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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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Evaluating model reduction under parameter uncertainty.

Håvard G Frøysa1, Shirin Fallahi2, Nello Blaser2

  • 1Department of Mathematics, University of Bergen, Mailbox 7803, Bergen, 5020, Norway. havard.froysa@uib.no.

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|July 29, 2018
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Summary

Evaluating reduced biochemical models with uncertain parameters is challenging. This study introduces a method using cluster analysis to select the best reduced model, showing parameter uncertainty dictates the extent of reduction needed.

Keywords:
ClusteringModel reductionParameter uncertaintySystems biology

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Area of Science:

  • Systems Biology
  • Computational Biology
  • Biochemical Network Modeling

Background:

  • Biochemical networks are often modeled using large systems of ordinary differential equations with numerous parameters.
  • Model reduction techniques like lumping, sensitivity analysis, and time-scale separation are crucial for simplifying these complex models.
  • Evaluating the efficacy of reduced models is difficult, especially when model parameters have uncertainty, lacking established criteria.

Purpose of the Study:

  • To develop a robust method for comparing different reduced biochemical network models.
  • To establish criteria for selecting the optimal reduced model that preserves the dynamics and uncertainty of the original full model.
  • To investigate the influence of parameter uncertainty on the choice and extent of model reduction.

Main Methods:

  • Simulated diverse parameter sets based on assumed parameter distributions for the full biochemical model.
  • Employed cluster analysis to compare the dynamics and variability of multiple reduced models against the full model across all simulated parameter sets.
  • Utilized the clustering results to identify and select the smallest reduced model that accurately approximates the full model's behavior.

Main Results:

  • The cluster analysis successfully identified reduced models that closely mirrored the dynamics and variability of the original model.
  • A direct correlation was observed between the level of parameter uncertainty and the optimal degree of model reduction.
  • Demonstrated that high parameter uncertainty necessitates further model reduction, while low uncertainty permits less reduction.

Conclusions:

  • A novel method for comparing and selecting reduced models under parameter uncertainty has been successfully developed and demonstrated.
  • This method is broadly applicable to various model reduction techniques used in systems biology.
  • The degree of parameter uncertainty is a critical factor that significantly influences the selection of an appropriate reduced model.