13th International Conference on Membrane Computing - MTA Sztaki

Maintenance of chronobiological information by P system mediated assembly
of control units for oscillatory waveforms and frequency
these slight modifications are sufficient to obtain frequency dividers 1:3, 1:5, and
1:6. Section 4 deals with a second application study. Here, we focus on the almost
sinusoidal core oscillator found in the suprachiasmatic nucleus. We arrange
an initial setting of 12 core oscillator instances within four layers. Core oscillators
placed in adjacent layers are unidirectionally coupled releasing their signals
downstream. In this scenario, we estimate the quality of synchronisation taken
in the final layer subject to the top level oscillator’s phase differences. Then, we
add two auxiliary core oscillators. It turns out that this action – just managed
by replication of two core oscillators and their connectivity – stabilizes the entire
system and contributes to an improved signal quality.
2 A P Meta Framework Capturing Assembly of
Non-probabilistic P Modules
In [16], we introduced the term of non-probabilistic P modules complementary
to other forms [25] and in accordance with the notion of modules in systems biology.
Each non-probabilistic P module represents a container encapsulating an
explicite specification of the dynamical behaviour of a reaction unit based on a
deterministic scheme like discretised reaction kinetics or event-driven methods.
In addition to the inherent dynamical behaviour, a non-probabilistic P module
defines its interface by dedicated input and output species whose temporal
concentration or abundance courses reflect the data managed by the reaction
unit. Interacting non-probabilistic P modules communicate via shared molecular
species. We define a non-probabilistic P module by a triple
π =(π ↓ ,π ↑ ,π □ )
where π ↓ = {I 1 ,...,I i } indicates a finite set of input signal identifiers, π ↑ =
{O 1 ,...,O o } a finite set of output signal identifiers, and π □ the underlying system
specification processing the input signals and producing the output signals
with or without usage of auxiliary inherent signals not mentioned in the interface.
Each signal is assumed to represent a real-valued temporal course, hence a
specific function σ : R ≥0 −→ R (R ≥0 : non-negative real numbers).
A collection of prototypic specification examples subsumed by nonprobabilistic
P modules might include:
– metabolic P systems, for instance of the form
M =(X, R, V, H, Φ, ν, μ, τ), cf. [4, 10, 19]
– P systems for cell signalling modules (CSM) of the form
Π CSM =(V,V ′ ,R 1 ,...,R r , f 1 ,...,f r ,A,C,Δτ), cf. [14]
– P systems for cell signalling networks (CSN) of the form
Π CSN =(V,V ′ ,E,M,n), cf. [13]
– ordinary differential equations (ODEs) in conjunction with an appropriate
numerical solver. The ODEs should be derived from reaction or diffusion
kinetics, cf. [8].
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