Nd logical parameters was implemented in the software GINsim (Naldi et al., 2009) (see Supplementary File two). This logical regulatory graph was then converted into Petri net framework using the export choice offered in GINsim. The exported standard Petri net was converted into Timed Continuous Petri net employing the software Snoopy (Heiner et al., 2012). This Petri net was modified by assigning rates and delays to transitions determined by biological observations (see Supplementary File 1).Hassan et al. (2018), PeerJ, DOI ten.7717/peerj.6/FigureThe workflow employed within this study. Full-size DOI: 10.7717/peerj.4877/fig-Hassan et al. (2018), PeerJ, DOI ten.7717/peerj.7/Figure four A toy BRN with two entities X and Y , where X is activating Y (shown by the edge labeled with +1) and Y inhibiting X (shown by an edge labeled with -1). Full-size DOI: ten.7717/peerj.4877/fig-RenThomas’ logical formalismIn the late 1970s, RenThomas presented kinetic logic Phortress Technical Information formalism for qualitative modeling of Biological Regulatory Networks (BRNs) (Thomas, 1991). This graph based formalism has its benefits over other boolean formalisms due its ability to permit interaction threshold levels above “1”. It has been proved that Kinetic Logic can capture the the dynamics in equivalent way to differential equations, however, it keeps the method much less complex as a consequence of discretization (Thomas, 1991) of expression levels. Moreover, it permits asynchronous dynamics to model cyclic trajectories which was not probable within the synchronous boolean formalism (Kauffman, 1969; Inoue, 2011). Thomas’ formalism uses graph theory to model Biological Regulatory Networks (BRNs). The components of a BRN incorporate entities plus the interactions amongst them. The expressions of an entity are shown by discrete levels and their interactions are threshold dependent, i.e., after the threshold is reached the interaction can requires location (see Fig. 4). The Fenobucarb medchemexpress semantics of Kinetic Logic Formalism is depending on Graph Theory. We adopt the semantics of this formalism from various studies (Ahmad et al., 2012; Bernot et al., 2004; Thomas, 2013; Ahmad et al., 2006). Definition 1 (Directed Graph): A graph G = (V ,E) is actually a tuple exactly where: V represents the set of vertices E V V represents the set of edges (ordered pairs of vertices). Definition two (Biological Regulatory Network): A biological regulatory network is usually a labeled directed graph G(V ,E) exactly where V will be the set of biological entities and E V V may be the ordered set of directed interactions among them. Each edge (vi , vj ) includes a pair (l,tvi ,vj ) as its label exactly where l is the sign of interaction (`+’ for activation and `-‘ for inhibition) and tvi ,vj 1,2,…,rvi could be the threshold of the interaction where rvi is much less than or equal for the out-degree of vi . All edges of a BRN are labeled in line with the threshold level and kind of interaction (as an instance see Fig. 4). The resources of an entity will depend on the presence and absence of its activators or inhibitors at any instant of time. In Fig. four, when X = 1 then it truly is the resource of Y and when Y = 0 then it truly is the resource of X (the absence of inhibitor is treated as a resource). The discrete expression levels of an entity is the set containing the integers 0 toHassan et al. (2018), PeerJ, DOI ten.7717/peerj.8/its highest threshold inside the BRN. By way of example, the expression levels of X and Y is the same set 0,1 as each have their highest thresholds equal to 1. A state of a BRN is an element from the Cartesian product in the sets of express.
