Clustering reveals limits of parameter identifiability in multi-parameter models of biochemical dynamics.

Karol Nienałtowski,Michał Włodarczyk,Tomasz Lipniacki,Michał Komorowski

doi:10.1186/s12918-015-0205-8

Abstract

BackgroundCompared to engineering or physics problems, dynamical models in quantitative biology typically depend on a relatively large number of parameters. Progress in developing mathematics to manipulate such multi-parameter models and so enable their efficient interplay with experiments has been slow. Existing solutions are significantly limited by model size.ResultsIn order to simplify analysis of multi-parameter models a method for clustering of model parameters is proposed. It is based on a derived statistically meaningful measure of similarity between groups of parameters. The measure quantifies to what extend changes in values of some parameters can be compensated by changes in values of other parameters. The proposed methodology provides a natural mathematical language to precisely communicate and visualise effects resulting from compensatory changes in values of parameters. As a results, a relevant insight into identifiability analysis and experimental planning can be obtained. Analysis of NF- κB and MAPK pathway models shows that highly compensative parameters constitute clusters consistent with the network topology. The method applied to examine an exceptionally rich set of published experiments on the NF- κB dynamics reveals that the experiments jointly ensure identifiability of only 60 % of model parameters. The method indicates which further experiments should be performed in order to increase the number of identifiable parameters.ConclusionsWe currently lack methods that simplify broadly understood analysis of multi-parameter models. The introduced tools depict mutually compensative effects between parameters to provide insight regarding role of individual parameters, identifiability and experimental design. The method can also find applications in related methodological areas of model simplification and parameters estimation.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-015-0205-8) contains supplementary material, which is available to authorized users.

Highlights

Compared to engineering or physics problems, dynamical models in quantitative biology typically depend on a relatively large number of parameters
Methods to understand the relationship between parameters and model properties are of particular interest in the context of biochemical dynamics and related phenomena
A priori methods focus on determining whether this condition is satisfied prior to data collection. This can be done either based on model structure, often by attempting to find functional relationships between parameters [6], or by analysing model responses to local perturbations in parameter values. The latter is achieved by examining the Fisher information matrix (FIM)

Summary

Introduction

Compared to engineering or physics problems, dynamical models in quantitative biology typically depend on a relatively large number of parameters. A priori methods focus on determining whether this condition is satisfied prior to data collection This can be done either based on model structure, often by attempting to find functional relationships between parameters [6], or by analysing model responses to local perturbations in parameter values. The latter is achieved by examining the Fisher information matrix (FIM). MI-CCA, when employed in a hierarchical clustering, provides statistically meaningful and precise information about mutual compensability of parameters. It can be used as an assistance tool to validate parameters identifiability in experimental planning. We show how the method can be used to guide further experiments

Methods

Results

Conclusion