UC San Diego

Mathematical models are indispensable for understanding the architecture and behavior of biological systems using engineering science approaches. Systems biology, analogous to reaction network theory in chemical engineering, enables researchers to investigate the dynamics and behaviors of biological systems beyond what is experimentally feasible. However, despite the successful application of systems biology to studying numerous biological systems, three key challenges limit the predictability of models, including epistemic uncertainty, uncertain model parameters, and incorporation of noisy and sparse experimental data. In this thesis, we propose that uncertainty quantification (UQ)—the field of computational mathematics that models uncertainties—can address these challenges. Recent advances in fluorescent microscopy and protein engineering, which enable near-real-time biological measurements, provide data with the resolution necessary to apply UQ methods.First, we address the estimation of model parameters from noisy and sparse experimental data. To investigate this, we examined the effects of data noise, data quality, parameter identifiability, and parameter sensitivity on our ability to estimate model parameters. In doing so, we developed a framework for parameter estimation that leverages identifiability and sensitivity analysis to pre-process the parameter space and then applies Bayesian inference to learn model parameters. Second, we address the problem of epistemic uncertainty, which commonly arises because our understanding of biology is still evolving. This often leads to the availability of multiple models of the same system. To make predictions with multiple models, we applied a methodology called Bayesian multimodel inference, which combines the specified models to yield a single consensus estimator. We found that multimodel inference increases the certainty of systems biology models by reducing predictive variance, increasing robustness to poor-quality data, and selecting models that best explain the data. Third, we demonstrate how UQ enables the modeling of a system for which we have experimental data, but few published models exist. Specifically, we leveraged high-quality experimental measurements from the Jin Zhang lab (UCSD Dept. of Pharmacology) and applied the methods established in the first two sections to develop a new model of the AMP-activated protein kinase signaling pathway. Through these interdisciplinary studies, we find that UQ addresses key challenges in systems biology, enabling data-informed modeling. Together, these methods constitute a broadly applicable workflow for UQ in systems biology and computational modeling applications. Uncertainty quantification has the potential to drive new biological discoveries by enhancing mechanistic predictability through principled incorporation of experimental data and systematic accounting of uncertainties.