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Actually, the transition rate K
iC1;i
stands for a control input to the cells proliferation
model and is dependent on excitation received from circadian oscillators.
The PDE model of the cell cycle is given by
@
@t
i
C
@
@a
Œ
v
i
.a/
i
C Œd
i
C K
i;iC1
i
D 0
v
i
.0/
i
.t;a D 0/ D
R
a0
K
i1;i
.t;a/
i1
.t;a/
da
2iI
(5.1)
1
.t;a D 0/2
R
a0
K
I;1
.t;a/
I
.t;a/
da
where
P
iD1
R
a0
i
.t;a/
da
D 1,
v
i
.a/ denotes a speed function of age a in phase
i with respect to time t and K
i;iC1
.t;a/ D
i
.t/
1
faa
i
g
.a/. The transition rates
i
.t/
1
faa
i
g
.a/ have the following significance: a minimum age a
i
must be spent in
phase i, and a dynamic control t!
i
.t/ is exerted on the transition from phase i to
phase i C1. Functionals
i
are dependent on physiological control, that is hormonal
or circadian, as well as on pharmacological factors. From the above, it is concluded
that circadian oscillators indeed affect the cells' cycle. They may also have an effect
on cell's cycle through the death rate d
i
.
It has been verified that the cells's growth is controlled by proteins known as
cyclines and cycline-dependent kinases (CDK) and in turn the concentration of
cyclines is controlled by circadian oscillators. Cyclines and CDKs, apart from
circadian control can be pharmacologically controlled. Anticancer drugs, such as
alcylating agents act by damaging DNA and thus triggering p53 protein which
provokes cell cycle arrest. It has been shown that p53 protein, on the one hand,
and many cellular drug detoxification mechanisms (such as reduced glutathione),
on the other hand, are dependent on the cell circadian clock, showing 24 h
periodicity. Consequently, the circadian neurons affect cell cycle's transitions in
both physiological and pathological conditions. By disrupting the circadian clock
cells' proliferation and tumor development can be triggered. Moreover, by infusing
anticancer drugs in time periods which are in-phase with high levels of proteins
which arrest the cell cycle and which are controlled by the circadian mechanism
one can anticipate a more efficient anticancer treatment. Finally, altering the period
of the oscillations of the circadian cells with disruptive inputs from cytokines and
drugs is an approach to improving the efficacy of chemotherapy [
106
].
It is also known that light through the retino-hypothalamic tract modulates
equally for all neurons. A higher risk of cancer is related with circadian disruption
induced by dark/light rhythm perturbations. Disruptive inputs can be due to
circulating molecules such as cytokines (e.g., interferon and interleukin) either
secreted by the immune system in the presence of cancer cells or delivered by
therapy. These inputs are known to have a disruptive effect on circadian neurons
mostly at the central pacemaking revel. It is also known that elevated levels of
cytokines are associated with fatigue.
Finally a note is given about transmission pathways from central to peripheral
circadian cells. These pathways maybe provided by the autonomic nervous system,
neurohormonal ways using the hypothalamocorticosurrenal axis. In a simple way
communication between circadian neurons may be based on intercentral, hormonal,
such as adrenocorticotropic hormone (ACTH) and peripheral tissue terminal inputs
(such as cortisol).
