13th International Conference on Membrane Computing - MTA Sztaki

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
M = {(brusselator, 1), (repressilator, 1), (goodwin, 1), (separator, 1), (mod17, 1)}
P = {0 :ModuleConnect(repressilator[1] → mod17[1], {(Z, C)})}
goodwin[1]
brusselator[1]
T T T T
B B B 3 B 4 B 5
separator[1]
B 1
T
1
repressilator[1]
C
C
mod17[1]
0 0 0 1 1
0.8
0
0
0
1
1
1
1
0
1
0
concentration (a.u.)
0.6
0.4
0
1
1
1
0
0.2
0
1
0
0
1
T
1 2
0
1 0
0
0
0
0 200 400 600 800 1000 1200
time (a.u.)
Fig. 8. Dynamical behaviour of the frequency divider 1:6 obtained by replacing the
Brusselator with the Repressilator module and skipping the binary signal separator
again (left: cycle of state transitions, right: counts together with divider output)
leads to the observation that now a frequency divider 1:6 with reliable operation
occurred, see Figure 8. After a short transient phase, a stable cycle consisting
of six state transitions emerged when the Repressilator’s parameterisation as
introduced before is applied. We assume the reason for that is a deterministically
maintained perturbance of the binary function’s computation in the logical
unit. Contrary to the previously discussed frequency divider 1:5, the Repressilator
implies an undersupply of the counting signal with its logical 1-level. This
prevents the system from completing the computation and forces the release of
an intermediate computational state taken as output.
3.5 Frequency Divider 1:3 by Usage of the Goodwin Module
The Goodwin module along with its capability of rudimentary plated oscillatory
signal generation appears to be another interesting candidate to drive our
frequency divider. By means of the P meta framework
Π FD3 =(M,P) with
M = {(brusselator, 1), (repressilator, 1), (goodwin, 1), (separator, 1), (mod17, 1)}
P = {0 :ModuleConnect(goodwin[1] → mod17[1], {(X, C)})}
we achieve once more a modified qualitative behavioural pattern, this time a
frequency division 1:3, see Figure 9. After a short transient phase, the system
persistently cycles through three states out of 17 from the original model. It
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