COMPUTER AIDED OPTIMIZATION OF CARBON ATOM LABELING … · Computer Aided Optimization of Carbon Atom Labeling for Tracer Experiments 275 Fig. 4. Screenshot of Metabolic Network Navigator:

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270

COMPUTER AIDED OPTIMIZATION OF CARBON ATOMLABELING FOR TRACER EXPERIMENTS

BENJAMIN SEFA MENKUC CHRISTOPH [email protected] [email protected]

HERMANN-GEORG HOLZHUTTER

[email protected]

Medical Faculty of the Humboldt University Berlin, Charite, Institute of Biochem-

istry, Monbijoustr. 2, 10117 Berlin, Germany

Isotopomer tracer experiments are indispensable for the determination of flux rates in

already known pathways as well as for the identification of new pathways. The informa-tion gained from such experiments depends on the labeling of the feed tracer metabolite,i.e. the atom positions carrying a label. Here we present an algorithm and a software

tool to find an optimal carbon labeling pattern that assures the label to disseminate pre-dominantly into those parts of the network under study. Our implementation is based oncarbon fate maps and distinguishes between homotopic and prochiral atoms. In addition,the software can be used to generate carbon transition probability matrices, which can

be used for the study of biochemical reaction mechanisms. In this article we present thealgorithms and show an application of the software for glycolysis and the TCA cycle.

Keywords: isotopomer tracer experiments; metabolic network; compound transition ma-trix; systems biology

1. Introduction

Isotopomer tracer experiments are essential for determining fluxrates of known path-ways [4, 8] as well as for elucidating new pathways [3, 11] and reaction mechanisms.In typical isotopomer tracer experiments labeled compounds are taken up by anorganism and the distribution of the label within certain compounds is observed.

The set of metabolites which will carry the label after a certain amount oftime depends on the labeling pattern of the feed metabolite. For the analysis it isadvantagous to achieve a preferential labeling of those metabolites that belong tothe pathway under investigation. If, however, the label is disseminated into manydifferent pathways the labeled fraction of each metabolite is low and therefore theaccuracy of the measurement is reduced.

Computer programms already exist to simulate the distribution of labels inmetabolic networks over time. Simulation of isotopomer tracer experiments requiresatom mappings between substrates and products [2]. The mapping can be con-structed using common subgraphs in molecule structures [1]. Another database ofatom correspondence [10] was established by Mu et al. using a MCS (maximum


Computer Aided Optimization of Carbon Atom Labeling for Tracer Experiments 271

common subgraph) algorithm [5]. In this database prochirality is considered andthe systematic Inchi naming scheme for compound atoms is used.

Here we present a novel software to track the distribution of the label using agraphical pathway view. It can be used to optimize the labeling pattern by probingall possible feed labelings.

2. Methods

Using the carbon fate mapes [10] we created carbon transition probability matri-ces. These matrices enable us to compute the fate of a labeled carbon atom ina certain reaction. For example the glycolytic enzyme Fructose Bisphosphate Al-dolase (R01070) that converts beta D-Fructose 1,6-Bisphosphate (C03578) to Dihy-droxyacetone Phosphate (C00118) and Glyceraldehyde 3-Phosphate (C00111) has2 transition matrices:

PC05378,C00118 =

0 0 0 1 0 01 0 0 0 0 00 0 1 0 0 0

PC05378,C00111 =

0 0 0 0 1 00 1 0 0 0 00 0 0 0 0 1

(1)

The numbering for atom positions in a compound follows the Inchi canonical-ization scheme [12] and can be computed by using the Inchi software. However,homotopic atoms cannot be numbered uniquely. This fact becomes important forprochiral compounds. For the hydrolysis of Acetylcholine and Choline, the number-ing is shown in Figures 1 and 2.

Fig. 1. Acetylcholine with Inchi atom numbering applied.

The distribution of labeled atoms for substrate beta D-Fructose 1,6-Bisphosphate in reaction R01070 can be calculated like this

lC00111 = PC05378,C00111lC05378 lC00118 = PC05378,C00118lC05378 (2)


272 B.S. Menkuc, C. Gille & H.G. Holzhutter

where P are the transition matrices and l are the labelvectors which contain zerosfor unlabeled positions, otherwise the probability for being labeled. For compoundsthat do not contain homotopic atoms, the transition matrices result directly fromthe carbon fate maps. For example if substrate atom number 5 becomes productatom number 4, the matrix entry at row 5 and column 4 will be 1. However, if thereare homotopic atoms in a compound, the compound is checked for prochirality.Only in the absence of prochirality the corresponding rows or columns of the carbontransition probability matrix P are permutated and divided by n!, where n is thenumber of homotopic atoms. For example in Acetylcholine (C01996) the atoms 2,3,4are homotopic to each other. Thus columns have to be permutated to generate 6transition matrices. Then these matrices are summed up and the resulting matrix isdivided by 6 to form the final transition matrix. The Acetylcholineesterase (R01026),which hydrolyses Acetylcholine to Acetate (C00033) and Choline (C00114), is usedas an example here. To create the matrix PC01996,C00114 the algorithm starts withthe transition matrix that was created without considering homotopicity:

PC01996,C00114 =

0 1 0 0 0 0 00 0 1 0 0 0 00 0 0 1 0 0 00 0 0 0 1 0 00 0 0 0 0 1 0

(3)

Since the nitrogen bound methy groups with carbons 2,3,4 of the substrate arehomotopic, columns 2,3,4 are permutated in the following scheme (2,3,4), (2,4,3),(3,4,2), (3,2,4), (4,2,3), (4,3,2) which results in the following matrix:

PC01996,C00114 =

0 1

313

13 0 0 0

0 13

13

13 0 0 0

0 13

13

13 0 0 0

0 0 0 0 1 0 00 0 0 0 0 1 0

(4)

If there are homotopic atoms that are not prochiral in the substrate the sameprocedure has to be applied to the corresponding rows of the matrix, except if the

Fig. 2. Choline with Inchi atom numbering applied



homotopic atoms are the same as in the substrate which is the case here. In thiscase atoms 1,2,3 of Choline are homotopic.

However if homotopic groups contribute to prochirality of a compound, thecorresponding matrix lines are not permutated.

As an example, the second carbon of Acetylcholine is labeled which results ina labelvector IC05378 = (0, 1, 0, 0, 0, 0, 0)T . The calculation of the labeled atoms incholine is done like this

IC00114 =

0 1

313

13 0 0 0

0 13

13

13 0 0 0

0 13

13

13 0 0 0

0 0 0 0 1 0 00 0 0 0 0 1 0

0100000

=

131313

00

(5)

This example demonstrates how homotopic atoms lead to dissemination of labelsin metabolic networks.

3. Results

We have created a software, Metabolic Network Navigator, that assists in findingthe appropriate atoms to be labeled in tracer experiments. It is possible to specifya labeled feed metabolite and let Metabolic Network Navigator perform in silicotracer experiments, which aids in finding appropriate atoms for labeling.

The selection of reactions that are used for simulation is done by chosing aKegg [7] organism or by manually selecting Kegg reaction IDs. It is recommendedto manually refine the list of reactions, because the genome based organisms thatare predefined in Metabolic Network Navigator usually show a lot of differences toreal organisms.

It has been observed that broad dissemination of the label is predicted whenall reactions are regarded as reversible. Therefore we added the possibility to thesoftware to manually assign directions to reactions.

To demonstrate how a labeled carbon atom propagates in a metabolic network,we have chosen glycolysis and the TCA cycle as an example. Reaction directionshave been assigned manually. As a feed metabolite, alpha D-Glucose was labeledat the first carbon atom. Fig. 3 shows how this label changes its number withinthe different molecules along glycolysis until it enters the TCA cycle as the firstcarbon of Acetyl-CoA. In the first cycle the labeled carbon propagates as a singlelabel through the TCA cycle until it reaches Succinate. Here, the label has equallypartitioned itself because of the homotopic groups within Succinate. The two labelsthen reach Oxaloacetate, where they enter, together with a new Acetyl-CoA, a newround of the TCA cycle. The labels that originate from the labeled Oxaloacetate ofthe first round are shown in the lower brackets.



Fig. 3. Labeled Glucose enters glycolysis and the TCA where its label disseminates.

Metabolic Network Navigator offers the possibility to simulate every possibletracer distribution for position within a certain feed compound and to list the totalnumbers of labeled compounds and iterations in a table (see Fig. 4).

For example, if it is desired that the label just goes into the pentosephosphatepathway, the result suggests to label the third or fourth carbon of alpha D-Glucose,which will become CO2 during Glycolysis and therefore will not enter the TCAcycle.



Fig. 4. Screenshot of Metabolic Network Navigator: Tracer propagation for different positions of

D-Glucose as feed compound. The atoms of the target metabolite Oxaloacetate that are labeledby the tracer are shown in the second column. The third column contains the number of labeledmetabolites and the forth the number of steps which were neccessary to complete the simulation.

4. Discussion

At the moment there are two critical factors hampering the application of ourmethod: the first is lacking reactions in genome based databases (and thus in thecarbon fate maps), the second is the correct assignment of reversibility to reactions.

We have experienced that rendering every reaction reversible leads to nonreal-istic effusive dissemination of the labeled atoms. Therefore it is desirable for thefuture to automatically assign a direction to each reaction. The reversibility of re-actions depends mainly on ∆G, substrate and product concentrations [6]. For mostreactions, there are estimates for the ∆G values [9], therefore it is possible to pre-dict the direction when the metabolite concentrations are known. If enough aboutthe organism is known, it is possible to perform a flux balance analysis and gaindirection properties from that.

The reason for missing reactions in genome based databases is that mostmetabolic networks contain reactions that are very specific for the purpose thenetwork is modelled, i.e. biomass reactions. However, using the methods from [10]it is possible to create carbon fate maps for new reactions. For the future it would beuseful to be able to make creating carbon fate maps for new reactions more easily,i.g. by creating a wizzard that assists the user.

References

[1] Arita, M., Metabolic reconstruction using shortest paths., Simulation Pract. Theory,8:109–125, 2000.

[2] Arita, M., In Silico Atomic Tracing by Substrate-Product Relationships in Escherichiacoli Intermediary Metabolism., Genome Res., 13(11):2455–2466, 2003.

[3] Berl, S., Nicklas, W. J., Clarke, D. D., Compartmentation of citric acid cycle



metabolism in brain: labeling of glutamate, glutamine, aspartate and gaba by severalradioactive tracer metabolites., J. Neurochem., 17(7):1009–1015, 1970.

[4] Buxton, D. B., Schwaiger, M., Nguyen, A., Phelps, M. E., Schelbert, H. R., Radi-olabeled acetate as a tracer of myocardial tricarboxylic acid cycle flux., Circ. Res.,63(3):628–634, 1988.

[5] Hattori, M., Okuno, Y., Goto, S., Kanehisa, M., Development of a chemical structurecomparison method for integrated analysis of chemical and genomic information inthe metabolic pathways., J. Am. Chem. Soc., 125(39):11853–11865, 2003.

[6] Hoppe, A., Hoffmann, S., Holzhutter, H.G., Including metabolite concentrations intoflux-balance analysis: Thermodynamic realizability as a constraint on flux distribu-tions in metabolic networks., BMC Syst. Biol., 1(1):23, 2007.

[7] Kanehisa, M., Goto, S., KEGG: kyoto encyclopedia of genes and genomes., NucleicAcids Res., 28(1):27–30, 2000.

[8] Kelleher, J. K., Analysis of tricarboxylic acid cycle using [14C]citrate specific activityratios., Am. J. Physiol., 248(2 Pt 1):E252–E260, 1985.

[9] Mavrovouniotis, M. L., Estimation of standard Gibbs energy changes of biotransfor-mations., J. Biol. Chem., 266(22):14440–14445, 1991.

[10] Mu, F., Williams, R. F., Unkefer, C. J., Unkefer, P. J., Faeder, J. R., Hlavacek, W. S.,Carbon-fate maps for metabolic reactions, Bioinformatics, 23(23):3193–3199, 2007.

[11] Noronha, S. B., Yeh, H. J., Spande, T. F., Shiloach, J., Investigation of the TCA cycleand the glyoxylate shunt in Escherichia coli BL21 and JM109 using (13)C-NMR/MS.,Biotechnol. Bioeng., 68(3):316–327, 2000.

[12] http://old.iupac.org/inchi/

[13] http://www.genome.ad.jp/

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COMPUTER AIDED OPTIMIZATION OF CARBON ATOM LABELING … · Computer Aided Optimization of Carbon Atom Labeling for Tracer Experiments 275 Fig. 4. Screenshot of Metabolic Network Navigator: