Introduction to dynamical systems analysis in quantitative systems pharmacology: basic concepts and applications

Quantitative systems pharmacology (QSP) can be regarded as a hybrid of pharmacometrics and systems biology. Here, we introduce the basic concepts related to dynamical systems theory that are fundamental to the analysis of systems biology models. Determination of the fixed points and their local stabilities constitute the most important step. Illustration of a phase portrait further helps investigate multistability and bifurcation behavior. As a motivating example, we examine a cell circuit model that deals with tissue inflammation and fibrosis. We show how increasing the severity and duration of inflammatory stimuli divert the system trajectories towards pathological fibrosis. Simulations that involve different parameter values offer important insights into the potential bifurcations and the development of efficient therapeutic strategies. We expect that this tutorial serves as a good starting point for pharmacometricians striving to widen their scope to QSP and physiologically-oriented modeling.