Metabolic Dissipative Structures - Systems Biology of Metabolic and Signaling Networks - page 184

the significant advances made, we still lack a quantitative description of the
effective functional structures involved in enzymatic activity coordination.
Functional connectivity quantifies how much the dynamics of one variable is
statistically dependent on the dynamics of another. Therefore, although structural
and functional connectivity are obviously related (i.e., structure shapes function),
there is a striking difference between them: it is possible to have two variables
which are functionally related (thus highly correlated) but structurally unconnected.
The reason is because function can go beyond structure through neighbor-neighbor
interactions. In order to quantify the functional structure arising from glycolytic
enzymes catalyzing irreversible steps under dissipative conditions, the effective
connectivity between enzyme and enzyme interactions, which account for the
influence that the activity of one enzyme has on the future of another, was analyzed
by transfer entropy (TE).

8.2.1 Determining the Rates of Irreversible Enzymatic Steps
in Glycolysis

Although the kinetic behavior in vivo of most enzymes is unknown, in vitro studies
can provide kinetic parameters and enzymatic rates. We used the latter strategy; for
hexokinase we adopted a rate equation depending on glucose and ATP (Viola
et al. 1982 ); for phosphofructokinase and pyruvate kinase a concerted transition
model was applied (Goldbeter and Lefever 1972 ; Markus et al. 1980 ).

8.2.2 Modeling Glycolytic Processes Under Dissipative
Conditions

In Fig. 8.1 , the classical topological structure characterized by the specific location
of enzymes, substrates, products, and feedback-regulatory metabolites is shown.
When the metabolite S (glucose) feeds the glycolytic system, it is transformed by
the first enzyme E 1 (hexokinase) into the product P 1 (glucose-6-phosphate). The
enzymes E 2 (phosphofructokinase) andE 3 (pyruvatekinase) transform the substrates
P 0 1 (fructose 6-phosphate) and P 0 2 (phosphoenolpyruvate) into the products P 2
(fructose 1-6-bisphosphate) and P 3 (pyruvate), respectively. The steps P 1 ! P 0 1 and

P 0 are reversible. A part of P 1 is removed from the pathway with a constant
rate of q 1 which is related to the activity of pentose phosphate pathway; likewise, q 2
is the constant rate for the sink of the product P 3 which is related to the activity of
the pyruvate dehydrogenase complex.
Kinetic modeling with ordinary differential equations (ODE) is commonly used
for studying metabolic systems. Consistently with the theory of dynamical systems,
delays can be modeled by adding to the original variables other auxiliary functional

P 2 !