13th International Conference on Membrane Computing - MTA Sztaki

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
see Figure 10. Obviously, the reaction network attempts to calculate the next
step but is unable to do so in time for the next count. This effect preserves for
any rate constant k0.9, there
is no restriction in the frequency divider’s functionality.
Finally, let us return to the life
cycle of periodical cicadas which
gave the crucial inspiration for our
studies. We are aware that the
mechanisms evolved in this life
form are most probably far away
from a binary counter modulo 17.
Up to now, we failed in retrieving
any scientific publication on potential
or even verified mechanisms. A
more or less speculative hypothesis
aims at a combination of two processes,
a slow growth on the one
hand and a threshold on the other.
Growth means a successive accumulation
of a dedicated species. As
soon as its concentration exceeds
T
1 B
concentration (a.u.)
1
0.8
0.6
0.4
0.2
C
0
0 1000 2000 3000 4000 5000
time (a.u.)
Fig. 10. Dynamical behaviour of the original
frequency divider model 1:17 after slowing
down all reactions within the logical unit for
one order of magnitude
an inherently set threshold, the finalisation of the life cycle is initialised indicating
the elapsed amount of 17 years. A successive accumulation organised for
instance in annual cycles is useful for a high precision. To this end, a core oscillator
could provide an annually altering signal of the form a +sin(bt) subject to
time t. A simple signal integration then produces a temporal course of the form
at + c · sin(bt + d) with a successive, staircase-shaped growth. Nevertheless, this
strategy is more prone to premature or late alert than an n-ary counter.
4 Core Oscillator’s Interplay in Suprachiasmatic Nucleus
A second application study is intended to demonstrate in brief the descriptional
capacity of our P meta framework. Let us consider the suprachiasmatic nucleus,
a region of the human brain, in which each neuron comprises a core oscillator
for generation of a circadian rhythm characterised by a controllable period close
to 24 hours. A cyclic gene regulatory network consisting of 10 molecular species
and 18 reactions including an inhibitory negative feedback forms this core oscillator
whose dynamical behaviour had been formalised via specific ODEs based
on mass-action and second-order Hill kinetics. For a full description, we refer
to [3]. The neuronal core oscillators within the suprachiasmatic nucleus appear
to be hierarchically organised in several layers. A small group of independently
oscillating neurons constitutes the so-called master-clock layer. Neurons in down-
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