Chapter 37 Leaving the Steady State: Analysis of Progress Curves The HENRI –MICHAELIS–MENTEN-law v D dŒP dt D dŒS dt D V max ŒS K m C ŒS (37.1) can be integrated (assuming ŒP 0 = 0 at t = 0), leading to: ŒP t t D V max C K m ln 1 ŒP t ŒS 0 t (37.2) or, if the decrease in substrate is measured ŒS 0 ŒS t t D V max K m ln ŒS 0 ŒS t t (37.3) (HENRI-equation). Thus K m and V max can be determined from a single reaction, plotting ŒP t t as a function of ln 1 ŒP t ŒS 0 t or, alternatively, ŒS 0 ŒS t t as a function of ln ŒS 0 ŒS t t . This would obviously result in great savings in time and material. For enzymes that use several substrates, all substrates except that being studied have to be held at near saturating concentration (say, 10 K m ). However, the precision for the parameters V max and K m determined this way is much lower than by the conventional variation of ŒS. Also, since all measure- ments are obtained from a single experiment, they are highly correlated and normal least-square ﬁtting techniques give artiﬁcially low error estimates for the parameters. Therefore, this method is rarely used. However, [83, 304] give details on it, if the need arises. E. Buxbaum, Biophysical Chemistry of Proteins: An Introduction to Laboratory Methods, DOI 10.1007/978-1-4419-7251-4 37, © Springer Science+Business Media, LLC 2011 367

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Page 1: Biophysical Chemistry of Proteins || Leaving the Steady State: Analysis of Progress Curves

Chapter 37Leaving the Steady State: Analysisof Progress Curves

The HENRI–MICHAELIS–MENTEN-law

v D dŒP �

dtD �dŒS�

dtD Vmax � ŒS�

Km C ŒS�(37.1)

can be integrated (assuming ŒP �0 = 0 at t = 0), leading to:

ŒP �tt

D Vmax C Km �ln

�1 � ŒP �t

ŒS�0

�

t(37.2)

or, if the decrease in substrate is measured

ŒS�0 � ŒS�tt

D Vmax � Km �ln

�ŒS�0ŒS�t

�

t(37.3)

(HENRI-equation). Thus Km and Vmax can be determined from a single reaction,

plotting ŒP �tt

as a function ofln

�1� ŒP �t

ŒS�0

�

tor, alternatively, ŒS�0�ŒS�t

tas a function

ofln

�ŒS�0ŒS�t

�

t. This would obviously result in great savings in time and material. For

enzymes that use several substrates, all substrates except that being studied have tobe held at near saturating concentration (say, 10 � Km).

However, the precision for the parameters Vmax and Km determined this wayis much lower than by the conventional variation of ŒS�. Also, since all measure-ments are obtained from a single experiment, they are highly correlated and normalleast-square fitting techniques give artificially low error estimates for the parame-ters. Therefore, this method is rarely used. However, [83, 304] give details on it, ifthe need arises.

E. Buxbaum, Biophysical Chemistry of Proteins: An Introductionto Laboratory Methods, DOI 10.1007/978-1-4419-7251-4 37,© Springer Science+Business Media, LLC 2011

367