# Visual exploration of isotope labeling networks in 3D

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## Abstract

Isotope labeling networks (ILNs) are graphs explaining the flow of isotope labeled molecules in a metabolic network. Moreover, they are the structural backbone of metabolic flux analysis (MFA) by isotopic tracers which has been established as a standard experimental tool in fluxomics. To configure an isotope labeling experiment (ILE) for MFA, the structure of the corresponding ILN must be understood to a certain extent even by a practitioner. Graph algorithms help to analyze the network structure but produce rather abstract results. Here, the major obstruction is the high dimension of these networks and the large number of network components which, consequently, are hard to figure out manually. At the interface between theory and experiment, the three-dimensional interactive visualization tool CumoVis has been developed for exploring the network structure in a step by step manner. Navigation and orientation within ILNs are supported by exploiting the natural 3D structure of an underlying metabolite network with stacked labeled particles on top of each metabolite node. Network exploration is facilitated by rotating, zooming, forward and backward path tracing and, most important, network component reduction. All features of CumoVis are explained with an educational example and a realistic network describing carbon flow in the citric acid cycle.

## Keywords

Metabolic flux analysis Isotope labeling networks Network visualization Cumomer networks Interactive network analysis## Abbreviations

- ILN
Isotope labeling network

- MFA
Metabolic flux analysis

- ILE
Isotope labeling experiment

- CumoVis
Cumomer network visualization tool

- M
Metabolite symbols

- M#101
Isotopomer notation (M, metabolite symbol; 0, unlabeled; 1, labeled)

- M#1X1
Cumomer notation (M, metabolite symbol; X, don’t care; 1, labeled)

- M#
*abc* Enumeration of atom positions

*v*: A→BReaction notation

- 3D
Three dimensional

- WL
Weight level

- CC
Connected component

- SCC
Strongly connected component

- DAG
Directed acyclic graph

- AcCoA
Acetyl-CoA

- AcN
*cis*-Aconitate- AKG
Alpha-Ketoglutarate

- Cit
Citrate

- CO2
Carbon dioxide

- Fum
Fumarate

- GlyOx
Glyoxylate

- ICit
Isocitrate

- Mal
Malate

- OAA
Oxaloacetate

- Pyr
Pyruvate

- Succ
Succinate

- SucCoA
Succinyl-CoA

## Notes

### Acknowledgments

The project was partly funded by the German Ministry BMBF (SysMAP Project), and the German Research Foundation (DFG, project grant WI 1705/13).

## References

- 1.Wiechert W (2001) 13C metabolic flux analysis. Metab Eng 3:195–206CrossRefGoogle Scholar
- 2.Sauer U (2006) Metabolic networks in motion: 13C-based flux analysis. Mol Syst Biol 2:62CrossRefGoogle Scholar
- 3.Szyperski T (1998) 13C -NMR, MS and metabolic flux balancing in biotechnology research. Q Rev Biophys 31:41–106CrossRefGoogle Scholar
- 4.Sauer U (2004) High-throughput phenomics: experimental methods for mapping fluxomes. Curr Opin Biotechnol 15:58–63CrossRefGoogle Scholar
- 5.Marx A, Graaf AAd, Wiechert W, Eggeling L, Sahm H (1996) Determination of the fluxes in central metabolism of
*Corynebacterium glutamicum*by NMR spectroscopy combined with metabolite balancing. Biotechnol Bioeng 49:111–129CrossRefGoogle Scholar - 6.Ratcliffe RG, Shachar-Hill Y (2006) Measuring multiple fluxes through plant metabolic networks. Plant J 45:490–511CrossRefGoogle Scholar
- 7.Winden WAv, Gulik WMv, Schipper D, Verheijen PJT, Krabben P, Vinke JL, Heijnen JJ (2003) Metabolic flux and metabolic network analysis of
*Penicillium chrysogenum*using 2D [13C, 1H] COSY NMR measurements and cumulative Bondomer simulation. Biotechnol Bioeng 83:75–92CrossRefGoogle Scholar - 8.Kelleher JK (2004) Probing metabolic pathways with isotopic tracers: insights from mammalian metabolic physiology. Metab Eng 6:1–5CrossRefGoogle Scholar
- 9.Malloy CR, Sherry AD, Jeffrey FMH (1990) Analysis of tricarbocylix acid cycle of the heart using 13C isotope isomers. Am J Physiol 259:987–995Google Scholar
- 10.Drysch A, El Massaoudi M, Wiechert W, de Graaf AA, Takors R (2004) Serial flux mapping of
*Corynebacterium glutamicum*during fed-batch L-lysine production using the sensor reactor approach. Biotechnol Bioeng 85:497–505CrossRefGoogle Scholar - 11.Fischer E, Sauer U (2005) Large-scale in vivo fluxes reveal rigidity and suboptimal performance of B. subtilis metabolism. Nat Genet 37:636–640CrossRefGoogle Scholar
- 12.Blank LM, Kuepfer L, Sauer U (2005) Large-scale 13C-flux analysis reveals mechanistic principles of metabolic network robustness to null mutations in yeast. Genome Biol 6:R49CrossRefGoogle Scholar
- 13.Strohhäcker J, Graaf AAd, Schoberth SM, Wittig RM, Sahm H (1993) 31P nuclear magnetic resonance studies of ethanol inhibition in
*Zymomonas mobilis*. Arch Microbiol 159:484–490CrossRefGoogle Scholar - 14.Tesch M, Graaf AAd, Sahm H (1999) In vivo fluxes in the ammonium-assimilatory pathways in
*Corynebacterium glutamicum*studied by 15N nuclear magnetic resonance. Appl Environ Microbiol 65:1099–1109Google Scholar - 15.Antoniewicz MR, Kelleher JK, Stephanopoulos G (2007) Elementary metabolite units (EMU): a novel framework for modeling isotopic distributions. Metab Eng 1:68–86CrossRefGoogle Scholar
- 16.Christensen B, Nielsen J (1999) Isotopomer analysis using GC-MS. Metab Eng 1:282–290CrossRefGoogle Scholar
- 17.Graaf AAd (2000) Use of 13C labelling and NMR spectroscopy in metabolic flux analysis, Chap. 4. In: Barbotin J-N, Portais J-C (eds) NMR in biotechnology: theory and applications, Horizon Scientific Press, WymondhamGoogle Scholar
- 18.Wiechert W (2002) An introduction to 13C metabolic flux analysis. Genet Eng Princ Methods 24:215–238Google Scholar
- 19.Wiechert W, Möllney M, Isermann N, Wurzel M, de Graaf AA (1999) Bidirectional reaction steps in metabolic networks. Part III: Explicit solution and analysis of isotopomer labeling systems. Biotechnol Bioeng 66:69–85CrossRefGoogle Scholar
- 20.Möllney M, Wiechert W, Kownatzki D, de Graaf AA (1999) Bidirectional reaction steps in metabolic networks. Part IV: Optimal design of isotopomer labeling experiments. Biotechnol Bioeng 66:86–103CrossRefGoogle Scholar
- 21.Schmidt K, Carlsen M, Nielsen J, Villadsen J (1997) Modelling isotopomer distribution in biochemical networks using isotopomer mapping matrices. Biotechnol Bioeng 55:831–840CrossRefGoogle Scholar
- 22.Fischer E, Zamboni N, Sauer U (2004) High-throughput metabolic flux analysis based on gas chromatography: mass spectrometry derived 13C constraints. Anal Biochem 325:308–316CrossRefGoogle Scholar
- 23.Rantanen A, Mielikäinen T, Rousu J, Maaheimo H, Ukkonen E (2006) Planning optimal measurements of isotopomer distributions for estimation of metabolic fluxes. Bioinformatics 22:1198–1206CrossRefGoogle Scholar
- 24.Winden Wv, Heijnen JJ, Verheijen PJT (2002) Cumulative bondomers: a new concept in flux analysis from 2D [13C,1H] COSY data. Biotechnol Bioeng 80:731–745CrossRefGoogle Scholar
- 25.Klapa MI, Park SM, Sinskey AJ, Stephanopoulos G (1999) Metabolite and isotopomer balancing in the analysis of metabolic cycles: I. Theory Biotechnol Bioeng 62:375–391CrossRefGoogle Scholar
- 26.Weitzel M, Nöh K, Wiechert W (2007) The topology of metabolic carbon labeling networks. BMC Bioinf 8:315CrossRefGoogle Scholar
- 27.Katz J, Wals P, Lee W-NP (1993) Isotopomer studies of gluconeogenesis and the Krebs cycle with 13C-labeled lactate. J Biol Chem 268:25509–25521Google Scholar
- 28.Wiechert W, Möllney M, Petersen S, de Graaf AA (2001) A universal framework for 13C metabolic flux analysis. Metab Eng 3:265–283CrossRefGoogle Scholar
- 29.Dauner M, Sauer U (2000) GC-MS analysis of amino acids rapidly provides rich information for isotopomer balancing. Biotechnol Prog 16:642–649CrossRefGoogle Scholar
- 30.Nöh K, Wahl A, Wiechert W (2006) Computational tools for isotopically instationary 13C labelling experiments under metabolic steady state conditions. Metab Eng 8:554–577CrossRefGoogle Scholar
- 31.Wiechert W, Siefke C, Graaf AAd, Marx A (1997) Bidirectional reaction steps in metabolic networks. Part II: Flux estimation and statistical analysis. Biotechnol Bioeng 55:118–135CrossRefGoogle Scholar
- 32.Zamboni N, Fischer E, Sauer U (2005) FiatFlux: a software for metabolic flux analysis from 13C-glucose experiments. BMC Bioinf 6:209CrossRefGoogle Scholar
- 33.Klapa MI, Park SM, Sinskey AJ, Stephanopoulos G (1999) Metabolite and isotopomer balancing in the analysis of metabolic cycles: I. Theory Biotechnol Bioeng 62:375–391CrossRefGoogle Scholar
- 34.Park SM, Shaw-Reid C, Sinskey AJ, Stephanopoulos G (1997) Elucidation of anaplerotic pathways in
*Corynebacterium glutamicum*via 13C-NMR spectroscopy and GC-MS. Appl Microbiol Biotechnol 47:430–440CrossRefGoogle Scholar - 35.Jeffrey FMH, Rajagopal A, Malloy CR, Sherry AD (1991) 13C-NMR: a simple yet comprehensive method for analysis of intermediary metabolism. TIBS 16:5–10Google Scholar
- 36.Sriram G, Shanks JV (2004) Improvements in metabolic flux analysis using carbon bond labeling experiments: bondomer balancing and Boolean function mapping. Metab Eng 6:116–132CrossRefGoogle Scholar
- 37.Forbes NS, Clark DS, HW Blanch (2001) Using isotopomer path tracing to quantify metabolic fluxes in pathway models containing reversible reactions. Biotechnol Bioeng 74:196–211CrossRefGoogle Scholar
- 38.Sherry AD, Jeffrey FMH, Malloy CR (2004) Analytical solutions for 13C isotopomer metabolic conditions: substrate oxidation, multiple andgluconeogenesis. Metab Eng 6:12–24CrossRefGoogle Scholar
- 39.Donato LD, Rosiers CD, Montgomery JA, David F, Garneau M, Brunengraber H (1993) Rates of gluconeogenesis and citric acid cycle in perfused livers, assessed from the mass spectrometric assay of the 13C labeling pattern of glutamate. J Biol Chem 268:4170–4180Google Scholar
- 40.Arita M (2005) Introduction to the ARM database: database on chemical transformations in metabolism for tracing pathways, In: Nishioka MtaT (eds) Metabolomics: the frontier of systems biology, Springer Tokyo, TokyoGoogle Scholar
- 41.Arita M, Fujiwara Y, Nakanishi Y (2006) Map editor for the atomic reconstruction of metabolism (ARM), in plant metabolomics. Springer, BerlinGoogle Scholar
- 42.Brandes U, Dwyer T, Schreiber F (eds) (2003) Visualizing related metabolic pathways in two and a half dimensions. Springer lecture notes in computer science, vol 11. International symposium on graph drawing, Springer, BerlinGoogle Scholar
- 43.Wiechert W, Wurzel M (2001) Metabolic isotopomer labeling systems. Part I: Global dynamic behaviour. Math Biosci 169:173–205CrossRefGoogle Scholar
- 44.Jünger M, Mutzel P (2003) Graph drawing software. Springer, New YorkGoogle Scholar
- 45.Karp P, Paley SM (1994) Automated drawing of metabolic pathways. In: Third international conference on bioinformatics and genome researchGoogle Scholar
- 46.Rost U, Kummer U (2004) Visualisation of biochemical network simulations with SimWiz. IEE Syst Biol 1:184–189CrossRefGoogle Scholar
- 47.Noack S, Wahl A, Qeli E, Freisleben B, Wiechert W (2007) Visualizing regulatory interactions in metabolic networks. BMC Biol 5:46CrossRefGoogle Scholar
- 48.Wegner K (2005) SimWiz3D: visualising biochemical simulation results. In: Medical information visualisation: biomedical visualisation, 2005 (MediVis 2005). Proceedings. Third International Conference on 77–82Google Scholar
- 49.Koike H (1993) The role of another spatial dimension in software visualization. ACM Trans Inf Syst 11:266–286CrossRefGoogle Scholar
- 50.Cohen RF, Eades P, Lin T, Ruskey F (1995) Three-dimensional graph drawing. In:Tamassia R, Tollis IG (eds) Proceedings graph drawing, pp 1–11Google Scholar
- 51.Frati F, Battista GD (2007) Three dimensional drawings of bounded degree trees. In: Kaufmann M, Wagner D (eds) Proceedings graph drawing, pp 89–94Google Scholar
- 52.Ho J, Hong S-H (2006) Drawing clustered graphs in three dimensions. In: Healy P, Nikolov NS (eds) Proceedings graph drawing, pp 492–502Google Scholar
- 53.Dickerson JA, Yang Y, Blom K, Reinot A, Lie J, Cruz-Neira C, Wurtele ES (2004) Using virtual reality to understand complex metabolic networks. In: Atlantic symposium comp biol genomic info systems technolGoogle Scholar
- 54.Hong S-H (2006) MultiPlane: a new framework for drawing graphs in three dimensions. In: Graph drawing, pp 414–415Google Scholar
- 55.Brandes U, Corman S (2002) Visual unrolling of network evolution and the analysis of dynamic discourse. In: IEEE symposium on information visualization (INFOVIS ‘02), pp 145–151Google Scholar
- 56.Wiechert W (2001) 13C metabolic flux analysis. Metab Eng 3:195–206CrossRefGoogle Scholar
- 57.Wiechert W, Graaf AAd (1996) In vivo stationary flux analysis by 13-C labelling experiments. Adv Biochem Eng Biotechnol 54:109–154Google Scholar
- 58.Wiechert W, Graaf AAd (1997) Bidirectional reaction steps in metabolic networks. Part I: Modeling and simulation of carbon isotope labelling experiments. Biotechnol Bioeng 55:101–117CrossRefGoogle Scholar
- 59.Sugiyama K, Tagawa S, Toda M (1981) Methods for visual understanding of hierarchical systems. IEEE Trans Syst Man Cybern SMC 11(2):109–125CrossRefGoogle Scholar