13th International Conference on Membrane Computing - MTA Sztaki

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
3.2 Composing the Original Frequency Divider 1:17
The original frequency divider 1:17 can be obtained by sequential coupling of the
Brusselator with the separator which in turn becomes finally connected with the
mod17 module. To do so, we define a P meta framework initially creating a pool
consisting of one instance from each module specified by multiset M. Program
P generates the connective structure by producing graph G.
Π FD17 =(M,P) with
M = {(brusselator, 1), (repressilator, 1), (goodwin, 1), (separator, 1), (mod17, 1)}
P = {0 :ModuleConnect(brusselator[1] → separator[1], {(S, O0 F )}),
0:ModuleConnect(separator[1] → mod17[1], {(O3 F ,C)})}
Figure 6 sketches the coupling (upper part) and depicts the dynamical behaviour
of the resulting reaction system. Periodically after receiving 17 counts, the output
temporarily releases a plated pulse (lower part).
repressilator[1]
1
goodwin[1]
T
B
T
1 C
B 1
brusselator[1] separator[1] mod17[1]
1
C
C
0.8
0.8
concentration (a.u.)
0.6
0.4
concentration (a.u.)
0.6
0.4
0.2
0.2
0
0 200 400 600 800 1000 1200
0
0 500 1000 1500 2000 2500 3000 3500 4000
time (a.u.)
time (a.u.)
Fig. 6. Dynamical behaviour of the frequency divider 1:17 (left: divider output B1
T
during a period of 17 counts, right: B1
T for a longer amount of time, C: counts)
3.3 Frequency Divider 1:5 by Removal of the Binary Signal
Separator
The binary signal separator is responsible for normalisation and binarisation
of the core oscillator’s output. Primarily, we were going to figure out whether
or not this module is essential for the function of the entire frequency divider.
Interestingly, the corresponding knockout P meta framework
Π FD5 =(M,P) with
M = {(brusselator, 1), (repressilator, 1), (goodwin, 1), (separator, 1), (mod17, 1)}
P = {0 :ModuleConnect(brusselator[1] → separator[1], {(S, O0 F )}),
234