How to get from biology to mathematics

Core model structures

At the core of every mathematical model lie two essential elements: the model components and their associated model equations. Together, they form a mathematical representation of a biological process by capturing both the entities involved and the interactions between them.

Model components are the biological elements whose behavior or dynamics we aim to study and understand — such as proteins, mRNAs, metabolites, the incidence of a disease, or the frequency of a mutation, to name just a few.

The model equations describe how these components influence one another over time. Their form depends on the modelling framework being used. For example, in one framework, equations may describe reaction rates (as in kinetic models); in another, they might encode regulatory rules (as in logical or Boolean models); or they may use if/then conditions to define state transitions.