of variation in the correlation’s strengths, with a more significant trend in the correlations between substrates and enzymes than between reaction products and enzymes. On the other hand, ter Kuile and Westerhoff [ 19 ] found that fluxes through steps in the biochemical pathways did not correlate proportionally with the concentrations of the corresponding biochemical enzymes, and Moxley et al . [ 20 ] also report low correlation coefficients between transcripts of metabolic enzymes and related metabolite fluxes ( r = 0.07–0.8) in yeast.

More concerningly for pure correlation-based approaches, Bradley [ 21 ] noted that both the direction and magnitude of correlation between metabolites and related genes could vary significantly between experimental conditions.

As well as using standard correlation coefficients, such as Pearson’s or Spearman’s, there are also other methods for measuring correlation the Goodman and Kruskal gamma test, which only takes into account the up/down regulation of each metabolite/gene, e.g. [ 22 ] robust linear models, which look at each transcripts’ ability to predict each metabolite [ 23 ] and partial correlations [ 24 , 25 ], which evaluate those correlations that are independent of the other colinear measurements. For instance, what is the independent correlation of gene A and metabolite B, given that they are both correlated to gene C, can be calculated through a partial correlation computation.

In many experimental designs, we know that the changes in the metabolome and the transcriptome will not be simultaneous, and therefore it will be best to obtain a time course of samples for each omics. In these cases, it has been shown that by firstly aligning the data through techniques such as Dynamic Time Warping will help the detection of associated metabolites and transcripts [ 26 ].

In mammalian systems, data integration is often performed on source-matched data sets, where the RNA and metabolomics samples were acquired from different tissues. This complicates the expected correlation patterns. For instance, linking plasma metabolic changes to liver transcript changes in a source-matched study of fenofibrate and fish oil treatments in mice [ 27 ]. Lu et al . found that the expression of genes involved in fatty acid metabolism were associated with levels of plasma cholesterol and phosphatidycholine.

This section shows that a straightforward application of Pearson or Spearman correlation has many potential problems and is not overly suited to the task of metabolomic–transcriptomic data integration. Those elements that are known to be closely related in the pathways, often do not show a correlative link, while correlations can also occur at great distances across the network. More work needs to be undertaken to see if partial correlations can aid the identification of the most direct connections. There are also issues of time that obscure the correlative links between transcriptomic and metabolomic samples taken at matched time points, with metabolomic changes being connected to a transcriptomic changes at a much earlier time points and vice versa. In cases where the time course data exist, alignment will be an important step before the correlative associations are evaluated.


How to integrate transcriptomics data with kinetic metabolic models? - Biology

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Conclusion

The above methods have been used to not only integrate expression data from a variety of sources but to also make progress toward overcoming key challenges in the field of systems biology. For instance, iMAT, highlighting its applicability in multi-cellular organisms, was used to curate the human metabolic network reconstruction and predict tissue-specific gene activity levels in ten human tissues (Duarte et al., 2007 Shlomi et al., 2008). Additionally, both E-Flux and PROM have been used to discover novel drug targets in Mycobacterium tuberculosis (Colijn et al., 2009 Chandrasekaran and Price, 2010).

Given the recent success with using genome-scale metabolic network reconstructions as a platform for integrating expression data, efforts should focus on multi-omics data integration. A handful of methods have already been introduced that integrate two or more types of omics data into genome-scale metabolic network reconstructions. For example, despite the current dearth of quantitative metabolomics data, a method has been developed that demonstrates how semi-quantitative metabolomics data can be used with transcriptomic data to curate genome-scale metabolic network reconstructions and identify key reactions involved in the production of certain metabolites (Cakir et al., 2006). Another algorithm, called Integrative Omics-Metabolic Analysis (IOMA), integrates metabolomics data and proteomics data into a genome-scale metabolic network reconstruction by evaluating kinetic rate equations subject to quantitative omics measurements (Yizhak et al., 2010). Furthermore, Mass Action Stoichiometric Simulation (MASS) uses metabolomic, fluxomic, and proteomic data to transform a static stoichiometric reconstruction of an organism into a large-scale dynamic network model (Jamshidi and Palsson, 2010). And finally, building off of iMAT, the Model-Building Algorithm (MBA) utilizes literature-based knowledge, transcriptomic, proteomic, metabolomic, and phenotypic data to curate the human metabolic network reconstruction to derive a more complete picture of tissue-specific metabolism (Jerby et al., 2010). Such algorithms show promise in their ability to easily integrate high-throughput data into genome-scale metabolic network reconstructions to generate phenotypically accurate and predictive computational models.


Studying plant physiology with kinetic models

Various aspects of plant physiology have been analysed extensively with kinetic models, and the field has a history going back for more than two decades. Detailed surveys of these models, the pathways they are addressing, and the techniques used can be found in Morgan and Rhodes (2002) and Rios-Estepa and Lange (2007). A recent review ( Arnold and Nikoloski, 2011) was devoted to a quantitative comparison and ranking of all the kinetic models that have been published on the Calvin–Benson cycle. This information will not be repeated here instead, the purpose of this section is 2-fold. First, a summary of recent plant kinetic models that have been published since the last comprehensive review by Rios-Estepa and Lange (2007) is presented in Table 1. Importantly, the scope of these models is not limited to primary metabolism, but extends to secondary metabolism, the metabolism of xenobiotics, as well as gene-regulatory networks.

Recent kinetic models of plant metabolism

Pathway Comment References
Essential oil biosynthesis Monoterpenoid biosynthesis in peppermint identified controlling enzymes for essential oil composition Rios-Estepa et al. (2008, 2010)
Benzenoid network Discussed in main text Colón et al. (2010)
Aspartate metabolism Discussed in main text Curien et al. (2009)
Flavonoid pathway Minimal kinetic model of temperature compensation and regulation of the pathway in Arabidopsis temperature effects modelled with Arrhenius equation Olsen et al. (2009)
Glucosinolate metabolism Kinetic model of multifunctional enzymes in glucosinolate biosynthetic pathway incorporating measured enzymatic properties model predicts different glucosinolate chain length profiles Knoke et al. (2009)
Fenclorim metabolism Modelled metabolism of the herbicide safener fenclorim (which enhances gene expression of detoxifying enzymes such as glutathione transferases) in Arabidopsis parameters estimated by fitting to time-courses Liu et al. (2009)
Photosystem II Chlorophyll a fluorescence transients in pea leaves modelled with eight models with different reaction schemes but comprising the same electron carriers Lazár and Jablonský (2009)
Plastoquinone kinetics Three-state-variable model of plastoquinone-related electron transport kinetics in photosynthesis, describing delayed fluorescence model validated with data from healthy and drought-stressed soybean plants Guo and Tan (2009)
Hydrogen production Bioreactor model of transition from oxygenic growth to anoxic H2 production in Chlamydomonas reinhardtii dependence on light and sulphur availability Fouchard et al. (2009)
Sucrose metabolism Discussed in main text Uys et al. (2007)
Circadian clock Three-feedback-loop model of the plant clock gene-regulatory network in Arabidopsis incorporating data on experimentally established feedbacks between regulatory proteins and genes the model predicts coupled morning and evening oscillators Locke et al. (2006)
RuBisCO activation kinetics Detailed kinetic model of the elementary reaction steps in the mechanism of RuBisCO from spinach leaves rate constants of carbamylation, activation, carboxylation, and inhibition determined by fitting to multiple experimental data sets McNevin et al. (2006)
Pathway Comment References
Essential oil biosynthesis Monoterpenoid biosynthesis in peppermint identified controlling enzymes for essential oil composition Rios-Estepa et al. (2008, 2010)
Benzenoid network Discussed in main text Colón et al. (2010)
Aspartate metabolism Discussed in main text Curien et al. (2009)
Flavonoid pathway Minimal kinetic model of temperature compensation and regulation of the pathway in Arabidopsis temperature effects modelled with Arrhenius equation Olsen et al. (2009)
Glucosinolate metabolism Kinetic model of multifunctional enzymes in glucosinolate biosynthetic pathway incorporating measured enzymatic properties model predicts different glucosinolate chain length profiles Knoke et al. (2009)
Fenclorim metabolism Modelled metabolism of the herbicide safener fenclorim (which enhances gene expression of detoxifying enzymes such as glutathione transferases) in Arabidopsis parameters estimated by fitting to time-courses Liu et al. (2009)
Photosystem II Chlorophyll a fluorescence transients in pea leaves modelled with eight models with different reaction schemes but comprising the same electron carriers Lazár and Jablonský (2009)
Plastoquinone kinetics Three-state-variable model of plastoquinone-related electron transport kinetics in photosynthesis, describing delayed fluorescence model validated with data from healthy and drought-stressed soybean plants Guo and Tan (2009)
Hydrogen production Bioreactor model of transition from oxygenic growth to anoxic H2 production in Chlamydomonas reinhardtii dependence on light and sulphur availability Fouchard et al. (2009)
Sucrose metabolism Discussed in main text Uys et al. (2007)
Circadian clock Three-feedback-loop model of the plant clock gene-regulatory network in Arabidopsis incorporating data on experimentally established feedbacks between regulatory proteins and genes the model predicts coupled morning and evening oscillators Locke et al. (2006)
RuBisCO activation kinetics Detailed kinetic model of the elementary reaction steps in the mechanism of RuBisCO from spinach leaves rate constants of carbamylation, activation, carboxylation, and inhibition determined by fitting to multiple experimental data sets McNevin et al. (2006)

Recent kinetic models of plant metabolism

Pathway Comment References
Essential oil biosynthesis Monoterpenoid biosynthesis in peppermint identified controlling enzymes for essential oil composition Rios-Estepa et al. (2008, 2010)
Benzenoid network Discussed in main text Colón et al. (2010)
Aspartate metabolism Discussed in main text Curien et al. (2009)
Flavonoid pathway Minimal kinetic model of temperature compensation and regulation of the pathway in Arabidopsis temperature effects modelled with Arrhenius equation Olsen et al. (2009)
Glucosinolate metabolism Kinetic model of multifunctional enzymes in glucosinolate biosynthetic pathway incorporating measured enzymatic properties model predicts different glucosinolate chain length profiles Knoke et al. (2009)
Fenclorim metabolism Modelled metabolism of the herbicide safener fenclorim (which enhances gene expression of detoxifying enzymes such as glutathione transferases) in Arabidopsis parameters estimated by fitting to time-courses Liu et al. (2009)
Photosystem II Chlorophyll a fluorescence transients in pea leaves modelled with eight models with different reaction schemes but comprising the same electron carriers Lazár and Jablonský (2009)
Plastoquinone kinetics Three-state-variable model of plastoquinone-related electron transport kinetics in photosynthesis, describing delayed fluorescence model validated with data from healthy and drought-stressed soybean plants Guo and Tan (2009)
Hydrogen production Bioreactor model of transition from oxygenic growth to anoxic H2 production in Chlamydomonas reinhardtii dependence on light and sulphur availability Fouchard et al. (2009)
Sucrose metabolism Discussed in main text Uys et al. (2007)
Circadian clock Three-feedback-loop model of the plant clock gene-regulatory network in Arabidopsis incorporating data on experimentally established feedbacks between regulatory proteins and genes the model predicts coupled morning and evening oscillators Locke et al. (2006)
RuBisCO activation kinetics Detailed kinetic model of the elementary reaction steps in the mechanism of RuBisCO from spinach leaves rate constants of carbamylation, activation, carboxylation, and inhibition determined by fitting to multiple experimental data sets McNevin et al. (2006)
Pathway Comment References
Essential oil biosynthesis Monoterpenoid biosynthesis in peppermint identified controlling enzymes for essential oil composition Rios-Estepa et al. (2008, 2010)
Benzenoid network Discussed in main text Colón et al. (2010)
Aspartate metabolism Discussed in main text Curien et al. (2009)
Flavonoid pathway Minimal kinetic model of temperature compensation and regulation of the pathway in Arabidopsis temperature effects modelled with Arrhenius equation Olsen et al. (2009)
Glucosinolate metabolism Kinetic model of multifunctional enzymes in glucosinolate biosynthetic pathway incorporating measured enzymatic properties model predicts different glucosinolate chain length profiles Knoke et al. (2009)
Fenclorim metabolism Modelled metabolism of the herbicide safener fenclorim (which enhances gene expression of detoxifying enzymes such as glutathione transferases) in Arabidopsis parameters estimated by fitting to time-courses Liu et al. (2009)
Photosystem II Chlorophyll a fluorescence transients in pea leaves modelled with eight models with different reaction schemes but comprising the same electron carriers Lazár and Jablonský (2009)
Plastoquinone kinetics Three-state-variable model of plastoquinone-related electron transport kinetics in photosynthesis, describing delayed fluorescence model validated with data from healthy and drought-stressed soybean plants Guo and Tan (2009)
Hydrogen production Bioreactor model of transition from oxygenic growth to anoxic H2 production in Chlamydomonas reinhardtii dependence on light and sulphur availability Fouchard et al. (2009)
Sucrose metabolism Discussed in main text Uys et al. (2007)
Circadian clock Three-feedback-loop model of the plant clock gene-regulatory network in Arabidopsis incorporating data on experimentally established feedbacks between regulatory proteins and genes the model predicts coupled morning and evening oscillators Locke et al. (2006)
RuBisCO activation kinetics Detailed kinetic model of the elementary reaction steps in the mechanism of RuBisCO from spinach leaves rate constants of carbamylation, activation, carboxylation, and inhibition determined by fitting to multiple experimental data sets McNevin et al. (2006)

Secondly, three examples of plant kinetic models (one from the author’s own work) are discussed in greater detail to illustrate specific aspects of the modelling techniques and approaches.

Top-down model assembly

As outlined above, one of the problems associated with building kinetic models is that often the kinetic data for the constituent enzymes are not available. In such cases, kinetic parameters can be obtained from a ‘top-down’ approach by fitting the model parameters to experimental data from the intact system, for example fluxes and metabolite concentrations.

This ‘top-down’ method was followed by Colón et al. (2010) to develop a model of the benzenoid network in petunia flowers. The model comprises a network of 31 biochemical reactions describing the conversion of phenylalanine to various benzenoid volatiles. The experimental data used for fitting were metabolite pool sizes and labelling patterns obtained by feeding three different concentrations of deuterated phenylalanine to the flowers. Independent validation data were provided by transgenic flowers in which one of the pathway enzymes, BPBT, was down-regulated using RNA interference. The model was subsequently subject to MCA, showing that the enzyme phenylacetaldehyde synthase exerted the bulk of the control on the phenylacetaldehyde branch of the network. However, in other branches flux control was widely distributed. The significance of the results in this study is 2-fold: first, construction and assembly of the model enabled the authors to perform MCA with the model. This would not have been experimentally feasible for every step in the pathway. Secondly, the MCA was able to identify key flux-controlling steps and thus suggested possible future metabolic engineering strategies for perturbing secondary plant metabolism by targeting steps with large flux control coefficients, for example with a view to boosting secondary metabolite production.

Bottom-up model assembly

In contrast to the previous example, the ‘bottom-up’ approach entails assembling all the available data on the isolated pathway components (such as enzyme kinetic parameters, etc., see above) into a model, and then appraising how well this model replicates the behaviour of the entire system. Curien et al. (2009) followed this strategy to build a detailed kinetic model of aspartate biosynthesis in Arabidopsis thaliana. The authors performed in vitro kinetic measurements on the constituent enzymes of the pathway, and then compiled and collated these into a detailed kinetic model, which could reproduce in vivo experimental measurements. The strength of this approach is that the authors could demonstrate that in vivo behaviour of the pathway can actually be explained in terms of independently collected in vitro data. The modelling results are significant for their explanatory power in identifying and clarifying the role of allosteric interactions, of which there are a great number in this pathway. The model identified some of these allosteric feedbacks whose function is not to couple supply and demand for an intermediate (as is commonly the case), but rather to ensure that fluxes in competing pathways function and are regulated independently. In addition, the model explicitly included the different isoforms for the enzymes aspartokinase, dihydrodipicolinate synthase, and homoserine dehydrogenase. Significantly, the model could provide insight into their role in vivo: because of their different kinetic properties, isoforms of the same enzyme varied greatly in terms of their control coefficients and their contribution to flux regulation, implying that they are not redundant but each has its specific function in the pathway. Finally, the model identified threonine as a potential high-level regulator as its concentration was the most sensitive variable in the system.

Modelling sucrose metabolism in sugarcane

In the remainder of this section, a brief overview of the author’s own work on the kinetic modelling of sugarcane will be provided. As explained earlier in this review, elementary mode analysis identified a number of substrate cycles in sugarcane metabolism this concurrent sucrose breakdown and re-synthesis has also been demonstrated experimentally ( Komor, 1994 Whittaker and Botha, 1997 Zhu et al., 1997). This prompted the construction of a kinetic model of the substrate cycling process, together with sucrose accumulation in the vacuole. The model, constructed with the ‘bottom-up’ approach, could replicate independent experimental flux and metabolite concentration validation data without resorting to parameter fitting (in no case was the discrepancy greater than a factor of two Rohwer and Botha, 2001). Based on MCA, the control of each reaction on the substrate cycling of sucrose (defined as the control of the flux ratio between sucrose breakdown and sucrose accumulation into the vacuole) could be quantified. The five reactions with the numerically largest control coefficients were the uptake of fructose and glucose into the cytoplasm (–0.86 and –0.90, respectively), the transport of sucrose into the vacuole (–0.51), phosphorylation of glucose by hexokinase (1.09), and breakdown of sucrose by neutral invertase (0.71). Rohwer and Botha (2001) found that a decrease in substrate cycling is predicted to translate into increased sucrose accumulation, and on the basis of these results predicted that overexpression of the plasma membrane glucose and fructose transporters, as well as of the vacuolar sucrose importer, and attenuation of neutral invertase would be the most promising biotechnological targets for reducing this futile cycling of sucrose and increasing sucrose accumulation. By way of experimental validation, Rossouw et al. (2007) demonstrated an increase in sucrose accumulation in sugarcane suspension cells by decreasing neutral invertase activity through RNA interference, albeit at the expense of reduced respiration and growth. Thus, while the increase in sucrose accumulation was correctly predicted by the model, its scope did not extend far enough to predict the effect of changes in neutral invertase activity on respiration and growth, perhaps suggesting that the cycling of sucrose is not ‘futile’ after all but fulfils another—as yet unidentified—function. More recently, these results were repeated in transgenic sugarcane plants, with Rossouw et al. (2010) demonstrating increased sucrose and decreased hexose levels, as well as reduced substrate cycling in the culm tissues of transgenics with reduced neutral invertase activity.

Growth modelling of a sugarcane stalk in segments

The model of Rohwer and Botha (2001) is specific to medium-mature tissue of a single internode. However, the expression of metabolic enzymes changes significantly with growth, stem elongation, and internodal maturation ( Botha et al., 1996) these effects are most pronounced during the first 10 internodes of the sugarcane stalk, and higher numbered internodes can be regarded as mature. This prompted the extension of the original sugarcane model to include more detail about culm biochemistry. Specifically, the isoforms of sucrose synthase and fructokinase were made explicit, carbon partitioning to respiration and fibre formation were treated separately, and partitioning to respiration occurred via either phosphofructokinase (PFK) or pyrophosphate-dependent PFK, on to aldolase and lower glycolysis ( Uys et al., 2007). The stoichiometry of this extended network is shown in Fig. 3.

Metabolic reactions of the extended model of sucrose accumulation and futile cycling in sugarcane parenchymal tissue ( Uys et al., 2007). Metabolites are indicated by a small circle, enzymes by a numbered grey box. Isozymes are grouped by a surrounding box and numbered a, b, and c where applicable.


Watch the video: Απώλεια Βάρους με EFT -Πρόγραμμα Αποδέσμευσης Περιττού Βάρους- 211. Liana Telioni (September 2022).


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