Mathematical Biology

Mathematical biology reconstructs biochemical networks as systems of ODEs via mass-action kinetics: each reaction species is a state variable, each reaction is a rate function, and the stoichiometric matrix encodes which species participate in which reactions. These networks are the substrate from which compartmental pharmacokinetic models are built; drug molecules diffuse between compartments, bind to receptors, are metabolised by enzymes, each process following mass-action laws. Quantitative systems pharmacology extends this framework to multi-compartment, multi-target reaction networks where we ask which species affect measurable output and what controls that mapping.