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Quantitative Biology

, Volume 6, Issue 4, pp 287–306 | Cite as

Experimental design and model reduction in systems biology

  • Jenny E. Jeong
  • Qinwei Zhuang
  • Mark K. Transtrum
  • Enlu Zhou
  • Peng QiuEmail author
Review
  • 29 Downloads

Abstract

Background

In systems biology, the dynamics of biological networks are often modeled with ordinary differential equations (ODEs) that encode interacting components in the systems, resulting in highly complex models. In contrast, the amount of experimentally available data is almost always limited, and insufficient to constrain the parameters. In this situation, parameter estimation is a very challenging problem. To address this challenge, two intuitive approaches are to perform experimental design to generate more data, and to perform model reduction to simplify the model. Experimental design and model reduction have been traditionally viewed as two distinct areas, and an extensive literature and excellent reviews exist on each of the two areas. Intriguingly, however, the intrinsic connections between the two areas have not been recognized.

Results

Experimental design and model reduction are deeply related, and can be considered as one unified framework. There are two recent methods that can tackle both areas, one based on model manifold and the other based on profile likelihood. We use a simple sum-of-two-exponentials example to discuss the concepts and algorithmic details of both methods, and provide Matlab-based code and implementation which are useful resources for the dissemination and adoption of experimental design and model reduction in the biology community.

Conclusions

From a geometric perspective, we consider the experimental data as a point in a high-dimensional data space and the mathematical model as a manifold living in this space. Parameter estimation can be viewed as a projection of the data point onto the manifold. By examining the singularity around the projected point on the manifold, we can perform both experimental design and model reduction. Experimental design identifies new experiments that expand the manifold and remove the singularity, whereas model reduction identifies the nearest boundary, which is the nearest singularity that suggests an appropriate form of a reduced model. This geometric interpretation represents one step toward the convergence of experimental design and model reduction as a unified framework.

Keywords

experimental design model reduction model manifold profile likelihood 

Notes

Acknowledgments

This work is supported by funding from the National Science Foundation (CCF1552784). Peng Qiu is an ISAC Marylou Ingram Scholar.

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jenny E. Jeong
    • 1
  • Qinwei Zhuang
    • 2
  • Mark K. Transtrum
    • 3
  • Enlu Zhou
    • 4
  • Peng Qiu
    • 5
    • 6
    Email author
  1. 1.School of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.School of Biological SciencesGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of Physics and AstronomyBrigham Young UniversityProvoUSA
  4. 4.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  5. 5.Department of Biomedical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  6. 6.Emory UniversityAtlantaUSA

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