On the validity and errors of the pseudo-first-order kinetics in ligand-receptor binding

The simple bimolecular ligand-receptor binding interaction is often linearized by assuming pseudo-first-order kinetics when one species is present in excess. Here, a phase-plane analysis allows the derivation of a new condition for the validity of pseudo-first-order kinetics that is independent of the initial receptor concentration. The validity of the derived condition is analyzed from two viewpoints. In the first, time courses of the exact and approximate solutions to the ligand-receptor rate equations are compared when all rate constants are known. The second viewpoint assesses the validity through the error induced when the approximate equation is used to estimate kinetic constants from data. Although these two interpretations of validity are often assumed to coincide, we show that they are distinct, and that large errors are possible in estimated kinetic constants, even when the linearized and exact rate equations provide nearly identical solutions.