Target-mediated drug disposition (TMDD) of mAbs – Paradoxical increase of terminal half-life of therapeutic antibodies with increasing target amount : the

David Ternant(1), Nicolas Azzopardi(1), Gilles Paintaud(1), Sten Madek(2), Vincent Perrolaz(2)

(1) EA 7501 GICC, Université de Tours, Tours, France; (2) UMR CNRS 7350, Université de Tours, Tours, France

Objectives: From the last two decades, the pharmacokinetics of therapeutic monoclonal antibodies (mAbs) has been repeatedly reported to be influenced by its target. Indeed, the kinetics of target turnover, of binding and of mAb-target complex elimination may cause nonlinear elimination decay. The joint kinetics of mAb and target is described by target-mediated drug disposition (TMDD) models [1,2]. In most of cases, the terminal elimination half-life (T½-R) of mAbs decreases with increased target amount (R). However, we previously reported a paradoxical increase in the T½-R of rituximab (anti-CD20 mAbs) with higher tumor volume in diffuse large B-cell lymphoma patients [3]. Some other publications suggested similar behaviour for bevacizumab (anti-VEGF), trastuzumab (anti-HER2) and infliximab (anti-TNF) [4]. We interpreted this phenomenon as a retention of mAb by target antigen that we called « sponge effect », which may occur for low elimination rates of mAb-target complexes [5]. The aim of the present work was to investigate the asymptotic behaviour of the TMDD system to determine the conditions of sponge effect emergence.

Methods: We first worked on a simplified 3-compartment TMDD system, where the kinetics of unbound mAb is described using an one compartment model as follows :

dC/dt = In(t) – k₁₀.C – k_on.C.R + k_off. R_C

dR/dt = k_in – k_out.R – k_on.C.R + k_off.R_C

dR_C/dt = k_on.C.R – k_off.RC – k_int.R_C

Where C is mAb concentration in central compartment, R and R_C are concentrations free antigen target and mAb-target complexes, respectively, In(t) is mAb input function, k₁₀ is elimination rate constant, k_syn and k_deg are endogenous zero-order production and first-order destruction rate constants, respectively, k_on and k_offare second-order and first order association and dissociation rate constants of mAb, its target and the complex, respectively, and k_int is first-order complex destruction rate constant. The initial condition of target amount is R₀ = k_in/k_out. As in previous studies [6], we proceeded to an adimensionalisation of the 3-compartment TMDD system and we made an asymptotic analysis of system return towards the equilibrium in function of R₀. We finally propose a conjecture to generalize our results to the general 4-compartment TMDD model under the assumption of asymptotic decay towards the beta-phase of unbound mAb, with beta = ½ . (k₁₂+k₂₁+k₁₀+((k₁₂+k₂₁+k₁₀)² – 4.k₂₁.k₁₀)^½)

Where k₁₂ and k₂₁ are central to peripheral and peripheral to central transfer rate constants, respectively.

Results: Our analysis allowed us to demonstrate the theorem of “sponge effect”, which states that the increase/decrease of T½-R depends only on the ratio k₁₀/k_int:

– if k₁₀/k_int > 1, then T½-R decreases for increasing R₀ (the most frequent situation)

– if k₁₀/k_int < 1, then T½-R increases for increasing R₀ (sponge effect).

In the case of the 4-compartment TMDD system, under the assumption of asymptotic equilibrium toward the beta elimination phase :

– if beta/k_int > 1, then T½-R decreases for increasing R₀ (the most frequent situation)

– if beta/k_int < 1, then T½-R increases for increasing R₀ (sponge effect).

Conclusions: The emergence of sponge effect depends only on the ratio between unbound and bound mAb elimination rates. Therefore, sponge effect occurs if and only if the elimination of mAb-target complexes is slower than the elimination of unbound mAb. This phenomenon may explain situations where elimination half-life of mAbs was higher than the well-known theoretical value of 21 days.

References:
[1] Mager DE, Jusko WJ. General pharmacokinetic model for drugs exhibiting target-mediated drug disposition. J Pharmacokinet Pharmacodyn. 2001;28(6):507-32.
[2] Gibiansky L, Gibiansky E, Kakkar T, Ma P. Approximations of the target-mediated drug disposition model and identifiability of model parameters. J Pharmacokinet Pharmacodyn. 2008;35(5):573-91.
[3] Tout M, Casasnovas O, Meignan M, Lamy T, Morschhauser F, Salles G, et al. Rituximab exposure is influenced by baseline metabolic tumor volume and predicts outcome of DLBCL patients: a Lymphoma Study Association report. Blood. 2017;129(19):2616-23.
[4] Ternant D, Azzopardi N, Raoul W, Bejan-Angoulvant T, Paintaud G. Influence of Antigen Mass on the Pharmacokinetics of Therapeutic Antibodies in Humans. Clin Pharmacokinet. 2019;58(2):169-87.
[5] Peletier LA, Gabrielsson J. Dynamics of target-mediated drug disposition: characteristic profiles and parameter identification. J Pharmacokinet Pharmacodyn. 2012;39(5):429-51.
[6] Aston PJ, Derks G, Raji A, Agoram BM, van der Graaf PH. Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting in vivo potency. J Theor Biol. 2011 ;281(1):113-21.

Reference: PAGE () Abstr 9389 [www.page-meeting.org/?abstract=9389]

Poster: Methodology - Other topics