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For MP systems where matter conservation holds, the energy orientation require-
ment can be stated by means of the following
cycle dissipation
principle (no free
reaction cycle may exist).
Cycle dissipation principle
When an MP system is time-unbounded and has a reaction cycle, then surely
a substance has to be present in the system that is consumed during the appli-
cation of the reactions of the cycle.
Figure 3.38 shows the abstract idea underlying the cycle dissipation principle.
The intuition of such a phenomenon can be understood with the metaphor of a wa-
termill, where the wheel activity of this device needs an external water flow sup-
porting the necessary mechanical energy providing the dynamics of the system. If
matter-boundedness is assumed in a metabolic system with a reaction cycle, then
according to the cycle dissipation principle, the input matter feeding the internal
cycle needs to be coupled with output rules expelling matter.
Fig. 3.38
The principle of cycle dissipation for metabolic systems, in the form of an (abstract)
watermill
In the following discussion we consider MP systems which are assumed to sat-
isfy the conservation principle and the cycle dissipation principle. The results we
derive show the importance of open systems and their relationship with oscillatory
dynamics.
Lemma 3.5.
Any closed MP system has to be time-bounded.
