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CumoVis

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CumoVis is an Omix plug-in for three dimensional visualization of the entire atom transport layer of a metabolic network. The atom transport layer is a graph that explains the fate of all individual atoms of all metabolite molecules involved in a metabolic network. CumoVis uses the third dimension in order to show all atom mappings. Furthermore, CumoVis can visualize the so called isotopomer graph and cumomer graph arising from the atom transport layer. In CumoVis you can perform network decomposition and atom path tracing.

Background

1.1.1. From Metabolic Networks to Isotopomer Networks

A metabolic network is a graph discribing how small molecules are converted into each other in a biological system:

Metabolic Layer
Metabolic layer


The individual molecules consist of a atoms which are transported from the educt molecules to the product molecules of a reaction. The description of this transport is called an atom mapping or atom transition. In an atom mapping, series of atoms can be split, joined as well as recombined. The totality of the atom mappings of all reactions lead to the atomic layer:

Atomic layer
Atomic layer (atom transport network)


Isotope labeling is an inportant tool in metabolic flux analysis. Here, the input substrate given into the biological system is isotopically labeled at specific positions in the molecule. The labeled substrate is metabolized by the system and thus, the isotopic labeling is distributed all over the metabolic network. The isotopic enrichment can be measured and allows inference on metabolic flux rates within the network.

A molecule with n labeling positions (being the atoms of the chemical element used for isotope labeling, e.g. carbon) has 2n different possible labeling states which we call isotopomers. The isotopomer network describes how these individual isotopomers are transported, split, joined and recombined in the biological system:

Isotopomer Network
Isotopomer network

1.1.2. The Cumomer Network

Isotopomers have a specific weight which is the number of labels. From a mathematical point of view, the challenge in solving the isotopomer network lies in reactions where isotopomers of a certain weight are joined to an isotopomer of higher weight because this leads to non-linear equations in the underlying equation system. One approach to handle this challenge is called the cumomer network (Wiechert 1999):

Cumomer Network
Cumomer network


Shortly spoken, cumomers are cumulative sets of isotopomers. Instead of tracing labeled atoms, the cumomer network describes the fate of labeled molecule fragments. By this, splitting reactions does no longer have to be considered and the entire network can be substructured in a cascade of different levels. Inside of such a level, all cumomers have the same weight, i.e. no splitting or joining steps have to be considered.

1.1.3. Network Decomposition

Each weight level of the cumomer cascade can be decomposed into so called connected components (CC). A CC is a complete set of nodes that are connected with each other. There is no connection between different CCs. By this the CCs of a weight level describe all independent subnetworks within the level.

A CC can be further decomposed into different stroncly connected components (SCC) by considering the actual edge direction. An SCC is a set of nodes within a CC whereas each nodes can reach all other nodes via a certain path. This, SCCs represent the cyclic subnetworks in a CC.

1.1.4. Concept of Visualization

CumoVis visualized the atomic layer, isotopomer network and cumomer cascade by using the two-dimensional layout of the metabolic network in Omix and stacking the corresponding atoms / isotopomers / cumomers on top of the metabolites.

Concept of visualization in CumoVis
Concept of visualization in CumoVis

1.2. Using CumoVis

Working with CumoVis requires a well prepared network model in Omix equipped with atom mappings for each reaction in the Atomic Layer Plug-In. Currently, CumoVis can only visualize the mappings of carbon atoms and arising isotopomer/cumomer networks. It is recommended to use atom mappings that base upon chemical structures.

1.2.1. Startup

Start CumoVis by selecting the corresponding entry in the Extras menu:

Starting CumoVis
Starting CumoVis


Now, CumoVis opens as an additional window and loads the metabolic network model given in Omix.
The network appears different from the classic design known from Omix. The metabolites are displayed with their respective chemical structure if available. Otherwise, a tube-like item us shown filled with as many spheres as labeling positions the metabolite has. The metabolite's position corresponds to its position in the Omix diagram. A text label on top of the chemical structure item shows the metabolites name.

Biochemical reaction in CumoVis
Biochemical reaction in CumoVis


Biochemical reactions in CumoVis are displayed as red spheres placed at the same position as in the Omix diagram. However, the connections in CumoVis do not use the edge shape from Omix. Instead, a standard curve progression is computed from the positions of the connected nodes which is similar for all types and levels of graphs visualized by CumoVis.

Screenshot of CumoVis
Screenshot of CumoVis

On top, a toolbar provides access to different functionality of the tool. In the center of the window the network is shown in 3D. The left side of CumoVis is the component view for navigating between atomic layer, isotopomer network and cumomer cascade.

1.2.2. Mouse & Key Navigation

It is possible to move, rotate and scale the scene and camera, respectively, by mouse and key navigation.
  • Moving the mouse with pressed left mouse button rotates the camera around the scene center point.
  • Moving the mouse with pressed right mouse button moves the camera relative to the scene center (up, down, left, right).
  • Using the mouse wheel moves the camera towards or away from the scene center point.
  • Arrow keys ↑ and ↓ move the network fore- and backwards.
  • Arrow keys ← and → rotate the network scene around its yaw axis.
  • Page up and down keys rotate the network scene around its pitch axis.
  • + and - keys can be used to zoom in and out.
  • Key "u" moves the camera up and "d" moves it down.
The ThermoVis toolbar contains a "Home" button. By pressing this button, the scene and camera positions are reset to their respective home position.

Mouse & Key Navigation
Mouse & Key Navigation

1.2.3. Displaying Different Networks Types

The component view on the left side shows the different types of graph that can be visualized with CumoVis:
  • "Cumomer Cascade"
  • "Isotopomer Graph"
  • "Atom Transition Graph"
  • "Metabolic Network"
By clicking on Atom Transition Graph, the network of the atom mappings is visualized on top of the metabolic network. In order to reduce the complexity of the visual impression, you can optionally hide the underlying metabolic layer. Therefore, uncheck the corresponding checkbox on bottom of the component view.

Atomic layer
Atomic layer


CumoVis visualizes the atom mappings by showing individual items for the single atoms. Their connections show how the atom is transported in the biochemical reaction:

Atom mapping in CumoVis (cf. biocemical reaction above)
Atom mapping in CumoVis (cf. biocemical reaction above)


In order to view the isotopomer network and cumomer cascade click on the corresponding entries in the component view. The internal model of the cumomer and isotopomer network is only generated on demand because depending on the network size it can be very memory and runtime expensive. Thus, CumoVis will ask you to confirm loading the cumomer / isotopomer network.

Isotopomer network (a) and cumomer cascade (b)
Isotopomer network (a) and cumomer cascade (b)


The nodes in the atomix layer, isotopomer network as well as cumomer levels do not display the metabolite name by default. However, you can cause the metabolite name of individual items to be displayed by moving the mouse curser over the corresponding item in the scene.

1.2.4. Visual Network Decomposition

The "Atom Transition Graph" item in the component view contains child elements for the subgraphs (CCs) of the network. Furthermore, the subgraph items contain child elements for the cyclic subgraphs (SCCs). By clicking on a subgraph or cyclic subgraph item, the corresponding nodes and edges are displayed while all others disappear.

Cyclic subgraph of the atomic layer
Cyclic subgraph of the atomic layer


The "Cumomer Cascade" item contains one child element for each weight level of the cascade. By clicking on a weight level item, only the selected weight level is displayed in the scene.

Weight level 2 of a cumomer cascade. The visualization shows the transport of all posible fragments with two labeled atoms.
Weight level 2 of a cumomer cascade. The visualization shows the transport of all posible fragments with two labeled atoms.


For the isotopomer network, no network decomposition is provided.

1.2.5. Path Tracing

CumoVis allows to trace individual atoms or groups of atoms through the network. Therefore, press the button "Start Path Tracing". Subsequently, the following dialog appears:

Specifying path tracing source node
Specifying path tracing source node


Here, you have to specify the start metabolite and select the atoms to be traced (start isotopomer). You have to select at lease one atom position up to all available positions. After confirming the dialog, a second dialog appears where you have to configure the path tracing:

Configuring path tracing
Configuring path tracing


Here, you have following options:
  • Target - If you speficy a target isotopomer CumoVis searchs for all possible paths between the start and end node through the network.
  • Maximal Depth - Since path tracing is a extreme complex computational task highly depending on the network size, the maximal depth restricts the search to the environment of the start isotopomer. Take a small maximal depth and increase it iteratively.
  • Tracing - You have the coice betreen path tracing on the cumomer weight level or in the isotopomer network. If you select weight level, the path tracing does not include paths where weight is lost or fragments are recombined.
  • "Atom specific" - means that each individual atom of the start node is color coded and the successor nodes display the colors of the source atom.
  • "Direction" - you can decide to perform path tracing in forward as well as in backward direction. Furthermore, you can decide if reversible reactions are traced in both directions or if only their nominal direction is taken into account.
After configuring the path tracing the process is started and finally the search result is displayed in the scene. Initially, only the start isotopomer is displayed. The toolbar at the bottom of the window provides functionality to manage the path tracing result:

Path tracing toolbar
Path tracing toolbar


The path tracing result usually consists of a certain number of paths through the network. On the left side of the toolbar you find a spinbox where you can select the currently displayed path. By pressing the "Shortest" button you can restrict the available paths to the shortest ones (usually multiple). By pressing the "Longest" button the longest paths are shown. By pressing "Show all" all paths are displayed simultaneously.

Furhermore, the displayed path depth can be specified. This is initially 1 which causes only the start node to be displayed. The slider in the center of the toolbar can be used in order to manually specify the path depth. Furthermore, you can customize the number of simultaneously displayed path subsections by changing the length in the spinbox (center).

The media-player-like controls allow to visualize the path tracing as animation.

The path tracing results can be saved as CSV file in list or matrix form.

By pressing "Continue" you can perform another path tracing step at the end of the paths of the current path tracinf result.

1.2.6. Configuring CumoVis

Several configurations of CumoVis can be changed. Therefore, select the configure button on the uller toolbar.

CumoVis configuration dialog
CumoVis configuration dialog


In the subsequently appearing configuration window you can specify following program settings:
  • Coordinate scale - specify a scale factor which is applied to the coordinates taken from the Omix diagram layout. This option is useful if the distance of the metabolite items is too high or low.
  • Edge shape resolution - the shape of the connecting edges is the most expensive part of the 3D scene. In order to improve memory and runtime performance reduce the resolution. In order to get better visual results increase it.
  • Chemical structures - you can force CumoVis not to display chemical structures but to use the tube-like shapes instead.
  • Item fonts - you can customize the font of metabolites and reactions.

1.2.7. Image and Animation Export

You can export the current view of the scene to image in PNG, JPG or GIF format (see image export button on the upper toolbar). Furthermore, you can select to continually save the visualization to image files. This image series can later be rendered to video file with corresponding video applications (external).

1.3. Further Reading

  • 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 66:69–85
  • Wiechert W, Wurzel M (2001) Metabolic isotopomer labeling systems. Part I: Global dynamic behaviour. Math Biosci 169:173–205
  • Weitzel, M., Wiechert, W., and Nöh, K. 2007. The topology of metabolic isotope labeling networks. BMC Bioinformatics, 8 (1), 315.
  • Nöh, K., Weitzel, M., and Wiechert, W. 2008. From Isotope Labeling Patterns to Metabolic Flux Rates. In U. H. E. Hansmann, J. H. Meinke, S. Mohanty, W. Nadler, and O. Zimmermann (Eds.) From Computational Biophysics to Systems Biology (CBSB08), vol. 40 of NIC Series, (pp. 345–348).
  • Droste, P., Weitzel, M., and Wiechert, W. 2008b. Visual Exloration of Isotope Labeling Networks in 3D. Bioprocess and Biosystems Engineering, 31 (3), 227–239.