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John says:
>Everybody appears to define an elasticity as a partial derivative, but
>opinions seem more divided as to whether the control coefficient
>definitions are best expressed as total or partial derivatives.
>>Your comments will be gratefully received ...
>> ... John Woods
I had a recent argument with one of our distinguished members a few weeks
ago on this point who wanted control coefficients to be partial.
I almost always use totals for control coefficents, I don't think I've
ever used partials. Here is my reasoning......
The reason why I use partials for elasticities
and totals for control coefficients is simply to make clear
that elasticities refer to a local response, i.e a partial
response - only one metabolite is allowed to move - and control
coefficients are measured while allowing all metabolites (except the
boundaries of course) to move, a total response. Thus with respect to
elasticities, we measure only a partial response of an intact pathway, while
with control coefficients we measure the total response of an intact pathway.
There will be some of course who will say, yes but with a control
coefficient we only change the activity of a single enzyme (lets say)
and keep all other enzyme activiities fixed, so
isn't the control coefficient measuring a partial response aswell? Well yes
it is, but we know what the TOTAL response of a pathway is, it's given
by the summation theorems.
I guess it's also to do with what level we're
at. If we're interested in the interaction of a single enzyme with the
intact pathway then we can stick to partials for elasticities and totals
for control coefficients. On the other hand if we're interested in the
interaction of intact pathways with the genetic pathways (which act at
more than one enzyme at a time) then maybe we might make the control
coefficients partial and the activity changes at the genes (eg promoter
efficiency) total. If one ever attempts to derive from first principles
the relationship between the control coefficients
and elasticites then depending on your organisational skills, it becomes
critical to distinguishing between the partials and the total.
Herbert Sauro
