Formal modeling of biological systems

As biomedical research advances into more complicated systems, there is an increasing need to model and analyze these systems to better understand them. For decades, biologists have been using diagrammatic models to describe and understand the mechanisms and dynamics behind their experimental observations. Although these models are simple to be built and understood, they can only offer a rather static picture of the corresponding biological systems, and scalability is limited. Thus, there is an increasing need to develop formalism into more dynamic forms that can capture time-dependent processes, together with increases in the models scale and complexity. In this invited review paper, we argue that the formal modeling formalisms can be applied fruitfully to biological systems, and can be complementary to the traditional mathematical descriptive modeling approaches used in systems biology. We also discuss one example: a stochastic hybrid model of the effect of estrogen at different levels in species' population in a freshwater ecosystem.