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Empirical vs Mechanistic models (was Re: Is it MCT or MCA)

Johann M. Rohwer JR at AKAD.SUN.AC.ZA
Tue Aug 29 02:24:09 EST 2000


On 28 Aug 2000, at 9:49, Petr Kuzmic wrote:

>[...] 
> I also understand the need to move away from mechanisms in those cases
> where we do not know what they are.  For example, we've all see enzyme
> reactions with a complex substrate-velocity dependence similar to this
> (sigmoidal increase to a maximum, followed by a decrease to an
> asymptote):
> [...] 
> This behavior could have many different mechanistic interpretations, so
> why not just describe it by some rational polynomial,
> 
> 	V = (a + b[S] + c[S]^2 + ...) / (d + e[S] + f[S]^2 + ...),
> 
> determine the coefficients a, b, c, ... from the available data, and use
> the polynomial model  without ever even trying to ascribe physical
> meaning to a, b, c, etc.  But what are the limitations of this empirical
> (as opposed to mechanistic) model building?  Isn't it true that the
> empirical model so built is only applicable to the exact conditions that
> were used to construct it?

Well, if the conditions are sufficiently general, that should be no 
problem. In other words, if the range of S-concentrations that 
were used to fit the above polynomial is wider than the S-
concentrations calculated by a larger model in which you use 
this rate eqn, you should be OK. Of course, if [S] moves either 
higher or lower, we have a problem with emprical fitting, as the 
best fit over a range of data often has the worst predictive power 
beyond the data range.

However, "mechanistic" rate equations suffer from similar 
shortcomings as emprically fitted ones. Km's, Ki's, Hill 
coefficients, etc., fitted on experimental enzyme kinetic data often 
depend on temperature, ionic strength, pH, etc. It is very seldom 
that these conditions are exactly physiological. Therefore, if you 
assemble those kinetic data into a model to simulate the 
behaviour of a metabolic pathway in vivo, you are equally 
restricted whether you use mechanistic kinetic parameters or 
empirically fitted ones. In both cases, the parameters may not 
truly reflect the kinetic behaviour of the enzyme beyond the 
experimental conditions that were used to determine them.

As you point out, the only advantage is that mechanistic 
parameters have a physical interpretation (affinity, etc.). But if we 
want to model larger pathways, this may not be of such 
importance.

Johann


--
Johann M. Rohwer
Dept. of Biochemistry, Univ. of Stellenbosch
Private Bag X1, 7602 Matieland
SOUTH AFRICA
Tel.: +27-21-8085843
Fax: +27-21-8085863
E-mail: jr at maties.sun.ac.za
WWW: http://www.sun.ac.za/biochem/
--


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