Abstract

BackgroundUtilizing kinetic models of biological systems commonly require computational approaches to estimate parameters, posing a variety of challenges due to their highly non-linear and dynamic nature, which is further complicated by the issue of non-identifiability. We propose a novel parameter estimation framework by combining approaches for solving identifiability with a recently introduced filtering technique that can uniquely estimate parameters where conventional methods fail. This framework first conducts a thorough analysis to identify and classify the non-identifiable parameters and provides a guideline for solving them. If no feasible solution can be found, the framework instead initializes the filtering technique with informed prior to yield a unique solution.ResultsThis framework has been applied to uniquely estimate parameter values for the sucrose accumulation model in sugarcane culm tissue and a gene regulatory network. In the first experiment the results show the progression of improvement in reliable and unique parameter estimation through the use of each tool to reduce and remove non-identifiability. The latter experiment illustrates the common situation where no further measurement data is available to solve the non-identifiability. These results show the successful application of the informed prior as well as the ease with which parallel data sources may be utilized without increasing the model complexity.ConclusionThe proposed unified framework is distinct from other approaches by providing a robust and complete solution which yields reliable and unique parameter estimation even in the face of non-identifiability.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0500-9) contains supplementary material, which is available to authorized users.

Highlights

  • Utilizing kinetic models of biological systems commonly require computational approaches to estimate parameters, posing a variety of challenges due to their highly non-linear and dynamic nature, which is further complicated by the issue of non-identifiability

  • There are no general methods for introducing constraints into the estimation process in unscented Kalman filter (UKF), which is crucial in biological modelling to ensure biologically meaningful parameter values [16]

  • The square-root variation of UKF (SR-UKF) proposed by Merwe and Wan, 2001 solves the numerical stability problem of the UKF but does not have the mechanism to introduce constraints into its estimation procedure. These issues have been addressed with the development of the constrained square-root unscented Kalman filter (CSUKF), a constrained extension of the SR-UKF, which was designed for use with biological models [17]

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Summary

Introduction

Utilizing kinetic models of biological systems commonly require computational approaches to estimate parameters, posing a variety of challenges due to their highly non-linear and dynamic nature, which is further complicated by the issue of non-identifiability. The KF operates by approximating the probability density function of the parameters and can cope efficiently with multi-modality, asymmetries and discontinuities [10] This is a very powerful technique which can perform estimation even when the precise knowledge of the model is not available or the measurement data is noisy and incomplete [11]. The square-root variation of UKF (SR-UKF) proposed by Merwe and Wan, 2001 solves the numerical stability problem of the UKF but does not have the mechanism to introduce constraints into its estimation procedure These issues have been addressed with the development of the constrained square-root unscented Kalman filter (CSUKF), a constrained extension of the SR-UKF, which was designed for use with biological models [17]. The CSUKF estimates the parameters within a biologically meaningful parameter space while guaranteeing numerical stability of the filtering technique by ensuring positive definiteness of the covariance matrix

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