Discrete dynamic modeling: A network approach for systems pharmacology

Systems pharmacology is an interdisciplinary field that aims to apply the theoretical and experimental tools of systems biology to drug development. The goal is to go beyond the interaction between a drug and the target to which it binds to explore drug effects on the cellular networks affected by disease. Over the years, vast amounts of information about the regulatory relationships among genes, proteins, and small molecules have been acquired. Similarly, there is much known about the deregulation of these systems during disease. However, many knowledge gaps still exist. There is an abundance of qualitative or relative information related to the activation of signaling pathways, but a paucity of kinetic and temporal information. Discrete dynamic modeling provides a means to create predictive models of signal transduction pathways by integrating fragmentary and qualitative interaction information. Using discrete dynamic modeling, a structural (static) network of biological regulatory relationships can be translated into a mathematical model without the use of kinetic parameters. This model can describe the dynamics of a biological system over time, both in normal and in perturbation scenarios. In this chapter, we discuss the fundamentals of discrete dynamic modeling as it pertains to systems pharmacology. As an example, we apply this methodology to a previously constructed pharmacodynamic model of epidermal derived growth factor receptor (EGFR) signaling. We (1) translate this model into two types of discrete models, a Boolean model and a three-state model, (2) show how the effects of an EGFR inhibitor (such as gefitinib) can suppress tumor growth, and (3) model how genomic variants can augment the effect of EGFR inhibition in tumor growth. We argue that discrete dynamic models can be used to facilitate many of the goals of systems pharmacology. These include understanding how individual differences contribute to variability in drug response and determining which drugs would be best depending on individual genetic differences.