In article <5um75c$emj at mserv1.dl.ac.uk>, RUMYM at BGEARN.ACAD.BG writes
>Herbert, you have replied to a posting of mine in which the point was not
>clearly stated. I am not against the idealization leading to the summation
>theorem. However I think that the importance of this theorem is exaggerated -
>I think I have presented an example in which a single "unknown" channel
>reduces the sum of the coefficients to zero. Maybe it would be better for
>us to discuss first this example. If I am right (I am still not sure - I am
>so uninformed) and if the problem has not been dealt with (is there any
>solution?), a lot of complementary study should be done - otherwise the
>summation theorem alone seems useless.
>>Pentcho
Perhaps the importance of the summation theorem is exaggerated and in
fact I am more inclined to give the greatest importance to the
connectivity theorem which connects the elasticities to the control
coefficients. The summation theorem is important for a number of reasons
however:
1. The summation implies that the control coefficient is not an
intrinsic property of a particular enzyme but a property of the whole
system, since changing one will lead to changes in all others (to
satisfy the sumamtion theorem).
2. That control, at least in principle, is shared among all enzyme
steps, therefore the old idea of the rate-limiting step is not a good
model - but still discussed even in text books dated 1997, as I
discovered on a trip to a book shop recently!
3. It provides a normalisation criterion for the connectivity theorems
which allows us to solve for the control coefficients.
4. The sum, sum Cji = 1 implies that on average the value of any
particular coefficient is small, hence the robustness discovered
recently by Leibler and Barkai in their nature paper (and quoted in new
scientist).
5. The operational proof of the summation theorem leads on naturally to
a derivation of the branching theorems and then on to the Universal
method snd all variations of the method and thus a possible means for
re-engineering metabolism for our own benefit.
Herbert
--
Herbert M Sauro
email: HSauro at fssc.demon.co.uk
Telephone: 01974 282428
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