Determination of Parameters in Chemical and Biochemical Non-Linear Models using Simulated Data with Gaussian Noise Perturbation

Keywords

Chemical and biochemical models, Data simulation, Gaussian noise

Abstract

The Michaelis-Menten kinetics is a well-known model in biochemistry, widely used in enzyme-substrate interaction (Nelson and Cox, 2008). The same mathematical formula is called Langmuir equation (Masel, 1996) when is used to model generic adsorption of chemical species, and finally, an empirical equation of this form is applied to microbial growth and it is called J. Monod kinetics (Martinez-Luaces, 2008). A typical problem in chemistry and/or biochemistry consists in determining the parameters of these equations from experimental data. In order to solve this problem, several methods were proposed, Lineweaver-Burk, Hanes-Woolf, Hofstee, Scatchard and Cornish-Bowden-Eisenthal are the most important ones (Nelson and Cox, 2008). In this paper, all these methods are analysed and compared in terms of exactitude and precision. For this purpose, simulated data were generated and perturbed using Gaussian noise with different amplitudes. The same methodology was used in a previous work (Martinez-Luaces, 2009). Absolute and relative errors of the different methods are compared, and taking into account the results, general conclusions about their robustness are obtained. This is particularly important in order to choose the best method when the relation between trend and noise tends to increase.

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