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Fig. 3.42
Gene-expression networks and MP graphs: co-promotion-inhibition and anti-
promotion-inhibition
of an MP system approximate to differentials and EMA reduces to a numerical in-
tegration performed according to the Euler method [77]. However, when the time
interval cannot be approximated to an infinitesimal time, MP models introduce a
perspective which is radically different from the ODE perspective [83, 115], more
related to the transformations of the systems along observation steps, rather than
to the real kinetic of reactions, and to the chemo-physical mechanisms underlying
biochemical processes. However, the different perspective of MP systems has com-
putational and modeling advantages, by opening the possibility of algorithmic and
algebraic procedures for disclosing regulation logics of metabolic systems. Namely,
dynamical inverse problems can be solved (via the LGSS algorithm) and the math-
ematical form of regulators can be discovered in a systematical way.
In ODE models, and in stochastic models [80, 74, 51, 79] a critical point is con-
stituted by the evaluation of kinetic rates or stochastic parameters. This is a hard
and unreliable task, because very often the exact microscopic dynamics of reactions
is not completely known, or even when it can be completely studied in vitro, its in
vivo behavior could significantly differ from its experimental evidence.
