Estimating Enzyme Kinetic Parameters from Apparent KMs and Vmaxs

The kinetic properties of enzymes are often reported using the apparent KM and Vmax appropriate to the standard Michaelis-Menten enzyme. However, this model is inappropriate to enzymes that have more than one substrate or where the rate expression does not apply for other reasons. Consequently, it is desirable to have a means of estimating the appropriate kinetic parameters from the apparent values of KM and Vmax reported for each substrate. We provide a means of estimating the range within which the parameters should lie and apply the method to data for glutamate dehydrogenase from the nematode parasite of sheep Teladorsagia circumcincta.




References:
[1] L. Michaelis and M. L. Menten, "Die Kinetik der Invertinwirkung,"
Biochemische Zeitschrift, vol. 49, pp. 333-369, 1913.
[2] N. Muhamad, D. C. Simcock, K. C. Pedley, H. V. Simpson, and S.
Brown, "The kinetics of glutamate dehydrogenase of Teladorsagia
circumcincta and the lifestyle of the parasite," Comparative
Biochemistry and Physiology, submitted for publication, 2011.
[3] C. M. Hill, R. D. Waight, and W. G. Bardsley, "Does any enzyme
follow the Michaelis-Menten equation?," Molecular and Cellular
Biochemistry, vol. 15, pp. 173-178, 1977.
[4] K. Dalziel, "The interpretation of kinetic data for enzyme-catalysed
reactions involving three substrates," Biochemical Journal, vol. 114,
pp. 547-556, 1969.
[5] K. R. F. Elliott and K. F. Tipton, "A kinetic analysis of enzyme systems
involving four substrates," Biochemical Journal, vol. 141, pp. 789-805,
1974.
[6] A. Chang, M. Scheer, A. Grote, I. Schomburg, and D. Schomburg,
"BRENDA, AMENDA and FRENDA the enzyme information system:
new content and tools in 2009," Nucleic Acids Research, vol. 37, pp.
D588-D592, 2009.
[7] G. E. Briggs and J. B. S. Haldane, "A note on the kinetics of enzyme
action," Biochemical Journal, vol. 19, pp. 338-339, 1925.
[8] U. Borgmann, K. J. Laidler, and T. W. Moon, "Four- and five-step
kinetic models of lactate dehydrogenase," Canadian Journal of
Biochemistry, vol. 54, pp. 915-918, 1976.
[9] J. A. Urbina and V. Azavache, "Regulation of energy metabolism in
Trypanosoma (Schizotrypanum) cruzi epimastigotes. II. NAD+-
dependent glutamate dehydrogenase," Molecular and Biochemical
Parasitology, vol. 11, pp. 241-255, 1984.
[10] R. E. Moore, Methods and applications of interval analysis.
Philadelphia: Society for Industrial and Applied Mathematics, 1979.
[11] W. G. Bardsley, P. Leff, J. Kavanagh, and R. D. Waight, "Deviations
from Michaelis-Menten kinetics. The possibility of complicated curves
for simple kinetic schemes and the computer fitting of experimental
data for acetylcholinesterase, acid phosphatase, adenosine deaminase,
arylsulphatase, benzylamine oxidase, chymotrypsin, fumarase,
galactose dehydrogenase, ß-galactosidase, lactate dehydrogenase,
peroxidase and xanthine oxidase," Biochemical Journal, vol. 187, pp.
739-765, 1980.
[12] J. Mayer, K. Khairy, and J. Howard, "Drawing an elephant with four
complex parameters," American Journal of Physics, vol. 78, pp. 648-
649, 2010.
[13] J. R. Kinghorn and J. A. Pateman, "NAD and NADP L-glutamate
dehydrogenase activity and ammonium regulation in Aspergillus
nidulans," Journal of General Microbiology, vol. 78, pp. 39-46, 1973.
[14] G. L. Abrahams and V. R. Abratt, "The NADH-dependent glutamate
dehydrogenase enzyme of Bacteroides fragilis Bf1 is induced by
peptides in the growth medium," Microbiology, vol. 144, pp. 1659-
1667, 1998.
[15] C. Frieden, "Glutamic dehydrogenase. III. The order of substrate
addition in the enzymatic reaction," Journal of Biological Chemistry,
vol. 234, pp. 2891-2896, 1959.
[16] J. E. Rife and W. W. Cleland, "Kinetic mechanism of glutamate
dehydrogenase," Biochemistry, vol. 19, pp. 2321-2328, 1980.
[17] D. P. Hornby, M. J. Aitchison, and P. C. Engel, "The kinetic
mechanism of ox liver glutamate dehydrogenase in the presence of the
allosteric effector ADP. The oxidative deamination of L-glutamate,"
Biochemical Journal, vol. 223, pp. 161-168, 1984.
[18] NC-IUB Nomenclature Committee of the International Union of
Biochemistry, "Symbolism and terminology in enzyme kinetics.
Recommendations 1981," European Journal of Biochemistry, vol. 128,
pp. 281-291, 1982.
[19] S. Brown, "Developing the enzyme-machine analogy: a nonmathematical
approach to teaching Michaelis-Menten kinetics,"
Orbital, vol. 2, pp. 92-100, 2010.
[20] D. P. Bertsekas, Constrained optimization and Lagrange multiplier
methods. Belmont: Athena Scientific, 1996.