13th International Conference on Membrane Computing - MTA Sztaki

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
with appropriate reaction kinetics. From now on, we call them core oscillators.
They have in common that the chemical concentration course of one or more
dedicated species over time symbolises the oscillation. The reactions and kinetic
parameterisation forming a core oscillator are assumed to be fixed. This comes
along with the observation that the genetic template composing a core oscillator
is often highly conserved against mutations to keep its oscillatory function.
In addition to core oscillators, a collection of reaction network motifs has
been identified which allows a dedicated conversion, modification, and combination
of oscillatory signals for postprocessing purposes. In this context, a simple
linear reaction cascade can act as a low-pass filter. At the same time, it is able
to convert spiking or plated oscillations into an almost sinusoidal shape. Vice
versa, a mutually entwined scheme of catalysed reactions whose products catalyse
the reactions of the next stage embodies a binary signal separator. This unit
succeeds in conversion of sinusoidal or spiking signals into a plated oscillation.
A chemical differentiator employed on plated oscillations generates spikes while
an exponentiation of sinusoidal signals has the same effect. Finally, catalysts
operating in concert can emulate switches and logic gates [15].
Our recent studies on generators and processing units for oscillatory signals
in terms of biological computations led to a comprehensive collection of reaction
networks, each of them individually formalised using appropriate P systems
or ordinary differential equations, and analysed by means of simulation studies.
What we intend to explore next is the interplay of those units towards new
or improved phenomena. Hence, we aim at an assembly of reaction units on
the fly. This objective has been flanked by the idea of an higher-level evolution
which “plays” with different compositions of reaction units leaving intact
the units themselves. Individual units interact via shared species as described
in [16] using non-probabilistic P modules. The general concept of P systems
provides an excellent formalism to capture dynamical structures especially concerning
reaction networks. Thus, we are going to employ this framework to trace
the recombination as well as the exchange of reaction units towards more complex
behavioural patterns. To this end, we introduce a corresponding P meta
framework that compiles an evolutionary program by assembly and subsequent
exchange of reaction units taken from an initial pool.
In Section 2, we familiarise the reader with all denotational and formal prerequisites
of our P meta framework for P system mediated assembly of nonprobabilistic
P modules which in turn define core oscillators and selected postprocessing
units. Section 3 is dedicated to our first application study inspired by
the synchronous life cycle of cicadas. It is based on a chemical reaction model of
a binary counter modulo 17. This initial model comprises three units: a spiking
core oscillator (Brusselator, [1, 28]), a binary signal separator, and a logical unit.
In its original form, the entire model acts as a frequency divider 1:17. In a first
scenario, we remove the binary signal separator. Afterwards, we just exchange
the Brusselator by the Goodwin oscillator (configurable to be plated or almost
sinusoidal, [12]) and by the Repressilator (configurable to be almost sinusoidal
or plated, [9]). Please note that we do not modify the logical unit. Interestingly,
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