Amplifying the Impact of Kidney Microphysiological Systems: Predicting Renal Clearance Using Mechanistic Modelling Based on Reconstructed Drug Secretion

The micro-perfusion model ......................................................................................................................................... 7 Assumptions and modelling steps .............................................................................................................................. 8 Software implementation ............................................................................................................................................ 9 9 In vitro to in vivo extrapolation (IVIVE) .......................................................................................................9

We acknowledge that using animal derived consumables such as antibodies, fetal bovine serum and collagen matrix perpetuates the use of animal-based research products. Nonetheless, the percentage of serum used in our cultures was limited to 1% (v/v). The sourcing of alternative antibodies for the tubular markers selected for this study, the validation of their specificity and optimization of experimental conditions was outside of our scope. The material used in our study had been previously validated and the target specificity of the antibodies used well documented in the literature, which facilitated our assays design. The same holds true for the use of rat tail collagen I gel. Although synthetic gels are available, implementing a new matrix would require extensive optimization, which was outside of our scope.

Fig. S1: Specificity of drug transporter antibodies evaluated in overexpression cell lines
Commercially available antibodies against membrane drug transporters are often reported as lacking specificity for their intended targets. To confirm that the antibodies used in this study recognize the drug transporters analyzed, immunostainings were performed in cell lines overexpressing OCT2 (HEK), OAT1 (HEK) or P-gp (MDCK). HEK-OCT2 (A) and HEK-mock transfected cells (D) were used to test the OCT2 antibody (dil. 1:500). HEK-OAT1 FlpIn (B) and HEK-FlpIn mock transfected cells (Zou et al., 2018) (E) were used to test the OAT1 antibody (dil. 1:500). MDCK-P-gp (C) and MDCK wild type cells (F) were used to test the P-gp antibody (dil. 1:1000). Secondary antibodies were used diluted 1:500 in combination with Hoechst33342 1:1000.

Fig. S2: Cellular localization of OCT2 and P-gp in RPTEC in 2D-Plastic culture
The spatial localization of OCT2 and P-gp was determined using reconstructed confocal Z-stacks consisting of eight frames each (2 μm apart) after staining for f-actin (Phalloidin 488: green) and OCT2 or P-gp (Alexa555: red). F-actin is seen delineating the cell boundaries in the orthogonal views. OCT2 is mostly localized intracellularly and does not colocalize with the membrane (A). P-gp is expressed both intracellularly and in the membrane, evident from the yellow stain that results from f-actin and P-gp co-localization (B). Gene expression statistical analysis Statistically significant differences between -ΔCt values were determined for each sample relative to 2D-Plastic using un-paired t-tests corrected for multiple comparisons using the Holm-Sidak method, assuming the same scatter (SD) among samples, with α=0.05. Calculations were performed using GraphPad Prism 8.

Apparent permeability and trans-epithelial flux calculations
The apparent permeability (Papp) of metformin and cidofovir was determined in a conventional 2D-transwell assay, in the apical-to-basolateral (A2B) direction and the basolateral-to-apical (B2A) direction. The efflux ratio (ER) was determined as Papp(B2A)/Papp(A2B). An ER > 2 indicates that active transport is involved in the drug permeability.

= . .
Papp is defined as the change in concentration (dQ) in the recipient compartment (A or B) over time (dt), crossing a barrier area (cell grow surface: A) relative to the initial concentration (Ci) in the donor compartment (A or B). Units: cm.s -1 .10 -6 Trans-epithelial flux (J) calculations were performed to evaluate the movement of drugs from B2A in 2D-transwell and kidney-MPS. This permeability analysis accounts for the quantity of a drug (m) crossing the area of a barrier (A) to a recipient compartment over time (t), independently of the initial concentration in the donor compartment. Units: µmol.cm -2 .min -1 .

Shear stress calculations in Kidney-MPS
To estimate the shear stress experienced by RPTEC in the kidney-MPS chip, an online microfluidic flow rate and shear stress calculator was used (https://darwin-microfluidics.com/blogs/tools/microfluidic-flowrate-and-shear-stresscalculator). The dimensions of the tubule embedded in the MPS chip matrix were used (diameter: 125 µm; length: 5.8 mm), together with a viscosity of 0.7978 cP and flow rates of either 0.5 µL/min (kidney-MPS culture conditions) or 1 µL/min (kidney-MPS assay conditions) were used to estimate shear stress.  Figure S4: Depiction of the cell count workflow in Kidney-MPS using ImageJ Cell density in the renal tubule was estimated by counting the number of nuclei present in renal tubules. The renal tubule was split into 9 sections (A) and confocal stacks of 25 images (20x) from the midsection to the boundary of the tubule were acquired using a CV7000 imager (B-C). In ImageJ each image stacks were projected to compile all structures present in one section (B) and the nucleus number was calculated. ImageJ instructions used were as follows: 1. Load image. Image -> Type -> 8 bit colour 2. Process -> Binary -> make binary 3. Process -> Binary -> Watershed 4. Analyse -> analyse particles 5. Show: outlines 6. Display results 7. Summarize 8. In situ show. The number of nuclei estimated reflects ½ of a tubule, and assuming a homogenous distribution of cells in the tubules, the values were doubled to estimate the whole renal tubule. Confocal stacks of the whole circumference of the renal tubule were not used since this would skew the total number of cells given that both the nucleus from the bottom and top half of the tubule are super-imposed.

Metformin and cidofovir perfusion cytotoxicity
To evaluate any cytotoxic effects in the kidney-MPS after perfusion with metformin or cidofovir live-dead assays were applied. Assays were performed after a 6 h perfusion with metformin or cidofovir together with the inhibitors imipramine or probenecid, respectively.

Quantification of trans-epithelial drug transport in the micro-perfusion platform
The micro-perfusion model A semi-mechanistic modelling approach, schematically illustrated in Figure 6 panel A (main text), was developed to evaluate drug disposition in the kidney-MPS chip. The model considers the net diffusion of drug cross the physical extracellular matrix volume section Vtot separating the loading and renal microfluidic channels, and further the basolateral-to-apical transport into the renal channel (Table S8). Vtot is split into ntr well-stirred transit compartments of equal volume Vtr=Vtot/ntr to accommodate for the transit time through the matrix. The flux of drug at any time t into the first transit compartment is proportional to the concentration Cl(t) in the loading channel, as defined by a first-order rate constant Qtr [μL/min] (Eq. S1). The same rate constant further defines flux into subsequent transit volumes and, in the cell-free chip presenting no epithelial cell barrier to passage, also transport into the renal channel (Eq. S2-S4). Drug is in turn leaving the renal channel at a rate governed by the chip perfusion rate Qp [μL/min] on its path to the outlet collection port. In presence of a RPTEC monolayer, drug translocate from the extracellular matrix to the renal channel either by diffusion down its concentration gradient (trans-or paracellularly) or by transporter-mediated secretion, categorized here as 'passive' and 'active' transport, respectively (Eq. S5). We expect the amount of drug transported to depend on the tubular area formed by the RPTECs, and hence define the rate constants as permeability-surface area products, denoted PSp and PSa [μL/min] for active and passive transport, respectively. A set of ordinary differential equations following mass-action principles forms a mathematical representation of the above. The rate by which the amount of drug Xtr,i changes over time is given by ,1 = × ( ( ) − ,1 ) Eq. S1 for the first transit compartment i=1 where Cl(t) represents the concentration in the loading channel. Change in subsequent compartments i=2:ntr-1 follows , = × ( , −1 − , ) Eq. S2 Eq. S3 defines flux into and out of the last transit compartment i= ntr. The rate equation follows the assumption that sink conditions apply, with continuous flow thought the tubule, and passive reabsorption is negligible. Following the reasoning above, change to the amount in the renal channel Xr is expressed as at empty cell-free chip conditions, whereas for the situation with a renal tubule Xr is governed by where Qp, PSp and PSa represent the perfusion rate, active and passive permeability-surface areas, respectively.

Assumptions and modelling steps
In the micro-perfusion model described, kinetic parameters Qtr, PSp and PSa and number of transit compartments ntr are not directly given by experimental conditions (Table S8) and need estimation through optimization of a likelihood function of the fit to observed concentrations. Identification required the following general assumptions: i) flux of drug through the loading channel and subsequent dispersion into the extracellular matrix in presence of a RPTEC monolayer can be approximated in a cell-free chip setup, ii) concentration-time profiles at the outlet ports of each circuit are useful surrogates for profiles in the channels through the matrix chamber and iii) the loading and renal channels can be considered well-mixed compartments. The loading outlet profile after perfusion of drug through a cell-free chip over 6 h demonstrates significant overlap to observations from chip with RPTEC tubule ± selective inhibitors ( Figure S6). This suggests that of the continuously introduced drug, the fraction dispersed into the extracellular matrix is relatively insensitive to the experimental condition over this time period, supporting assumption i). For reasons indicated above, including the consequence of flow profile and interactions with material, we expect a broadening of the concentration-time build-up along the length of each microfluidic circuit, also downstream of the matrix chamber. However, as loading and renal profiles are expected to be similarly convoluted, actual channel profiles -provided linear kinetics -will be interchangeable with observed port profiles in assessing exchange cross the channels, in support of assumption ii. Finally, given the small volume and short residence time in the matrix loading and renal channels (<0.1 min at experimental conditions), influence of axial concentration gradients is negligible, in line with assumption iii). Parameters defining renal secretion in the MPS system, PSp and PSa ultimately used to predict human renal clearance, were for each drug estimated by a sequential fitting procedure. The cell-free chip profiles were used to calibrate the model's baseline behavior. Firstly, the loading channel Cl(t) was modelled empirically by curve-fitting of a sigmoidal three-parameter function to the loading channel outlet concentration.
( ) = 1 + 10 (log( 50 )−log( )) * Eq. S6 Definition of Top (concentration at the plateau), t50 (time at which Cl=Top/2) and  (slope factor) allowed for simulation of the concentration driving flux into the extracellular matrix (Eq. S1) at any time t. This in turn enabled subsequent estimation of Qtr by fitting the micro-perfusion model to the corresponding renal outlet profile ( Figure 6 panels B1, C1, main text). Keeping Cl(t) and Qtr frozen, basolateral-to-apical transport of the epithelial cell layer, represented by parameters PSp and PSa, was assessed by simultaneous fit to renal channel outlets in absence and presence of selective inhibitors of the carrier-mediated pathway ( Figure 6 panels B2, C2, main text). Parameter estimates for metformin and cidofovir are collected in Table 1 (main text). Estimates were found to be insensitive to number of transit compartments ≥ 3. Reported estimates were obtained for ntr = 3.

Software implementation
The micro-perfusion model was implemented in MATLAB (Release 2017a, The MathWorks, Inc., Natick, Massachusetts, US). Fitting applied a naïve pooled approach using the non-linear least squares solver lsqnonlin with the default trust-region-reflective algorithm. Model selection was guided by a composite of likelihood function optimization and visual inspection of the residual graphs. Confidence intervals were generated by Monte-Carlo simulations (n=500) of concentration-time profiles on basis of parameter values randomly chosen from the multivariate normal distribution of the estimates, generated from the mvnrnd function, as implemented in MATLAB. At each simulated timepoint, upper and lower bounds were given by the 97.5 th and 2.5 th percentiles, respectively.

In vitro to in vivo extrapolation (IVIVE)
The renal clearance in human was predicted from PSp and PSa on basis of the tubular surface area in the microfluidic system relative to that of the in vivo physiology following the scaling method established by Kunze et al (Kunze et al., 2014). In brief, the approach expresses kidney organ clearance CLr,org as the net result of glomerular filtration CLr,fil, tubular secretion CLr,sec, and fractional tubular reabsorption freab. Eq. S9 Filtration is calculated from the glomerular filtration rate GFR and the fraction unbound in blood fub , = × Eq. S10 whereas secretion is derived from the renal blood flow rate Qr,b, fub and the scaled intrinsic clearance of tubular transport CLint,sec , = , × × , , + × , Eq. S11 applying the well-stirred liver model concept. Reabsorption from the tubule fluid is calculated as Eq. S12 where the intrinsic clearance of reabsorption in vivo CLint,reab constitutes the passive portion of CLint,sec.
The in vivo intrinsic clearances where upscaled from the MPS determined permeability-surfaces areas , = ( + ) × Eq. S13 , = × Eq. S14 where SAvivo is the estimated total surface area of a human proximal tubules and SAMPS is the surface area of the RPTEC tubule layer in the microphysiological system: Physiological values (Table S9) for the proximal tubule diameter dPT and length lPT, number of nephrons per kidney nneph, number of kidneys nkid and body weight BW were taken from literature (Lote, 2013) following the steps of Kunze et al. (2014). Sensitivity of metformin and cidofovir predicted renal clearance to variation of in vitro (MPS surface area) and physiological (in vivo surface area, GFR and renal blood flow) scaling parameters are shown in Figure S7. A 3fold change of each parameter resulted predicted renal clearance within a factor of 2 of the point estimate, with the expectation of GFR for which the clearance was within a factor of 3.

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The steady-state model The permeability-surface area products (PSpassive and PSactive) were derived at steady-state, when drug concentration in the loading channel reaches a constant input, approximately 200 min after perfusion is initiated. In Eq. S7 Cd and Cr are approximated by the loading and renal channel outlet concentrations and Vr/t is the flow rate (1 µL/min in this setup