Where to look and how to look: Combining global sensitivity analysis with fast/slow analysis to study multi-timescale oscillations
•Global sensitivity analysis is combined with fast/slow geometric analysis to find and understand the effects of key model parameters.•The analysis demonstrates that global sensitivity analysis can be a good tool for determining which parameters to focus on, while fast/slow analysis can be a good to...
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Veröffentlicht in: | Mathematical biosciences 2019-08, Vol.314, p.1-12 |
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Sprache: | eng |
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Zusammenfassung: | •Global sensitivity analysis is combined with fast/slow geometric analysis to find and understand the effects of key model parameters.•The analysis demonstrates that global sensitivity analysis can be a good tool for determining which parameters to focus on, while fast/slow analysis can be a good tool for understanding the dynamics underlying the effects of key parameters.•The analysis also demonstrates that different parameters will be key in different regimes of bursting oscillations.
Parameterized systems of nonlinear ordinary differential equations, the type of system that is often used in mathematical models for biological systems, can be of sufficient complexity that it can take years to appreciate the full range of behaviors that can be produced. Global sensitivity analysis is one tool that has been developed for determining which parameters have the largest impact on the behavior of the model. Thus, it provides the user with a tool to know where to look in parameter space for important changes in behavior. However, it says nothing about the underlying mechanism mediating a change in behavior. For this, other tools exist. If the system dynamics occur over multiple highly-separated time scales then one useful analysis tool is fast/slow geometric analysis, also known as geometric singular perturbation analysis. This is based on bifurcation analysis of a fast or slow subsystem, and can shed light on the influence that a parameter has on structures of either subsystem, and thus on the system dynamics. Hence, once one knows where to look in parameter space for interesting behavior, this technique describes how to look at the system to extract information about how parameter changes influence the behavior of the system. In this study, we combine the two techniques in the analysis of bursting behavior in a model of insulin-secreting pancreatic β-cells, with the goal of determining the key parameters setting the period of the bursting oscillations, and understanding why they are so influential. This can be viewed as a case study for combining mathematical techniques to build on the strengths of each and thereby achieve a better understanding of what most influences the range of model behaviors and how this influence is brought about. |
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ISSN: | 0025-5564 1879-3134 |
DOI: | 10.1016/j.mbs.2019.05.004 |