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Hi All
I have a question regarding the calculation of kinetic parameters like
Km's and Vmax's, when the drug follows either a biphasic or sigmoidal
kinetics in microsomes (assessed by Eadie-Hofstee plots). Is there an
equation to fit the observed data points in an Eadie-Hofstee plot, when
the drug displays either a biphasic pattern or sigmoidicity?. If so,
how to comeup with the input parameters (estimates) that are initially
used for fitting the observed data points?. Although I know of using
Hills and other equations for the v Vs S plots, I would like to
specifically know if there is anything like that for v Vs v/S plots
(Eadie-Hofstee). I would appreciate your help in this regard.
Thanks in advance
Ragini Vuppugalla
Gradaute Student
Texas Tech School of Pharmacy
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A biphasic pattern might indicate 2 different enzymes.
Look at Enzyme Kinetics by Irwin H. Segel, 1975, from John Wiley &
Sons. It
will probably have what you're looking for.
Ron Kavanagh
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Dear Vuppugalla,
There is a paper reviewing the aspects of atypic kinetic profiles in
microsomal metabolic reactions: J.M. Hutzler and T.S. Tracy, Drug
Metabolism and Disposition 30:355-362, 2002.
In my understanding of your question, you have: 1) used the
Eadie-Hofstee plot to visualize the occurrence of atypical kinetics, 2)
determined the equation to use for data fitting, and then 3) visualized
this equation in the V vs S plot. Then, you'd like to visualize the
curve corresponding to that equation in the Eadie-Hofstee plot,
wouldn't you ? I would try to see how a data fitting software such as
GraFit deals with that issue. There is a forum about the applications
of this software at www.erithacus.com, maybe you'll find there some
interesting information.
Hope this helps. Please let me(us) know eventually.
Frederic MASSIERE, Ph.D.
frederic.massiere.-a-.oroxcell.com
Dear Ragini,Back to the Top
Why would you want to fit the data points in an Eadie-Hofstee plot? The
E-D plot, as well as the L-B and other such plots are best used only for
visual analysis of data. These days, kinetic analysis is done directly
on the V vs. S plot using nonlinear regression software. I use
SigmaPlot, but there are dozens of applications that can do this. You
can estimate some initial parameters by visual inspection of the E-H and
L-B plots.
A two-phase E-D plot usually means you have two enzymes involved, while
a sigmoidal v vs. S plot indicates allosteric interactions. Try fitting
with the Michaelis-Menten 2 enzyme or Hill equations, respectively.
Peter J Rix
Drug Safety and Disposition
Ligand Pharmaceuticals, Inc.
San Diego, CA 92121
Email: PRix.at.ligand.com
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The reason I want to fit the data points in an Eadie-Hofstee plot is
because we can visually assess the goodness of the fit, when the drug
displays either a biphasic or sigmoidal pattern . Whereas, if I fit the
data points that are clearly biphasic on E-D plot using nonlinear
regression, I will still get a good fit (Using AIC and Schwartz
criteria) even if I use a simple michaelis-menten equation (one
enzyme). The other thing is, I agree with you in saying that we can get
some estimates of the initial parameters from the Eadie-Hofstee plot if
the drug follows a biphasic pattern, but what if the drug follows
sigmoidicity?. When I was trying to fit my data (showing sigmoidicity)
using different initial parameters I am getting very different final
parameters. In that case, which fitting should I really trust. I would
appreciate your response in this regard.
Thank you
Ragini Vuppugalla
Graduate Student
Texas Tech School of Pharmacy
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Ragini,
Goodness of fit can be adequately assessed after direct non linear
regression of the v vs. S plot (saturation plot). I don't think you
benefit in this respect by trying to use the E-H or L-B plot. Of
course, one does benefit by using the shape of the E-H plot as a "guide"
as to which model to attempt to fit.
Beside the obvious minimization of both the R^2 and the standard errors
of the predicted parameters, the most important criteria one should look
for is a random distribution of residuals around zero when assessing the
model selected. This is where you will hopefully see a clear skewing
when trying to fit a one enzyme MM model to data better described by a 2
enzyme MM or Hill model. If this does not produce an obvious 'winner',
there are many more exotic criteria that have been developed for this
purpose, but I must admit that I am not a modeling expert, and others
may be more qualified to comment. I would caution that analysis of
covariance may not be a good discrimination tool because in
Michaelis-Menten models, Vmax and Km share a common rate constant in
their derivations, and are by definition, intrinsically correlated.
As to getting very different final parameters based on different initial
parameters, you may find that only one of the predicted set of
parameters passes a "reality check" and the others are often nonsense
solutions.
Peter J Rix
Ligand Pharmaceuticals, Inc.
San Diego, CA
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