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 K_D and the other which is valid only for a large drug dose or for a small value of K_D. Both of these formulae show that the potency achieved by increasing the association constant k_on can be very different from the potency achieved by decreasing the dissociation constant k_off. In particular, there is a saturation effect when decreasing k_off where the increase in potency that can be achieved is limited, whereas there is no such effect when increasing k_on. Thus, for certain monoclonal antibodies, an increase in potency may be better achieved by increasing k_on than by decreasing k_off.