Biology Reference
In-Depth Information
X
C
i
i
X
ε
¼
0
:
(3.7)
This relationship also applies for the concentration control coefficients
(Westerhoff and Chen
1984
), as shown by (
3.8
) and (
3.9
):
X
C
i
i
ε
X
¼
0
;
X
6¼
Y
(3.8)
with the exception of
X
C
i
i
ε
X
¼
1
(3.9)
The connectivity laws empower control analysis with the ability to describe how
fluctuations in the concentrations of network components pathway propagate
through the chain of reactions so as to be annihilated by the system's response
(Westerhoff and Chen
1984
). The kinetic properties of each process attenuate the
perturbation to and from its immediate neighbours (Kholodenko et al.
2002
).
The connectivity laws also reflect another characteristic of biological systems,
i.e. that components are determined more by the collective of all processes than by
themselves. For the signal transduction network of Fig.
3.3
, one finds for the extent
to which the kinase controls the phosphorylation state of E:
1
C
EP
=
E
C
EP
=
E
kinase
¼
phosphatase
¼
:
(3.10)
phosphatase
EP
=
E
kinase
ε
EP
=
E
þ ε
This shows that it is impossible for kinase to be the only factor in control and that
the control of the kinase depends on properties of both the kinase and the phospha-
tase. If the kinases and phosphatases are product insensitive, the dependence on
kinase properties even drops from the equation, and the extent to which the kinase
affects transcription does not depend on kinase properties. The importance of the
phosphatase also reflects on the response of the transcription rate to changes in the
concentration of the external signal:
RNApolymerase
EP
kinase
signal
ε
ε
=
E
R
transcription
signal
¼
:
(3.11)
phosphatase
EP
=
E
kinase
ε
EP
=
E
þ ε
The equations also generalise the case of zero-order ultrasensitivity which
requires that both the kinase and phosphatase are insensitive to the fractional
phosphorylation of the signal transduction protein E, leading to elasticity
coefficients close to zero. Ortega et al. (
2002
) have shown that this situation is
biochemically unlikely. Network topology and component elasticities together
determine the magnitudes of the control coefficients in complex networks of signal
transduction that may include gene expression and metabolism. In a sense systems
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