Kinetic Models in Life Science — Contributions to Methods and Applications

Doctoral thesis, 2017

Kinetic models in life science combine mathematics and biology to answer questions from areas such as cell biology, physiology, biotechnology, and drug development. The idea of kinetic models is to represent a biological system by a number of biochemical reactions together with mathematical expressions for the reaction kinetics, i.e., how fast the reactions occur. This defines a set of mass balance differential equations for the modeled biochemical variables, whose solution determines the variables' temporal dynamics. Good kinetic models describe, predict, and enable understanding of biological systems, and provide answers to questions which are otherwise technically challenging, unethical, or expensive to obtain directly from experiments. This thesis investigates the workflow for building and using kinetic models. Briefly, the model question determines a suitable mathematical framework for the mass balance equations, prior knowledge informs selection of relevant reactions and kinetics, and unknown parameters are estimated from experimental data. A validated model is used for simulation and analysis, which is interpreted to gain biological insights. Three kinetic models were created to illustrate the workflow. First, a model of the antiplatelet drug ticagrelor and the investigational antidote MEDI2452 was developed for the mouse. The model unraveled the biological mechanisms of the pharmacokinetic interaction and predicted free ticagrelor plasma concentration, thereby contributing to the pharmaceutical development of MEDI2452. Second, a model of the Kv1.5 potassium ion channel was integrated within an existing electrophysiological model of a canine atrial cell. The effect of Kv1.5 block on the action potential was simulated, which improved understanding of blocking mechanisms and enabled assessing pharmacological treatment of atrial fibrillation. Third, a nonlinear mixed effects (NLME) model, with population-level distributions of kinetic parameters, was successfully used to describe cell-to-cell variability of the yeast transcription factor Mig1. This model demonstrated the innovative idea of applying NLME modeling to single cell data. Two studies of kinetic model-building methods are also presented. First, a novel parameter estimation algorithm for NLME models is explained. It computes exact gradients using sensitivity-equations, and represents a substantial advancement over its predecessor. Second, a modeling framework is proposed that combines stochastic differential equations with NLME modeling. This promising framework extends the current scope of NLME models by considering uncertainty in the model dynamics.