13th International Conference on Membrane Computing - MTA Sztaki

An analysis of correlative and quantitative causality in P systems
series Gluc6P and F ruc6P being direct causes for AT P and AMP (recall that
r F ruc6P,AT P = r Gluc6P,AT P ) and to AT P being directly correlated with AMP .
5.2 The Signal Transduction Cascades
Cyclic motifs are extremely common in biochemical networks. They can be
found in metabolic, genetic, and particularly signaling pathways. These motifs
are often composed in order to form a vertical signaling cascade, which have
been used in [8] to model the mitotic oscillator in early amphibian embryos involving
cyclin and cdc2 kinase, Figure 5. Cyclin is synthesized at a constant rate,
v i , and triggers, in a first cycle, the transformation of inactive (i.e., phosphorylated),
m + , into active, m (i.e., dephosphorylated), cdcd2 kinase by enhancing
the rate of a phosphatase. A kinase reverts this modification by allowing the
transformation from m to m + . In the second cascade cycle, cdc2 kinase drives
the transformation from the inactive, x + , into the active, x, form of a protease
which degrades the cyclin. This second cycle is closed by a reaction regulated by
a protease, which elicits the transition from x to x + . The constants V i , 1 ≤ i ≤ 4,
represent the kinetics of the enzyme involved in the two cycles of post-translation
modification. The dynamics of this model, obtained by a numerical solution of
Fig. 5. The Goldbter’s cascade model for mitotic oscillation in early amphibian embryos
[8].
the set of differential equations proposed in [8], considering the initial conditions
c = 0.01µM and m = x = 0.01, shows an oscillatory behaviour in the activation
of the three model’s substances, that repeatedly go through a state in which
cells enter in a mitotic cycle. We sampled the dynamics with τ = 1 minute to
obtain 100 macro observation of the substances’ dynamics. After that, we studied
correlative causality among the substances. As it was expected, since in a
cyclic motif the concentration of species activated by a stimulus have a constant
amount, we obtained that both ρ(m + , m) and ρ(m + , m) are approximately equal
to −1, and both |ρ Call (m + , m)| and |ρ Call (m + , m)| are above 0.2. Moreover, we
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