Biology Reference
In-Depth Information
by coincidence, whereas the quantitative test has a much smaller such chance,
depending on the experimental accuracy.
2.2.
Inability to deal with emergence
A second limitation also derives from the lack of being quantitative but, para-
doxically, pertains to failure to test the prediction of qualitative phenomena. The
behaviour of systems of independent components is nothing but the simple addi-
tion of the behaviour of those components. In sufficiently nonlinear systems and
even in linear systems with certain networking (for simplicity we shall here call
the latter also 'nonlinear'), qualitatively new behaviour may emerge, which is
often important for biological function. In fact for survival of living organisms,
a number of properties is essential that are absent from the individual molecules
in those organisms. They must emerge from certain nonlinear interactions. We
shall refer to those nonlinear interactions as 'essential' nonlinearities. Examples
include oscillations in networks of components that would themselves never
oscillate (Goldbeter et al., 2001), and free-energy transduction between compo-
nents that would themselves only dissipate free energy (Westerhoff & van Dam,
1987). For biological macromolecules, the nonlinearity varies between condi-
tions, as it depends on their environment. We briefly illustrate this by considering
what may be the rate equation of an enzyme in an intracellular network:
S
ยท
V
K
m
+
v
=
(1)
S
where v, [S], K
m
and V refer to the actual reaction rate, the concentration of the
substrate of the reaction, the Michaelis-Menten 'constant' and the 'maximum'
reaction rate, respectively. The way in which the enzyme affects the behaviour
(both in the qualitative and in the quantitative sense) of the network is fairly well
described by the elasticity coefficients for the metabolites with which it interacts,
in this simplest case, the substrate S. This elasticity coefficient corresponds to the
log-log derivative of the rate with respect to the concentration of the substrate, i.e.
ln v
lnS
=
K
m
K
m
+
S
=
(2)
S
The equation shows that the role of the enzyme in the system is not only
determined by that enzyme itself (through K
m
) but also by its environment (i.e.
by S) and by how it interacts with that environment (in terms of S/K
m
).
The new behaviour that emerges depends on the type of nonlinearity that
reigns in the network, e.g. on the value of the above elasticity coefficient
(Westerhoff & van Dam, 1987). Consequently any theory explaining the occur-
rence of oscillations will only predict oscillations for certain states of the system
