Modeling and controlling uncertainty in multi-level biological systems

Abstract

Mathematical modeling is essential to the understanding and design of biological systems. Modeling uncertainty, which variously represents lack of data, variability between individuals and between different measurements of a single individual, ambiguity in the proper model form, and others, is essential to explaining the limitations of our understanding and constraining the confidence of our predictions. Current methods for modeling uncertainty provide a rich mathematical means of analyzing simple forms of uncertainty in self-contained models. However, real biological systems of interest exhibit many forms of uncertainty simultaneously and may require the composition of multiple levels of models to create useful predictions. I develop and test new methods for characterizing and propagating uncertainty through multi-level models in order to better make clinically relevant predictions. These methods are applied to three systems.

First, a selenium chemoprevention clinical trial's patients were modeled at the cellular metabolic, mutation accumulation, and cancer detection levels. Metabolite, demographic, and epidemiological data were integrated to produce predictions of prostate cancer risk and putative trial outcomes. The value of information - from doing experiments to reduce uncertainty in a targeted manner - was evaluated on trial design. Second, a population pharmacokinetics/ pharmacodynamics model was created to guide preclinical studies of antibody-drug conjugates targeting breast cancer. An optimal experimental design method was created to efficiently reduce uncertainty in estimates of drug-related parameters of interest. The contributions of inter-individual variability and parameter uncertainty are specially handled by sampling and propagating ensembles of models.

Third, a two-level drug efficacy and cellular dynamics model was created to analyze the efficacy of targeted liposomal-doxorubicin in multiple nucleolin-overexpressing cell lines. A single model topology (but with selected species- and cell line-independent parameters) adequately described the measured behavior in all cell lines. These were then used predict drug uptake and cell killing as a function of surface receptor density. In each system, a modeling framework that integrates data from multiple sources and different forms of uncertainty is applied to make predictions, quantify gaps in knowledge (and help fill them), and guide decision making in controlling clinically important outcomes.