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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.

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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→B:

Reaction 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

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Acknowledgments

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

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Authors and Affiliations

  1. Simulation Group, Institute of Systems Engineering, Faculty 11/12, University of Siegen, 57068, Siegen, Germany

    P. Droste, M. Weitzel & W. Wiechert

Authors
  1. P. Droste
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  2. M. Weitzel
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  3. W. Wiechert
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Corresponding author

Correspondence to W. Wiechert.

Appendix: Implementation details

Appendix: Implementation details

CumoVis (cumomer graph visualization tool) is implemented in Java version 1.5 (http://www.java.sun.com). The three-dimensional visualization of the cumomer network is realized with Java3D (https://java3d.dev.java.net), an OpenGL (http://www.opengl.org) based library for Java. This library requires graphics hardware with full 3D acceleration. CumoVis is available via the authors’ Internet presentation http://www.uni-siegen.de/fb11/simtec/software.

The visualization of an ILN in CumoVis is split into three main tasks (cf. Fig. 8).

Fig. 8
figure 8

Data flow diagram of visualizing cumomer networks. The first step is to analyze a carbon transition network given in FluxML to get information about the cumomer graph with its partition in WLs, CCs and SCCs. In a parallel task the underlying metabolite network is designed to get a two-dimensional layout. Alternatively, a horizontal graph layout can be generated automatically. On the basis of this layout information, CumoVis generates the three-dimensional visualization of the cumomer graph

Full size image

Analysis of a carbon transition network

The network generation algorithm introduced in [26] translates the carbon atom transition network given in FluxML (a new file format developed at the University of Siegen in conjunction with 13C flux simulation) into a cumomer network graph with a partition in WLs and a connectivity analysis of the individual WLs of the cumomer network graph reveals their CCs and SCCs. This analysis is not part of the CumoVis software but of an external tool. The obtained information is serialized into a document of another XML language, the CGraph (.cg) format developed for this purpose. It keeps all information about the cumomer network, i.e.

  • all metabolites with all possible cumomers,

  • all reactions with a reference to the involved metabolites,

  • the network partition with all WLs, their reaction edges, their CCs and SCCs and the uplinks between different WLs.

Design of the metabolic network

The underlying metabolic network layout is also designed independently from CumoVis. For that purpose, a flux map editor called Omix can be used. Omix is a follow-up tool of MetVis [47]. It is developed at the University of Siegen in a companion project. For a better lucidity of metabolic networks, Omix—and therefore CumoVis—supports duplicated nodes which are often applied for co-metabolites, like CO2 and H2O.

The Omix output format (Omix Graph Layout .ogl) keeps metabolite and reaction nodes with their coordinates in a two-dimensional layer. Both file formats “ogl” and “cg” are specified in XML. Functionally linked data in aforementioned file formats are associated by the unambiguous names of reactions and metabolites. If no layout data is available, CumoVis can automatically generate a hierarchical layout of the metabolic network by analyzing the topology of the metabolic graph that yields a directed acyclic graph (DAG) of CCs and SCCs. This DAG is designed according Sugiyama’s layered approach [59].

Generating the three-dimensional cumomer graph

Having collected this input data, the CGraph data can be visualized based on the 2D layout in the CumoVis application. Generating the three-dimensional scene of the cumomer network occurs as follows:

  • Arranging the cumomer nodes according the underlying metabolic nodes: The X and Y coordinates of every cumomer result from the underlying metabolite node in level 0 (cf. Fig. 4). Their Z position arises from the position of the appropriate weight level and the position of the single cumomer in that level. In a weight level, all cumomers of the same metabolite are arranged in a pile sorted by their binary number. The height of a weight level arises from the largest number of cumomer nodes of the same metabolite.

  • Generating the edges between the cumomer nodes:

The drawing of edge shapes is quite more difficult than that of nodes, because the positions of their start, control, and end points cannot be taken from the metabolite graph. A reason for this lies on the one hand in the difference between metabolite and cumomer graphs. A metabolite graph is a hyper graph, i.e. every edge can have several sources and destinations whereas edges in a cumomer network have always one source and one destination node (cf. “Cumomer networks” section). On the other hand, a reaction edge in the metabolic network splits into multiple edges in the cumomer network. If the reaction is reversible this number of cumomer edges is even doubled.

To solve this problem of designing edges in the cumomer network automatic layout methods were developed. Every cumomer node sorts its incoming and outgoing edges by the position of the aim node. According to this sort sequence, their start respectively end points are arranged alongside the cumomer. For the shape of the edges a cubic Bézier curve was chosen.

The computation of all edges takes the largest share of the time to generate the 3D network. For example, it needs up to 20 s to build up the citric acid graph, which cannot be avoided.

Certainly, the visualization of full “genome wide” networks makes no sense because they can have more than 100,000 cumomer nodes with stacks of up to 16,000 cumomers. For this reason, the visual approach is limited to medium-sized networks. However, it should be pointed out that MFA is traditionally concerned with the central metabolic pathways, which fulfill this condition.

The graphical user interface contains a selection area that contains the structure of the cumomer graph divided into WLs, CCs, SCCs and single cumomers to control the complexity of the cumomer graph and to choose the path visualization.

The path tracing functionality is solved with a recursive depth search algorithm which searches for a target cumomer and with a maximum depth. In the case of no specified target all possible paths with the given depth are returned. If a cycle is detected, the algorithm breaks the recursion. In order to visualize the aforementioned carbon permutations the sequence of labeled atoms of the source cumomer is permutated according the reactions along the depth search.

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Droste, P., Weitzel, M. & Wiechert, W. Visual exploration of isotope labeling networks in 3D. Bioprocess Biosyst Eng 31, 227–239 (2008). https://doi.org/10.1007/s00449-007-0177-1

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