(371p) Time-Varying Model Identification of Nonlinear Systems with Partially Known Model Structure: Application to NF?B Signaling Pathway Induced by LPS and BFA

One obstacle in the model development for a new chemical process is the lack of quantitative, systems-level information regarding the underlying chemical reaction network [1]. Specifically, for a new or partially understood process, its reaction network topology, the reaction mechanisms, and involved reaction intermediates are partially known or unknown beforehand [1, 2]. In this work, we propose a numerical scheme to construct a time-varying model to accurately represent a partially known chemical reaction network based on a nominal model available from the literature. Here, a nominal model refers to a preliminary model, which represents the chemical reaction network of interest constructed based on the available experimental observations as well as the previous studies. The proposed methodology consists of sequential implementation of global sensitivity analysis, unsupervised machine learning for data clustering, and parameter estimation. First, a set of important parameters of the nominal model is determined by performing the global sensitivity analysis, and these identified parameters are allowed to be piecewise constants while the remaining parameters are time-invariant. Second, the available experimental measurements are clustered into several temporal subdomains, where these important model parameters take different values in each temporal subdomain. In this study, motivated by the recent studies, an unsupervised learning technique is proposed to cluster experimental data, and the optimal number of temporal subdomains is determined by maximizing intracluster similarity and minimizing intercluster dissimilarity [3, 4]. Lastly, a least-squares problem is solved to estimate the values of the parameters in each temporal subdomain by minimizing the difference between the experimental measurements and model predictions. In order to ensure the validity of the estimated parameters’ values, constraints can be given to the least-squares problem if the physical ranges of the parameters’ values are known a priori.

The validity of the proposed method was demonstrated by developing a time-varying model for the NFκB signaling pathway induced by brefeldin A (BFA). Although the NFκB system has been extensively studied because of its importance in cellular survival and inflammation, it is not yet fully characterized. This is partially because the NFκB signaling pathway can be activated by around 100 different stimuli with different corresponding reaction mechanisms, and the NFκB signaling pathway initiated by only a few stimuli such as LPS is well characterized. Compared to LPS, the NFκB dynamics induced by BFA are only partially understood with the limited model availability. Based on the fact that the NFκB signaling dynamics induced by both LPS and BFA share core mechanisms, the proposed mechanism was implemented to construct a time-varying model for the BFA-induced NFκB signaling pathway based on the model for the LPS-induced dynamics and flow cytometry measurements [5]. Compared to the time-invariant model developed in the previous study [5], the proposed model was able to predict the signaling dynamics more accurately, which demonstrated the validity of the proposed methodology. In summary, the proposed methodology can reduce the overall time required for the model development without compromising the prediction accuracy when the underlying chemical reaction network is only partially known.

References

[1] Willis, M.J.; von Stosch, M. Inference of chemical reaction networks using mixed integer linear programming, Computers and Chemical Engineering 2016, 90, 31-43.

[2] Cho, K.-H.; Choo, S.-M.; Jung, S.H.; Kim, J.-R.; Choi, H.-S.; Kim, J. Reverse engineering of gene regulatory networks, IET Systems Biology 2007, 1, 149 – 163.

[3] Tan, M.P.; Broach, J.R.; Floudas, C.A. A novel clustering approach and prediction of optimal number of clusters: global optimum search with enhanced positioning, Journal of Global Optimization 2007, 39, 323 - 346.

[4] Narasingam, A.; Siddhamshetty, P.; Kwon, J. S. Temporal clustering for order reduction of nonlinear parabolic PDE systems with time‐dependent spatial domains: Application to a hydraulic fracturing process. AIChE Journal 2018, 63, 3818-3831.

[5] Lee, D.; Ding, Y.; Jayaraman, A.; Kwon, J.S. Mathematical modeling and parameter estimation of intracellular signaling pathway: application to LPS-induced NFκB activation and TNFα production in macrophages, Processes 2018, 6, 21.