I asked:
> 2. Is the general proof of the theorem based on the thought experiment<
>in which the concentrations are kept constant? <
Paul answered:
Only the concentration of the substrate for the first step, and the <
concentrations of all chemical species outside of the pathway are assumed <
constant. <
But this converts the pathway in something like an isolated system, plus
an input and output. Pedro Mendes once wrote that the coefficients are
global properties of the system, i.e. depend on all elements in the system.
I cannot see this dependence. If the first step is not controlled by a
feedback, its coefficient is unity and the rest are zero. If it is controlled
by a feedback, its coefficient is not unity and this is compensated by some
next coefficient. That seems to be all. All dependencies are within
the pathway.
Can you describe some hypothetical simple case in which the theorem
gives an obvious advantage in the theoretical analysis of a pathway? If we
are to analyse an isolated pathway, a system of differential equations
would give us much richer information than what the theorem offers. If the
pathway is surrounded by metabolism, the restrictions you mention seem to
make the theorem useless. It is quite improbable that increase in some
enzyme concentration would affect only the substrate concentrations of a
particular pathway. Or, if it does so, the pathway is naturally isolated
and therefore not interesting in this respect. I hope experts have much to
say about this.
Pentcho
