The Control Analysis of Signal Transduction - Systems Biology of Metabolic and Signaling Networks - page 43

for transient time, and area-under-the-curve control coefficients:
X

C τ i
i

¼ 1 (3.5)

i

where the summations are over all the reactions in the system. This may include not
only the steps in the pathway of interest but also those of other pathways linking
in. X j may refer to any free variable in the system that does not have the dimension
of time, such as the ratio of the phosphorylated to the non-phosphorylated form of a
signal transduction protein, the ATP/ADP ratio, or the intracellular concentration of
cAMP. Summation laws may be verified for the examples in Fig. 3.1 and Table 3.1 .
The summation law proves that systems biology is essential for the understand-
ing of life. Let us look at a linear pathway, where there is but a single steady-state
flux and flux control coefficients are non-negative, and suppose that the flux control
by the third enzyme equals 1. This implies that the first enzyme has no control on its
own flux. The effect that enzyme has on life (which is through the flux that it
enables) is not at all determined by the enzyme catalysing reaction 1, nor by the
gene encoding that enzyme. Figure 3.1 gives other examples where no enzyme fully
controls its own function, but the enzymes do this collectively.
An example from signal transduction can be found in the work of Kolodkin
et al. ( 2010 ). They examined the control of the components of the signal transduction
pathways of one nuclear hormone receptor (NR) on the flux through the signalling
pathway of another nuclear hormone receptor. In contrast to cascade process signal-
ling such as in the MAP kinase pathway (Hornberg et al. 2005a , b ), in the case of
nuclear hormone receptor signalling the signal flux equals a material flux, i.e. that of
the nuclear hormone receptor itself. The nuclear hormone receptors serve as alter-
native cargos of a single transport system which uses a single transport channel (the
nuclear pore complex, NPC). Hence the nuclear hormone receptors and their signal
transduction pathways compete with one another (Fig. 3.2a ). Kolodkin
et al. calculated the extent to which a particular NR pathway flux would be con-
trolled by both its own input, NPC, and output processes and those of the other NRs.
If we first inspect the case with the lowest number of nuclear hormone receptors
(i.e. n

2 in Fig. 3.2b, c ), then we see that the input process of NR1 controlled its
own signal transduction flux for only some 25 %. The control by its own output and
transport processes amounted to some 45 % and 25 %, respectively, the three
controls adding up to 100 %, but all differing from zero. As the number of NRs
using this same channel exceeded 6, the control by the input over its own signal flux
control went up to some 45 % but never got even close to 100 %.
Much of the control, i.e. some 25 %, of the signal flux through the NR1
pathway was carried by the input reactions of the other NR when n

¼

2. This
control was negative because the processes were competing. The transport and
output processes of the second signal transduction route also controlled the flux
through the first. The flux control coefficients all added up to 100 %, again
suggesting that there was indeed full control but that this control is likely to be
distributed, as is confirmed by the computations.

¼