Target-Mediated Drug Disposition Model for Bispecific Antibodies: Properties, Approximation, and Optimal Dosing Strategy

Abstract

Bispecific antibodies (BsAbs) bind to two different targets, and create two binary and one ternary complex (TC). These molecules have shown promise as immuno-oncology drugs, and the TC is considered the pharmacologically active species that drives their pharmacodynamic effect. Here, we have presented a general target-mediated drug disposition (TMDD) model for these BsAbs, which bind to two different targets on different cell membranes. The model includes four different binding events for BsAbs, turnover of the targets, and internalization of the complexes. In addition, a quasi-equilibrium (QE) approximation with decreased number of binding parameters and, if necessary, reduced internalization parameters is presented. The model is further used to investigate the kinetics of BsAb and TC concentrations. Our analysis shows that larger doses of BsAbs may delay the build-up of the TC. Consequently, a method to compute the optimal dosing strategy of BsAbs, which will immediately create and maintain maximal possible TC concentration, is presented.

Figure 1

Schematic of bispecific binding kinetics (a), full bispecific target‐mediated drug disposition (TMDD) model (b), quasi‐equilibrium (QE) approximation (c), and QE approximation with total constant receptors (d). Solid boxes reflect the necessity of a differential equation for this state, and the dotted boxes reflect that these states are explicitly available. The peripheral compartment is marked as a dashed box.

Figure 2

Diagram showing the relationship between total bispecific antibody (BsAb) concentration C _tot and the ternary complex RC _AB simulated with the equilibrium binding model. (a) The typical bell‐shaped curve is shown, and the area between the dashed bars shows the optimal working range of the BsAb. Parameter settings are K_{D 1} = K_{D 2} = 0.01 nM, $R_{\mathrm{totA}}^0$ = 10 nM, $R_{\mathrm{totB}}^0$ = 100 nM and α = 1. To visualize the effect of varying parameter values, only one parameter is changed at a time, over a wide range. Further the y‐axis was normalized. (b and c) The effect of K_{D 1} and K_{D 2} is shown, (d) the effect of α, (e) the effect of $R_{\mathrm{totA}}^0$.

Figure 3

Comparison of the free bispecific antibody (BsAb) concentration C and the ternary complex concentration RC_AB simulated with the full model. (a) The free BsAb concentration for two different i.v. bolus doses 50 mg (solid line) and 250 mg (dash‐dotted line). (b) Visualizes the effect on the build‐up of the ternary complex.

Figure 4

Overall behavior of all six model components C,R_A,R_B,RC_A,RC_B, and RC_AB simulated with the full model. The effect of recovery of the free receptors R_A and R_B on the free bispecific antibody concentration C is shown and the relation to the complexes RC_A,RC_B and RC_AB can be observed.

Figure 5

Optimal dosing strategy for i.v. and s.c. administration is visualized. The first example (a–c) considers constant total receptors and an i.v. bolus administration. (a) Free bispecific antibody (BsAb) concentration is shown after administration of the optimal i.v. bolus dose to keep the total BsAb concentration in the optimal working range (b) resulting in the maximal possible concentration of the ternary complex (c). Example was produced with the quasi‐equilibrium approximation with constant total receptors. The second example (d–f) considers nonconstant total receptors and an s.c. administration simulated with the full model.