A simple method for identifying parameter correlations in partially observed linear dynamic models.

Pu Li,Quoc Dong Vu

doi:10.1186/s12918-015-0234-3

Pu Li, Quoc Dong Vu

Open Access

https://doi.org/10.1186/s12918-015-0234-3

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Abstract

BackgroundParameter estimation represents one of the most significant challenges in systems biology. This is because biological models commonly contain a large number of parameters among which there may be functional interrelationships, thus leading to the problem of non-identifiability. Although identifiability analysis has been extensively studied by analytical as well as numerical approaches, systematic methods for remedying practically non-identifiable models have rarely been investigated.ResultsWe propose a simple method for identifying pairwise correlations and higher order interrelationships of parameters in partially observed linear dynamic models. This is made by derivation of the output sensitivity matrix and analysis of the linear dependencies of its columns. Consequently, analytical relations between the identifiability of the model parameters and the initial conditions as well as the input functions can be achieved. In the case of structural non-identifiability, identifiable combinations can be obtained by solving the resulting homogenous linear equations. In the case of practical non-identifiability, experiment conditions (i.e. initial condition and constant control signals) can be provided which are necessary for remedying the non-identifiability and unique parameter estimation. It is noted that the approach does not consider noisy data. In this way, the practical non-identifiability issue, which is popular for linear biological models, can be remedied. Several linear compartment models including an insulin receptor dynamics model are taken to illustrate the application of the proposed approach.ConclusionsBoth structural and practical identifiability of partially observed linear dynamic models can be clarified by the proposed method. The result of this method provides important information for experimental design to remedy the practical non-identifiability if applicable. The derivation of the method is straightforward and thus the algorithm can be easily implemented into a software packet.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-015-0234-3) contains supplementary material, which is available to authorized users.

Highlights

Parameter estimation represents one of the most significant challenges in systems biology
In a recent study [15], we proposed a method that is able to analytically identify both pairwise parameter correlations and higher order interrelationships among parameters in nonlinear dynamic models
We propose a simple method which can be used for identifying pairwise and higher order parameter correlations in partially observed linear dynamic models

Summary

Introduction

Parameter estimation represents one of the most significant challenges in systems biology This is because biological models commonly contain a large number of parameters among which there may be functional interrelationships, leading to the problem of non-identifiability. Many biological models contain a large number of parameters to be estimated, among which some parameters may have functional interrelationships. More important is that biologists experiment with living cells and the possibilities to stimulate the cells are limited, i.e. the control signals and the initial condition cannot be chosen at will This limitation leads to challenges in parameter estimation [11,12,13], Li and Vu BMC Systems Biology (2015) 9:92 in particular, the model can be non-identifiable, which is the concern of this paper

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