Metabolic Dissipative Structures - Systems Biology of Metabolic and Signaling Networks - page 189

each variable was in a given state. The set of all variables is given by α , β , and γ in

( 8.4 ).
The units of TE are in information bits, as the Log function appearing in the
Shannon information is calculated on base 2. All the values were normalized to the
maximum, thus the value of 1.00 corresponding in all cases to the TE between E 2
and E 3 which was the maximum in the system; the other values represent the ratio
of information with respect to this maximum flow.
In Fig. 8.2 the biomolecular information flows between the irreversible enzymes
of glycolysis are plotted. The values of functional influence obtained range from
0.58 TE 1.00 (with mean SD ¼ 0.79 0.12), which in general terms indicates
a high effective connectivity in the multienzymatic subsystem.

8.2.5 Emergence of an Integrative Functional Structure
in the Glycolytic Metabolic Subsystem

The data showed that the flows of functional connectivity can change significantly
during the different metabolic transitions analyzed, exhibiting high TE values. The
maximum source of information corresponds to the E 2 enzyme (phosphofructo-
kinase) at the edge of chaos, when complex quasiperiodic oscillations emerge
(cf. Fig. 8.2 ). This finding seems to be consistent with other studies showing that
complexity is maximal when a dynamic system operates at the edge between order
(e.g., periodic behavior) and chaos (Bertschinger and Natschlager 2004 ; Kauffman
and Johnsen 1991 ).
The level of influence in terms of causal interactions between the enzymes is not
always the same but varies depending on substrate fluxes and the particular
dynamic regime. As a result of the dissipative self-organization, a biomolecular
informative structure emerges in the metabolic subsystem, which is capable of
modifying the catalytic activities of the glycolytic irreversible enzymes. The self-
organization of the metabolic subsystem shapes a functional dynamic structure able
to send biomolecular information between its catalytic elements, in such a way that
the activity of each irreversible enzymatic step could be considered an information
event. Each irreversible catalytic activity depends on the molecular information
given by the substrate fluxes and regulatory signals, performing three simultaneous
functions: as signal receptor, as signal integrator, and as a source of new molecular
information. As a result of the overall process, the enzymatic activities are coordi-
nated, and the metabolic subsystem operates as an information processing system
which, at every moment, defines sets of biochemical instructions that make each
irreversible enzyme evolve in a particular and precise catalytic pattern.
The simulations also show that for all cases analyzed the maximum effective
connectivity corresponds to the transfer entropy from E Z to E Z, indicating the
biggest information flow in this system. The total information flow was also
analyzed as the difference between the TE output from an enzyme minus the total