The Control Analysis of Signal Transduction - Systems Biology of Metabolic and Signaling Networks - page 48

Table 3.2 Control coefficients of various levels kinases and phosphatases for the degree of
phosphorylation at the next level down, for the signalling pathway shown in Fig. 3.4
Enzymes Kinase 1 Ptase 1 Kinase 2 Ptase 2 Kinase 3 Ptase 3

C X levelA
i Aþ 1 ; SS

0.15 0.15 0.21 0.21 0.32 0.32

Note : Ptase denotes Phosphatase

concentration is not linear such as when a process is catalysed by two proteins, or
when proteins are substrates rather than catalysts such as in signal transduction, the
protein concentration-based control coefficients will not conform to the above
summation laws (Van Dam et al. 1993 ).
The alternative to experimental determination of the measurement of control
coefficient is the computational determination, either from complete replica models
of the network (e.g. Bakker et al. 1999 ; Conradie et al. 2010 ), or by inversion of the
matrix of elasticity coefficients (Westerhoff and Kell 1987 ).
This indicates that the phosphorylation and dephosphorylations processes are
equally important for steady-state signalling. This is clearest for a simple signal
transduction cascade where there is only one kinase and one phosphatase per level:

C X iþ 1 C X iþ 1

phosphatase ¼ kinase :

(3.12)

3.8 Control and Signal Transduction

Kahn and Westerhoff ( 1991 ) developed HCA for signal transduction cascades at
steady state, where extra control laws apply between the cascade levels: The steady-
state degree of phosphorylation of a protein at any next level in the cascade is
controlled by the protein, and the control by that kinase and that phosphatase adds
up to zero:

X

n Aþ 1

C X level A

i Aþ 1 ; SS ¼

0 : (3.13)

i Aþ 1 ¼ 1

In Table 3.2 this summation law is demonstrated for the signalling pathway
shown in Fig. 3.4 .
This kind of signal transduction process is of interest in protein kinase cascades,
such as the MAP kinase pathway. Here the first kinase activates the second by
phosphorylation, which then activates the third, again by phosphorylation, and so
on. The phosphorylated last kinase activates transcription. The above HCA implies
that corresponding protein phosphatases deserve as much interest as the kinases for
the ultimate steady-state levels, a conclusion that breaks with the research history,
which focused on the kinases. Hornberg et al. ( 2005a , b ) extended HCA mathemat-
ically to describe the maximum phosphorylation level obtained in the time-
dependent functioning of the cascade. In this case the same summation law