Robust network calibration and therapy design in systems biology

Abstract

Mathematical modeling of biological networks is under active research, receiving attention for its ability to quantitatively represent the modeler's systems-level understanding of network functionalities. Computational methods that enhance the usefulness of mathematical models are thus being increasingly sought after, as they face a variety of difficulties that originate from limitations in model accuracy and experimental precision. This thesis explores robust optimization as a tool to counter the effects of these uncertainty-based difficulties in calibrating biological network models and in designing protocols for cancer immunotherapy. The robust approach to network calibration and therapy design aims to account for the worst-case uncertainty scenario that could threaten successful determination of network parameters or therapeutic protocols, by explicitly identifying and sampling the region of potential uncertainties corresponding to worst-case. Through designating individual numerical ranges that uncertain model parameters are each expected to lie within, the region of uncertainties is defined as a hypercube that encompasses a particular uncertainty range along each of its dimensions. For investigating its applicability to parameter estimation, the performance of the optimization method that embodies this robust approach is examined in the context of a model of a unit belonging to the mitogen-activated protein kinase pathway. For its significance in therapeutic design, the method is applied to both a canonical mathematical model of the tumor-immune system and a model specific to treating superficial bladder cancer with Bacillus Calmette-Guirin, which have both been selected to examine the plausibility of applying the method to either discrete-dose or continuous-dose administrations of immunotherapeutic agents. The robust optimization method is evaluated against a standard optimization method by comparing the relative robustness of their respective estimated parameters or designed therapies. Further analysis of the results obtained using the robust method points to properties and limitations, and in turn directions for improvement, of existing models and design frameworks for applying the robust method to network calibration and protocol design. An alternative mathematical formulation to solving the worst-case optimization problem is also studied, one that replaces the sampling process of the previous method with a linearization of the objective function's parameter space over the region of uncertainties. This formulation's relative computational efficiency additionally gives rise to a novel approach to experimental guidance directed at improving modeling efforts under uncertainties, which may potentially further fuel the advancement of quantitative systems biological research.