Supplementary Table 1: Parameters and Variables used in model

Parameter / Units / Definition
K0 / moles/min / Synthesis rate of endogenous IgG
Rorgan / M / Endosomal concentration of FcRn
FR / Fraction of FcRn-bound IgG recycled to plasma
τ / min / Transit time between endosomal sub-compartments
τLY / min / Lymph node transit time
F1 / Coefficient modulating endosomal uptake rate
F2 / Coefficient modulating the vascular reflection coefficient
CLup, organ / L/min / Endosomal uptake rate
Vpl / L / Volume of plasma
Qpl / L/min / Plasma flow rate
Qtissue / L/min / Tissue plasma flow rate
Ltissue / L/min / Tissue lymph flow rate
Vv, tissue / L / Tissue vascular volume
Ve, tissue / L / Tissue endosomal volume
Vi, tissue / L / Tissue interstitial volume
σV, tissue / Tissue vascular reflection coefficient
σL, tissue / Tissue lymphatic reflection coefficient
KA, endo , KA, Ab / M-1 / Equilibrium association constant for IgG-FcRn
kon, endo , kon, Ab / M-1min-1 / IgG-FcRn association rate constant
koff, endo , koff, Ab / min-1 / IgG-FcRn dissociation rate constant
nPttissue / M / Baseline tissue interstitial receptor concentration
KD / M / Equilibrium dissociation constant for IgG-FcRn
ksyn, tissue / M/min / Production rate of target receptor in tissue
kdeg / min-1 / Elimination rate of unbound receptor
ktmd / min-1 / Elimination rate of mAb-receptor complexes
futissue / mAb fraction unbound in interstitial space
Cpl, endo , Cpl, Ab / M / IgG plasma concentration
Cv tissue, endo , Cv tissue, Ab / M / IgG tissue vascular concentration
Ce tissue, endo , Ce tissue, Ab / M / Free IgG tissue endosomal concentration
Ci tissue, endo , Ci, tissue, Ab / M / IgG tissue interstitial concentration
Ce tissue, endo complex , Ce tissue, Ab complex / M / IgG-FcRn complex endosomal concentration
Ce tissue, FcRn / M / Free FcRn endosomal concentration
Xly, endo , Xly, Ab / mole / Amount of IgG in the lymph node

Abbreviations: Endo represents endogenous IgG and Ab represents administered IgG

Model Equations:

1.  Plasma

Vpl×dCpl, endodt=K0+Qlung-Llung×Cv lung, endo-LGI tract+Lspleen+Qliver+Qheart+Qskin+Qmuscle×Cpl, endo+(1τLY)×Xly, endo×(0.28+0.72×KA, endoKA,endo+650000)

Vpl×dCpl, Abdt=Qlung-Llung×Cv lung, Ab-LGI tract+Lspleen+Qliver+Qheart+Qskin+Qmuscle×Cpl,Ab+(1τLY)×Xly, Ab×(0.28+0.72×KA, AbKA,Ab+650000)

2.  Lung

2.1. Vascular Space

Vv, lung×dCv lung, endodt=Qliver-Lliver×CV liver, endo+Qheart-Lheart×Cv heart, endo+Qkidney-Lkidney×CV kidney, endo+Qskin-Lskin×Cv skin, endo+Qmuscle-Lmuscle×Cv muscle, endo-CLup, lung×Cv lung, endo+FR×CLup, lung×Ce5 lung, endo complex-1-σV, lung×Llung×Cv lung, endo-(Qlung-Llung)×Cv lung, endo

Vv, lung×dCv lung, Abdt=Qliver-Lliver×CV liver, Ab+Qheart-Lheart×Cv heart, Ab+Qkidney-Lkidney×CV kidney, Ab+Qskin-Lskin×Cv skin, Ab+Qmuscle-Lmuscle×Cv muscle, Ab-F1×CLup, lung×Cv lung, Ab+FR×F1×CLup, lung×Ce5 lung, Ab complex-F2×1-σV, lung×Llung×Cv lung, Ab-Qlung-Llung×Cv lung,Ab

2.2. Endosomal Space

2.2.1.  Sub-compartment 1 (pH 7.4)

dCe1 lung, endodt=CLup, lungVe, lung×Cv lung, endo+Ci lung, endo-kon1, endo×Ce1 lung, endo×(Ce1 lung, FcRn+Rlung)+koff1,endo×Ce1 lung, endo complex-1τ×Ce1 lung, endo

dCe1 lung, endo complexdt= kon1, endo×Ce1 lung, endo×Ce1 lung, FcRn+Rlung-koff1,endo×Ce1 lung, endo complex-1τ×Ce1 lung, endo complex

dCe1 lung, Abdt=F1×CLup, lungVe, lung×Cv lung, Ab+fulung×Ci lung, Ab-kon1, Ab×Ce1 lung, Ab×(Ce1 lung, FcRn+Rlung)+koff1,Ab×Ce1 lung, Ab complex-1τ×Ce1 lung, Ab

dCe1 lung, Ab complexdt= kon1, Ab×Ce1 lung, Ab×(Ce1 lung, FcRn+Rlung)-koff1,Ab×Ce1 lung, Ab complex-1τ×Ce1 lung, Ab complex

dCe1 lung, FcRndt=1τ×Ce1 lung, FcRn+Rlung+Ce1 lung, endo complex+Ce1 lung, Ab complex-kon1, endo×Ce1 lung, endo×(Ce1 lung, FcRn+Rlung)+koff1, endo×Ce1 lung, endo complex-kon1, Ab×Ce1 lung, Ab×(Ce1 lung, FcRn+Rlung)+koff1, Ab×Ce1 lung, Ab complex-1/τ×(Ce1 lung, FcRn+Rlung)

2.2.2.  Sub-compartment 2 (pH 7.0)

dCe2 lung, endodt=1τ×Ce1 lung, endo-kon2, endo×Ce2 lung, endo×Ce2 lung, FcRn+Rlung+koff2,endo×Ce2 lung, endo complex-1τ×Ce2 lung, endo

dCe2 lung, endo complexdt=1τ×Ce1 lung, endo complex+kon2, endo×Ce2 lung, endo×Ce2 lung, FcRn+Rlung-koff2, endo×Ce2 lung, endo complex-1τ×Ce2 lung, endo complex

dCe2 lung, Abdt=1τ×Ce1 lung, Ab-kon2, Ab×Ce2 lung, Ab×Ce2 lung, FcRn+Rlung+koff2,Ab×Ce2 lung, Ab complex-1τ×Ce2 lung, Ab

dCe2 lung, Ab complexdt=1τ×Ce1 lung, Ab complex+kon2, Ab×Ce2 lung, Ab×Ce2 lung, FcRn+Rlung-koff2, Ab×Ce2 lung, Ab complex-1τ×Ce2 lung, Ab complex

dCe2 lung, FcRndt=1τ×Ce1 lung, FcRn+Rlung-kon2, endo×Ce2 lung, endo×Ce2 lung, FcRn+Rlung+koff2, endo×Ce2 lung, endo complex-kon2, Ab×Ce2 lung, Ab×Ce2 lung, FcRn+Rlung+koff2, Ab×Ce2 lung, Ab complex-1/τ×(Ce2 lung, FcRn+Rlung)

2.2.3-2.2.4: Sub-compartments 3-4 (pH 6.5 and pH 6.0)

Equations are similar to 2.2.2

2.2.5: Sub-compartment 5 (pH 6.0)

dCe5 lung, endodt=1τ×Ce4 lung, endo-kon4, endo×Ce5 lung, endo×Ce5 lung, FcRn+Rlung+koff 4, endo×Ce5 lung, endo complex-CLup, lungVe, lung×Ce5, lung, endo

dCe5 lung, endo complexdt=1τ×Ce4 lung, endo complex+kon4, endo×Ce5 lung, endo×Ce5 lung, FcRn+Rlung-koff4, endo×Ce5 lung, endo complex-CLup, lungVe, lung×Ce5 lung, endo complex

dCe5 lung, Abdt=1τ×Ce4 lung, Ab-kon4, Ab×Ce5 lung, Ab×Ce5 lung, FcRn+Rlung+koff 4, Ab×Ce5 lung, Ab complex-F1×CLup, lungVe, lung×Ce5, lung, Ab

dCe5 lung, Ab complexdt=1τ×Ce4 lung, Ab complex+kon4, Ab×Ce5 lung, Ab×Ce5 lung, FcRn+Rlung-koff4, Ab×Ce5 lung, Ab complex-F1×CLup, lungVe, lung×Ce5 lung, Ab complex

dCe5 lung, FcRndt=1τ×Ce4 lung, FcRn+Rlung-kon4, endo×Ce5 lung, endo×Ce5 lung, FcRn+Rlung+koff 4, endo×Ce5 lung, endo complex-kon4, Ab×Ce5 lung, Ab×Ce5 lung, FcRn+Rlung+koff 4, Ab×Ce5 lung, Ab complex-CLup, lungVe, lung×Ce5 lung, FcRn+Rlung

2.3. Interstitial Space

Vi, lung×dCi lung, endodt=CLup, lung×1-FR×Ce5 lung, endo complex-Ci lung, endo+1-σV, lung×Cv lung, endo-(1-σL, lung)×Ci lung, endo

Vi, lung×dCi lung, Abdt=F1×CLup, lung×1-FR×Ce5 lung, Ab complex-fulung×Ci lung, Ab+F2×1-σV, lung×Cv lung, Ab-1-σL, lung×fulung×Ci lung, Ab-ktmd×1-fulung×Ci lung, Ab

dnPtlungdt=ksyn, lung-kdeg×nPtlung-ktmd-kdeg×1-fulung×Ci lung, Ab

fulung=1-KD+nPtlung+Ci lung, Ab-KD+nPtlung+Ci lung, Ab2-4×Ci lung, Ab×nPtlung2×Ci lung, Ab

3.  Liver

3.1. Vascular Space

Vv liver×dCv liver, endodt=QGI tract-LGI tract×Cv GI tract, endo+Qspleen-Lspleen×Cv spleen, endo+Qliver-QGI tract-Qspleen+LGI tract+Lspleen×Cpl, endo-Qliver-Lliver×Cv liver, endo-CLup, liver ×Cv liver, endo+FR×CLup, liver×Ce5 liver, endo complex-1-σV, liver×Lliver×Cv liver, endo

Vv liver×dCv liver, Abdt=QGI tract-LGI tract×Cv GI tract, Ab+Qspleen-Lspleen×Cv spleen, Ab+Qliver-QGI tract-Qspleen+LGI tract+Lspleen×Cpl, Ab-Qliver-Lliver×Cv liver, Ab-F1×CLup, liver ×Cv liver, Ab+FR×F1×CLup, liver×Ce5 liver, Ab complex-F2×1-σV, liver×Lliver×Cv liver, Ab

3.2-3.3: Endosomal and Interstitial Spaces

Equations are similar as 2.2-2.3

4.  Other organs

4.1. Vascular Space

Vv tissue×dCv tissue, endodt=Qtissue×Cpl, endo-Qtissue-Ltissue×Cv tissue, endo-CLup, tissue ×Cv tissue, endo+FR×CLup, tissue×Ce5 tissue, endo complex-1-σV, tissue×Ltissue×Cv tissue, endo

Vv tissue×dCv tissue, Abdt=Qtissue×Cpl, Ab-Qtissue-Ltissue×Cv tissue, Ab-F1×CLup, tissue ×Cv tissue, Ab+FR×F1×CLup, tissue×Ce5 tissue, Ab complex-F2×1-σV, tissue×Ltissue×Cv tissue, Ab

4.2-4.3: Endosomal and Interstitial Spaces

Equations are similar as 2.2-2.3

5.  Lymph Node

dXly, endodt=1-σL, lung×Llung×Ci lung, endo+1-σL, GI tract×LGI tract×Ci GI tract, endo+1-σL, spleen×Lspleen×Ci spleen, endo+1-σL, liver×Lliver×Ci liver, endo+1-σL, heart×Lheart×Ci heart, endo+1-σL,kidney×Lkidney×Ci kidney, endo+1-σL,skin×Lskin×Ci skin, endo+1-σL,muscle×Lmuscle×Ci muscle, endo-1τLY×Xly, endo

dXly, Abdt=1-σL, lung×Llung×fulung×Ci lung, Ab+1-σL, GI tract×LGI tract×fuGI tract×Ci GI tract, Ab+1-σL, spleen×Lspleen×fuspleen×Ci spleen, Ab+1-σL, liver×Lliver×fuliver×Ci liver, Ab+1-σL, heart×Lheart×fuheart×Ci heart, Ab+1-σL,kidney×Lkidney×fukidney×Ci kidney, Ab+1-σL,skin×Lskin×fuskin×Ci skin, Ab+1-σL,muscle×Lmuscle×fumuscle×Ci muscle, Ab-1τLY×Xly, Ab