Parameter identifiability analysis and visualization in large-scale kinetic models of biosystems

Abstract

BackgroundKinetic models of biochemical systems usually consist of ordinary differential equations that have many unknown parameters. Some of these parameters are often practically unidentifiable, that is, their values cannot be uniquely determined from the available data. Possible causes are lack of influence on the measured outputs, interdependence among parameters, and poor data quality. Uncorrelated parameters can be seen as the key tuning knobs of a predictive model. Therefore, before attempting to perform parameter estimation (model calibration) it is important to characterize the subset(s) of identifiable parameters and their interplay. Once this is achieved, it is still necessary to perform parameter estimation, which poses additional challenges.MethodsWe present a methodology that (i) detects high-order relationships among parameters, and (ii) visualizes the results to facilitate further analysis. We use a collinearity index to quantify the correlation between parameters in a group in a computationally efficient way. Then we apply integer optimization to find the largest groups of uncorrelated parameters. We also use the collinearity index to identify small groups of highly correlated parameters. The results files can be visualized using Cytoscape, showing the identifiable and non-identifiable groups of parameters together with the model structure in the same graph.ResultsOur contributions alleviate the difficulties that appear at different stages of the identifiability analysis and parameter estimation process. We show how to combine global optimization and regularization techniques for calibrating medium and large scale biological models with moderate computation times. Then we evaluate the practical identifiability of the estimated parameters using the proposed methodology. The identifiability analysis techniques are implemented as a MATLAB toolbox called VisId, which is freely available as open source from GitHub (https://github.com/gabora/visid).ConclusionsOur approach is geared towards scalability. It enables the practical identifiability analysis of dynamic models of large size, and accelerates their calibration. The visualization tool allows modellers to detect parts that are problematic and need refinement or reformulation, and provides experimentalists with information that can be helpful in the design of new experiments.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-017-0428-y) contains supplementary material, which is available to authorized users.

Nonlinear robust adaptive control strategies for a lactic fermentation process

“…The development of large‐scale kinetic models is one of the key issues in biotechnology. Many kinetic models of biosystems consist of ordinary (or partially) differential equations which can have many unknown parameters . Two major problems should be solved in these systems: the parameter identifiability analysis and the design of parameter estimators .…”

“…Many kinetic models of biosystems consist of ordinary (or partially) differential equations which can have many unknown parameters . Two major problems should be solved in these systems: the parameter identifiability analysis and the design of parameter estimators . Parameter estimation in large‐scale nonlinear models is a challenging problem due to issues such as the lack of identifiability, ill‐conditioning, multimodality and over‐fitting .…”

“…30,31 Two major problems should be solved in these systems: the parameter identifiability analysis and the design of parameter estimators. 31,32 Parameter estimation in large-scale nonlinear models is a challenging problem due to issues such as the lack of identifiability, ill-conditioning, multimodality and over-fitting. 31 Usually, complex optimization and regularization techniques are applied in order to calibrate medium-and large-scale biological models with moderate or large computation times.…”

“…31,32 Parameter estimation in large-scale nonlinear models is a challenging problem due to issues such as the lack of identifiability, ill-conditioning, multimodality and over-fitting. 31 Usually, complex optimization and regularization techniques are applied in order to calibrate medium-and large-scale biological models with moderate or large computation times. 31 The model of the continuous fermentation process used for lactic acid production may be considered as a medium-scale model, consisting of eight nonlinear differential equations with about 20 parameters.…”

“…31 Usually, complex optimization and regularization techniques are applied in order to calibrate medium-and large-scale biological models with moderate or large computation times. 31 The model of the continuous fermentation process used for lactic acid production may be considered as a medium-scale model, consisting of eight nonlinear differential equations with about 20 parameters. This size of the model does not raise significant problems concerning the complexity and the computation time for parameter estimation and further for the control laws design.…”