On the Way to More Convenient Description of Drug-Plasma Protein Binding

The theoretical case is considered where the total amount of plasma protein is conserved, but the drug is eliminated after its single application. After a single drug application at time t = 0, the total drug concentration is measured at times ti,…,tk and the total drug concentration at time ti is denoted by {\phi}i. Our discussion is limited to one protein binding site. The quantity of plasma protein ({\Lambda}), the association constant (Ka) and the total concentration of the drug {\phi}i at time ti are considered as independent variables. Free drug concentration, plasma protein bound concentration and free drug fraction are given as functions of these “new” variables. The aim of this communication is to derive the formula that allows to calculate the free drug concentration at any time after the drug application, based on 3 parameters: the association constant of the drug, the total plasma concentration of the drug and the concentration of the protein. If the plasma protein quantity ({\Lambda}) and the association constant (Ka) are known, then from the knowledge of the total drug concentration {\phi}i at time ti it is possible to determine the free drug concentration at time ti.

💡 Research Summary

The paper presents a concise mathematical framework for describing drug‑plasma protein binding under a set of simplifying assumptions. It assumes that the total concentration of the binding protein (Λ) remains constant over time, that a single dose of drug is administered at time zero and then eliminated from the system, and that each protein molecule possesses only one binding site, leading to a 1:1 interaction model. Starting from the law of mass action, the association constant (Ka) relates free drug concentration