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In-Depth Information
a
b
5
5
20
0
0
0
−5
−5
5
10
15
20
25
30
35
40
0
20
40
0
20
40
time
time
time
1
1
4
0
0
2
0
−
1
−1
5
10
15
20
25
30
35
40
0
20
40
0
20
40
time
ti
m
e
ti
m
e
0.5
0.05
4
0
0
2
0
−0.5
−0.05
5
10
15
20
25
30
35
40
0
20
40
0
20
40
time
time
time
Fig. 5.7
Test 5: (
a
) Synchronization of state variables x
i
(i D 1;4: frq mRNA concentration,
i D 2;5: FRQ protein concentration in cytoplasm, i D 3;6: FRQ protein concentration in nucleus)
between the two circadian cells (
red continuous line
denotes concentration in cell 1 whereas the
dashed blue line
denotes concentration in cell 2) (
b
) Estimation of disturbance inputs and of their
derivatives (
blue lines
) with the use of the Derivative-free nonlinear Kalman Filter
a
b
5
5
4
2
0
0
0
−5
−5
5
10
15
20
25
30
35
40
0
20
40
0
20
40
time
time
time
1
1
1
0.5
0
0
0
−1
−1
5
10
15
20
25
30
35
40
0
20
40
0
20
40
time
time
time
0.2
0.05
1
0.5
0
0
0
−0.2
−0.05
5
10
15
20
25
30
35
40
0
20
40
0
20
40
time
time
time
Fig. 5.8
Test 6: (
a
) Synchronization of state variables x
i
(i D 1;4: frq mRNA concentration,
i D 2;5: FRQ protein concentration in cytoplasm, i D 3;6: FRQ protein concentration in nucleus)
between the two circadian cells (
red continuous line
denotes concentration in cell 1 whereas the
dashed blue line
denotes concentration in cell 2) (
b
) Estimation of disturbance inputs and of their
derivatives (
blue lines
) with the use of the Derivative-free nonlinear Kalman Filter
5.9
Conclusions
The problem of robust synchronization of coupled circadian oscillators and the
problem of the nonlinear control of the associated protein synthesis has been
studied. Control of the periodic variations of protein levels in circadian cells is
important because it affects several functions performed by living organisms. When
the periodicity of circadian cells is disrupted pathological situations such as tumor
growth may appear. On the other hand, knowing the effect of the circadian cycle on
the variation of proteins levels can help in administering more efficiently anticancer
treatment. The chapter has proposed a synchronizing control method for coupled
