13th International Conference on Membrane Computing - MTA Sztaki

T. Hinze, B. Schell, M. Schumann, C. Bodenstein
all life forms known up to now. Molecular mechanisms responsible for creation
and maintenance of a phenotype based on genotypic information imply an iterative
nature of underlying translational and transcriptional processes. This is due
to compensate or counteract the degradation of chemical substances making an
organism to be alive. Resulting gene expressions typically oscillate over time, for
example consecutive activation peaks repeat within few hours for replacement of
rapidly dissociating substances and up to several days for robust proteins [22].
Even procaryotes, the simplest long-term surviving life forms on earth, regularly
reproduce themselves by intrinsically cycling processes, mostly by binary
fission or budding [18]. Regarding eucaryotic cells, the cell cycle as a more complex
mechanism assures periodical cell division by passing through a number of
dedicated phases [26]. Subject to distinct species, individual properties, and environmental
conditions, the periods of cell cycling range from approximately six
hours in some fungi up to about 24 hours in some mammals [21]. For humans,
the duration of cell cycles typically varies between 19 and 20 hours according to
the specific cell type [17]. Most notably, the time span between two cell divisions
much more deviates in different tissues. While cells forming the inner surface of
the stomach renew in average every three days [7], more than ten years seem to
be enough for the osteocytic cellular skeleton of bones [7].
Beyond phenomena directly related with gene expression, we find a plethora
of oscillating processes spanning a much larger diversity of periodicities within
each individual organism. Let us consider humans for example. Firing neurons
are able to send spikes every 10 milliseconds with a peak time of 2 milliseconds
[11]. Several hundred spikes passing a neural axon in a sequence induce a
high frequential oscillatory signal by mutual regulation of ion channels [11]. The
molecular oscillator residing in the sinu-atrial node commonly generates between
40 and almost 210 heart beats per minute [23]. The suprachiasmatic nucleus as
a part of the brain consistently provides the circadian rhythm with a period of
approximately one day [3]. Infradian rhythms include monthly cycles like the
menstruation. There is also some evidence for saisonally altering hormone concentrations
indicating winter and summer [24]. Among other effects, this annual
cycle leads to a slight reduction of the average human body temperature within
a magnitude of 0.1 ◦ C during winter [6].
All together, we are aware of a broad spectrum of frequencies caused by
biological rhythms. It appears that several molecular oscillators exist independently
from each other. They operate simultaneously by individual generation
of oscillatory signals, which in turn can act as periodical triggers for regulation
of subsequent processes or behavioural patterns. The coexistence of a large
number of molecular oscillators in living organisms is no surprise since a simple
cyclic reaction scheme comprising at least one feedback loop suffices for obtaining
a persistent oscillation. Probably, there are many evolutionary origins and
resulting mechanisms of molecular oscillators.
Envisioning a more holistic view, the question arises how those oscillators
interact in a way that their signal courses can interfere with each other. Downstream
reaction systems can benefit from this richness by utilising a majority
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