Supporting and supplemental information for the paper "Unruly Motifs - No Convergent Evolution of Network Topologies"

Schematic Protein / Genome / Environment interaction of differentiated cells.
On this web page you will find supporting information for the paper "Unruly Motifs - No Convergent Evolution of Network Topologies". The commented, full Java source code will be made available as well as results of newer experiments. There is an extended version of this article now, please look at that paper resp. webpage for newest results.

What is in the paper?
Abstract   Methods that analyse the topological structure of networks have recently become quite popular. Whether motifs, subgraph patterns that occur more often than in randomized networks, have specific functions as elementary computational circuits has been cause for debate. As the question can not be resolved with currently available biological data we elucidate the issue using networks that abstractly model natural Genetic Regulatory Networks (GRNs) which are evolved to show dynamical behaviors.
Specifically one group was evolved to show differentiation, i.e. to be able to perform an additional behavior as compared to the original, single target behavior. Comparing these GRNs we find motif distribution differences within the groups to be larger than differences between groups, indicating that evolutionary niches (target functions) do not necessarily mold network structure uniquely. These results suggest that variability operators can have a stronger influence on network topologies than selection pressures, especially when many topologies can create similar dynamics. When considering single networks only we do find significantly overrepresented motifs. Checking for their functional relevance by lesioning however renders them not more important than other parts of the network.

Network dynamics visualization with a Java Applet
Not as reliable as statistics, but gives you an impression of what the network structure looks like!
Please choose between five sample networks by selecting from the drop-down menu: 
The source code for this applet can be found in the section "Java code".

Java source code
Please feel free to download the full Java source code. Structuring of the code in quite a few classes has hopefully increased readability.
  • motifAnalysis.zip (188kb) - Java network analysis software as used for the analysis presented in the paper - Does not include data which you can generate yourself with the code provided here ("original") and here ("differentiation") or we can send you a DVD ;).
  • motifTools.zip - The code above is rather specific to the GRN model used here; this a more generic code version usable for all kinds of networks. Have a look at the README.txt included in the zip file (most important classes: network.java and main.java)!
  • netAppletLesionIndSource.zip (140kb) - Java Applet for visualizing network dynamics.
This software is distributed under the GNU General Public License (GNU GPL).

Additional results
Jump directly to a subsection:
  • Impact of lesioning; random damage vs most significant 3-node motif damaged after 500 generations and random damage vs most significant 4-node motif damaged after 1000 generations



    Average reduction in fitness when one edge in a network is removed for the original (left) and differentiated GRNs (right). In each pair, the diagonally striped bar shows the impact when any edge can be chosen while for the grid patterned bar an edge from the nets most significant network motif was removed. On average the differences are very small and the standard deviations huge.
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  • Distribution of THREE node motif patterns after generations 500, 750 and 1000




    Three groups ($N=80$ each) are compared: Original evolutionary setting for one task (light gray), evolved for differentiation (dark gray) and randomly evolved (medium gray). Only subgraph patterns that have more than the cut-off value of 0.5 occurences on average in at least one of the groups are shown.
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  • Distribution of FOUR node motif patterns after generations 500, 750 and 1000




    Three groups ($N=80$ each) are compared: Original evolutionary setting for one task (light gray), evolved for differentiation (dark gray) and randomly evolved (medium gray). Only subgraph patterns that have more than the cut-off value of 0.5 occurences on average in at least one of the groups are shown.
    go back to top of additional results section
    • Motif #7, sub-structure distribution after generation 1000 (not present above cut-off value before)


      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #13, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #22, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #31, sub-structure distribution after generation 1000 (not present above cut-off value before)


      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #37, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #38, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #45, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #73, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #74, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #75, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #82, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #89, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #90, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #91, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #105, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #109, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #211, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section
    • Motif #219, sub-structure distribution after generations 500, 750 and 1000




      light-gray: one function networks, dark-gray: two function networks, medium gray: randomly evolved networks
      go back to top of additional results section

Lookup tables mentioned in the paper
Due to space reasons we could only mention that the four bit decay rate per protein, the three bit saturation values and the four bit binding proportion parts of the genome are decoded by taking values from a lookup table. Here you find the arrays from our Java implementation (see code) used for generating the results reported in the paper: 
  
  public static double[] decayRates={0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.0,1.0,1.0,1.0,1.0,1.0}; //\in [0..1]
  public static double[] saturationValues={10,25,50,100,150,200,300,500};
  public static double[] bindingProportions={0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.0,1.0,1.0,1.0,1.0,1.0}; //\in [0..1]

Reference / Bibtex

Knabe, J. F., Nehaniv, C. L. and Schilstra, M. J. Unruly Motifs - No Convergent Evolution of Network Topologies. Submitted to IPCAT, 7th intl. Workshop on Information Processing In Cells and Tissues

Please cite the extended version of this article!


2006-10-30; University of Hertfordshire, Hatfield AL10 9AB, UK; Version 1.0
You might want to visit Johannes Knabe's homepage and other publications as well.