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
of those signals in parallel which enables astonishing capabilities and complex
response towards an evolutionary advantage.
A fascinating example in this context is given by cicadas, insects of the species
Magicicada. Populations in northern America share a synchronous life cycle of 17
years while those in central America prefer 13 years [20]. Most of its existence is
spent underground in a dormant state. Shortly before the end of the life cycle, all
the adults of a brood emerge at roughly the same time to reproduce for several
weeks. After laying their eggs, the adults die off and the cycle begins again.
What stands out is that 17 and 13 are prime numbers, which ensures that the
reproduction period does not coincide with the life cycles of potential predators.
The simultaneous mass awakening of a brood also ensures that predators are
overwhelmed by the number of cicadas so that a large number can survive. In
order to guarantee a concerted awakening of all members of a brood, the species
needs a precise molecular mechanism to measure the passage of the appropriate
amount of time. Since it seems that there is no external stimulus with a natural
period of 13 or 17 years, its exact estimation exclusively based on annual or even
shorter cycles becomes a complicated task [27]. Furthermore, it is worthwhile
toknowwhetherornotalow number of slight evolutionary changes within
the molecular mechanism is sufficient to toggle the life cycle between a variety
of years. Having this feature at hand, it becomes plausible how a widespread
range of life times could emerge where those forming prime numbers resist the
evolutionary selection driven by predators.
Complementary to the frequency, also the waveform of oscillatory signals can
contain crucial information that might help organisms to optimise their response
or adaptation regarding relevant environmental stimuli. Most of the biological
rhythms studied so far are characterised by one out of three types of oscillatory
waveforms. Sinusoidal or almost sinusoidal signal courses enable a gradual and
smooth alteration such that the transfer between minimal and maximal signal
levels consumes a notable amount of time. Commonly, a sinusoidal oscillation
passes a stable limit cycle which acts as an attractor. This makes the oscillator
quite robust against perturbations affecting the signal course. In contrast, spiking
signals are a good choice to exhibit triggers. They can be outlined by an intensive
signal peak active for a short moment followed by a quiet course close to zero for
a much longer duration. The fast raise or fall of the signal value might be easy
to detect for subsequent processing units. Remarkably, the average signal value
can be kept low which might imply a reduced amount of energy necessary to
sustain the oscillation. Contrary to sinusoidal signals, addition of phase-shifted
isofrequential spiking oscillations can induce higher frequential overall oscillations
in terms of an effective signal amplification. Furthermore, plated signal
courses reflect a more or less bistable oscillatory behaviour. Here, the waveform
over time resembles an almost rectangular shape similar to a binary clock signal.
Plated oscillations combine the advantage of fast toggling with the ability for a
balanced or weightable ratio between high-level and low-level signal values. To
each of all three waveform types, corresponding oscillators can be assigned just
by consideration of small or medium-sized chemical reaction networks together
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