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Parameter inference in dynamical systems with co-dimension 1 bifurcations.

Elisabeth Roesch¹, Michael P H Stumpf¹

¹Melbourne Integrative Genomics, School of BioScience and School of Mathematics & Statistics, University of Melbourne, Parkville, Australia.

Royal Society Open Science

|December 12, 2019

Summary

Understanding biological systems requires analyzing bifurcations. This study reveals that identifying the bifurcation diagram is crucial before inferring kinetic parameters from data.

Keywords:

bifurcation parameter inference stability analysis

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Area of Science:

Biology
Dynamical Systems
Theoretical Biology

Background:

Biological processes often exhibit complex dynamics governed by dynamical systems.
Bifurcations, where small parameter changes cause qualitative shifts in behavior, are common in biology.
Inferring the structure and parameters of these systems from empirical data is challenging.

Purpose of the Study:

To investigate the impact of bifurcations on inferring model parameters and initial conditions from data.
To analyze the relationship between system dynamics, specifically bifurcations, and the ability to estimate kinetic parameters.
To provide practical implications for analyzing biological dynamical systems with unknown structures.

Main Methods:

Focus on canonical co-dimension 1 bifurcations.
Comprehensive analysis linking system dynamics to parameter inference capabilities.
Theoretical investigation of bifurcations' influence on data-driven modeling.

Main Results:

The presence of bifurcations significantly affects the identifiability of model parameters and initial conditions.
A nuanced relationship exists between the qualitative dynamics (bifurcation diagram) and quantitative parameter estimation.
Inference challenges are heightened near bifurcation points.

Conclusions:

Identifying the bifurcation diagram is a critical prerequisite for accurate kinetic parameter inference in biological dynamical systems.
Understanding the qualitative dynamics should precede attempts at quantitative parameter estimation.
This approach enhances the reliability of modeling complex biological behaviors.