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
0:ModuleConnect(separator[1] → mod17[1], {(O3 F ,C)}),
200 : ModuleDisconnect(brusselator[1] ↔ separator[1]),
200 : ModuleConnect(brusselator[1] → mod17[1], {(S, C)})}
repressilator[1]
goodwin[1]
B T 1
T
B 2
T
B 3
T
B 4
T
B 5
0 0 0 1 1
0 0 1 1 1
0 1 1 1 1
0 1 0 1 1
1 1 0 0 0
separator[1] brusselator[1] mod17[1]
B 1
T
concentration (a.u.)
4
3.5
3
2.5
2
1.5
1
0.5
0
C
0 200 400 600 800 1000 1200
time (a.u.)
C
Fig. 7. Dynamical behaviour of the frequency divider 1:5 obtained by skipping the
binary signal separator (left: cycle of state transitions, right: counts together with
divider output)
reveals a frequency divider 1:5 although no changes within the logical unit were
made. The same effect can be observed if the Brusselator is directly connected
with the logical unit from the beginning while avoiding any temporary connection
with the binary separator module. Figure 7 shows the behavioural pattern. It
appears that a majority of state transitions skip by leaving a reduced scheme
with identical signal courses of b 4 and b 5 persistently cycling through five states
(after a short transient phase). A most likely reason for that can be found in
the waveform in concert with the quantitatively high-valued oscillatory signal
released by the Brusselator. Most of the time, its course indicates the logical
value “1” solely interrupted by extremely short drops at the 0-level. Since the
flip flops had been designed to be set or reset at the 1-level, the circuit loses
its synchronicity due to the variable cascade lengths in computing the boolean
functions. This in turn might entail a scenario where intermediate stages in the
computation of a bit b ′ i interfere with the computation of another bit b′ j .
3.4 Frequency Divider 1:6 by Repressilator Instead of Brusselator
Due to its nature to induce almost sinusoidal and hence more symmetric signal
courses, the question arises whether or not the Repressilator module in its function
as core oscillator could be able to restore the original qualitative behaviour
of the entire system on its own when renouncing the binary signal separator
again. Checking out this scenario by the P meta framework
Π FD6 =(M,P)
with
235