Development of a Physiologically Based Pharmacokinetic Model for a Domain Antibody in Mice

Development of a physiologically based pharmacokinetic model for A domain antibody in mice using THE TWO-pore theory-

Supplementary information.

Armin Sepp1, Alienor Berges2, Andrew Sanderson1, and Guy Meno-Tetang2

1BioPharm Innovation, Biopharm R&D, GlaxoSmithKline, Cambridge, UK, 2Clinical pharmacology, Modelling and Simulation, GlaxoSmithKline, Stockley Park, UK

Address correspondence to: Guy Meno-Tetang, Ph.D, Clinical pharmacology, Modelling and Simulation, GlaxoSmithKline, Stockley Park, Uxbridge, UB11 1BT, UK.

E-mail:

Domain antibody protein expression and purification: VHD2-AST-VD1 fusion protein (dAb2, EVQLLESGGGLVQPGGSLRLSCAASGVNVSHDSMTWVRQAPGKGLEWVSAIRGPNGSTYYADSVKGRFTISRDNSKNTLYLQMNSLRAEDTAVYYCASGARHADTERPPSQQTMPFWGQGTLVTVSSASTDIQMTQSPSSLSASVGDRVTITCRASQSISSYLNWYQQKPGKAPKLLIYAASSLQSGVPSRFSGSGSGTDFTLTISSLQPEDFATYYCQQSYSTPNTFGQGTKVEIKR) in pDOM10, a pUC119-based expression vector [1], was transformed into E. coli HB2151 cells from Agilent Technologies (Santa Clara, US) and expressed in 500ml TB OnEx autoinduction medium from Merck Serono (Feltham, UK) supplemented with 100 mg/ml carbenicillin from Sigma-Aldrich (Dorset, UK) at 30°C for 72 hrs. Secreted protein was purified from clarified culture supernatant sequentially by affinity chromatography on 20 ml of protein A streamline resin from GE Healthcare (Chalfont St. Giles, UK). Briefly, protein in clarified culture supernatant was batch-bound to resin for 4 hrs at room temperature before washing with 10 column volumes (CV) of 25 mM Na Acetate from Sigma-Aldrich, pH 6. Bound protein was eluted with 4 CV 25 mM Na Acetate, pH 3, into 1/10th CV 1 M Na-Tris.HCl from Sigma-Aldrich, pH 8. Eluted protein was concentrated using 3.5 kDa MWCO Vivaspin20 devices from Sartorius-Stedim (Epsom, UK) and then purified by anion exchange on HiTrap SP FF (GE Healthcare) and size exclusion chromatography on Superdex 200 HR 10/30 from GE Healthcare column..Molecular integrity of the protein was confirmed by SDS-PAGE on Invitrogen 4-12% SDS Tris-Tricine gels from Life Technologies. Endotoxin was removed from the protein using Vivapure Q Mini from Sartorius (Epsom, UK), the final value being 0.6 EU/mg, as measured using Endosafe LAL cartridges from Charles River (Margate, UK).

Radiolabelling: dAb2 protein labelling, dosing and mouse QWBA was performed by Quotient Bioresearch (Rushden) Ltd. (Rushden, UK). Briefly, 1.6 mCi of N-succinimidyl[2,3-3H]propionate ([3H]-NSP) from Perkin-Elmer (Seer Green, UK) was dispensed into a vial and the solvent was evaporated under nitrogen gas at room temperature. The remaining residue was dissolved in DMSO from Sigma-Aldrich, added to 0.5mg protein in PBS and allowed to stand at +4 °C for approximately 16 hours (overnight). Any remaining unincorporated [3H]-NSP was removed by gel filtration using PD-10 desalting columns from GE Healthcare, yielding dAb2 with specific activity of 326.8 µCi/mg. The radiochemical purity of the dose prior to and after dosing was greater than 99 %, before being diluted with unlabelled dAb2 to 58.6µCi/mg at 1 mg/mL in PBS for dosing.

Stokes radius of dAb2. The hydrodynamic radius ae of a spherical protein can be expected to depend linearly on the cubic root of its volume and also molecular weight, given the tight packing of well-folded proteins. In order to estimate the ae for dAb2, we first established an empirical relationship between the experimentally measured Stokes radius values and their molecular weights for proteins ranging from 6380 Da for bovine pancreas trypsin inhibitor (BPTI) to 440 kDa fibronectin [2-8] and including ae=1.84nm value calculated for a monomeric dAb using Hydropro [9] and the x-ray structure of the Hel4 VH dAb 1OHQ.pdb by Jespers et al. [10]. An empirical quadratic relationship was observed between ae and 3MW values (R2=0.985), most likely reflecting increasing deviation from spherical shape as the size of the molecule increases (Figure 1S).

ae=0.5614×3MW+0.09611×23MW (1S)

Using Equation 1S we calculated ae=2.49nm for dAb2 with 25.6kDa molecular weight.

Figure 1S: Semi-empirical relationship between the molecular weight of the protein and its Stokes radius ae.

The two-pore hypothesis (2PH) of extravasation that takes into account both diffusion and filtration of the protein solute has been developed by Rippe and Haraldsson [5] .

In the case of homoporous membrane, according to non-equilibrium thermodynamics, the flow rate Jorg of solvent is expressed as

Jorg=LPS×ΔP-σ×Δπ (2S)

where LPS is hydraulic conductance, ΔP is the transmembrane hydrostatic pressure gradient, Δπ is the transmembrane osmotic pressure gradient and σ is the reflection coefficient for the solute.

According to Poiseuille law, the hydraulic conductance in Equation 2S depends on the total pore area Ao, viscosity of the solution η, the pores length Δx and pore radius r.

LPS=AoΔx× r28η (3S)

The solute dissolved in the medium is transported across the membrane in flux Js according to Kedem-Katchalsky equation [11]

Js=Jorg×1-σ×C+PS×ΔC (4S)

where C is the mean intramembrane solute concentration, ΔC the concentration gradient across the membrane, σ the reflection coefficient and PS is the permeability-surface area product for the solute.

The integrated form of Equation 4A is known as Patlak equation for global convection/diffusion in steady-state conditions [12]

Js=Jorg×1-σ×Cv-Ci×e-Pe1-e-Pe (5S)

where Pe is the modified Peclet number

Pe=Jorg×1-σPS (6S)

PS, the solute permeability-surface area product, depends on the diffusion constant Ds and the pore area available for diffusion A for the given solute

PS=Ds×AΔx (7S)

DS is the free diffusion constant of the solute according to Stokes-Einstein solution

Ds=R×T6×π×η×N×ae (8S)

R is gas constant, T is absolute temperature, η is viscosity and N is Avogadro number.

The solute reflection coefficient σ is calculated using an empirical equation

1-σ=1-(163×γ2-203×γ3+73×γ4) (9S)

γ is the ratio of the Stokes radius of the solute ae over that of the pore, r.

γ=aer (10S)

The ratio A/Ao also depends on γ

AAo=(1-γ)2×1-2.105×γ+2.087-1.707×γ5+0.726×γ61-0.7586×γ5 (11S)

Functions 9S and 11S are empirically defined at 0≤γ≤1.

Equation 7S can be rearranged to include ratio AoΔx, substituted using Equation 3S

PS=Ds×AAo×AoΔx=Ds×AAo×8×η×LPSr2 (12S)

LpS in Equation 12S can be expressed as a ratio of Jv and (ΔP-σ×Δπ) from function 2S

PS=Ds×AAo×8×η×Jorgr2×(ΔP-σ×Δπ) (13S)

Diffusion coefficient Ds from Equation 8S can be substituted into Equation 13S

PS=R×T6×π×N×ae×AAo×8×Jorgr2×(ΔP-σ×Δπ) (14S)

Equation 14S links the permeability-surface area product PS to the flow rate Jv because both take place through the same pores at the same time.

In the case of heteroporous membrane model applied to PBPK, the fraction of flow passing through large and small pores is determined by their respective fractional hydraulic conductance values LPSL and LPSS defined through dimensionless coefficients αL and αS and are expressed per unit of tissue, as well as flow of lymph Jorg for different organs.

LPS=LPSS+LPSL (15S)

LPSL=αL× LPS (16S)

LPSS=αS×LPS=1- αL×LPS (17S)

αS=1-αL (18S)

The small and large pore permeability-surface area products PSS and PSL are solute-dependent functions on the respective relative pore areas available for diffusion ASAoS and ALAoL in a given tissue, as well as pore radius values rS and rL.

PSS=Ds×ASAoS×AoSΔxS=Ds×ASAoS×LpSS×8×ηrS2=Ds×ASAoS×(1-αL)×LpS×8×ηrS2==Ds×ASAoS× (1-αL)×8×η×JorgrS2×(ΔP-σa×Δπ)=

=R×T6×π×N×ae×ASAoS×8×(1-αL)×JorgrS2×(ΔP-σa×Δπ)=XP×ASAoS×(1-αL)×JorgrS2 (19S)

PSL=Ds×ALAoL×AoLΔxL=Ds×ALAoL×LpSL×8×ηrL2=Ds×ALAoL×αL×LpS×8×ηrL2==Ds×ALAoL×αL×8×η×JorgrL2×(ΔP-σa×Δπ)=

=R×T6×π×N×ae×ALAoL×8×αL×JorgrL2×(ΔP-σa×Δπ)=XP×ALAoL× αL× JorgrL2 (20S)

Equations 19S-20S share a common factor XP and the Starling pressure expression (ΔP-σa×Δπ).

XP=8×R×T6×π×N×ae×(ΔP-σa×Δπ) (21S)

In physiological steady-state conditions σa is the effective reflection coefficient for plasma proteins and is hereby assumed to be equal to that of albumin, the dominant plasma protein, with reflection coefficients σS,a and σL,a at both small and large pores respectively.

σa=αL×σL,a+αS×σS,a (22S)

In two-pore model the oncotic pressure gradient across the membrane gives rise to local isogravimetric circular flow Jiso which affects the net flow of through large and small pores Jorg,L and Jorg,S respectively.

Jorg,L=Jiso+αL×Jorg (23S)

Jorg,S=-Jiso+αS×Jorg (24S)

By substituting LpS from Equation 2S, isogravimetric flow Jiso too is linearly related to the net flow rate Jv and the Starling forces (ΔP-σa×Δπ)

Jiso=αL×αS×LpS×σS,a-σL,a×Δπ=αL×αS×σS,a-σL,a×Δπ(ΔP-σa×Δπ)Jv=XJ×Jorg (25S)

Unlike XPS and XPL, XJ is solely determined by physiological steady state parameters and does not depend on properties of proteins added in trace amounts.

XJ=αL×αS×σS,a-σL,a×Δπ(ΔP-σa×Δπ) (26S)

Nonlinear transfer according to Equation 4S in the case of two-pore membrane the total flux of solute Js includes fractions JsL and JsS passing through large and small pores respectively.

Js=JsL+JsS=Jorg,L×1-σL.s×CL+PSL×ΔC+Jorg,S×1-σS.s×CS+PSS×ΔC (27S)

CL and CS are the mean intramembrane concentrations of the solute in large and small pores.

Using the integrated Patlak Equation 5A for fluxes through large and small pores

Js=Jorg,L×1-σL,s×Cv-Ci×e-PeL1-e-PeL+Jorg,S×1-σS,s×Cv-Ci×e-PeS1-e-PeS (28S)

Flux Js of solute is determined by its vascular and interstitial concentrations Cv and Ci,, fractional flow rates Jorg,L, Jorg,S, reflection coefficients σL and σS, as well as Peclet values PeL and PeS.

The Peclet number values do not vary between different tissues as long as long as the pore sizes and ratio does remain unchanged because permeability-surface area product is expressed as a function of lymph flow rate Jorg.

PeL=Jorg,L×(1-σL)PSL=Jiso+αL×Jorg×1-σL×rL2XP×(ALAoL)×αL×Jorg=XJ×Jorg+αL×Jorg×1-σL×rL2XP×(ALAoL)×αL×Jorg=XJ+αL×1-σL×rL2XP×(ALAoL)×αL

(29S)

PeS=Jorg,S×(1-σS)PSS=-Jiso+αS×Jorg×1-σS×rS2XP×(ASAoS)×αS×Jorg=-XJ×Jorg+αS×Jorg×1-σS×rS2XP×(ASAoS)×αS×Jorg=-XJ+αS×1-σS×rS2XP×(ASAoS)×αS (30S)

Calculation of Peclet numbers for dAb2

For large pores filtration slightly dominates over diffusion

PeL=Jorg,L×(1-σL)PSL=Jiso+αL×Jorg×1-σLXPL×Jorg=XJ×Jorg+αL×Jorg×1-σLXPL×Jorg=XJ+αL×1-σLXPL=0.34+0.042×1-0.05170.27=0.360.27=1.33 (31S)

For small pores diffusion dominates over filtration

PeS=JvS×(1-σS)PSS=-Jiso+αS×Jorg×1-σSXPS×Jorg=-XJ×Jorg+αS×Jorg×1-σSXPS×Jorg=-XJ+αS×1-σSXPS=-0.34+0.958×1-0.7125.7=0.185.7=0.031 (32S)

Cross-correlation of lymph flow rate (L) and isogravimetric flow rate (Jiso) values used and calculated by Ferl et al. [7].

Figure 2S: Cross-correlation of lymph flow (L) and isogravimetric flow Jiso values used and calculated by Ferl et al. [7]. A-without standard errors, B- with standard error bars.

Table S1: Different organs’ clearances of dAb2 from the PBPK model.

Muscle / Skin / Liver / Kidney / Total
kint×Vmuscle,vs / kint×Vskin,vs / Kliv×Vliv,vs / QGFR×θGFR
Clearance / ml/min / 0.0024 / 0.0018 / 0.00015 / 0.1296 / 0.134
Relative Clearance / % / 1.8 / 1.3 / 0.1 / 96.8 / 100

Table S2: Derived per cent of plasma flow diverted to lymph in different organs.

Heart / Lung / Bone / GIT / Spleen / Brain / Muscle / Skin / Liver / Kidney / Total
Jorg x10-3
(ml/min/g) / 3.01 / 0.65 / 1.59 / 0.97 / 0.09 / 0 / 0.49 / 0.88 / 2.36 / (1.44)
Morg (g) / 0.15 / 0.20 / 2.82 / 1.04 / 0.127 / 0.485 / 11.3 / 5.02 / 1.930 / 0.525
Jorg, total
x10-3
(ml/min) / 0.45 / 0.13 / 4.48 / 1.01 / 0.011 / 0 / 5.54 / 4.42 / 4.60 / 0.756 / 21.4
Qorg
(ml/min) / 0.608 / 6.217 / 0.25 / 1.25 / 0.136 / 0.197 / 1.435 / 1.173 / 1.56 / 1.142 / 6.217
Jorg, totalQorg ×100% / 0.084 / 0.002 / 1.2 / 0.088 / 0.017 / 0 / 0.36 / 0.29 / 0.12 / (0.07) / 0.34
Note: Jorg for kidney was not fitted

Table S3: Relative contribution of filtration and diffusion to dAb2 extravasation through small and large pores in all organs (except for kidney).

Large pores / Small pores / All pores
Peclet number[1] / 1.33 / 0.031
Filtration / 0.36 / 00.18 / 00.54
Diffusion / 0.27 / 05.70 / 05.97
Filtration + Diffusion / 0.63 / 05.88 / 06.51
Relative filtration % / 5.50 / 02.75 / 08.25
Relative diffusion % / 4.15 / 87.60 / 91.75

Table S4: Parameter cross-correlation for the PBPK model in SAAM2.

Cgfr / LbneSp / LgitSp / LhrtSp / LlngSp / LlvrSp / LmscSp / LsknSp / LsplSp / VkdyT
Cgfr / 1 / -0.06801 / -0.05606 / -0.08903 / -0.01295 / -0.07549 / -0.01255 / 0.41805 / 0.23653 / 0.02413
LbneSp / -0.06801 / 1 / -0.01094 / 0.05995 / -0.01026 / -0.03515 / -0.0072 / 0.00917 / -0.06021 / -0.02053
LgitSp / -0.05606 / -0.01094 / 1 / 0.031 / 0.00397 / 0.02266 / 0.0181 / 0.02743 / -0.036 / -0.01923
LhrtSp / -0.08903 / 0.05995 / 0.031 / 1 / 0.01003 / 0.09846 / 0.04691 / 0.02239 / -0.04644 / -0.02078
LlngSp / -0.01295 / -0.01026 / 0.00397 / 0.01003 / 1 / 0.00086 / 0.0133 / 0.02891 / -0.01498 / -0.01452
LlvrSp / -0.07549 / -0.03515 / 0.02266 / 0.09846 / 0.00086 / 1 / 0.05447 / 0.06471 / -0.06518 / -0.02977
LmscSp / -0.01255 / -0.0072 / 0.0181 / 0.04691 / 0.0133 / 0.05447 / 1 / -0.00391 / -0.05398 / -0.05658
LsknSp / 0.41805 / 0.00917 / 0.02743 / 0.02239 / 0.02891 / 0.06471 / -0.00391 / 1 / 0.02562 / -0.10871
LsplSp / 0.23653 / -0.06021 / -0.036 / -0.04644 / -0.01498 / -0.06518 / -0.05398 / 0.02562 / 1 / 0.02034
VkdyT / 0.02413 / -0.02053 / -0.01923 / -0.02078 / -0.01452 / -0.02977 / -0.05658 / -0.10871 / 0.02034 / 1
Cgfr is the glomerular filtration coefficient θGFR, LorgSp is the specific lymph flow rate Jorg, VkdyT is the VBCLH

Table S5. Sensitivity analysis of the impact of VBCLH value on the AUC of dAb2 in plasma and kidney (Shah and Betts [13])

AUC (VBCLH) M×min / AUC (0.5×VBCLH) M×min / %Change / AUC (1.5×VBCLH) M×min / %Change
Plasma / 437 / 437 / 0 / 437 / 0
Kidney / 6334 / 3294 / 48 / 9244 / -46

%Change=AUCSIM-AUC±50%AUCSIM×100%

Supplementary references

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