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Open Access Highly Accessed Methodology article

Efficient characterization of high-dimensional parameter spaces for systems biology

Elías Zamora-Sillero123*, Marc Hafner134, Ariane Ibig23, Joerg Stelling23 and Andreas Wagner1356

Author Affiliations

1 Department of Biochemistry, University of Zurich, Zurich, Switzerland

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

3 Swiss Institute of Bioinformatics, Lausanne, Switzerland

4 School of Computer and Communication, EPFL, Lausanne, Switzerland

5 The Santa Fe Institute, Santa Fe, New Mexico, USA

6 Department of Biology, University of New Mexico, Albuquerque, New Mexico, USA

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BMC Systems Biology 2011, 5:142  doi:10.1186/1752-0509-5-142

Published: 15 September 2011

Abstract

Background

A biological system's robustness to mutations and its evolution are influenced by the structure of its viable space, the region of its space of biochemical parameters where it can exert its function. In systems with a large number of biochemical parameters, viable regions with potentially complex geometries fill a tiny fraction of the whole parameter space. This hampers explorations of the viable space based on "brute force" or Gaussian sampling.

Results

We here propose a novel algorithm to characterize viable spaces efficiently. The algorithm combines global and local explorations of a parameter space. The global exploration involves an out-of-equilibrium adaptive Metropolis Monte Carlo method aimed at identifying poorly connected viable regions. The local exploration then samples these regions in detail by a method we call multiple ellipsoid-based sampling. Our algorithm explores efficiently nonconvex and poorly connected viable regions of different test-problems. Most importantly, its computational effort scales linearly with the number of dimensions, in contrast to "brute force" sampling that shows an exponential dependence on the number of dimensions. We also apply this algorithm to a simplified model of a biochemical oscillator with positive and negative feedback loops. A detailed characterization of the model's viable space captures well known structural properties of circadian oscillators. Concretely, we find that model topologies with an essential negative feedback loop and a nonessential positive feedback loop provide the most robust fixed period oscillations. Moreover, the connectedness of the model's viable space suggests that biochemical oscillators with varying topologies can evolve from one another.

Conclusions

Our algorithm permits an efficient analysis of high-dimensional, nonconvex, and poorly connected viable spaces characteristic of complex biological circuitry. It allows a systematic use of robustness as a tool for model discrimination.