Sameed Ahmed (1*), Miandra Ellis (2*), Hongshan Li (3*), Luca Pallucchini (4*), Andrew M. Stein (5)
(1) Department of Mathematics, University of South Carolina (2) School of Mathematical and Statistical Sciences, Arizona State University (3) Department of Mathematics, Purdue University ? (4) Department of Mathematics, Temple University (5) Novartis Institute for BioMedical Research (*) These authors contributed equally to this abstract
Objectives:
In guiding dose selection for monoclonal antibodies, the methods for predicting receptor occupancy (RO) vary in their level of complexity.
A simple approach was used for atezolizumab [1]. This approach asserted that the following equation held for predicting RO in a tumor: RO = B·Cavg/(B·Cavg + Kd), where B is the fraction of drug from circulation that makes it to the tumor, Cavg is the average drug concentration at steady state (trough concentration could also be used), and Kd is the dissociation constant for the drug. This equation was used without a clear statement of all assumptions needed; in particular, using Kd implicitly assumes that receptor internalization and shedding are unimportant.
A more complex approach was used for pembrolizumab [2]. Here, a physiological model for drug distribution was combined with a receptor binding model and a tumor kinetic model. In this case, all assumptions were clearly stated, but the model was more complex than necessary and this complexity can make it challenging to mathematically understand the model and to explain it to decision-making boards that are unfamiliar with quantitative systems pharmacology.
In this work, we derive a simple expression for target engagement for a physiological model of drug distribution and target binding and we show that this simple expression accurately approximates target engagement for the more complex physiological model. This expression is more accurate than the RO equation above and is easier to explain than the full physiological model.
Methods:
A new parameter was recently derived for characterizing target engagement in circulation for the standard target mediated drug disposition (TMDD) model [3]. Here, this work is extended to estimate the Average Free Tissue target to Initial target Ratio (AFTIR). The extended model includes distribution of the drug and target from circulation to the tissue of interest, binding of the drug to both a membrane-bound and soluble receptor, shedding of receptor from the cell surface, and elimination of both drug, target, and complex. A mathematical derivation of AFTIR is shown and simulations using realistic parameters for trastuzumab, atezolizumab, pembrolizumab, and bevacizumab were performed to check that AFTIR accurately characterizes target engagement.
Results:
The following equation holds under the assumptions listed further below.
AFTIR = Tavg/T0 = Kssd·Tfold/(B·Cavg)
Tavg is the free target concentration at steady state; T0 is the baseline target level in tissue; Kssd is the steady state binding coefficient with distribution (defined further below); Tfold is the fold-change of target in tissue upon binding the drug; and B and Cavg are as described above. Analytical expressions for each of the terms were calculated explicitly from the system parameters and dosing regimen.
The steady state binding coefficient with distribution is given by Kssd = (kint + kshed + kdist + koff)/kon, where kint is the drug-target complex elimination rate; kshed is the complex shedding rate (for membrane-bound targets, zero otherwise); kdist is the rate of distribution of the complex from tissue back to circulation; and koff and kon are the unbinding and binding constants. When kdist=kshed=0, then Kssd=Kss, the steady state binding constant [4]. When koff >> kint + kshed + kdist and when Tfold = 1, this formula agrees with the simpler RO equation from [1].
The expression above requires the assumptions that the tumor can be treated as a homogenous tissue, and that the drug concentration in the tissue of interest is much larger than the target concentration. When these assumptions are met, simulations of target engagement for the full physiological system matched the AFTIR equation. To apply this equation in practice, additional assumptions are often needed, including estimates for B, Tfold, and the value of AFTIR needed for efficacy.
Conclusions:
To predict target engagement in the tissue of interest, a simple equation for AFTIR has been derived and the set of assumptions needed to apply this equation have been provided. This simple expression shows how four lumped parameters: Kssd, Tfold, B, and Cavg impact target engagement and this formula together with the necessary assumptions can be used to guide Phase 2 dose selection for a monoclonal antibody. This methodology can be readily explained to decision making boards and is more accurate than the simple receptor occupancy equation used previously [1].
References:
[1] Deng, R, et al., Preclinical pharmacokinetics, pharmacodynamics, tissue distribution, and tumor penetration of anti-PD-L1 monoclonal antibody, an immune checkpoint inhibitor.” MAbs, 8, 593, 2016
[2] Lindauer, A, et al. “Translational pharmacokinetic/pharmacodynamic modeling of tumor growth inhibition supports dose-range selection of the anti–PD-1 antibody pembrolizumab.” CPT:PSP, 6.1, 11, 2017
[3] Stein, AM, and Ramakrishna R, “AFIR: A dimensionless potency metric for characterizing the activity of monoclonal antibodies.” CPT:PSP 6, 258, 2017.
[4] Ma, P, “Theoretical considerations of target-mediated drug disposition models: simplifications and approximations.” Pharmaceutical research 29, 866, 2012.
Reference: PAGE 27 (2018) Abstr 8446 [www.page-meeting.org/?abstract=8446]
Poster: Methodology - Other topics