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Open Access Highly Accessed Methodology article

A method for zooming of nonlinear models of biochemical systems

Mikael Sunnåker123*, Gunnar Cedersund456 and Mats Jirstrand1

Author Affiliations

1 Fraunhofer-Chalmers Research Centre for Industrial Mathematics, 412 88 Gothenburg, Sweden

2 Department of Biosystems Science and Engineering, ETH Zurich, Switzerland

3 Competence Center for Systems Physiology and Metabolic Diseases, ETH Zurich, Switzerland

4 Department of Clinical and Experimental Medicine, Diabetes and Integrative Systems Biology, Linkoping University, 581 85 Linkoping, Sweden

5 Freiburg Institute of Advanced Sciences, Freiburg University, D79104 Freiburg, Germany

6 Department of Mathematical Sciences, Gothenburg University, 412 96 Gothenburg, Sweden

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BMC Systems Biology 2011, 5:140  doi:10.1186/1752-0509-5-140

Published: 7 September 2011



Models of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model.


In this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in baker's yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved.


We introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to nonlinear models.