Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling

• Published in: PLoS computational biology Vol. 16; no. 12; p. e1008472
• Main Authors: Lee, Dongheon, Jayaraman, Arul, Kwon, Joseph S.
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 14.12.2020; Public Library of Science (PLoS)
• Subjects: Accuracy; Algorithms; Apoptosis; Biology and Life Sciences; Biomolecules; Case studies; Cellular signal transduction; Computer and Information Sciences; Correlation analysis; Differential equations; Error-correcting codes; Gene expression; Intracellular; Intracellular signalling; Knowledge; Least-Squares Analysis; Lipopolysaccharides - pharmacology; Mathematical models; Medicine and Health Sciences; Metabolism; Neural networks; Neural Networks, Computer; NF-kappa B - metabolism; Ordinary differential equations; Physical Sciences; Signal transduction; Signal Transduction - drug effects; Signaling; Terminology; United States
• ISSN: 1553-7358; 1553-734X; 1553-7358
• DOI: 10.1371/journal.pcbi.1008472

Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NF κ B signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively.