Jim Anderson asked:
>Ok, I'll bite - what DID M-M plot?
They plotted v against log[S]. This is not a trivial point as they used a
specific property of the semilog plot (the fact that its maximum slope is
0.576V) as a way of estimating V and then they got log Km as the value of
log[S] where v = V/2. A more naive approach would have taken log Km as the
value of log[S] at the point of inflection, but Michaelis and Menten were
intelligent enough to realize that this would be very inaccurate, and also
that it would be inaccurate to try to get the parameters directly from a
plot of v against [S].
Incidentally, if you multiply 0.576 by 4 you'll get a less
arbitrary-looking number (recognizable to people who grew up before
electronic calculators made interconversion of different kinds of logs a
trivial matter).
>And, did L-B plot anything?
>They plotted both 1/v against 1/[S] (the plot usually attributed to them)
and also [S]/v against [S] (the plot variously attributed to Hanes (who
gave the equation but didn't mention a plot), to Woolf (who didn't publish
any of the common plots but was credited with having discovered all of the
common ones in the German edition of Haldane's book), or to various other
people like Eadie or Hofstee (who didn't do anything in particular with
this plot but who are sometimes credited with it by people who are bit
vague about who did what)).
However, they didn't get their parameter values by reading them directly
off either of the plots they described. Instead they used linear
regressionweighting each 1/v value with the fourth power of v (i.e. the
method developed in more sophisticated form by Wilkinson and independently
by Johansson & Lumry nearly 30 years later and popularized by Cleland).
Although their method isn't quite as precise as what Wilkinson and
Johansson & Lumry described it's as good as one good reasonably aspire to
with the computing equipment available in 1934 (pencil, paper and log
tables, I expect). Moreover, unlike Wilkinson etc. they didn't base their
weights on an assumption about error behaviour but on measurements of their
actual error behaviour.
athel
--
Athel Cornish-Bowden athel at ibsm.cnrs-mrs.frhttp://ir2lcb.cnrs-mrs.fr/~athel/homepage.htm
Phone: + 33 491 16 41 38; fax: + 33 491 16 45 78
CNRS-BIP, B.P. 71, 13402 Marseille Cedex 20, France
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