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Fig. 1 | BMC Systems Biology

Fig. 1

From: Stochastic simulation of Boolean rxncon models: towards quantitative analysis of large signaling networks

Fig. 1

Principles of the rxncon formalism and the bipartite Boolean modeling. a Bipartite Boolean modeling based on rxncon format. Two protein-protein interactions between B and C (B_ppi_C), and between A and B (A_ppi_B), produce the B--C and A--B complexes, respectively. Note that these complexes are not mutually exclusive. Instead, they correspond to all complexes containing B & C and A & B. The trimeric A-B-C complex corresponds to the intersection between these two sets. The symbol “*=” means that the value of left side at time t + 1 will be equal to the value of right side at time t. b In a specific state description, these reactions translate into a network with three possible complexes (AB, BC and ABC) and four different reactions. Hence, the elemental reactions in (a) are generic statements that map to several distinct specific reactions in (b). If the specific reactions corresponding to a single elemental reaction occur with different rates, then the elemental reaction is contingent on one or more of elemental states. There are six such possible contingencies (c); absolute requirement (A_ppi_B; ! B--C)(corresponding to rate k_re1 = 0 in (B)); positive effect (K+)(k_re1 < k_re2 in (B)); neutral (0)(k_re1 = k_re2 in (B)); negative (K-)(k_re1 > k_re2 in (B)) and absolutely inhibitory (x)(k_re2 = 0 in (B)). Unknown effects (?) are treated as neutral. In a qualitative Boolean model, only absolute requirements or inhibitions affect the update functions, while the probabilistic model can account also for the quantitative modifiers (K+/K-), as can be seen in the direct comparison between the two model formats c: In this table, protein-protein interaction B_ppi_C is omitted. The false rules (blue lines in red box) correspond to noise in biological systems, and can be set to any value between 0 (no noise) and 1 (no signal). The second Boolean functions in the rows “A_ppi_B; K+ B--C” and “A_ppi_B; K- B--C” (red lines) only appear in the probabilistic model, allowing it to account for quantitative modifiers (K+/K-), which was not possible with the qualitative version. In the probabilistic Boolean modeling, one of the Boolean functions is chosen randomly at each time step according to the probability assigned to it

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