Abstract
Immunodeficient mice are crucial models to evaluate the efficacy of monoclonal antibodies (mAbs). When studying mAb pharmacokinetics (PK), protection from elimination by binding to the neonatal Fc receptor (FcRn) is known to be a major process influencing the unspecific clearance of endogenous and therapeutic IgG. The concentration of endogenous IgG in immunodeficient mice, however is reduced, and this effect on the FcRn protection mechanism and subsequently on unspecific mAb clearance is unknown, yet of great importance for the interpretation of mAb PK data. We used a PBPK modelling approach to elucidate the influence of altered endogenous IgG concentrations on unspecific mAb clearance. To this end, we used PK data in immunodeficient mice, i.e. nude and severe combined immunodeficiency mice. To avoid impact of target-mediated clearance processes, we focussed on mAbs without affinity to a target antigen in these mice. In addition, intravenous immunoglobulin (IVIG) data of immunocompetent mice was used to study the impact of increased total IgG concentrations on unspecific therapeutic antibody clearance. The unspecific clearance is linear, whenever therapeutic IgG concentrations, i.e. mAb and IVIG concentrations are lower than FcRn; it can be non-linear if therapeutic IgG concentrations are larger than FcRn and endogenous IgG concentrations (e.g., under IVIG therapy). Unspecific mAb clearance of immunodeficient mice is effectively linear (under mAb doses as typically used in human). Studying the impact of reduced endogenous IgG concentrations on unspecific mAb clearance is of great relevance for the extrapolation to clinical species, e.g., when predicting mAb PK in immunosuppressed cancer patients.
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Acknowledgements
S.F. acknowledges fruitful discussions with Hans Peter Grimm (F. Hoffmann-La Roche Ltd, Basel, Switzerland).
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Appendix
Appendix
Extension of the generic PBPK model to account for FcRn-dependent clearance kinetically linked to interstitial fluid of organs
In order to account for FcRn-dependent clearance kinetically linked to interstitial fluid of organs, we make use of the organ extraction ratio \(E_{\text{org}}\). The extraction ratio is estimated for two groups of organs, dependent on the tightness and leakiness of the vessel wall. Intrinsic clearance from interstitial fluid of organs \(\text{CLint}_{\text{int}}\) is determined via tissue extraction ratio.
Linear clearance from plasma (\({\text{CLpla}}\)) is calculated via total clearance (\(\text{CL}_{\text{tot}}\)) and the plasma clearance corresponding to the different intrinsic clearances from the organs as
FcRn concentration [nM] in interstitial fluid was estimated for two groups of tissues. Fraction unbound \({\text{fu}}_{{\text{IgG}}}\) is calculated dependent on total IgG concentration (i.e. therapeutic IgG and endogenous IgG) and FcRn concentration, both in interstitial fluid of the organs. \({\text{fu}}_{{\text{IgG}}}\) is determined by one of the methods described in section ‘Theoretical’.
Hence, intrinsic clearance is calculated based on total IgG:
Endogenous IgG synthesis rate \(k_{\text{syn}}\) in [nmol/min] is determined via clearance processes (from plasma and interstitial fluid of organs) and baseline (steady state) endogenous plasma concentration \({\text{IgG}}_{{\text{endo}},{\text{baseline}}}\):
Baseline concentration of endogenous IgG in interstitial fluid is computed from \({\text{IgG}}_{{\text{endo}},{\text{baseline}}}\) via \({\text{ABC}}_{\text{int}}\):
Total \({\text{CLpla}}\) is estimated from the the PBPK model in Eqs. (1)–(2) with constant \({\text{CLpla}}\) and with extraction ratios set to zero (see Table 6). Then, the herein presented PBPK model was used to estimate the organ extraction ratios and FcRn concentrations for two groups of tissues. As already explained in the Discussion, predictions for mAb PK in FcRn wild-type mice, nude and SCID mice with FcRn salvage kinetically linked to plasma are indistinguishable to predictions based on the herein presented extension for FcRn linked to the two groups of organs.
Modelling FcRn-dependent clearance with almost tenfold difference in binding affinity of murine and human IgG to mouse FcRn
Zhou et al. [45] report an almost tenfold difference in binding affinity with higher affinity of human IgG than murine IgG to mouse FcRn (\({\text{hK}}_{\text{D}}\) = 82 nM versus \({\text{mK}}_{\text{D}}\) = 750 nM, respectively). We used the equilibrium binding model with different \({\text{K}}_{\text{D}}\) values to predict the influence of human IgG (IVIG) on murine IgG (murine mAb and endogenous IgG) clearance in FcRn wild-type mice. The model cannot describe quantitatively the experimentally measured mAb concentrations following IVIG therapy resulting in a too strong protection mechanism of FcRn for IVIG, see Figure 12. However qualitatively it predicts the influence of IVIG on murine IgG clearance and endogenous IgG concentrations very well. Following a higher binding affinity of IVIG for mouse FcRn, IVIG is more protected from elimination than murine IgG resulting in a lower IVIG clearance. After a significant decrease in endogenous IgG concentration, it takes time for endogenous IgG to return to baseline plasma concentration. This can be explained with the almost tenfold lower binding affinity of murine IgG for mouse FcRn resulting in a less protection by FcRn and a higher degradation within endo-lysosomes (see Figure 13 for kinetics of endogenous IgG and IVIG predicted by the model with twofold difference in \({\text{K}}_{\text{D}}\)).
Accounting for non-equilibrium binding effects on unspecific clearance
So far, we assume equilibrium binding with \({\text{K}}_{\text{D}} = ({\text{k}}_{\text{off}}/{\text{k}}_{\text{on}})\) to model FcRn–IgG interaction. Non-equilibrium binding with baseline rate of \({\text{fu}}_{{\text{IgG}}}\) > 0 may be explainable by a very slow and incomplete binding of total IgG to FcRn leading to a high amount of total IgG in lysosome or unregulated sorting resulting in FcRn within lysosomes. We used a non-equilibrium binding model (see Eq. (22)) and jointly estimated an unbound plasma clearance, total FcRn and a baseline clearance \(\text{CL}_\text{base}\) to predict mAb PK data in FcRn wild-type mice following IVIG treatment, nude mice and SCID mice. Following non-equilibrium binding, we obtained estimates for total FcRn and unbound plasma clearance, that are comparable for wild-type mice and immunodeficient mice with a baseline fraction unbound \({\text{fu}}_{\text{base}}\) of approx. 11% (data not shown).
To account for non-equilibrium binding, we parameterised the unspecific plasma clearance \({\text{CLpla}}\) in the model with equilibrium binding affinity (see Eq. (4)) in addition with a baseline clearance \({\text{CL}}_{\text{base}}\) as:
with \(\text{CL}_\text{base}\)= \({\text{fu}}_\text{base}\) \(\cdot\) \({\text{CLpla}}_{\text{u}}\).
Presence of tumour has no influence on mAb PK
Total tumour volumes (including vascular space) for nude mice were taken from [29] to be 0.472 mL and for SCID mice to be 0.250 mL based on [27]. We used the values reported in [56] to determine the tissue volume fraction of total tumour volume \((f_{\text{tis}} = 0.77)\), the vascular volume fraction of total tumour volume \((f_{\text{vas}}=0.06)\) and the interstitial volume fraction of tumour tissue volume \((f_{\text{int}}=0.42)\). Vascular volume was included in the blood volume \(V_{\text{blo}}\). Tumour growth was modelled using the estimated tumour growth rate \({\text{k}}_{\text{growth}}\) for LS174T tumour of approx. \(\text{6.35e-5}\) 1/min in [57]. Total tumour volumes were used as initial tumour volumes for the two mouse strains. Tumour plasma flow was set to 0.1 L/min as measured in [29] and tumour lymph flow rate was assumed to be 0.4% of tumour plasma flow. The two remaining unknown parameter values for the tumour, i.e., vascular reflection coefficient \(\sigma _{\text{vas}}\) and the antibody biodistribution coefficient \({\text{ABC}}_\text{tum}\) were estimated. The two parameters were estimated separately for nude and SCID mice due to differences in tumour cell lines and tumour inoculation. The generic PBPK model in Eqs. (1)–(2) with fixed total \({\text{CLpla}}\) (see Table 6) was used to estimate the parameters \(\sigma _{\text{vas}}\) and \({\text{ABC}}_{\text{tis}}\) of tumour. Parameters are summarised in Table 7. As can be inferred from the Figs. 14 and 15, the tumour has practically no influence on mAb clearance on the time scale of the experimental data.
The rate of change of the interstitial tumour volume \(V_{\text{tum}}(t)\) and the concentration in the interstitial space of the tumour \(C_{\text{tum}}(t)\) was described by the following system of ordinary differential equations (ODEs):
from which the concentration was determined by \(C_{\text{tum}}(t)=A_{\text{tum}}(t)/V_{\text{tum}}(t)\).
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Fuhrmann, S., Kloft, C. & Huisinga, W. Impact of altered endogenous IgG on unspecific mAb clearance. J Pharmacokinet Pharmacodyn 44, 351–374 (2017). https://doi.org/10.1007/s10928-017-9524-2
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DOI: https://doi.org/10.1007/s10928-017-9524-2