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GraTeLPy: graph-theoretic linear stability analysis.

Walther GR, Hartley M, Mincheva M - BMC Syst Biol (2014)

Bottom Line: GraTeLPy lists all critical fragments of the bipartite digraph of a given biochemical mechanism, thus enabling a preliminary analysis on the potential of a biochemical mechanism for some instability based on its topological structure.The correctness of the implementation is supported by multiple examples.The code is implemented in Python, relies on open software, and is available under the GNU General Public License.

View Article: PubMed Central - HTML - PubMed

Affiliation: Computational and Systems Biology, John Innes Centre, Norwich Research Park, Norwich, UK. gratelpy@gmail.com.

ABSTRACT

Background: A biochemical mechanism with mass action kinetics can be represented as a directed bipartite graph (bipartite digraph), and modeled by a system of differential equations. If the differential equations (DE) model can give rise to some instability such as multistability or Turing instability, then the bipartite digraph contains a structure referred to as a critical fragment. In some cases the existence of a critical fragment indicates that the DE model can display oscillations for some parameter values. We have implemented a graph-theoretic method that identifies the critical fragments of the bipartite digraph of a biochemical mechanism.

Results: GraTeLPy lists all critical fragments of the bipartite digraph of a given biochemical mechanism, thus enabling a preliminary analysis on the potential of a biochemical mechanism for some instability based on its topological structure. The correctness of the implementation is supported by multiple examples. The code is implemented in Python, relies on open software, and is available under the GNU General Public License.

Conclusions: GraTeLPy can be used by researchers to test large biochemical mechanisms with mass action kinetics for their capacity for multistability, oscillations and Turing instability.

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Critical fragments of the yeast Cdc42 mechanism. Critical fragments of order 5 of the yeast Cdc42 network reported in [32] and reproduced by GraTeLPy.
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Figure 10: Critical fragments of the yeast Cdc42 mechanism. Critical fragments of order 5 of the yeast Cdc42 network reported in [32] and reproduced by GraTeLPy.

Mentions: The bipartite digraph of the Cdc42 network is shown in Figure 9. The Cdc42 network has a corresponding stoichiometric matrix of rank 5. The necessary condition for Turing instability requires that a critical fragment of order 1≤k≤5 exists. GraTeLPy identifies 35 critical fragments – among which we find the two critical fragments reported in [32] and shown in Figure 10.


GraTeLPy: graph-theoretic linear stability analysis.

Walther GR, Hartley M, Mincheva M - BMC Syst Biol (2014)

Critical fragments of the yeast Cdc42 mechanism. Critical fragments of order 5 of the yeast Cdc42 network reported in [32] and reproduced by GraTeLPy.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4016541&req=5

Figure 10: Critical fragments of the yeast Cdc42 mechanism. Critical fragments of order 5 of the yeast Cdc42 network reported in [32] and reproduced by GraTeLPy.
Mentions: The bipartite digraph of the Cdc42 network is shown in Figure 9. The Cdc42 network has a corresponding stoichiometric matrix of rank 5. The necessary condition for Turing instability requires that a critical fragment of order 1≤k≤5 exists. GraTeLPy identifies 35 critical fragments – among which we find the two critical fragments reported in [32] and shown in Figure 10.

Bottom Line: GraTeLPy lists all critical fragments of the bipartite digraph of a given biochemical mechanism, thus enabling a preliminary analysis on the potential of a biochemical mechanism for some instability based on its topological structure.The correctness of the implementation is supported by multiple examples.The code is implemented in Python, relies on open software, and is available under the GNU General Public License.

View Article: PubMed Central - HTML - PubMed

Affiliation: Computational and Systems Biology, John Innes Centre, Norwich Research Park, Norwich, UK. gratelpy@gmail.com.

ABSTRACT

Background: A biochemical mechanism with mass action kinetics can be represented as a directed bipartite graph (bipartite digraph), and modeled by a system of differential equations. If the differential equations (DE) model can give rise to some instability such as multistability or Turing instability, then the bipartite digraph contains a structure referred to as a critical fragment. In some cases the existence of a critical fragment indicates that the DE model can display oscillations for some parameter values. We have implemented a graph-theoretic method that identifies the critical fragments of the bipartite digraph of a biochemical mechanism.

Results: GraTeLPy lists all critical fragments of the bipartite digraph of a given biochemical mechanism, thus enabling a preliminary analysis on the potential of a biochemical mechanism for some instability based on its topological structure. The correctness of the implementation is supported by multiple examples. The code is implemented in Python, relies on open software, and is available under the GNU General Public License.

Conclusions: GraTeLPy can be used by researchers to test large biochemical mechanisms with mass action kinetics for their capacity for multistability, oscillations and Turing instability.

Show MeSH