Conservation Analysis for Large Models

Information Provided by Ravi Rao

Update: (5 Dec 2005): This work is now available as a paper, and can be obtained from the Advance Access section of Bioinformatics (See Link: doi:10.1093/bioinformatics/bti800).

Models of biochemical networks are indicative of the complexity of the system represented. Often, the size of such models tends to increase as more data becomes known and the scope of the model is enhanced. This is even true of models that are built by combining smaller networks. Conservation analysis of such large networks using current set of tools is likely to be fraught with numerical error. This is due to the numerical instability of methods such as Gaussian Elimination (for e.g. used in Jarnac) and LU Decomposition (COPASI; PySCeS). We have developed a new algorithm that is robust for computing the conserved cycles of large systems. This method makes use of the Householder QR factorization to generate the correct conserved cycles.

In the following, four examples are used to show the capability of this method. The robustness and performance of this method is also compared with those used by other tools. These four examples include

1. iCS291 - H. pylori: 396 Species, 381 Reactions (xls, SBML, Jarnac, PySCeS) Ref: Schilling, C. H., et al., J. Bacteriology, 184(16): pp. 4582-4593 (2002).
2. iJE660a - E. coli: 537 Species, 739 Reactions (xls, SBML, Jarnac, PySCeS).
3. iJR904 - E. coli: 764 Species, 931 Reactions (xls, SBML, Jarnac, PySCeS) Ref: Reed, J. L., et al., Genome Biology, 4(9): pp. R54.1-R54.12 (2003).
4. iND750 - S. cerevisiae: 1072 Species, 1149 Reactions (xls, SBML, Jarnac, PySCeS) Ref: Duarte, N.C., et al., Genome Research, 14 (7), 1298-1309.

The SBML models were built using the Excel spread sheet versions developed by the Systems Biology Group at the University of California, San Diego (see In silico Organisms). The reactions comprising the network were extracted from the Excel spread sheets and used to build a Jarnac file. This Jarnac file was then used to generate the SBML file to be used by our conservation analysis algorithm. We are thankful to Brett Olivier for generating the equivalent PyCSeS formats for two of the models - iJR904 and iND750. (For the other two models, the PyCSeS format was generated by using a script written in PERL. A similar script was written to produce the Jarnac file as well. The PERL script reads the Excel file, after it has been saved as a tab-delimited file and parses the reaction information to build the equivalent Jarnac or Pysces files. These are two bare-bones PERL scripts - build_jarnac.pl and build_pysces.pl - with no documentation, so please contact me if you are interested in using them - and I will email instructions on using them. Please note that the scripts do not handle all special characters in the reactions and reaction names - so the generated scripts have to be checked to eliminate errors).

The results from conservation analysis on these models are listed below. These are saved in files that can be seen or downloaded following the links for each model. The results from our algorithm (Householder QR) are named as modelname_QR.txt while that for our implementation of the LU factorization are named as modelname_LU.txt. Results from Jarnac are given by modelname_JN.txt and those from PySCeS are given as modelname_PY.txt. (note that COPASI results are available as text files as the results could only be viewed, but not saved). The conservation laws obtained from each of these models are in bold letters.

Here is a picture of a part of the large network iJE660a showing the complexity involved. (Thanks to Anastasia Deckard for generating a PS file for the whole network) We will try to have similar images of the other large networks in near future.

Simulation Times (in seconds) - 10 Runs