Optimal Experimental Design for Parameter Estimation of an IL-6 Signaling Model

Abstract

IL-6 signaling plays an important role in inflammatory processes in the body. While a number of models for IL-6 signaling are available, the parameters associated with these models vary from case to case as they are non-trivial to determine. In this study, optimal experimental design is utilized to reduce the parameter uncertainty of an IL-6 signaling model consisting of ordinary differential equations, thereby increasing the accuracy of the estimated parameter values and, potentially, the model itself. The D-optimality criterion, operating on the Fisher information matrix and, separately, on a sensitivity matrix computed from the Morris method, was used as the objective function for the optimal experimental design problem. Optimal input functions for model parameter estimation were identified by solving the optimal experimental design problem, and the resulting input functions were shown to significantly decrease parameter uncertainty in simulated experiments. Interestingly, the determined optimal input functions took on the shape of PRBS signals even though there were no restrictions on their nature. Future work should corroborate these findings by applying the determined optimal experimental design on a real experiment.

Diverse cell stimulation kinetics identify predictive signal transduction models

“…The Fisher information matrix (FIM) analysis was used to estimate expected parameter uncertainty for different experiment designs (Apgar et al, 2010;Fox and Munsky, 2019;Hagen et al, 2013;Jetka et al, 2018;Komorowski et al, 2011). The FIM provides the amount of information an observable could provide around an unknown parameter, and it has been extensively used to estimate how well potential experiments will constrain model parameters (Apgar et al, 2008;Bandara et al, 2009;Fox and Munsky, 2019;Sinkoe et al, 2017;Stewart-Ornstein et al, 2017). The FIM -1 , the inverse of the FIM, known as the Cramer-Rao bound (CRB), is in particular useful as it provides a lower bound on the variance for any unbiased estimator of model parameters (Aitkin, 2010).…”

“…To date, most computational models have been fit to experiments at steady state in different environments (Hao and O'Shea, 2012) or under step-like perturbations from one baseline level to another (Klipp et al, 2005;Sinkoe et al, 2017) ( Figure 1A). However, life evolved to thrive in the presence of gradual changes (Harvey and Smith, 2009;Sorre et al, 2014), and recent studies have demonstrated that many cells respond differently to inputs of equal magnitudes based upon specific variations in input kinetics, such as different temporal frequencies (Albeck et al, 2013;Ashall et al, 2009;Cai et al, 2008;Hao and O'Shea, 2012;Hersen et al, 2008;Mettetal et al, 2008;Wang et al, 2012) or different spatial gradients (Harvey and Smith, 2009).…”

Special Issue on “Biological Networks”

“…Two papers in this Special Issue explore the model-based optimal design of experiments (MBDOE) via the Fisher information matrix (FIM). The paper by Sinkoe and Hahn [2] showcases the importance of optimizing experiments for improving the practical identifiability of model parameters, especially in connection to dynamic biological data and modeling. More specifically, the paper describes the application of the FIM-based D-optimality criterion and the Morris method for computing parametric sensitivities, to optimize dynamic input functions to the interleukin-6 signaling model.…”

The Impact of Global Sensitivities and Design Measures in Model-Based Optimal Experimental Design

“…In the literature, most implementations of MB-OED are based on local sensitivities as part of the Fisher information matrix (FIM) [12,14,16,[18][19][20]. Technically, the inverse of the FIM is used to approximate the covariance matrix of the parameter estimates [12,14,18].…”