13th International Conference on Membrane Computing - MTA Sztaki

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Maintenance of chronobiological information by P system mediated assembly
of control units for oscillatory waveforms and frequency
The Binary Signal Separator Module
Figure 4 illustrates a three-stage signalling cascade whose function consists in
binarisation of species concentration courses captured by O0 F .
O T
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O T
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O T
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O 3
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k, H
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O OF 1
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OF 2 OF
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Concentration
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Concentration
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Time scale
Fig. 4. Signalling cascade for binarisation of input species concentration course O F 0 .
Concentrations ≥ 1 and those close to 1 converge to 1 while values smaller than a
threshold H are forced down against 0. Michaelis-Menten kinetics and mass-action
kinetics describe the dynamical behaviour of the module. Chosen parameter setting:
H =0.6,k =0.1
The corresponding module separator = ({O F 0 }, {O F 3 },F) employs ODEs:
Ȯ T 0 = kH
O F 0 + H
Ȯ T i = k · O F i · O T i−1 − k · O T i · O F i−1 − k · O T i · (O F i ) 2 + k · O F i · (O T i ) 2 i =1, 2, 3
Ȯ F i = k · O T i · O F i−1 − k · O F i · O T i−1 − k · O F i · (O T i ) 2 + k · O T i · (O F i ) 2
The Logical Unit Forming a Binary Counter Modulo 17
Our construction of a chemical binary counter model modulo 17 is based on a
chemical representation of each boolean variable b ∈{0, 1} by two correlated
species B T and B F with complementary concentrations such that B F +B T =1.
The inequality B T ≪ B F indicates “false” (b =0)andB F ≪ B T “true” (b =1),
respectively. Following a commonly used requirement in circuit design, we intend
by denoting ≪ a deviation of at least one order of magnitude.
A chemical counterpart of a logic gate can be obtained if each line of the
transition table refers to a dedicated chemical reaction where the boolean input
variable values identify corresponding catalysts. These catalysts manage the
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