A mechanistic modelling approach for the determination of the mechanisms of inhibition by cyclosporine on the uptake and metabolism of atorvastatin in rat hepatocytes using a high throughput uptake method

Figures & data

Figure 1. Flow chart of high throughput assay starting from incubation and separation of hepatocytes from the media via an oil spin method (steps 1–4) to extraction and analysis via LC-MS (steps 5–9). Numbers in squares relate to the step number in time order as described in the Methods section. LC-MS: liquid chromatography–mass spectrometry.

Figure 2. Schematic of the micro-rate constant models (Models 1 and 2) consisting of medium, transporter and intracellular compartments, and macro-rate constant models (Models 3 and 4) consisting of medium and intracellular compartments. Atorvastatin following pre-incubation with CsA with competitive (a and c) and non-competitive (b and c) inhibition of uptake respectively were modelled. CsA: cyclosporine.

Table 1. Structural identifiability of the micro-rate constant models and macro-rate constant models, and goodness of fit values obtained during parameter estimation (Models 1–4).

Model	Inhibition type	No. of unknown parameters	No. of states	Identifiability result	No. of parameters to be identifiable (d.o.f.)	BIC (wBIC)	% RMSRE (ind + pop)
1	C	11	5	SI	0	5514.2 (0.45)	21 + 61 = 82
2	NC	12	6	SI	0	5513.8 (0.54)	21 + 49 = 69
3	C	8	3*	U	2: Km.up, KI.up, Km.met, KI.met	5608.0 (0)	29 + 94 = 123
4	NC	8	3*	U	2: Vmax.up, Kinact.up, Km.met, KI.met	5524.8 (0)	29 + 96 = 125

Best fitting model outlined in bold.

BIC: Bayesian information criterion; C: competitive; d.o.f.: degrees of freedom; NC: non-competitive; RMSRE: relative mean square root error; SI: structurally (locally) identifiable; U: unidentifiable; wBIC: weighted BIC.

Figure 3. Plots of atorvastatin cellular concentration against time following the addition of atorvastatin (0.05, 0.25, 0.5, 2.5, 5, 25, 50 and 150 nmol/ml) in the absence (circles) and presence (triangles) of 10 nmol/ml of CsA. Each time course represents one experiment from one Teflon block trough. Shapes are data from the three separate experiments, the solid line and dashed line is the average individual prediction from Model 2 in the absence and presence of 10 nmol/ml of CsA, bounded by the max and min individual predictions (shading). CsA: cyclosporine.

Figure 4. Plot of individual weighted residuals (IWRES) against time for Model 2 obtained using Monolix 2018R2. Points are IWRES, dashed lines are 95% confidence intervals and solid line is the locally estimated scatterplot smoothing of the IWRES.

Figure 5. Model 2 plots of the simulated amounts of atorvastatin bound to the transporter against time in the absence (dotted line) and presence (solid line) of cyclosporine (CsA). The dotted-dashed line is the amount of CsA bound to the transporter following pre-incubation, and the dashed line is the atorvastatin–transporter–CsA complex.

Table 2. Micro-rate constant model parameter estimates for the non-competitive inhibition of atorvastatin by CsA in rat hepatocytes (Model 2).

Parameter	Individual mode (min–max)
Passive
kfA (/min)	1.1 (0.2–23.3)
kbA (/min)	9.3 (0.6–36.5)
Transporter
kaA (/nmol/min)	2.6 (1.2–13.3)
kaC (/nmol/min)	0.36 (0.33–0.37)
kdA (/min)	0.017 (0.015–0.021)
kdC (/min)	0.16 (0.13–0.2)
To (nmol)	2.7 (2–3.6)
ktA (/min)	0.3 (0.2–0.3)
α	0.013 (0.007–0.023)
Metabolism
Vmax.met (pmol/min)	393 (285–500)
Km.met (nmol/ml)	18 (8–31)
KI.met (nmol/ml)	11 (6–29)

Data are the individual mode of the conditional distribution obtained from Monolix 2018R2, n = 3. All parameter estimates are scaled to per 1 × 10⁶ cells. V_max was scaled to pmol/min and K_m, K_I and K_inact were scaled to nmol/ml.