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A Method for Zooming of Nonlinear Models of Biochemical Systems

Journal article
Authors Mikael Sunnåker
Gunnar Cedersund
Mats Jirstrand
Published in BMC Systems Biology
Volume 5
ISSN 1752-0509
Publication year 2011
Published at Department of Mathematical Sciences
Language en
Links dx.doi.org/10.1186/1752-0509-5-140
https://gup.ub.gu.se/file/185592
Keywords model reduction, systems theory, biochemical reaction networks, lumping
Subject categories Applied mathematics, Optimization, systems theory, Systems engineering, Biochemistry, Cell and molecular biology

Abstract

BACKGROUND: 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. RESULTS: 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. CONCLUSIONS: 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.

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