On 13 May 98 at 16:37, JHS Hofmeyr and J Rhower wrote:
[A SUMMARY OF THE MAIN POINTS OF THEIR POSTING:]
> This brings us to the crux of the matter: It is the partial
> derivative terms (cv/cx) that are the crucial quantities and
> should have a name - we call them elasticity coefficients
> [...]
> Now, for the full metabolic system an exactly analogous situation
> exists [...]
> [...] However, from a mathematical point of view it remains the partial
> derivatives cJ/cp that we should use as a basis of definition for the
> response coefficients (actually, all coefficients of MCA). It is these
> quantities that enter the mathematical framework of MCA.
> [...]
> So, in our view, all our definitions should be in terms of partial
> derivatives.
Congratulations Jannie and Johann! You have explained this very clearly
and I could not disagree with a single point in your posting. My view is
exactly the same.
Just to add a very small point that should lend (even) more support for
this position:
If one takes a purely formalistic approach to MCA and departs from this
description of control coefficients as the partial derivatives of
state variables (fluxes and concentrations), one will arrive at the
summation theorems by using Euler's theorem for homogeneous functions of
degree one (flux-control coeffs) or degree zero (concentration-control
coeffs.); as indeed has been shown by Giersch. If control coefficients were
total derivatives then this would not be so in the general case (only when
the pathway was composed of a single step, where "summation" wouldn't even
make sense).
Pedro
Pedro Mendes Inst. Biological Sciences
prm at aber.ac.uk (home: pedro at enzyme.demon.co.uk) Univ. Wales, Aberystwyth,
http://gepasi.dbs.aber.ac.uk/pedro/prmhome.htm Ceredigion SY23 3DD, U.K.
http://gepasi.dbs.aber.ac.uk/softw/gepasi.html FAX: +44 (0)1970 622307
