Abstract
In biological regulatory networks represented in terms of signed, directed graphs, topological motifs such as circuits are known to play key dynamical roles. After reviewing established results on the roles of simple motifs, we present novel results on the dynamical impact of the addition of a short-cut in a regulatory circuit. More precisely, based on a Boolean formalisation of regulatory graphs, we provide complete descriptions of the discrete dynamics of particular motifs, under the synchronous and asynchronous updating schemes. These motifs are made of a circuit of arbitrary length, combining positive and negative interactions in any sequence, and are including a short-cut, and hence a smaller embedded circuit.
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Notes
- 1.
Classical terms of graph theory can be found in [3]. Moreover, we use here the following terminology:
- Isolated (elementary) circuit::
-
a connected directed graph with every vertex of in-degree and out-degree equal to 1;
- Circuit: :
-
a subgraph of a regulatory graph amounting to an isolated circuit;
- Flower-graph::
-
group of circuits sharing one single vertex;
- Chorded circuit::
-
circuit with a chord, possibly a self-loop;
- Cycle::
-
a subgraph of a state transition graph amounting to an isolated circuit.
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Remy, E., Mossé, B., Thieffry, D. (2016). Boolean Dynamics of Compound Regulatory circuits. In: Rogato, A., Zazzu, V., Guarracino, M. (eds) Dynamics of Mathematical Models in Biology . Springer, Cham. https://doi.org/10.1007/978-3-319-45723-9_4
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