Enumeration and extension of non-equivalent deterministic update schedules in Boolean networks

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Motivation: Boolean networks (BNs) are commonly used to model genetic regulatory networks (GRNs). Due to the sensibility of the dynamical behavior to changes in the updating scheme (order in which the nodes of a network update their state values), it is increasingly common to use different updating rules in the modeling of GRNs to better capture an observed biological phenomenon and thus to obtain more realistic models.

In Aracena et al. equivalence classes of deterministic update schedules in BNs, that yield exactly the same dynamical behavior of the network, were defined according to a certain label function on the arcs of the interaction digraph defined for each scheme. Thus, the interaction digraph so labeled (update digraphs) encode the non-equivalent schemes.

Results: We address the problem of enumerating all non-equivalent deterministic update schedules of a given BN. First, we show that it is an intractable problem in general. To solve it, we first construct an algorithm that determines the set of update digraphs of a BN. For that, we use divide and conquer methodology based on the structural characteristics of the interaction digraph. Next, for each update digraph we determine a scheme associated. This algorithm also works in the case where there is a partial knowledge about the relative order of the updating of the states of the nodes. We exhibit some examples of how the algorithm works on some GRNs published in the literature.

Availability and implementation: An executable file of the UpdateLabel algorithm made in Java and the files with the outputs of the algorithms used with the GRNs are available at: www.inf.udec.cl/ ∼lilian/UDE/


Supplementary information: Supplementary data are available at Bioinformatics online.

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