The Control Analysis of Signal Transduction - Systems Biology of Metabolic and Signaling Networks - page 40

process activities in the system. The corresponding sensitivity coefficients are called
control coefficients. This focus enabled MCA to discover and prove laws that capture
the dependencies of these control coefficients on each other. MCA also defines the
subset of properties of the processes that matter most for the control properties of the
system. This leads to the discovery of another set of laws relating systems properties to
component properties. These laws are absent when the processes occur in isolation and
are hence properties of the system only. They are among the first principles discovered
by systems biology [review: (Westerhoff 2008 )].
Together these laws enable the prediction of relative control exerted by each step
(enzyme) on the system's variables (such as fluxes and metabolite concentrations)
on the basis of certain kinetic properties of the component processes. As of the
operational nature of the definitions of the control coefficients, this control can also
be measured experimentally by applying a perturbation to the step being studied and
measuring the effect on the variable of interest after the system has settled to a new
steady state. By virtue of these properties, MCA is an example of systems biology.
In contrast to what its name suggests, metabolic control analysis is not limited to
the topic of metabolism. Its principles and definitions also apply to gene expression
and signal transduction pathways, where similar laws of “hierarchical control
analysis” apply in addition (Kahn and Westerhoff 1991 ; Westerhoff 2008 ). As the
methodology also applies to biology outside biochemistry, such as ecology (Getz
et al. 2003 ), we shall refer to the generalised form of metabolic control analysis as
control analysis.

3.3 The Control Coefficients

Control analysis relies on the proper definition of the system under investigation,
i.e. on specifying what are the system's borders, which are the (dependent)
variables, which are the parameters ( independent variables), and which are

process activities (Westerhoff and Dam 1987 ). The dependencies of the variables
on process activities are quantified in terms of control coefficients. A control
coefficient is the relative measure of the change in a system variable (e.g. flux or
concentration) upon perturbation of the activity of an elemental process (in -
non-channelled pathways corresponding to the enzyme activities) (Westerhoff
and Van Dam 1987 ). It is mathematically defined (Burns et al. 1985 ; Kholodenko
et al. 1995 )as

¼

d p
global

d x

dln x
d p
@ ln v i

v i
x ¼

C i

@p local

@p ;

(3.1)

@ v i

where “ x ” is the dependent variable (e.g. flux J , concentration X or potential ) and

v i is a process activity such as the activity ( V max in both directions) of an enzyme

ψ