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
b ′ 1 = ¯b 1 b 2¯b3¯b4¯b5
b ′ 2 = ¯b 1 b 2 ∨ ¯b 1 b 2¯b3¯b4¯b5
b ′ 3 = ¯b 1¯b2 b 3 ∨ ¯b 1 b 3¯b4 ∨ ¯b 1 b 2 b 3 b 5 ∨ ¯b 1¯b2 b 4¯b5
b ′ 4 = ¯b 1 b 4¯b5 ∨ ¯b 1 b 2 b 3 b 5 ∨ ¯b 1¯b2¯b3 b 5 ∨ ¯b 1¯b2¯b3 b 4 ∨ ¯b 1 b 2 b 3 b 4
b ′ 5 = ¯b 1¯b2¯b3¯b4 ∨ ¯b 1¯b2 b 3 b 4 ∨ ¯b 1 b 2 b 3¯b4 ∨ ¯b 1 b 2¯b3 b 4
For implementation of these functions, we exclusively use logic AND and OR
gates with two input variables and one output variable in a cascaded manner in
order to avoid an exponential growth of reactions whose number doubles with
any additional input variable. The corresponding cascade lengths (number of
subsequent gates to be passed by a binary signal) vary between 4 and 7. As a
consequence, the latencies of the cascades also deviate, which might imply an
evolutionary potential towards modified functionalities.
b b b b b
1 2 3 4 5
b ’ 1
&
&
NOR
NOR
b ’ 5
&
&
NOR
NOR
Fig. 5. Sketch of the logical unit representing a chemical model of a binary counter
modulo 17. A periodical trigger acts as input providing the counts. Bit b 1 accomplishs
the output. For all reactions within the logical unit, we utilise mass-action kinetics
along with rate constants consistently set to k = 1. This allows a fast toggling which
results in a short latency of approx. 10 time units per individual gate.
Figure 5 sketches the structure of the entire binary counter modulo 17. In
the chemical representation, the resulting module mod17 = ({C}, {B T 1 },F) consists
of 145 species and subsumes 416 individual reactions. The logical unit was
constructed by using standard techniques of circuit design known from engineering.
We consider this unit as a fixed module whose potential with respect to
additional, originally unintended functionalities is worth to be found out.
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