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
seems that the resulting toggling process runs slightly more fragile than in the
Repressilator study. This becomes visible by a pronounced signal tuning, which
exhibits damped high frequential micro oscillations in conjunction with output
switch. Even several modifications of the experimental setup confirm this behaviour,
for instance a more distinctive transient oscillation of the Goodwin
module (shown in Figure 9) as well as doubling the rate constants from k =0.05
to k =0.1 within the Goodwin module. Again, the core oscillator continuably
disturbes the computation of the bits b ′ 1 up to b ′ 5.
repressilator[1]
brusselator[1]
separator[1]
B 2
T
4
C
goodwin[1]
C
mod17[1]
B T 1
T
B 2
T
B 3
T
B 4
T
B 5
0 0 1 1 0
0
1
1
1
1
0
1
0
1
0
concentration (a.u.)
3.5
3
2.5
2
1.5
1
0.5
0
0 200 400 600 800 1000 1200
time (a.u.)
Fig. 9. Dynamical behaviour of the frequency divider 1:3 obtained by replacing the
Brusselator with the Goodwin module in absence of the binary signal separator (left:
cycle of state transitions, right: counts together with divider output). Instead of B1 T ,
we depict B2
T as divider output due to its more precisely toggling nature.
3.6 Discussion
The experimental results indicate that an originally designed frequency divider
1:17 might change its behaviour revealing division ratios of 1:3, 1:5, and 1:6
just by slight rewiring of few interacting modules. By using a binary counter
approach modulo 17, we intentionally employed a pure synthetic reaction system
derived from standard concepts in engineering. Although, those systems tend to
be quite resistent against evolutionary optimisation, there is some evidence for
achievement of new or extended functionalities. A detailed plausibilisation of the
observed behavioural pattern directly arises from the entirety of concentration
courses involved in carrying out the state transitions. In order to emphasise
this line of evidence, we conducted an additional simulation study by consistent
variation of the rate constants within the logical unit. Slowing down its reactions
by setting k =0.1 instead of k = 1 leads to complete loss of frequency division by
forwarding the core oscillator’s period instead. Here, the entire system exhibits
a fragile “cycle” at the edge of chaotic behaviour after a longer transient phase,
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