Regularization Techniques to Overcome Overparameterization of Complex Biochemical Reaction Networks

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

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 NFκB signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively.

An intracellular signaling pathway is often represented by a set of nonlinear ordinary differential equations, which translate our current knowledge about the signaling pathway into a testable mathematical model. However, predictions from such models are often subject to high uncertainty since many signaling pathways are only partially known beforehand. In this study, we propose a systematic approach to develop a hybrid model to improve model accuracy by combining machine learning and the first-principle modeling. Specifically, model correction terms are learned from discrepancy between model predictions and measurements, and these terms are added to the first-principle model to enhance the prediction accuracy. Once these correction terms are learned from the data, an artificial neural network (ANN) model is developed to find an empirical relation between the model and the correction terms so that the developed ANN can be used to posses improved predictive capabilities even in new operating conditions (i.e., generalizability). The final hybrid model is then constructed by coupling the first-principle model with the developed ANN.

MODELING INTER-KINGDOM REGULATION OF INFLAMMATORY SIGNALING IN HUMAN INTESTINAL EPITHELIAL CELLS

The human gastrointestinal (GI) tract is colonized by a highly diverse and complex microbial community (i.e., microbiota). The microbiota plays an important role in the development of the immune system, specifically mediating inflammatory responses, however the exact mechanisms are poorly understood. We have developed a mathematical model describing the effect of indole on host inflammatory signaling in HCT-8 human intestinal epithelial cells. In this model, indole modulates transcription factor nuclear factor κ B (NF-κB) and produces the chemokine interleukin-8 (IL-8) through the activation of the aryl hydrocarbon receptor (AhR). Phosphorylated NF-κB exhibits dose and time-dependent responses to indole concentrations and IL-8 production shows a significant down-regulation for 0.1 ng/mL TNF-α stimulation. The model shows agreeable simulation results with the experimental data for IL-8 secretion and normalized NF-κB values. Our results suggest that microbial metabolites such as indole can modulate inflammatory signaling in HTC-8 cells through receptor-mediated processes.

Application of Systems Engineering Principles and Techniques in Biological Big Data Analytics: A Review

In the past few decades, we have witnessed tremendous advancements in biology, life sciences and healthcare. These advancements are due in no small part to the big data made available by various high-throughput technologies, the ever-advancing computing power, and the algorithmic advancements in machine learning. Specifically, big data analytics such as statistical and machine learning has become an essential tool in these rapidly developing fields. As a result, the subject has drawn increased attention and many review papers have been published in just the past few years on the subject. Different from all existing reviews, this work focuses on the application of systems, engineering principles and techniques in addressing some of the common challenges in big data analytics for biological, biomedical and healthcare applications. Specifically, this review focuses on the following three key areas in biological big data analytics where systems engineering principles and techniques have been playing important roles: the principle of parsimony in addressing overfitting, the dynamic analysis of biological data, and the role of domain knowledge in biological data analytics.

Systems NMR: single-sample quantification of RNA, proteins and metabolites for biomolecular network analysis

Cellular behavior is controlled by the interplay of diverse biomolecules. Most experimental methods, however, can only monitor a single molecule class or reaction type at a time. We developed an in vitro nuclear magnetic resonance spectroscopy (NMR) approach, which permitted dynamic quantification of an entire 'heterotypic' network-simultaneously monitoring three distinct molecule classes (metabolites, proteins and RNA) and all elementary reaction types (bimolecular interactions, catalysis, unimolecular changes). Focusing on an eight-reaction co-transcriptional RNA folding network, in a single sample we recorded over 35 time points with over 170 observables each, and accurately determined five core reaction constants in multiplex. This reconstruction revealed unexpected cross-talk between the different reactions. We further observed dynamic phase-separation in a system of five distinct RNA-binding domains in the course of the RNA transcription reaction. Our Systems NMR approach provides a deeper understanding of biological network dynamics by combining the dynamic resolution of biochemical assays and the multiplexing ability of 'omics'.

Modeling the Dynamics of Human Liver Failure Post Liver Resection

Liver resection is an important clinical intervention to treat liver disease. Following liver resection, patients exhibit a wide range of outcomes including normal recovery, suppressed recovery, or liver failure, depending on the regenerative capacity of the remnant liver. The objective of this work is to study the distinct patient outcomes post hepatectomy and determine the processes that are accountable for liver failure. Our model based approach shows that cell death is one of the important processes but not the sole controlling process responsible for liver failure. Additionally, our simulations showed wide variation in the timescale of liver failure that is consistent with the clinically observed timescales of post hepatectomy liver failure scenarios. Liver failure can take place either instantaneously or after a certain delay. We analyzed a virtual patient cohort and concluded that remnant liver fraction is a key regulator of the timescale of liver failure, with higher remnant liver fraction leading to longer time delay prior to failure. Our results suggest that, for a given remnant liver fraction, modulating a combination of cell death controlling parameters and metabolic load may help shift the clinical outcome away from post hepatectomy liver failure towards normal recovery.