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When can sigmoidal data be fit to a Hill curve?

Published online by Cambridge University Press:  17 February 2009

Jack Heidel  and
John Maloney
Jack Heidel
Affiliation:
Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182
John Maloney
Affiliation:
Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182
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Abstract

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The Hill equation is a fundamental expression in chemical i kinetics relating velocity of response to concentration. It is known that the Hill equation is parameter identifiable in the sense that perfect data yield a unique set of defining parameters. However not all sigmoidal curves can be well fit by Hill curves. In particular the lower part of the curve can't be too shallow and the upper part can't be too steep. In this paper an exact mathematical criterion is derived to describe the degree of shallowness allowed.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 1 , July 1999 , pp. 83 - 92
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Godfrey, K. R., Compartmental Models and their Applications (Academic Press, New York, 1983).Google Scholar
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[3]Heidel, J. and Maloney, J., “An analysis of a fractal Michaelis-Menten curve”, J. Austral. Math. Soc. Ser. B to appear.Google Scholar