Graphical spreadsheet tools for learning enzyme kinetics

Simon Brown, David C. Simcock


Many students lack sufficient mathematical skill or confidence to be able to visualise a process just by looking at an equation. This is particularly apparent when students are working on the dynamics of enzyme action.  Understanding the basic concepts of enzyme kinetics is essential to any appreciation of the chemical processes that occur in living organisms.  Fortunately, learning can be enhanced by direct manipulation of the parameters while students observe the behaviour of the graphs of the functions.  Spreadsheets are described that enable students to analyse the significance of the parameters at several levels, to connect concepts between levels of treatment and to use the basic expression in the analysis of their own experiments.  Methods for constructing these spreadsheets in Excel and the essentials of the relevant theory are also summarised.

Full Text:



M. Aksu, "Student performance in dealing with fractions," Journal of Educational Research, vol. 90, pp. 375-380, 1997.

D. Arganbright, "Enhancing mathematical graphical displays in Excel through animation," Spreadsheets in Education, vol. 2, pp. 125-147, 2005.

A. Ault, "An introduction to enzyme kinetics," Journal of Chemical Education, vol. 51, pp. 381-386, 1974.

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.

M. Blunck and T. P. Mommsen, "Systematic errors in fitting linear transformations of the Michaelis-Menten equation," Biometrika, vol. 65, pp. 363-368, 1978.

G. E. Briggs and J. B. S. Haldane, "A note on the kinetics of enzyme action," Biochemical Journal, vol. 19, pp. 338-339, 1925.

S. Brown, "The units tell you what to do," Acta Didactica Napocensia, vol. 2, pp. 91-99, 2009.

S. Brown, "Developing the enzyme-machine analogy: a non-mathematical approach to teaching Michaelis-Menten kinetics," Orbital, vol. 2, pp. 92-100, 2010.

S. Brown, "The problem of translation: science and the language of science in the classroom," Journal of Didactics, vol. 3, pp. 1-15, 2012.

S. Brown, L. F. Blackwell, and D. G. Cooke, "Online fertility monitoring: some of the issues," International Journal of Open Information Technologies, vol. 5, pp. 85-91, 2017.

S. Brown, N. Muhamad, K. C. Pedley, and D. C. Simcock, "A simple confidence band for the Michaelis-Menten equation," International Journal of Emerging Sciences, vol. 2, pp. 238-246, 2012.

S. Brown, N. Muhamad, and D. C. Simcock, "Estimating enzyme kinetic parameters from apparent KMs and Vmaxs," International Journal of Chemical and Biological Engineering, vol. 3, pp. 200-205, 2010.

S. Brown and S. Salter, "Analogy in science and science teaching," Advances in Physiology Education, vol. 34, pp. 167-169, 2010.

S. Brown and D. C. Simcock, "Confidence bands for rational rate equations," International Journal of Emerging Sciences, vol. 3, pp. 15-27, 2013.

S. Brown and D. C. Simcock, "On series approximations of Michaelis-Menten kinetics," Scientia, vol. 126, pp. art01, 2014.

S. Brown and D. C. Simcock, "Structural and functional properties of glutamate dehydrogenases," in Handbook of microbial metabolism of amino acids, J. P. F. D'Mello, Ed. Wallingford: CAB International, 2017, pp. 1-14.

M. F. Bruist, "Use of a spreadsheet to simulate enzyme kinetics," Journal of Chemical Education, vol. 75, pp. 372-375, 1998.

B. Chance, "The kinetics of the enzyme-substrate compound of peroxidase," Journal of Biological Chemistry, vol. 151, pp. 553-577, 1943.

D. G. Cooke, L. F. Blackwell, and S. Brown, "A graphical trap for unwary users of Excel 2010," International Journal of Open Information Technologies, vol. 4, pp. 7-10, 2016.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, "On the Lambert W function," Advances in Computational Mathematics, vol. 5, pp. 329-359, 1996.

A. Cornish-Bowden, "Why is uncompetitive inhibition so rare? A possible explanation, with implications for the design of drugs and pesticides," FEBS Letters, vol. 203, pp. 3-6, 1986.

J. E. Dowd and D. S. Riggs, "A comparison of estimates of Michaelis-Menten kinetic constants from various linear transformations," Journal of Biological Chemistry, vol. 240, pp. 863-869, 1965.

R. G. Duggleby, "A nonlinear regression program for small computers," Analytical Biochemistry, vol. 110, pp. 8-18, 1981.

R. G. Duggleby, "Regression analysis of nonlinear arrhenius plots: an empirical model and a computer program," Computers in Biology and Medicine, vol. 14, pp. 447-455, 1984.

K. Ebert, H. Ederer, and T. L. Isenhour, Computer Applications in Chemistry. Weinheim: VCH Verlagsgesellschaft, 1989.

F. N. Fritsch, R. E. Shafer, and W. P. Crowley, "Algorithm 443: solution of the transcendental equation wew = x," Communications of the ACM, vol. 16, pp. 123-124, 1973.

C. Furió, R. Azcona, and J. Guisasola, "The learning and teaching of the concepts 'amount of substance' and 'mole': a review of the literature," Chemistry Education: Research and Practice, vol. 3, pp. 277-292, 2002.

N. Gains, "Unreliability of rate constants derived from a linear transformation of kinetic data, with special reference to cholesterol equilibration between phospholipid vesicles," Biochemical Journal, vol. 283, pp. 537-539, 1992.

M. L. Johnson, "Why, when, and how biochemists should use least squares," Analytical Biochemistry, vol. 206, pp. 215-225, 1992.

N. Jourdan, P. Cretchley, and T. Passmore, "Secondary-tertiary transition: what mathematics skills can and should we expect this decade?," presented at Mathematics: essential research, essential practice, Hobart, 2007.

H. Lineweaver and D. Burk, "The determination of enzyme dissociation constants," Journal of the American Chemical Society, vol. 56, pp. 658-666, 1934.

Р. В. Майер, "Решение физических задач с помощью электронных таблиц MS Excel," International Journal of Open Information Technologies, vol. 2, pp. 18-23, 2014.

D. W. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," Journal of the Society for Industrial and Applied Mathematics, vol. 11, pp. 431-441, 1963.

L. Michaelis and M. L. Menten, "Die Kinetik der Invertinwirkung," Biochemische Zeitschrift, vol. 49, pp. 333-369, 1913.

M. J. Moloney, "Simple acoustic source radiation near a large wall," American Journal of Physics, vol. 71, pp. 794-796, 2003.

J. Monod, J. Wyman, and J. -P. Changeux, "On the nature of allosteric transitions: a plausible model," Journal of Molecular Biology, vol. 12, pp. 88-118, 1965.

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, vol. 159B, pp. 71-77, 2011.

D. A. Phoenix, "Numeracy and the life scientist!," Journal of Biological Education, vol. 34, pp. 3-4, 1999.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C. The Art of Scientific Computing, 2 ed. Cambridge: Cambridge University Press, 1992.

I. H. Segel, Enzyme kinetics: behavior and analysis of rapid equilibrium and steady-state enzyme systems. Chichester: Wiley-Interscience, 1993.

V. Tariq, "Diagnosis of mathematical skills among bioscience entrants," in Diagnostic testing for mathematics, MathsTEAM, Ed. Birmingham: Learning and Teaching Support Network, 2003, pp. 14-15.

V. Tariq, "Defining the problem: mathematical errors and misconceptions exhibited by first-year bioscience undergraduates," International Journal of Mathematical Education in Science and Technology, vol. 39, pp. 889-904, 2008.

R. D. H. Warburton and J. Wang, "Analysis of asymptotic projectile motion with air resistance using the Lambert W function," American Journal of Physics, vol. 72, pp. 1404-1407, 2004.

J. L. Webb, Enzyme and metabolic inhibitors. New York: Academic Press Inc., 1966.

M. L. Witherspoon, "Fractions: in search of meaning," Arithmetic Teacher, vol. 40, pp. 482-485, 1993.

E. J. Wood, "Biochemistry is a difficult subject for both student and teacher," Biochemical Education, vol. 18, pp. 170-172, 1990.


  • There are currently no refbacks.

IT-EDU-2017   RTUWO 2017

ISSN: 2307-8162