Exploring simplification of a target-mediated drug disposition (TMDD) model for bispecific antibodies for potential application to data-driven modelling
Chihiro Hasegawa (1,2), Abhishek Gulati (3), Yasuhiro Tsuji (2), Stephen Duffull (4)
(1) MSD (Merck Sharp and Dohme), Japan (2) Nihon University, Japan (3) MSD (Merck Sharp and Dohme), USA (4) Certara, USA
Introduction: Bispecific antibodies are antibodies with two binding sites, directed against two different antigens or two different epitopes on the same antigen. These can be promising therapeutic modalities in different disease areas. For monoclonal antibodies target-mediated drug disposition (TMDD) may include a total of three states: drug, target antigen, and drug-target complex. The model becomes more complicated in the case of bispecific antibodies since there are two target antigens, with a total of six states of drug, target A, target B, drug-target A complex, drug-target B complex, and a ternary complex, resulting in parameter identifiability issues and difficulty in estimating model parameters using data from nonclinical/clinical studies. This is the case even after applying a quasi-equilibrium (QE) approximation [1], assuming this approximation meets the analysis needs.
Objectives: Simplifying the model by lumping some of the states in the full TMDD model may result in the model suitable for parameter estimation while retaining acceptable predictive performance depending on the aim of the modelling.
- Explore a lumping approach to reduce the bispecific TMDD model.
- Explore the possibility of applying automated proper lumping for the bispecific TMDD model.
Methods: Using the bispecific TMDD model in Schropp [1] as a starting point, concentration-time profiles from different sets of parameter values were simulated, by focusing on the difference in binding potency (kon1 vs kon2), amount of target antigens (target A vs target B at t=0), and turnover rates of target antigens (kdeg for target A vs kdeg for target B). With the same sets of parameter values, the lumped model for each set of parameter values was manually derived by merging two target antigen states into one state, as well as by merging three complex states into one state. The lumped model then consisted of three states, which is same as the general monospecific TMDD model. Parameter values for the lumped model were obtained by simply calculating the average of turnover rates for each target antigen and binding parameters, respectively. An internalization rate for the lumped complex state was assumed to be identical to that for ternary complex existing in the original model. An inductive linearization method [2] was coupled with proper lumping to explore the application of automated proper lumping (as per [3]). Parameter values for the lumped model were derived via the lumping formula for the linear model. The lumped model was then unlinearized for simulations. All simulations were conducted using NONMEM® 7.4 or MATLAB R2021a.
Results: (For the 1st objective) The lumping approach provided good performance for total drug concentrations and generally provided reasonable predictive performance for free drug concentrations. For the latter, this was however not the case when target antigens have slow turnover rate, or when it was doubtful to assume that the internalization rate for the lumped complex state was identical to that for ternary complex existing. (For the 2nd objective) The three-state lumped model (State 1: [Free drug] + State 2: [Target receptor A and B] + State 3: [Complex A and B and ternary complex]) was preferred for both the settings in which the focus was either free or total drug concentration. The two-state lumped model (State 1: [Free drug] + State 2: [The others grouped together]) performed well given finite time span (up to 70-100 days in this scenario), while the four-state model (State 1: [Free drug] + State 2: [Target receptor A and B] + State 3: [Complex A and B] + State 4: [ternary complex]) provided better model fit compared with the three-state model.
Conclusions: These findings suggest that while manual lumping can provide reasonable predictive performance, several assumptions need to be made, and such assumptions may not be appropriate in some situations. Automated proper lumping provided a reasonable alternative. The lumped model can be improved by either estimating parameters using data from nonclinical/clinical studies or increasing the number of unlumped states. These findings will need to be confirmed via a simulation-estimation study and/or modelling work using real data.
References:
[1] Schropp J, et al. CPT Pharmacometrics Syst Pharmacol (2019) 8: 177-87.
[2] Hasegawa C, Duffull SB. J Pharmacokinet Pharmacodyn (2018) 45: 35-47.
[3] Hasegawa C, Duffull SB. CPT Pharmacometrics Syst Pharmacol (2018) 7: 562-72.