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Identification of alterations in the Jacobian of biochemical reaction networks from steady state covariance data at two conditions

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Abstract

Model building of biochemical reaction networks typically involves experiments in which changes in the behavior due to natural or experimental perturbations are observed. Computational models of reaction networks are also used in a systems biology approach to study how transitions from a healthy to a diseased state result from changes in genetic or environmental conditions. In this paper we consider the nonlinear inverse problem of inferring information about the Jacobian of a Langevin type network model from covariance data of steady state concentrations associated to two different experimental conditions. Under idealized assumptions on the Langevin fluctuation matrices we prove that relative alterations in the network Jacobian can be uniquely identified when comparing the two data sets. Based on this result and the premise that alteration is locally confined to separable parts due to network modularity we suggest a computational approach using hybrid stochastic-deterministic optimization for the detection of perturbations in the network Jacobian using the sparsity promoting effect of \(\ell _p\)-penalization. Our approach is illustrated by means of published metabolomic and signaling reaction networks.

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Acknowledgments

We would like to thank Wolfram Weckwerth and Dirk Walther for pointing to the manuscript (Steuer et al. 2003) and for fruitful discussions.

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Authors and Affiliations

  1. Institute for Applied Mathematics and Statistics, University of Hohenheim, Schloss, 70599 , Stuttgart, Germany

    Philipp Kügler

  2. RICAM, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040 , Linz, Austria

    Philipp Kügler & Wei Yang

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  1. Philipp Kügler
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  2. Wei Yang
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Correspondence to Philipp Kügler.

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Kügler, P., Yang, W. Identification of alterations in the Jacobian of biochemical reaction networks from steady state covariance data at two conditions. J. Math. Biol. 68, 1757–1783 (2014). https://doi.org/10.1007/s00285-013-0685-3

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  • DOI: https://doi.org/10.1007/s00285-013-0685-3

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