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Journal of Chemistry
Volume 2017 (2017), Article ID 6560983, 12 pages
Research Article

Robust Nonlinear Regression in Enzyme Kinetic Parameters Estimation

1Faculty of Chemistry and Technology, University of Split, Ruđera Boškovića 35, 21000 Split, Croatia
2Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Ruđera Boškovića 32, 21000 Split, Croatia

Correspondence should be addressed to Tea Marasović; rh.bsef@vosaramt

Received 18 October 2016; Accepted 6 February 2017; Published 5 March 2017

Academic Editor: Murat Senturk

Copyright © 2017 Maja Marasović et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Accurate estimation of essential enzyme kinetic parameters, such as and , is very important in modern biology. To this date, linearization of kinetic equations is still widely established practice for determining these parameters in chemical and enzyme catalysis. Although simplicity of linear optimization is alluring, these methods have certain pitfalls due to which they more often then not result in misleading estimation of enzyme parameters. In order to obtain more accurate predictions of parameter values, the use of nonlinear least-squares fitting techniques is recommended. However, when there are outliers present in the data, these techniques become unreliable. This paper proposes the use of a robust nonlinear regression estimator based on modified Tukey’s biweight function that can provide more resilient results in the presence of outliers and/or influential observations. Real and synthetic kinetic data have been used to test our approach. Monte Carlo simulations are performed to illustrate the efficacy and the robustness of the biweight estimator in comparison with the standard linearization methods and the ordinary least-squares nonlinear regression. We then apply this method to experimental data for the tyrosinase enzyme (EC extracted from Solanum tuberosum, Agaricus bisporus, and Pleurotus ostreatus. The results on both artificial and experimental data clearly show that the proposed robust estimator can be successfully employed to determine accurate values of and .