13th International Conference on Membrane Computing - MTA Sztaki

R. Pagliarini, O. Agrigoroaiei, G. Ciobanu, V. Manca
data-sets can be useful to infer causality interactions. With the term causality,
we intend that the analysis of interactions establishes a directional pattern
in which species action may trigger or suppress and be triggered or suppressed
by the actions of other species in the network. Although this causal
connectivity alone is not sufficient to fully describe the dynamics of a network,
it reveals the logic of the systems which constraints its potential behaviour.
In more detail, a direct causal relationship x 1 → x 2 implies that the timeseries
of x 1 “influences” the time-series of x 2 . An indirect causal relationship
x 1 → x i1 → x i2 → . . . → x ik → x 2 is a link from x 1 to x 2 through a sequence of
direct casual relationships involving a set of one or more intermediates species
x i1 , x i2 , . . . x ik .
Usually, cell biologists use perturbations to prove the existence of cause-effect
relationships in biological pathways. An interesting hypothesis is that biological
networks constitute dynamical systems which are continuously subjects to
fluctuations and oscillations due to changes in the environment as well as to
patterns of regulations [17,18]. Dynamics changes induce variability in species
concentrations, propagate through the networks and generate emergent patterns
of time-lagged correlations. Therefore time-lags are ubiquitous in biological systems.
As a simple example, Figure 4 shows an experimental result in which a
time delay τ 1 between two genes is present. This implies that biological network
topologies, and then causality, involve many interlocked network motifs which
have inherent delays.
Fig. 4. A gene expression experimental result where time lag τ 1 could be an indication
of an underlying cascade of biochemical reactions.
Then, if we conduce computational experiments which allow the comparison
of shifted behaviours, it could be possible to identify directed causal-effect relationships
between time-series. This is rooted on the fact that time indicates
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