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
Fig. 1. Brusselator reaction network (left) composed of four reactions: (1) P +T k 1
−→ S;
(2) S +2T k 1
−→ 3T ;(3)Q k 3
−→ T ;(4)T k 4
−→ W for generation of persistently spiking
oscillations. The concentration course of species S over time (right) acts as module
output. Mass-action parameter setting: k 1 = k 2 = k 3 = k 4 =0.1; initial concentrations:
P (0) = 3,Q(0) = 1,W(0) = 0,S(0) = 0.5,T(0) = 0.5
The Repressilator Module
The Repressilator is represented by a cyclic gene regulatory network [9] where
a progressional inhibition on its own causes an almost sinusoidal oscillation due
to a negative feedback.
Fig. 2. Repressilator reaction network (left) composed of three inhibiting cycling reactions
along with degradation of each species. The concentration course of species Z
over time (right) acts as module output. Second order Hill kinetic’s parameter setting
H 1 = H 2 = H 3 =0.6,k i = 1 for i ∈{1,...,6} chosen to exhibit persistent almost
sinusoidal oscillations whose amplitude enables signal values between approx. 0.1 and
0.6; initial concentrations: X(0) = 0.3,Y(0) = 0.15,Z(0) = 0.55
We formalise the dynamical behaviour of the module repressilator = (∅, {Z},F)
using second-order Hill kinetics by three ODEs in F :
Ẋ = k 3H 2 3
Z 2 + H 2 3
− k 4 X Ẏ = k 1H 2 1
X 2 + H 2 1
− k 5 Y Ż = k 2H 2 2
Y 2 + H 2 2
− k 6 Z
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