densitometry on western blots

Dr Engelbert Buxbaum via (by engelbert_buxbaum At
Sun Dec 10 03:36:17 EST 2006

DK wrote:

> This maybe a factor for fits of very complex functions with many 
> parameters but I wouldn't think one notices a difference doing 
> simple binding curve or M-M kinetics. (?)

With a starting value near the obtimum (e.g. obtained from a
Lineweaver-Burk plot) Marquard-Levenberg is able to fit HMM-kinetics,
although I had cases were Simplex converged to a (slightly) better
optimum even with such simple a model.

But simple HMM is of more educational than real-life value, when you
have an enzyme with 4 co-operating catalytic sites and an additional
site for substrate inhibition (see Eur. J. Biochem. 265 (1999) 54-63)
then you separate wheat from chaff, even with near-perfect data. In that
particular case the data range was 5 orders of magnitude, even if
Marquard-Levenberg would not crash on a singular matrix on this 5-params
ratio of polynoms it would ignore the data at the bottom end as they
make no significant contribution to the sum of squared error (think of
data of 1.0 and 10,000, each with a relative error of 1%. That is 1.00
+/- 0.01 and 10,000 +/- 100). So you need to minimise Chi-square (sum of
squared relative errors) instead. And ML can't do that. 

Remember: If your only tool is a hammer, you'll treat all your problems
as nails. 

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