Metabolic Dissipative Structures - Systems Biology of Metabolic and Signaling Networks - page 193

When the dynamics of this network was analyzed in the presence of two
simultaneous external stimuli S1 and S2, a systemic metabolic structure emerged
spontaneously. The MSb12 is always in an active state (metabolic core) and the
MSb15 is always inactive whereas the remaining subsystems exhibit intermittent
catalytic activities (on-off changing states) (Fig. 8.4 ). The active catalytic
subsystems present complex output patterns with large periodic transitions between
oscillatory and steady-state behaviors (105 transitions per period). Figure 8.4 b1
displays a representative time series of activities from MSb12 showing
30 transitions between oscillatory and steady-state behavior.
When the external stimulus S2 was removed and only the stationary input flux of
substrate S1 was considered, the network undergoes a drastic dynamic reorganiza-
tion: flux (Almaas et al. 2005 ) and structural (Almaas et al. 2005 ; Almaas 2007 )
plasticity appear. The former involves persistent changes in all catalytic activities
(see some examples in Fig. 8.4 b2, c2), while the latter implies a persistent change in
the state of the MSb15, i.e., under conditions of both stimuli S1 and S2 the MSb15
was in an off state, while the presence of only S1 stimulus MSb15 locks into an
on-off changing dynamics. Despite the drastic catalytic changes observed in the
temporal evolution of the subsystems dynamics, the network preserves the systemic
metabolic structure, i.e., MSb12 is the metabolic core while the remaining
subsystems exhibit intermittent dynamics.
Interestingly, the network adjusts the internal metabolic activities to the new
environmental change (one or two stimuli) by means of flux and structural
plasticities. This kind of behavior has been experimentally observed in several
organisms as an adaptive response to external perturbations (Almaas et al. 2005 ).
The complex dynamic behavior and transitions exhibited by the network studied are
spontaneous and emerge from the regulatory structure, and nonlinear interactions.
8.3.1 Systemic Functional Structure of Biomolecular
Information Flows
Next, the amplitude of the different catalytic patterns was used to study the
effective connectivity based on transfer entropy.
For the condition corresponding to two simultaneous stimuli, the analyzed graph
of effective connections shows that there are only nine metabolic subsystems with
significant statistical values (Fig. 8.5 d1). The arrows in the graph illustrate that the
effective connectivity has directionality and the thickness is proportional to TE
values. The maximum value of TE equal to 0.179 information bits corresponds to
the link from MSb16 to MSb13.
Under conditions in which S2 was removed and only the stationary input flux of
substrate S1 was considered, the TE values obtained are depicted in Fig. 8.5 d2. It
can be observed how the structure of the effective information flows is much more
complex under one stimulus: (I) 10 of the 18 enzymatic sets have effective links,