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Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates.

Alexander P Browning1,2,3, Matthew J Simpson1,2

  • 1School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.

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Summary

Computational biology often struggles to balance model complexity with data limitations. This study introduces a geometric approach to extract biological insights from complex, non-identifiable models using simpler, identifiable surrogate models.

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Area of Science:

  • Computational biology
  • Mathematical modeling
  • Systems biology

Background:

  • Balancing data quality and quantity with model complexity is a persistent challenge in computational biology.
  • Existing tools like identifiability analysis struggle to resolve mismatches between experimental data and the granularity needed for complex biological models.
  • Simple phenomenological models are often identifiable, limiting biological insights from more complex, mechanistic models.

Purpose of the Study:

  • To develop a novel geometric approach for analyzing complex, non-identifiable mathematical models in computational biology.
  • To bridge the gap between complex mechanistic models and simple, identifiable surrogate models for extracting biological insights.
  • To provide a new layer of interpretation beyond traditional identifiability analysis for complex biological systems.

Main Methods:

  • Studying the geometry of parameter space mapping from complex to simple, identifiable surrogate models.
  • Quantitatively relating non-identifiable parameters in complex models to identifiable parameters in surrogate models.
  • Applying a geometric approach to analyze mathematical models of multicellular tumor spheroid growth with limited and noisy experimental data.

Main Results:

  • The geometric approach successfully predicts non-identifiabilities in complex models.
  • Non-identifiable parameter spaces were classified into identifiable parameter combinations linked to surrogate model features.
  • The method enhances biological insight extraction from complex, non-identifiable models, even with limited data.

Conclusions:

  • A geometric framework offers a powerful method to interpret complex, non-identifiable models in computational biology.
  • This approach allows for the extraction of meaningful biological insights from data-limited experiments by linking complex model parameters to identifiable ones.
  • The study demonstrates the utility of geometric analysis for understanding parameter identifiability and enhancing biological discovery.