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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.

Show MeSH
Fragment enumeration for double-layer MAPK mechanism. Number of fragments of different orders generated for the double-layer MAPK network (i) combinatorially (gray) and (ii) generated from the unique correspondence between fragments and edges-only subgraphs (black).
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Figure 4: Fragment enumeration for double-layer MAPK mechanism. Number of fragments of different orders generated for the double-layer MAPK network (i) combinatorially (gray) and (ii) generated from the unique correspondence between fragments and edges-only subgraphs (black).

Mentions: By using the method of one-to-one correspondence between fragments and subgraphs consisting of edges, we reduce the number of fragments generated by the combinatorial approach by multiple orders of magnitude. A reduction in the number of the generated fragments translates directly to a reduction in computational cost. Hence the latter approach for fragment generation is an important development in the implementation of GraTeLPy that allows for analyzing larger biochemical mechanisms. To highlight this reduction in computational cost we plot the number of fragments (of varying order) generated with both methods for the double-layer mitogen-activated protein kinase (MAPK) mechanism in Figure 4. The double-layer MAPK mechanism is discussed in more detail in the last example in Section Results and discussion.


GraTeLPy: graph-theoretic linear stability analysis.

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

Fragment enumeration for double-layer MAPK mechanism. Number of fragments of different orders generated for the double-layer MAPK network (i) combinatorially (gray) and (ii) generated from the unique correspondence between fragments and edges-only subgraphs (black).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Fragment enumeration for double-layer MAPK mechanism. Number of fragments of different orders generated for the double-layer MAPK network (i) combinatorially (gray) and (ii) generated from the unique correspondence between fragments and edges-only subgraphs (black).
Mentions: By using the method of one-to-one correspondence between fragments and subgraphs consisting of edges, we reduce the number of fragments generated by the combinatorial approach by multiple orders of magnitude. A reduction in the number of the generated fragments translates directly to a reduction in computational cost. Hence the latter approach for fragment generation is an important development in the implementation of GraTeLPy that allows for analyzing larger biochemical mechanisms. To highlight this reduction in computational cost we plot the number of fragments (of varying order) generated with both methods for the double-layer mitogen-activated protein kinase (MAPK) mechanism in Figure 4. The double-layer MAPK mechanism is discussed in more detail in the last example in Section Results and discussion.

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