Physiologically‐Based Pharmacokinetic Modeling Analysis for Quantitative Prediction of Renal Transporter–Mediated Interactions Between Metformin and Cimetidine

Abstract

Metformin is an important antidiabetic drug and often used as a probe for drug–drug interactions (DDIs) mediated by renal transporters. Despite evidence supporting the inhibition of multidrug and toxin extrusion proteins as the likely DDI mechanism, the previously reported physiologically‐based pharmacokinetic (PBPK) model required the substantial lowering of the inhibition constant values of cimetidine for multidrug and toxin extrusion proteins from those obtained in vitro to capture the clinical DDI data between metformin and cimetidine.¹ We constructed new PBPK models in which the transporter‐mediated uptake of metformin is driven by a constant membrane potential. Our models successfully captured the clinical DDI data using in vitro inhibition constant values and supported the inhibition of multidrug and toxin extrusion proteins by cimetidine as the DDI mechanism upon sensitivity analysis and data fitting. Our refined PBPK models may facilitate prediction approaches for DDI involving metformin using in vitro inhibition constant values.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

☑  Metformin is an important antidiabetic drug and a probe drug to predict drug–drug interactions (DDI) mediated by renal transporters. The previously reported physiologically‐based pharmacokinetic (PBPK) models required a substantial lowering of in vitro inhibition constant values to reproduce the observed DDI data, necessitating the development of PBPK models suitable for the bottom‐up prediction of the DDI potential.

• WHAT QUESTION DID THIS STUDY ADDRESS?

☑  This study aimed to develop a new PBPK model of metformin and to quantitatively predict DDI between metformin and cimetidine (an inhibitor of organic cation transporter 1/2 and multidrug and toxin extrusion proteins) using in vitro inhibition constant values.

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

☑  The constructed PBPK model incorporated the metformin transport process driven by the membrane potential kept constant and achieved the quantitative prediction of DDI incurred by cimetidine using in vitro inhibition constant values. The simulation results also supported the inhibition of multidrug and toxin extrusion proteins by cimetidine as the DDI mechanism.

• HOW MIGHT THIS CHANGE DRUG DISCOVERY, DEVELOPMENT, AND/OR THERAPEUTICS?

☑  This metformin PBPK model represents an important advancement in quantitatively capturing the DDI mediated by renal transporters using middle‐out approaches.

Metformin is a first‐line therapy for type 2 diabetes, but its response varies substantially, with about 30% of patients failing to achieve glycemic control2, 3 and the rare incidence of severe events of lactic acidosis.4 As such, it is important to understand the factors contributing to interindividual variation in metformin response and to quantitatively predict the potential for drug–drug interactions (DDIs) involving metformin.

The pharmacokinetics of metformin has been well characterized. The oral bioavailability of metformin is 50–60%.5, 6, 7, 8 Metformin undergoes negligible hepatic metabolism, but it is mainly excreted intact into the urine; its renal clearance exceeds the glomerular filtration rate, indicating tubular secretion. With negligible plasma protein binding, metformin slowly distributes to erythrocytes.6, 9 Metformin exists ionized at physiological pHs, relying on transporters for its translocation across cell membranes. Metformin is transported by the organic cation transporters (OCTs), particularly OCT1 in the liver10 and OCT2 in the kidney.11 Multidrug and toxin extrusion proteins (MATEs), namely MATE1 and MATE2‐K are also shown to mediate the extrusion of metformin from proximal renal tubular cells to urine.12 These transporters harbor genetic variations, some of which can impact the pharmacokinetics and pharmacodynamics of metformin.13, 14, 15

Cimetidine is an inhibitor of OCT2 and MATEs and incurs DDIs with metformin; the coadministration of cimetidine increased the systemic exposure of metformin in plasma by ~ 50%, whereas it decreased the renal clearance of metformin by ~ 30%.16, 17 The inhibition of OCT2 by cimetidine had been initially suspected as the DDI mechanism, but it was deemed unlikely as the reported values of the OCT2 inhibition constant (Ki) for cimetidine (ranging from 72.6–510 μM10, 11) are much higher than the maximal unbound plasma concentrations of cimetidine (C_max; ranging from 7.67–9.48 μM after the oral administration of 400 mg cimetidine).18, 19 The reported Ki values of cimetidine for MATEs range from 1.21–13.5 μM.20, 21, 22 The results from the mouse study (in vitro and in vivo) also supported the inhibition of MATEs as a likely mechanism for the DDI between cimetidine and metformin.21

Physiologically‐based pharmacokinetic (PBPK) modeling analysis allows for quantitative prediction of drug concentration‐time profiles and enhances our mechanistic understanding of DDI.1, 23, 24 For metformin, a minimal PBPK model was previously reported but with no consideration of transporter‐mediated processes.9 Later, whole‐body PBPK models were developed with the mechanistic components reflecting transporter‐mediated processes (by OCT1, OCT2, and MATEs), namely, the conventional model and the “electrochemical model” driven by dynamically changing electrochemical modulation.1 To reproduce clinical DDI data, these models required a substantial lowering of the Ki values of cimetidine for transporters from the in vitro reported values: for the conventional model, the lowering of the Ki values for OCT1 and OCT2 nearly by 500‐fold, and for the electrochemical model, the lowering of the Ki values for OCT1, OCT2, and MATEs by 8~18‐fold.1 Thus, there is a clear need to develop a PBPK model that can quantitatively predict DDIs involving metformin using Ki values obtained in vitro.

We developed a new metformin PBPK model by incorporating hepatic and renal transporter–mediated processes driven by the membrane potential, which is kept constant. Our PBPK model achieved quantitative prediction of DDIs between metformin and cimetidine using in vitro data, supporting the inhibition of MATEs by cimetidine as the major DDI mechanism.

Materials and Methods

Development of the metformin PBPK model

We modified the previously reported model1, 25 by adding erythrocyte compartments and implementing changes in the kidney and the liver (Figure  1 a). The physicochemical and pharmacokinetic parameters of metformin are summarized in Table  S1 , and relevant physiological parameters are summarized in Tables  S2 and S3 . Adipose, muscle, and skin are incorporated considering their contribution to the distribution volume. Rapid equilibrium was assumed using the tissue‐to‐plasma concentration ratios predicted in silico 26 by physicochemical properties.

Figure 1.

Structures of the physiologically‐based pharmacokinetic models for metformin (a) and cimetidine (b). Erythrocyte compartments were incorporated into all the tissues in the metformin model (red boxes). CL _met, metabolic clearance; p.o., per os.

Erythrocyte compartments

Considering its slow distribution to erythrocytes and time‐dependent changes in blood‐to‐plasma concentration ratios,6 the systemic circulation and capillary vessels in all tissues were divided into plasma and erythrocyte compartments. The distribution processes between plasma and erythrocytes are defined in Eqs. (1) and (2).

$$\frac{X_{\mathrm{erythro}}}{\mathrm{d}t}=k_{\mathrm{in},\mathrm{RBC}}\ast X_{\mathrm{plasma}}-k_{\mathrm{out},\mathrm{RBC}}\ast X_{\mathrm{erythro}},$$ (1)

$$\frac{X_{\mathrm{plasma}}}{\mathrm{d}t}=-k_{\mathrm{in},\mathrm{RBC}}\ast X_{\mathrm{plasma}}+k_{\mathrm{out},\mathrm{RBC}}\ast X_{\mathrm{erythro}}$$ (2)

where X _erythro and X _plasma are the amount of metformin in the erythrocyte and plasma compartment, respectively, and k _in,RBC and k _out,RBC are the partitioning rate constants of metformin from plasma to erythrocytes and from erythrocytes to plasma, respectively, and obtained in vitro by measuring time‐dependent blood cell distribution of metformin using human blood9 (Table  S1 ).

Liver model

A five‐compartment liver model was used as similar to our previous report.24 Biliary excretion was not included in the model as clinical data indicated that metformin is not excreted into bile. Considering that OCT1 is a bidirectional transporter driven by the membrane potential, the OCT1‐mediated transport is defined using Eq. (3),27 the Michaelis–Menten constant (K _m,OCT1), and the maximum rate (V_max,OCT1).

$$\begin{array}{cc}\hfill \text{OCT}1\text{transport}& =\mathrm{PS}{}_{\mathrm{OCT}1,\inf }\ast C_{\mathrm{EH}}-\text{PS}{}_{\mathrm{OCT}1,\mathrm{eff}}\ast C_{\mathrm{HC}}\hfill \\ & ={\mathrm{V}}_{\max ,\mathrm{OCT}1}\hfill \\ & \ast \left(\frac{C_{\mathrm{EH}}}{K_{\mathrm{m},\mathrm{OCT}1}+C_{\mathrm{EH}}}-\frac{e^N}{R_{\mathrm{OCT}1,\inf /\mathrm{eff}}}\ast \frac{C_{\mathrm{HC}}}{K_{\mathrm{m},\mathrm{OCT}1}+C_{\mathrm{HC}}}\right)\hfill \end{array}$$ (3)

$$N=\frac{z\ast \mathrm{\Phi }\ast F}{R\ast T}$$ (4)

where PS_OCT1,inf and PS_OCT1,eff are the intrinsic OCT1‐mediated clearance via influx into and efflux out of hepatocytes, respectively; C _HC and C _EH are the metformin concentrations inside and outside hepatocytes, respectively; R _OCT1,inf/eff is the OCT1‐mediated influx‐to‐efflux ratio; z, Φ, F, R, and T are the valence, the membrane potential, Faraday's constant, the gas constant, and the absolute temperature, respectively. The definitions for the other parameters are provided in the Supplemental Text .

Kidney model

The kidney model comprised the glomerulus, the proximal tubule (further divided into the S1, S2, and S3 regions), the distal tubule, and the collecting duct. The proximal tubule, the distal tubule, and the collecting duct were further divided into the three subcompartments representing the blood vessels, cells, and the urinary lumen, similar to the previous report.1 The active transport of metformin was assumed to occur only in the proximal tubule by OCT2 and MATEs at the basolateral and luminal sides, respectively. Reabsorption of metformin from the urinary lumen was assumed to be mediated by passive diffusion. Considering that OCT2 is a bidirectional transporter driven by the membrane potential, the transport process by OCT2 is defined using Eq. (5), the Michaelis–Menten constant (K _m,OCT2) and the maximum rate (V_max,OCT2).

$$\begin{array}{cc}\hfill \text{OCT}2\text{transport}& =\text{PS}{}_{\mathrm{OCT}2,\inf }\ast C_{\mathrm{r}}-{\text{PS}}_{\mathrm{OCT}2,\mathrm{eff}}\ast C_{\mathrm{rcell}}\hfill \\ & ={\mathrm{V}}_{\max ,\mathrm{OCT}2}\hfill \\ & \ast \left(\frac{C_{\mathrm{r}}}{K_{\mathrm{m},\mathrm{OCT}2}+C_{\mathrm{r}}}-\frac{e^N}{R_{\mathrm{OCT}2,\inf /\mathrm{eff}}}\ast \frac{C_{\mathrm{rcell}}}{K_{\mathrm{m},\mathrm{OCT}2}+C_{\mathrm{rcell}}}\right)\hfill \end{array}$$ (5)

where PS_OCT2,inf and PS_OCT2,eff are the OCT2‐mediated intrinsic clearance via influx into and efflux out of renal cells, respectively; R _OCT2,inf/eff is the influx‐to‐efflux ratio of OCT2; and C _r and C _rcell are the metformin concentrations in the blood vessels and renal cells, respectively.

As shown in Eq. (5), our model defined that the OCT2‐mediated transport process is driven by a constant membrane potential, different from the previously reported PBPK model where the membrane potential changed in response to time‐dependent changes in metformin concentrations.1 The transporter‐mediated processes in the liver were similarly defined using the membrane potential kept constant. Intrinsic clearance by MATEs was defined using Eq. (6), the Michaelis–Menten constant (K _m,MATE) and the maximum rate (V_max,MATE).

$$\text{PS}{}_{\mathrm{MATE}}=\frac{{\mathrm{V}}_{\max ,\mathrm{MATE}}}{K_{\mathrm{m},\mathrm{MATE}}}+C_{\mathit{in}}.$$ (6)

In the proximal tubule, based on the extended clearance concept,28 the parameters CL_int,sec, β_kidney, R _MATE/dif, γ_r, and γ_urine were defined using Eqs. (7), (8), (9), (10), (11), (12), (13), (14):

$${\text{CL}}_{\mathrm{int},\sec }={\text{PS}}_{\mathrm{r},\inf }\ast {\mathrm{\beta }}_{\mathrm{kidney}}={\text{PS}}_{\mathrm{r},\inf }\ast \frac{{\text{PS}}_{\mathrm{urine}}}{{\text{PS}}_{\mathrm{r},\mathrm{eff}}+{\text{PS}}_{\mathrm{urine}}}$$ (7)

$${\mathrm{\beta }}_{\mathrm{kidney}}=\frac{{\text{PS}}_{\mathrm{urine}}}{{\text{PS}}_{\mathrm{r},\mathrm{eff}}+{\text{PS}}_{\mathrm{urine}}}$$ (8)

$${\mathrm{R}}_{\mathrm{MATE}/\mathrm{diff}}=\frac{{\text{PS}}_{\mathrm{MATE}}}{{\text{PS}}_{\mathrm{urine},\mathrm{dif},\mathrm{eff}}}$$ (9)

$${\mathrm{\gamma }}_r=\frac{{\text{PS}}_{\mathrm{r},\mathrm{dif},\inf }}{{\text{PS}}_{\mathrm{r},\mathrm{dif},\mathrm{eff}}}=\frac{f_{\mathrm{o},\mathrm{union}}+\mathrm{\lambda }\ast f_{\mathrm{o},\mathrm{ion}}}{f_{\mathrm{i},\mathrm{union}}+e^N\ast \mathrm{\lambda }\ast f_{\mathrm{i},\mathrm{ion}}}\approx \frac{1}{e^N}=13.7$$ (10)

$${\mathrm{\gamma }}_{\mathrm{urine}}=\frac{{\text{PS}}_{\mathrm{urine},\mathrm{dif},\inf }}{{\text{PS}}_{\mathrm{urine},\mathrm{dif},\mathrm{eff}}}\approx \frac{1}{e^N}=12.3$$ (11)

$${\text{PS}}_{\mathrm{r},\inf }={\text{PS}}_{\mathrm{OCT}2,\inf }+{\text{PS}}_{\mathrm{r},\mathrm{dif},\inf }$$ (12)

$${\text{PS}}_{\mathrm{r},\mathrm{eff}}={\text{PS}}_{\mathrm{OCT}2,\mathrm{eff}}+{\text{PS}}_{\mathrm{r},\mathrm{dif},\mathrm{eff}}$$ (13)

$${\text{PS}}_{\mathrm{urine}}={\text{PS}}_{\mathrm{MATE}}+{\text{PS}}_{\mathrm{urine},\mathrm{dif},\mathrm{eff}}$$ (14)

where CL_int,sec is the intrinsic urinary secretion clearance; PS_r,inf and PS_r,eff are the intrinsic renal clearance via influx into and efflux out of renal cells, respectively; PS_urine is the intrinsic efflux clearance from renal cells to the urinary lumen; PS_r,dif,inf and PS_r,dif,eff are the intrinsic passive clearance via influx into and efflux out of renal cells, respectively; PS_{urine,dif,inf} and PS_{urine,dif,eff} are the intrinsic passive clearance via influx into cells from the urinary lumen and efflux out of cells to the urinary lumen; R_MATE/dif is the ratio of the intrinsic clearance of MATEs to the intrinsic passive diffusion clearance via efflux out of cells to the urinary lumen; γ_r and γ_urine are the passive influx‐to‐efflux ratio on the basolateral and luminal sides, respectively; λ is the ratio of passive diffusion for the ionized form to that for the unionized form; f _o,union and f _o,ion are the extracellular fractions of the unionized and ionized forms, respectively; f _i,union and f _i,ion are the intracellular fractions of the unionized and ionized forms, respectively; β_kidney is a hybrid parameter reflective of the major rate‐limiting steps of C_Lint,sec

Metformin (pKa of 12.3) exists mainly ionized at physiological pHs (thus, f _o,union = f _i,union = 0 and f _o,ion = f _i,ion = 1), and γ_r and γ_urine were calculated using the Nernst equation.29 Passive diffusion clearances of each compartment in the kidney were calculated using permeability measured in a parallel artificial membrane permeability assay system,30 surface area, γ_r, and γ_urine (Table  S3 ).29, 31

Optimization of model parameters

Other unknown parameters (absorption rate constant, k _a; transit rate constant from the transit compartment to the intestinal compartment, k _trans; and R _MATE/dif) were optimized by fitting to the two clinical data sets obtained after oral administration of metformin at 1,500 mg (time profiles of plasma and blood concentrations and urinary excretion)6 or 250 mg (DDI data between metformin and cimetidine).16 Because reliable β_kidney was not estimated from the observed metformin pharmacokinetic data, four different β_kidney values (0.1, 0.3, 0.5, and 0.8) were used to cover a wide range of rate‐determining step situations. Unknown parameters were optimized with β_kidney fixed (Table  1 ) and used as fixed values for DDI simulation. Under DDI conditions, the β_kidney value was not fixed and allowed to change as the renal transport processes became inhibited. Upon oral dosing, metformin showed a less than dose‐proportional increase of area under the curve (AUC), suggesting saturable intestinal absorption processes.32 To reflect such saturation, our PBPK model assumed that metformin is absorbed via first‐order kinetics with the intestinal availability set as 0.57 and 0.84 for the metformin oral doses of 1,500 and 250 mg, respectively (back‐calculated from the bioavailability data, Table  S1 ). Between the two data sets (metformin oral doses of 250 mg and 1,500 mg),6, 16 time of maximum concentration (Tmax) values varied (3.3 and 1.5 hours, respectively). The reported T_max values vary substantially even with the same doses,5, 14, 17 and the adjustment of T_max was deemed necessary in analyzing the two data sets together. As the same formulation was used in the two clinical studies,6, 16 the data of the 1,500 mg dose were used to obtain the optimized k _a value, which was then used for the data of the 250 mg dose. The k _trans and R _MATE/dif values were optimized by fitting to the observed data after oral dosing of 250 mg metformin16 using varying β_kidney values (0.1, 0.3, 0.5, and 0.8).

Table 1.

Optimized physiologically‐based pharmacokinetic model parameters (k _a, k _trans, and R _MATE/dif) after fitting to the oral metformin doses of 1,500 and 250 mg using differing β_kidney values

1,500 mg metformin
	Observed6	βkidney
		0.1	0.3	0.5	0.8
R MATE/dif	–	153 ± 18.1	213 ± 25.5	325 ± 39.2	814 ± 111
k a (/hour)	–	0.21 ± 0.013	0.21 ± 0.013	0.21 ± 0.013	0.21 ± 0.013
k trans (/hour)	–	2.4 ± 0.36	2.4 ± 0.36	2.4 ± 0.36	2.4 ± 0.36
AUC0–24 (mg•h/L)	21.4 ± 3.18	20.1	20.1	20.2	20.2
CLr (L/hour)	23.0 ± 3.87	29.8	29.8	30	30

250 mg metformin
	Observed16	βkidney
		0.1	0.3	0.5	0.8
RMATE/dif	–	183 ± 30.1	261 ± 43.3	402 ± 66.3	1,143 ± 186
k a (/hour)	–	0.21	0.21	0.21	0.21
k trans (/hour)	–	0.61 ± 0.044	0.61 ± 0.044	0.61 ± 0.044	0.61 ± 0.044
AUC0–12 (mg•hour/L)	3.75 ± 1.43	4.12	4.12	4.12	4.12
CLr (L/hour)	31.6 ± 9.90	28.5	28.6	28.6	28.6
Cmax (μg/L)	590 ± 240	502	502	502	502
Tmax (hour)	3.3 ± 0.8	3.72	3.72	3.72	3.72

AUC_0–24, area under the curve from 0–24 hours; AUC_0–12, area under the curve from 0–12 hours; CLr, renal clearance; C_max, maximum plasma concentration; T_max, time of maximum concentration; k_a,absorption rate; k_trans, the rate from transit compartment to intestine compartment; R_MATE/dif, the ratio of the intrinsic clearance of MATEs to the intrinsic passive diffusion clearance via efflux out of cells to the urinary lumen.

Development of the cimetidine PBPK model

The cimetidine PBPK model was developed by implementing several modifications to the metformin PBPK model (Figure  1 b, Supplemental Text ). At physiological pHs, cimetidine (pKa of 6.9) can exist as both ionized and unionized, and their fractions were calculated using the Henderson–Hasselbalch equation (Table  S3 ).24, 33 To calculate γ_h, γ_r, and γ_urine of cimetidine using Eq. (10), λ was set to be 0.1 as described previously.29

DDI simulation

DDI simulation was performed by combining the developed metformin and cimetidine PBPK models. Cimetidine was assumed to be a competitive inhibitor in the transport of metformin by OCT1, OCT2, or MATEs, as shown in Eq. (15):

$${\text{PS}}_{\mathrm{act}}\left(+I\right)=\frac{{\text{PS}}_{\mathrm{act}}\left(\text{control}\right)}{1+\frac{\left[I\right]}{\mathit{Ki}}}$$ (15)

where PS_act(control) and PS_act(+I) are the intrinsic active clearance of metformin in the absence and the presence of an inhibitor, respectively, and I is the inhibitor concentration.

In vitro Ki (or half maximal inhibitory concentration (IC₅₀)) values of cimetidine were obtained from the reports where the metformin concentration was sufficiently lower than its K_m value (Table  2 ).

Table 2.

Sensitivity analysis for AUC, C_max, and CLr ratios between control and drug–drug interaction conditions using different Ki values for OCT2 and MATEs

Sensitivity analysis of three different Ki values for OCT2 (72.6, 509, and 159 represent the lowest and highest values and the geometric mean of in vitro Ki values, respectively) and differing βkidney values. The Ki value for MATEs was fixed at the geometric mean value.
	Observed16	βkidney = 0.1			βkidney = 0.3			βkidney = 0.5			βkidney = 0.8
		Ki for OCT2 (μM)			Ki for OCT2 (μM)			Ki for OCT2 (μM)			Ki for OCT2 (μM)
		72.6	159	509	72.6	159	509	72.6	159	509	72.6	159	509
AUC ratio	1.47 ± 0.75	1.23	1.23	1.23	1.19	1.19	1.19	1.14	1.14	1.14	1.07	1.07	1.07
Cmax ratio	1.72 ± 0.97	1.32	1.32	1.32	1.26	1.26	1.26	1.19	1.19	1.19	1.08	1.08	1.08
CLr ratio	0.72 ± 0.32	0.75	0.75	0.75	0.80	0.80	0.80	0.84	0.84	0.84	0.90	0.90	0.90

Sensitivity analysis of three different Ki values for MATEs (1.22, 13.5, and 3.93 represent the lowest and highest values and the geometric mean of in vitro Ki values, respectively) and differing βkidney values. The Ki value for OCT2 was fixed at the geometric mean value.
	Observed16	βkidney = 0.1			βkidney = 0.3			βkidney = 0.5			βkidney = 0.8
		Ki for MATEs (μM)			Ki for MATEs (μM)			Ki for MATEs (μM)			Ki for MATEs (μM)
		1.22	3.93	13.5	1.22	3.93	13.5	1.22	3.93	13.5	1.22	3.93	13.5
AUC ratio	1.47 ± 0.75	1.44	1.23	1.10	1.40	1.19	1.07	1.30	1.14	1.05	1.15	1.07	1.03
Cmax ratio	1.72 ± 0.97	1.57	1.32	1.13	1.52	1.26	1.09	1.41	1.19	1.07	1.21	1.08	1.03
CLr ratio	0.72 ± 0.32	0.59	0.75	0.89	0.63	0.80	0.92	0.70	0.84	0.94	0.82	0.90	0.97

The geometric mean and the ranges of the reported in vitro Ki (μM) values of cimetidine were as follows: OCT1, 10411; OCT2, 159, 72.6–50910, 11, 20, 21, 34, 35; MATEs, 3.93, 1.22–13.520, 21, 22, 41 ^.

AUC, area under the curve; Ki, inhibition constant; C_max, maximum plasma concentration; CLr, renal clearance; β_kidney = PS_urine/(PS_r,eff+PS_urine); OCT2, organic cation transporter 2; MATEs, multidrug and toxin extrusion proteins.

The Numeric Analysis Program for Pharmacokinetics (version 2.31)34 was used for simulation and optimization of parameters using the nonlinear least‐squares method. The weight for the calculation was set as 1 (the square root of the value).

Results

Metformin PBPK model

The k _a, k _trans, and R _MATE/dif were optimized by fitting the model to the time profiles of plasma and blood concentrations and urinary excretion of metformin after a single oral dose of 1,500 mg metformin6 at varying β_kidney values (Table  1 ). Although the optimized R _MATE/dif varied from 150–800 at different β_kidney values, the optimized k _a and k _trans were 0.21 ± 0.01 hour⁻¹ and 2.4 ± 0.4 hour⁻¹, respectively, regardless of β_kidney values. The use of these optimized parameters well reproduced the observed data, including the increase of blood‐to‐plasma ratios over time (likely from slow distribution of metformin to erythrocytes; Figure  2 a–d, Figure  S1 ). Next, the k _trans and R _MATE/dif were optimized by fitting the model to the plasma concentration‐time profile after oral metformin dosing of 250 mg16 (intestinal availability adjusted to 0.84 as described in the Methods section) using differing β_kidney values (Figure  2 e–h, Table  1 ). The use of the optimized parameters yielded simulated T_max (3.72 hours) and AUC_0–12 (4.12 mg•h/L) comparable with the observed values (3.3 ± 0.8 hours and 3.75 ± 1.43 mg•h/L, respectively) at all four β_kidney values.

Figure 2.

Fitted and observed metformin plasma and blood concentration‐time profiles after single oral administration of 1,500 mg metformin (a–d), fitted and observed plasma concentration‐time profiles after a single oral administration of 250 mg metformin (e–h) and after a single oral administration of 400 mg cimetidine (i). The black circles and red triangles represent the observed concentration‐time profiles in plasma and blood, respectively. The black and red lines represent the fitted concentration‐time profiles in plasma and blood, respectively. Simulations were performed using differing β_kidney values; β_kidney = PS_urine/(PS_r,eff+PS_urine).

Cimetidine PBPK model

Parameters for the cimetidine PBPK model were from the reported data (Table  S4 )1, 10, 27, 30 and used with no further optimization. Our PBPK model yielded the simulation results that well reproduced the observed data after a single oral administration of 400 mg cimetidine (Figure  2 i).18 The simulated AUC (9.10 mg•h/L) was comparable with the observed value (10.4 ± 2 mg•h/L).

DDI simulation

The pharmacokinetic profiles under DDI conditions were simulated using the developed PBPK models for metformin and cimetidine and in vitro Ki values (geometric mean) of cimetidine for OCT1, OCT2, and MATEs at differing β_kidney values. The simulated plasma concentrations of metformin were increased with coadministration of cimetidine at all β_kidney values, but the extent of the changes showed some discrepancies between the simulated and observed values; the fold changes of AUC, C_max, and CLr in the simulations were 1.07–1.23, 1.08–1.32, and 0.75–0.90, respectively, whereas the observed fold changes were 1.47, 1.72, and 0.72, respectively (Table  2 , Figure  S2 ).

Sensitivity analysis for in vitro Ki values of cimetidine for OCT2 and MATEs

As the reported in vitro Ki values of cimetidine for OCT2 and MATEs vary widely (Table  2 ),10, 11, 20, 21, 22, 35, 36, 37 we conducted sensitivity analyses for Ki values. DDI simulations were initially conducted with three in vitro Ki values for OCT2 (72.6, 509, and 159 μM, corresponding to the smallest and largest values and the geometric mean of the reported values, respectively), whereas the Ki values for OCT1 and MATEs were fixed to the geometric means of 104 μM and 3.93 μM, respectively. The fold changes of AUC, C_max, and CLr were not impacted by the Ki values for OCT2 regardless of β_kidney values (Table  2 ). DDI simulations were also conducted with three in vitro Ki values for MATEs (1.22, 13.5, and 3.93 μM, corresponding to the smallest and largest values and the geometric mean of the reported values, respectively), whereas the Ki values of cimetidine for OCT1 and OCT2 were fixed to 104 μM and 159 μM, respectively. The fold changes in AUC, C_max, and CLr were impacted by the Ki values for MATEs (Table  2 ).

Estimation of the in vivo Ki value of cimetidine for MATEs

The in vivo Ki value of cimetidine for MATEs was estimated by fitting to clinical DDI data with k _trans and R _MATE/dif fixed to their optimized values at varying β_kidney values. Simulation using the estimated in vivo Ki values for MATEs at all four β_kidney values reproduced the observed fold changes in AUC, CLr, and C_max with less than 15% differences (Figure  3 , Table  3 ). The good agreement between the simulated and observed profiles regardless of β_kidney values appears to be consistent with our initial trial on reliable β_kidney estimation by fitting to the clinical metformin pharmacokinetic data. The estimated in vivo Ki values for MATEs were in the range of the in vitro reported Ki values with β_kidney values of 0.1 and 0.3 but not with 0.5 and 0.8 (corresponding to 0.52‐ and 0.18‐fold of the smallest in vitro reported Ki value (1.22 μM), respectively).

Figure 3.

Metformin plasma concentration‐time profiles under control and drug–drug interaction conditions using fitted in vivo inhibition constant values for multidrug and toxin extrusion proteins after oral administration of 250 mg metformin and 400 mg cimetidine. For the control condition, the optimized parameters shown in Table  1 for β_kidney value of 0.1 (a), 0.3 (b), 0.5 (c), or 0.8 (d) were used. For drug–drug interaction conditions, the optimized parameters were fixed, but the β_kidney value was not fixed and allowed to change as the renal transport processes became inhibited. The black circles and blue triangles represent the observed plasma concentrations under control and drug–drug interaction conditions, respectively, and the black and blue lines represent the corresponding simulation results; β_kidney = PS_urine/(PS_r,eff+PS_urine).

Table 3.

Observed and simulated AUC, C_max, and CL_r ratios of metformin between control and drug–drug interaction conditions with fitted in vivo Ki value for MATEs at various β_kidney values

βkidney a	Fitted in vivo Ki value for MATEs (μM)	Fold changes from simulations
		AUC (1.47 ± 0.75)16	Cmax (1.72 ± 0.97)16	CLr (0.72 ± 0.32)16
0.1	1.71 ± 0.74	1.40	1.52	0.63
0.3	1.34 ± 0.60	1.39	1.50	0.64
0.5	0.64 ± 0.34	1.42	1.54	0.61
0.8	0.23 ± 0.12	1.42	1.54	0.61

AUC, area under the curve; C_max, the maximum plasma concentration; CLr, renal clearance; Ki, inhibition constant; MATEs, multidrug and toxin extrusion proteins.

^aFor the control condition, the β_kidney value was set to 0.1, 0.3, 0.5, or 0.8, and the optimized parameters shown in Table  1 were used. For the drug–drug interaction conditions, the optimized parameters were fixed, but the β_kidney value was not fixed and allowed to change as the renal transport processes became inhibited.

Sensitivity analysis of Ki values of cimetidine for MATEs

For comparison with the previously reported model,1 we examined the impact of changing Ki values for MATEs on the fold changes in plasma AUC, CLr, or AUC in the proximal tubule cell segment 1 under DDI conditions. Initially, the sensitivity analysis of our PBPK model (β_kidney of 0.1) was compared with that of the conventional and electrochemical models reported previously (Figure  4 a–c).1 In our model, β_kidney values reflect the rate‐determining step of renal secretion in proximal tubule cells. Upon additional sensitivity analysis using varying β_kidney values (Figure  4 d–f), the sensitivity to changing Ki values for MATEs on plasma AUC, CLr, and AUC in proximal tubule segment 1 in our model tended to be greater than the previously reported model1 except for the extreme ends of the β_kidney ranges tested. For the plasma AUC of metformin, the observed fold change (1.47) under DDI conditions was recovered by lowering the Ki values for MATEs by ~ 1.5, 2.5, and 6‐fold from the smallest in vitro Ki value with β_kidney values of 0.3, 0.5, and 0.8, respectively (Figure  4 d). With a β_kidney of 0.1, the lowest reported Ki value (1.22 μM) yielded the observed 1.44‐fold change in the plasma AUC, close to the observed value. For the CLr, the observed fold change (0.72) was recovered using the Ki values for MATEs that fell within the range of the reported in vitro Ki values except for a β_kidney of 0.8; for a β_kidney of 0.8, the Ki for MATEs had to be lowered to 0.40 μM (approximately threefold lower than the smallest in vitro Ki value; Figure  4 e). For the AUC in proximal tubule segment 1, the fold change under DDI conditions was not available, but as β_kidney values increased, so did the sensitivity to changing Ki values for MATEs increase (Figure  4 f). Overall, the observed fold changes in the plasma AUC or CLr were reproduced using the Ki values for MATEs near and within the range of those obtained in vitro with β_kidney values of 0.1, 0.3, or 0.5 but not 0.8.

Figure 4.

Sensitivity analysis to examine the impact of changing Ki values for MATEs on the fold changes in plasma AUC (□), CLr (△), or AUC in the proximal tubule cell segment 1 (♢). For comparison, the initial analysis was performed using the conventional model (a) and the electrochemical model (b) reported by Burt et al.1 and our current PBPK model (c) using β_kidney = 0.1. For our current PBPK model, the impact of changing β_kidney values was examined on plasma AUC (d), CLr (e), and AUC in the proximal tubule cell segment 1 (f). The shaded area near the x‐axis indicates the range of in vitro Ki values for MATEs reported in the literature (geometric mean: 3.93 μM (1.22–13.5 μM)). The dotted horizontal lines indicate the observed fold changes in plasma AUC (1.47, black) or CLr (0.72, blue). (d–f) Red, orange, green, and blue symbols and lines represent the simulation results using optimized values shown in Table  1 for β_kidney values of 0.1, 0.3, 0.5, and 0.8, respectively. DDI, drug–drug interaction; Ki, inhibition constant; MATEs, multidrug and toxin extrusion proteins; PBPK, physiologically‐based pharmacokinetic. AUC, area under the curve; CLr, renal clearance; β_kidney = PS_urine/(PS_r,eff+PS_urine).

Discussion

Metformin is a clinically important antidiabetic drug and often used as a probe drug to examine the potential DDI mediated by renal transporters. Thus, there is a clear need to establish and refine PBPK models that can accurately and quantitatively predict the DDI potential between metformin and other drugs using in vitro data. To this end, the previous metformin PBPK model (“electrochemical model”)1 incorporated the transport process by OCTs driven by dynamically changing membrane potential in response to metformin levels. This electrochemical model reproduced the plasma concentration profile of metformin alone, but the extent of the fold changes in the plasma AUC under DDI conditions was recovered only when the Ki value for MATEs was set at 8.7‐fold lower values than the geometric mean value of the reported in vitro Ki values (3.93 μM). Although in vitro Ki values can substantially vary, the 8.7‐fold difference is rather substantial. To reconcile these differences, our model considered the electrogenic property of OCTs but kept the membrane potential constant. In the living cells and organisms, the electrochemical potential is regulated by concentration and permeability of multiple ions (e.g., potassium ion, sodium ion, chloride ion, typically at 100–200 mM) present at much higher concentrations.38 Thus, a reasonable assumption may be that drug‐induced changes in the electrochemical potential at the therapeutically relevant level to be modest extent. Our current PBPK model yielded in vivo simulated Ki values within the reported in vitro Ki values when β_kidney was 0.1 or 0.3 (Table  3 ). In the sensitivity analysis, the observed plasma AUC change was reproduced within 15% difference (Table  2 ) with the lowest in vitro Ki values and observed CLr change was reproduced in the range of in vitro Ki values (1.22–5 μM) except for a β_kidney of 0.8 (Figure  4 e). Overall, our model reproduced the clinical DDI data of metformin and cimetidine with in vitro Ki values when β_kidney was 0.3 or less. In addition, the results from sensitivity analysis were comparable between the previous electrochemical model and our model with a β_kidney of 0.8 (Figure  4 b,d,e). These results suggest that the rate‐determining step in the electrochemical model is likely the renal uptake, requiring one to greatly lower the Ki value for MATEs or OCT2 from in vitro Ki values to reproduce the observed DDI data. Thus, a β_kidney of 0.3 or less is recommended for future efforts to predict the potential DDI using in vitro Ki values. Of note, we could not obtain reliable β_kidney estimates by fitting to clinical metformin data (under control conditions). Our approach was to use a wide range of fixed β_kidney values (to cover situations with differing rate‐determining steps) under control conditions and to deduce optimal β_kidney ranges from sensitivity analysis. This approach may represent another strategy to indirectly estimate β_kidney.

In understanding how our model was capable of reproducing the clinical DDI data using in vitro Ki values and small β_kidney values, a mechanistic interpretation of the β_kidney values may shed some light on possible reasons. The extended clearance concept takes all intrinsic processes into account when assessing the overall elimination process. Incorporating the extended clearance concept, CL_int,sec is described as PS_r,inf·β_kidney (Eq. (7)). By converting the parameters with Eqs. (5) and (8), (9), (10), (11), (12), (13), (14), CL_int,sec can be transformed to Eq. (16).

$$\begin{array}{cc}\hfill {\text{CL}}_{\mathrm{int},\sec }=& \left({\text{PS}}_{\mathrm{OCT}2,\inf }+{\text{PS}}_{\mathrm{r},\mathrm{dif},\inf }\right)\hfill \\ & \ast \frac{{\text{PS}}_{\mathrm{MATE}}+{\text{PS}}_{\mathrm{urine},\mathrm{dif},\mathrm{eff}}}{\frac{e^N}{R_{\mathrm{OCT}2,\inf /\mathrm{eff}}}{\text{PS}}_{\mathrm{OCT}2,\inf }+{\text{PS}}_{\mathrm{r},\mathrm{dif},\mathrm{eff}}+{\text{PS}}_{\mathrm{MATE}}+{\text{PS}}_{\mathrm{urine},\mathrm{dif},\mathrm{eff}}}\hfill \end{array}$$ (16)

When β_kidney is 0.1, the values for individual parameters in Eq. (16) are as follows: PS_OCT2,inf, 732 L/hour; PS_r,dif,inf, 0.043 L/hour; PS_r,dif,eff, 0.0031 L/hour; PS_MATE, 4.47 L/hour; PS_{urine,dif,eff}, 0.024 L/hour; e ^N/R _OCT2,inf/eff, 0.055. When the transport of metformin by MATEs becomes inhibited to 20% in the presence of cimetidine (i.e., PS_MATE decreased to 0.89 L/hour), the β_kidney is changed from 0.1 to 0.022, and CL_int,sec is decreased from 73.5 to 16.3 L/hour, by ~ 4.5‐fold when compared with the control condition. A similar calculation can be performed when β_kidney is 0.8. The values for individual parameters in Eq. (16) are as follows: PS_OCT2,inf, 126 L/hour; PS_r,dif,inf, 0.043 L/hour; PS_r,dif,eff, 0.0031 L/hour; PS_MATE, 27.9 L/hour; PS_{urine,dif,eff}, 0.024 L/hour; e ^N/R _OCT2,inf/eff, 0.055. When the transport of metformin by MATEs becomes inhibited to 20% in the presence of cimetidine (i.e., PS_MATE decreased to 5.6 L/hour), β_kidney is changed from 0.8 to 0.45, and CL_int,sec is decreased from 101 to 56.4 L/hour, by ~ 1.8‐fold when compared with the control condition. These calculation results indicate that as β_kidney values become smaller, the inhibition of MATEs has a much greater impact on CL_int,sec.

A number of DDI cases have been reported between metformin and other drugs that can inhibit both OCT2 and MATEs (e.g., pyrimethamine,39, 40 dolutegravir,41 trimethoprim,37, 42 and vandetanib43). For pyrimethamine, in vitro Ki values for MATEs (0.059–0.15 μM) are much lower than those for OCT2 (4.1–23 μM).22, 38, 44 The observed C_max values of unbound pyrimethamine in plasma range from 0.30–0.40 μM after a 50 mg oral pyrimethamine dose,35, 45 suggesting the inhibition of MATEs as the likely DDI mechanism. In the case of dolutegravir, its in vitro Ki values for OCT2 and MATE1 are 1.9 and 6.3 μM,41 respectively. In a clinical DDI study, the coadministration of dolutegravir increased the plasma AUC of metformin by 79% and 145% when dolutegravir was coadministered as a single daily dose of 50 mg and two daily doses of 50 mg with a 12‐hour interval.41 With its unbound C_max values being much lower than the in vitro Ki values for OCT2 and MATE1, the inhibitions of OCT2 and MATE1 were deemed unlikely to explain the observed DDI, and the exact mechanism remains unknown. Our current PBPK model may aid the efforts to quantitatively predict the DDI and gain mechanistic insights into complex DDI cases between metformin and other drugs.

Our PBPK model for metformin may also have some utility in understanding the source of variable response and toxicity to metformin therapy. Drug concentrations in plasma or blood are often assumed to be associated with drug efficacy and toxicity. It is, however, increasingly recognized that it may not be the case if a drug is actively taken up into tissues or metabolized in the tissues.46 Although one third of patients did not respond to metformin,2, 3 the metformin levels in plasma are not predictive of blood lactate concentrations and the risk for lactic acidosis.4, 15, 47 In addition, the diabetic patients carrying the MATE1 promoter variant (g.‐66T→C) exhibit a greater response to metformin than those carrying the wildtype.15 By incorporating variables consistent with biologically plausible mechanisms (especially variables for transport processes by OCT1/2 and MATEs), it might be possible to gain mechanistic insights into interindividual variations in metformin response and side effects and to predict the pharmacokinetic profiles and clinical outcomes using the virtual clinical study method.48

In conclusion, we developed a refined PBPK model for metformin that successfully reproduced the DDI between metformin and cimetidine with in vitro Ki values. Our results supported the fact that the DDI between metformin and cimetidine is likely mediated by the inhibition of MATEs by cimetidine rather than by OCT2 inhibition.

Funding

No funding was received for this work.

Conflict of Interest

The authors declared no competing interests for this work.

Author Contributions

K.N., K.T., W.L., N.I., B.B., and Y.S. wrote the manuscript. K.N., K.T., and Y.S. designed the research. K.N., K.T., and Y.S. performed the research. K.N., K.T., and Y.S. analyzed the data.

Supporting information

Figure S1. Simulated (lines) and observed (open circles) time profiles of metformin urinary excretion after a single oral administration of 1,500 mg metformin using various β_kidney values.

Figure S2. Metformin plasma concentration time profiles of control and drug–drug interaction conditions using the lowest and geometric mean of inhibition constant values of cimetidine at differing β_kidney values after the administration of 250 mg metformin and 400 mg cimetidine.

Table S1. Various parameters used in the metformin physiologically‐based pharmacokinetic model and reported in vitro Km values for transporters of metformin parameters used in the metformin physiologically‐based pharmacokinetic model.

Table S2. Physiological parameters of blood volume, tissue volumes, hematocrit value, and blood flows.

Table S3. Physiological parameters, membrane potential, blood flow, and urinary flow in the kidney model.

Table S4. Parameters used in the cimetidine physiologically‐based pharmacokinetic model.

Supplementary Material S1. Model code file.

Supplementary Material S2. Model equations for metformin.