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Feedback Control in Systems Biology
book

Feedback Control in Systems Biology

by Carlo Cosentino, Declan Bates
October 2011
Intermediate to advanced content levelIntermediate to advanced
296 pages
9h 39m
English
CRC Press
Content preview from Feedback Control in Systems Biology
156 Feedback Control in Systems Biology
0 0.5 1 1.5 2 2.5 3
0
0.5
1
1.5
2
2.5
3
3.5
4
x
y
FIGURE 5.4: Phase plane of the simple chemical oscillator (5.7). The thick
curve denotes the limit cycle.
Example 5.1
On the basis of the results above, among the possible candidates for chemical
systems which exhibit limit cy c les, the s implest such reaction mechanism can
be shown to be, [4]:
X
k
1
−−
−−
k
1i
A, B
k
2
−→ Y, 2X + Y
k
3
−→ 3X. (5.6)
Applying the law of mass ac tion, the reaction kinetics are describ ed by
˙x = k
3
x
2
y + k
1i
a k
1
x (5.7)
˙y = k
2
b k
3
x
2
y (5.8)
The system exhibits a limit cycle for certain choices of the parameters, as
shown by the phase plane in Fig. 5.4 ...
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Publisher Resources

ISBN: 9781439816912