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Fitting ordinary differential equations to short time course data.

Daniel Brewer1, Martino Barenco, Robin Callard

  • 1Institute of Child Health, University College London, 30 Guilford Street, London WC1N 1EH, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 19, 2007
PubMed
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This study introduces an efficient new method for estimating parameters in ordinary differential equations (ODEs) using limited, noisy time-course data, crucial for systems biology. The technique combines spline collocation with alternating least squares and noise-free value estimation.

Area of Science:

  • * Mathematical Modeling
  • * Computational Biology
  • * Applied Mathematics

Background:

  • * Ordinary differential equations (ODEs) are fundamental in modeling diverse scientific systems.
  • * Parameter estimation from time-course data is vital but lacks robust computational methods, especially in systems biology.
  • * Existing numerical methods for ODEs are sophisticated, yet fitting ODEs to data remains a challenge.

Purpose of the Study:

  • * To survey and present existing algorithms for ODE parameter estimation.
  • * To introduce and evaluate a novel, efficient technique for estimating ODEs linear in parameters.
  • * To address challenges in parameter estimation with high noise and low data points.

Main Methods:

  • * A spline-based collocation scheme is employed for numerical approximation.

Related Experiment Videos

  • * Alternating linear least squares minimization steps with repeated estimates of noise-free variables.
  • * The approach is inspired by expectation-maximization methods for handling missing data or nuisance parameters.

    • Main Results:

    • * The new technique demonstrates efficiency in estimating parameters for ODEs.
    • * It is particularly effective in scenarios with high noise levels and sparse data.
    • * Performance is evaluated against existing methods, showing promise for practical applications.

    Conclusions:

    • * The developed method offers a significant improvement for ODE parameter estimation in data-limited, noisy conditions.
    • * This technique is well-suited for applications in systems biology and other fields relying on ODE modeling.
    • * Further development and application of this method can enhance the analysis of complex dynamic systems.