Mathematical analysis of the pharmacokinetic–pharmacodynamic (PKPD) behaviour of monoclonal antibodies: Predicting in vivo potency

We consider the relationship between the target affinity of a monoclonal antibody and its in vivo   potency. The dynamics of the system is described mathematically by a target-mediated drug disposition model. As a measure of potency, we consider the minimum level of the free receptor following a single bolus injection of the ligand into the plasma compartment. From the differential equations, we derive two expressions for this minimum level in terms of the parameters of the problem, one of which is valid over the full range of values of the equilibrium dissociation constant KDKD and the other which is valid only for a large drug dose or for a small value of KDKD. Both of these formulae show that the potency achieved by increasing the association constant konkon can be very different from the potency achieved by decreasing the dissociation constant koffkoff. In particular, there is a saturation effect when decreasing koffkoff where the increase in potency that can be achieved is limited, whereas there is no such effect when increasing konkon. Thus, for certain monoclonal antibodies, an increase in potency may be better achieved by increasing konkon than by decreasing koffkoff.

► Potency is measured by the minimum free receptor following an injection of ligand.
► Two approximations of this minimum are derived from the differential equations.
► A saturation effect is demonstrated when the dissociation constant koff is reduced.
► There is no such saturation when the association constant kon is increased.