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. 11. Hierarchical scheme of unidirectionally coupled neuronal core oscillators organised
in four layers. Individual oscillations synchronise by passing through these
layers. See text for detailed explanation.
stream layers synchronise their oscillation via unidirectional molecular coupling
in which the oscillatory outputs of superior layers directly affect oscillations in
adjacent subsequent layers. Neurons residing in the deepest layer release their
widely synchronised oscillatory signals to peripheral oscillators in other parts of
the organism. Figure 11 illustrates a small network composed of 14 core oscillators
called n[1] up to n[14] organised within four layers.
We are going to conduct two experimental studies: In a first scenario, we wish
to consider a pre-synchronised network with a single neuron in the master-clock
layer, see part A of Figure 11. This neuron propagates its oscillatory rhythm to
all downstream neurons causing a slight signal delay from layer to layer. After
a short transient phase, all 12 neurons incorporated in this scenario oscillate
synchronously. Although sufficient so far, a single master clock makes the system
error-prone and fragile, especially if the master-clock oscillation deviates from
its expected behaviour which can easily happen along with cell ageing. In this
case, an incorrect or insufficient oscillatory signal runs through all layers without
any correction or control. Additional master-clock neurons with full connectivity
to downstream layers can help to stabilise the function of the whole network.
Our second scenario depicted in part B reflects this aspect. Here, we add a
master clock neuron and a second-layer neuron completing the network of 14
neurons. Temporal signal offsets (so-called phase differences) among individual
master-clock oscillations are diminished while passing the downstream layers.
Finally, a robust “average” oscillatory signal derived from all master clocks is
released as global output. Our simulation shows that initial phase differences
within the master-clock layer can be reduced up to ≈ 2.6-fold by running through
three subsequent layers, widely independent of the coupling strength. Antiphasic
master-clock oscillations (half-periodic offset, phase difference 180 ◦ ) turn out to
be resistent against synchronisation by passing the layers almost unaffected.
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