Introduction to three mathematical model formalisms

There are several different types of mathematical model formalisms which are frequently applied throughout biological research. Which one to choose depends on the research questions targeted with the model and the type and amount of available data.

Mathematical model formalisms in biology can be categorised based on the following characteristics:

Brief overview of types of models we will consider:

• Boolean network models are a simple way to represent systems with elements that can only be in one of two states, typically “on” or “off” (or “true” or “false”, present or absent, low or high, …). In biology, these models are often used to describe regulatory processes. Illustrative applications are gene regulatory networks, where each gene is either expressed (“on”) or not expressed (“off”) depending on the regulation via transcription factors being expressed (“on”) or not expressed (“off”). 
• Difference equation models describe how the elements of a system change over time by looking at the state of the system time point by time point. These models use equations that calculate the system state at the next time point (one time step later) from the current state of the system. Therefore, the most illustrative applications are biological processes in which changes occur at regular intervals, such as population growth from one generation to the next, but these models also closely resemble the usual experimental setup of being able to take measurements only with a finite temporal resolution.
• Ordinary differential equation models describe how the state of a system continuously changes over time based on how each of the components gives rise to this change: e.g. the more enzyme we add in an enzymatic assay, the faster we will see a change in the readout. The influence of each model component on its own change and that of the other components is formalised in so called differential equations, which calculate the rate (change in value per unit time) at which each model component changes at every point in time.

Move on to the following sections to explore these models in further detail.