13th International Conference on Membrane Computing - MTA Sztaki

An analysis of correlative and quantitative causality in P systems
When we consider just one time-series, quantitative causality corresponds to
both direct correlation and to direct causality in the correlative causality framework.
For the case of several time-series considered together with multiplicities,
we need more data regarding the sets C xi and D xi to advance the correspondences
between correlative and quantitative causalities. A start towards establishing
such correspondences is made in the following section by analyzing two
case studies.
5 Case Studies
In this section we consider two examples which indicate how we can study in
a more general manner quantitative causality starting from correlative causality.
For the second one, we set 0.7 (a value indicating high correlation) as threshold
for correlations and cross-correlations, and 0.2 as threshold for partial correlations.
5.1 The Yeast Glycolytic Network
Glycolysis is at the heart of classical biochemistry and, as such, it has been
thoroughly studied. Glycolysis is the metabolic pathway that converts glucose
into pyruvate. The free energy released in this process is used to form the highenergy
compounds, ATP (adenosine triphosphate) and NADH (reduced nicotinamide
adenine dinucleotide). It is a definite sequence of ten reactions involving
several intermediate compounds. The intermediates provide entry points to glycolysis.
For example, most monosaccharides, such as fructose, glucose, and galactose,
can be converted to one of these intermediates. The intermediates may also
be directly useful. For instance, the intermediate dihydroxyacetone phosphate is
a source of the glycerol that combines with fatty acids to form fat.
We applied our framework on the first reactions from the upper part of
glycolysis pathway of Saccharomyces cerevisiae. These reactions represent the
pathway which leads to the degradation of glucose in order to yield energy
and building blocks for cellular processes. In [14], this pathway, as well as
the reactions balancing the energy currency ATP and ADP, have been translated
into a Metabolic P system 3 . This formulation provided us dynamics
in accordance with experimental values observed in [19] and differential models
developed in [9]. Starting from these dynamics, we applied the correlative
framework to infer a set R of rules modelling statistical causality associated
with the glycolisis pathway. Entering into the details, we have a set of species
X = {F ruc6P, Gluc6P, F ruc16P 2, AMP, AT P, ADP } having the following directed
correlation sets: C F ruc6P = {Gluc6P, F ruc16P 2}, C Gluc6P = {F ruc6P },
C F ruc16P 2 = {F ruc6P }, C AT P = {AMP }, C AMP = {AT P }, C ADP = ∅.
Moreover, we inferred the following sets expressing cause-effect relationships:
3 Metabolic P systems [12] are a class of deterministic P systems introduced for expressing
biological phenomena.
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