PKPD modelling to predict altered disposition of 1α,25-dihydroxyvitamin D₃ in mice due to dose-dependent regulation of CYP27B1 on synthesis and CYP24A1 on degradation

Abstract

Background and Purpose

Concentrations of 1α,25-dihydroxyvitamin D₃ [1,25(OH)₂D₃], the active ligand of the vitamin D receptor, are tightly regulated by CYP27B1 for synthesis and CYP24A1 for degradation. However, the dose-dependent pharmacokinetic (PK)-pharmacodynamic (PD) relationship between these enzymes and 1,25(OH)₂D₃ concentrations has not been characterized.

Experimental Approach

The pharmacokinetics of 1,25(OH)₂D₃ were evaluated after administration of single (2, 60 and 120 pmol) and repeated (2 and 120 pmol q2d ×3) i.v. doses to male C57BL/6 mice. mRNA expression of CYP27B1 and CYP24A1 was examined by quantitative PCR and 1,25(OH)₂D₃ concentrations were determined by enzyme immunoassay.

Key Results

CYP27B1 and CYP24A1 changes were absent for the 2 pmol dose and biexponential decay profiles showed progressively shorter terminal half-lives with increasing doses. Fitting with a two-compartment model revealed decreasing net synthesis rates and increasing total clearances with dose, consistent with a dose-dependent down-regulation of renal CYP27B1 and the induction of renal/intestinal CYP24A1 mRNA expression. Upon incorporation of PD parameters for inhibition of CYP27B1 and induction of CYP24A1 to the simple two-compartment model, fitting was significantly improved. Moreover, fitted estimates for the 2 pmol dose, together with the PD parameters as modifiers, were able to predict profiles reasonably well for the higher (60 and 120 pmol) doses. Lastly, an indirect response model, which considered the synthesis and degradation of enzymes, adequately described the PK and PD profiles.

Conclusions and Implications

The unique PK of exogenously administered 1,25(OH)₂D₃ led to changes in PD of CYP27B1 and CYP24A1, which hastened the clearance of 1,25(OH)₂D₃.

Tables of Links

TARGETS
Ion channelsa	Enzymesc
TRPV5	CYP24A1
TRPV6	CYP27A1
Nuclear hormone receptorsb	CYP27B1
Vitamin D receptor	CYP2R1

LIGANDS
1α,25-dihydroxyvitamin D3
25-hydroxyvitamin D3
PTH
Vitamin D

These Tables list key protein targets and ligands in this article which are hyperlinked to corresponding entries in http://www.guidetopharmacology.org, the common portal for data from the IUPHAR/BPS Guide to PHARMACOLOGY (Pawson et al., 2014) and are permanently archived in the Concise Guideto PHARMACOLOGY 2013/14 (^a,b,cAlexander et al., 2013a,b,c).

Introduction

Vitamin D, formed from 7-dehydrocholesterol in skin upon exposure to sunlight, is metabolized by CYP2R1 and CYP27A1 in liver to its major circulating form, 25-hydroxyvitamin D₃ [25(OH)D₃]. This relatively inactive metabolite is transported by the vitamin D binding protein (DBP) for activation by 1α-hydroxylase (CYP27B1) in the kidney to form the active ligand of the vitamin D receptor, 1α,25-dihydroxyvitamin D₃ [1,25(OH)₂D₃] (Jones et al., 1998). A major physiological role of 1,25(OH)₂D₃ is to regulate plasma calcium concentrations through the calcium ion channels, TRPV5 and TRPV6, in the kidney and intestine (den Dekker et al., 2003) and the calcium-sensing receptor (Carrillo-Lopez et al., 2008). Continuous bone turnover, including resorption of existing bone and deposition of new bone, is another process that is stimulated by 1,25(OH)₂D₃ and the parathyroid hormone (PTH) (Jones et al., 1998; Hoenderop et al., 2005).

Calcium and 1,25(OH)₂D₃ homeostasis is tightly controlled by 1,25(OH)₂D₃, calcium and PTH (Shinki et al., 1992; Masuda et al., 2005; Turunen et al., 2007). Plasma 1,25(OH)₂D₃ concentrations are regulated by two major enzymes: CYP27B1 for synthesis and CYP24A1 for degradation. CYP27B1, expressed predominantly in the kidney, responds positively to PTH at low plasma calcium concentrations (Shinki et al., 1992), but is down-regulated by high concentrations of 1,25(OH)₂D₃ (Brenza and DeLuca, 2000; Turunen et al., 2007). CYP24A1, distributed abundantly in the kidney and intestine, is responsible for the metabolism of 25(OH)D₃ to 24,25-dihydroxyvitamin D₃ and 1,25(OH)₂D₃ to 1α,24,25-trihydroxyvitamin D₃ (Holick et al., 1972; Kumar et al., 1978; Halloran and Castro, 1989). Because elevated concentrations of 1,25(OH)₂D₃ are known to cause hypercalcaemia (Jones et al., 1987; Makin et al., 1989), CYP24A1 expression in the kidney is up-regulated as a feedback mechanism to increase 1,25(OH)₂D₃ catabolism and reduce 1,25(OH)₂D₃ and 25(OH)D₃ stores (Clements et al., 1992). In contrast, intestinal CYP24A1 is regulated by 1,25(OH)₂D₃ and not PTH (Henry, 2001), suggesting that the induction of intestinal CYP24A1 is an acute response to the vitamin D receptor (Akeno et al., 1994).

Pharmacokinetic (PK) studies of 1,25(OH)₂D₃ are challenging due to assay sensitivity in measuring low 1,25(OH)₂D₃ concentrations and studies in rodents are further hampered by the limited plasma volume for sampling. Masuda et al. (2005) examined the decay of radiolabelled 1,25(OH)₂D₃ over 96 h in CYP24A1(+/−) and CYP24A1(−/−) mice, confirming that CYP24A1 is the major enzyme involved in the metabolism of 1,25(OH)₂D₃. CYP24A1(−/−) mice exhibited a longer t_1/2 compared with CYP24A1(+/−) mice. In a phase I clinical trial, where 2 to 10 μg 1,25(OH)₂D₃ was administered s.c., the derived t_1/2 proved to be ill-defined due to inadequate sampling over 12 h (Smith et al., 1999). In a human study in which prolonged sampling was conducted following p.o. and i.v. doses of 4 μg 1,25(OH)₂D₃, a t_1/2 of 26 h was observed, along with a plasma clearance (dose/AUC_∞) of 0.17 mL·min⁻¹·kg⁻¹ and bioavailability of 0.71 after 72 h of sampling (Brandi et al., 2002). C3H/HeJ mice treated with 0.125 or 0.5 μg 1,25(OH)₂D₃ i.p., with sampling up to 24 h, produced an apparent clearance (dose/AUC_0→24), but a debatable terminal t_1/2 due to limited sampling (Muindi et al., 2004). Chow et al. (2013) reported an apparent terminal t_1/2 of 6.8 h after sampling for 48 h in mice treated with 0.05 μg 1,25(OH)₂D₃ i.p. and showed that both plasma and tissue 1,25(OH)₂D₃ concentrations fell below basal levels at 24 h due to the induction of CYP24A1. None of these studies provided an in-depth interpretation of the PK when describing the net rate of synthesis (R_syn) of endogenous 1,25(OH)₂D₃ nor accounted for pharmacodynamic (PD) changes on the inhibition of CYP27B1 or induction of CYP24A1.

In this study, we examined the PD changes driven by 1,25(OH)₂D₃ PK in relation to basal concentrations of 1,25(OH)₂D₃. Single and repeated i.v. doses were administered to mice to appraise the dose- and time-dependent PK of 1,25(OH)₂D₃. Fitting with a simple two-compartment model yielded a decreasing R_syn and increasing total plasma clearance (CL_total), observations consistent with the inhibition of CYP27B1 and induction of CYP24A1 with dose. Inclusion of parameters associated with PD changes in mRNA expression for the down-regulation of CYP27B1 and the induction of CYP24A1, obtained upon regression of mRNA expression fold change (FC) of enzymes in tissue versus 1,25(OH)₂D₃ plasma concentration, significantly improved model fitting criteria. Lastly, an indirect response model was able to provide similar parameters as the PD-linked model and predicted the temporal PK and PD data for the different doses administered. The composite data show that changes in the PD of CYP27B1 and CYP24A1 with increasing 1,25(OH)₂D₃ doses resulted in altered PK of 1,25(OH)₂D₃.

Methods

Pharmacokinetic study

The concentration of 1,25(OH)₂D₃ in anhydrous ethanol was assayed spectrophotometrically at 265 nm (UV-1700, Shimadzu Scientific Instruments, Mandel Scientific, Guelph, Ontario, Canada) and diluted with sterile 0.9% saline containing 1% ethanol. Male C57BL/6 mice (8 weeks old), weighing 25.5 ± 1.6 g (mean ± SD), were purchased from Charles River Canada (Saint-Constant, Quebec, Canada). Mice were given water and food ad libitum and maintained under a 12:12 h light and dark cycle in accordance with approved protocols by the Animal Care and Use Committee at the University of Toronto. All studies involving animals are reported in accordance with the ARRIVE guidelines for reporting experiments involving animals (Kilkenny et al., 2010; McGrath et al., 2010). A total of 130 mice were used in the experiments described. Mice were randomly assigned to treatment with single (0, 2, 60 or 120 pmol) or repeated (0, 2 or 120 pmol q2d ×3) i.v. doses of 1,25(OH)₂D₃ on days 0, 2 and 4 at 0900 h. Serial blood sampling from the saphenous vein was performed at 1, 5, 15, 30 or 60 min. Thereafter, mice were anaesthetized with ketamine and xylazine i.p. (150 and 10 mg·kg⁻¹ respectively) before blood collection by cardiac puncture with a 1 mL syringe-23G 3/4″ needle set that was pre-rinsed with heparin (1000 IU·mL⁻¹). The depth of anaesthesia was assessed by monitoring the heart rate and pedal reflex. Tissues were harvested at each sampling point (3, 6, 9, 12, 24 and 48 h) from the treated mice (n = 3–4 per time point). For the vehicle-treated group (n = 9), sampling was conducted at 0 h on days 0 and 4 and averaged, as described previously (Chow et al., 2013), to provide basal concentrations. Plasma was obtained by centrifugation of blood at 3000× g for 10 min. After flushing the lower vena cava with ice-cold saline, the kidneys and ileum (6 cm proximal to the ileocecal junction) were removed over ice as outlined previously (Chow et al., 2011). Samples were snap-frozen in liquid nitrogen and stored at −80°C.

Plasma 1,25(OH)2D₃ analysis

Plasma 1,25(OH)₂D₃ concentrations were measured by enzyme immunoassay (EIA) (Chow et al., 2013).

Quantitative real-time PCR (qPCR)

Total RNA, obtained from kidney tissues and scraped ileal enterocytes, was extracted using the TRIzol extraction method (Sigma-Aldrich, Mississauga, Ontario, Canada) in accordance with the manufacturer's protocol, with modifications (Chow et al., 2011). A total of 1.5 μg of cDNA was synthesized from RNA using the high capacity cDNA reverse transcription kit (Applied Biosystems® by Life Technologies, Burlington, Ontario, Canada) and qPCR was performed with SYBR Green detection system. Kidney and intestinal mRNA data were normalized to cyclophilin and villin, respectively, for calculation of the relative change in gene expression (Chow et al., 2009).

PK and PD analysis

Non-compartmental analysis

The AUC from 0 to 48 h (AUC_0→48h) was estimated by the trapezoidal rule. The extrapolated area from the last datum point to time infinity (AUC_48h→∞) was calculated upon dividing the measured plasma concentration, C_48h, by the terminal slope (β). Other parameters included: t_1/2β or terminal half-life, estimated from data between 6 and 48 h and calculated as 0.693/β, and CL_total, estimated as dose/AUC_∞.

Estimation of PD parameters for inhibition and induction

The mRNA expression of renal CYP27B1 and renal and ileal CYP24A1 was normalized to basal levels (vehicle-treated mice) and the FC was plotted against the plasma 1,25(OH)₂D₃ concentration. For CYP27B1, the inhibition function or FC of CYP27B1 (CYP27B1_FC) was (1)

For CYP24A1, the induction function or FC of CYP24A1 (CYP24A1_FC) was (2) with C_p as the plasma 1,25(OH)₂D₃ concentration, the maximal FC as I_max and E_max for inhibition and induction factors, and IC₅₀ and EC₅₀ as the plasma concentrations that result in 50% of I_max and E_max (Mager et al., 2009). The E_max, EC₅₀, I_max and IC₅₀ estimates were obtained upon non-linear regression of single and repeated dose and combined data from all doses with Equations 1994 and 2013a using Scientist® (version 2.0; Micromath, St. Louis, Missouri, USA).

Fitting without consideration of PD: simple two-compartment model

Fitting was conducted with Scientist with appropriate weighting schemes (unity, 1/observation and 1/observation²) or with ADAPT5 (version 5; Biomedical Simulations Resource, University of Southern California, Los Angeles, California, USA). Assuming stationary kinetics and dynamics, we estimated the volume of the central compartment (V₁), net synthesis rate (R_syn) controlled by CYP27B1 and the micro-rate constants (k₁₂, k₂₁, k₁₀) during the first 48 h of sampling. The fit for each of the single 2, 60 or 120 pmol dose levels was obtained with a simple two-compartment model (Figure A and equations in Appendix A). The steady-state volume of distribution (V_ss) was estimated as V₁·(1 + k₁₂/k₂₁). Values of k₁₂ for the 60 and 120 pmol doses are expressed as multiples of k₁₂, relative to the 2 pmol dose, for the combined fit of all data (1.5× and 5.7× the k₁₂ value of the 2 pmol dose). Parameter estimates obtained from the single doses were used as initial estimates for the combined fit to all data upon repeated dosing.

Figure 1.

Fitting of 1,25(OH)₂D₃ data using (A) a simple two-compartment model, (B) a PD-linked model and (C) an indirect response model. For the compartmental models, it is assumed that synthesis and elimination of 1,25(OH)₂D₃ are occurring from the central compartment.

Integrated PKPD model

Parameters governing changes in CYP27B1 and CYP24A1 expression were incorporated into a two-compartment model (Figure B and Appendix B) to modify R_syn and k₁₀. Based on the assumption that there was no down-regulation of CYP27B1 nor induction of CYP24A1 for the 2 pmol dose, fitted parameters for this dose (V₁, k₁₂, k₂₁, R_syn and k₁₀) from the two-compartment model were used as initial estimates, together with averaged estimates of I_max, IC₅₀, E_max and EC₅₀ (Table 3), for combined fitting of data for the first doses (2, 60 and 120 pmol) and data from all doses. Fitting was repeated upon addition of scaling factors, then Hill coefficients (Appendix B). Again, k₁₂ values for the 60 and 120 pmol doses were scaled to account for possible changes in the distribution of 1,25(OH)₂D₃ in the simultaneous fits. The PD-linked models were compared with the simple two-compartment model using the F-test (Boxenbaum et al., 1974).

Table 3.

Pharmacodynamic parameters estimated from CYP27B1 or CYP24A1 fold change versus plasma 1,25(OH)₂D₃ concentration

	Renal CYP27B1		Renal CYP24A1		Ileal CYP24A1
	Imaxa	IC50 (pM)	Emaxa	EC50 (pM)	Emaxa	EC50 (pM)
For first dose	8 ± 2b	100 ± 9	82 ± 19	300 ± 23	1000 ± 129	500 ± 62
For repeated third dose	24 ± 2	150 ± 15	107 ± 16	1480 ± 90	939 ± 126	3630 ± 220
For first and third doses	24 ± 4	150 ± 24	107 ± 19	1480 ± 189	970 ± 218	3630 ± 272

^aI_max and E_max values are expressed as fold change relative to baseline.

^bSD of parameter estimate.

Fitting with the indirect response model

The indirect response model (Figure C), which describes an indirect mechanism of action and incorporates transit compartments (A_transit1 and A_transit2) containing a time-delay function (τ) (Appendix C), relates temporal differences between drug concentrations and responses (Mager et al., 2003). The indirect response model was used to explain the time delay for the CYP27B1 effects, assuming CYP27B1 is indirectly stimulated by PTH-induced activation of the vitamin D receptor. Similar to the PD-linked model, scaling factors and Hill coefficients were incorporated for fitting purposes.

Statistical analysis

The mRNA data are expressed as mean ± SEM. One-way anova and a post hoc Tukey honest significant difference test were used to evaluate differences between mean mRNA expression of groups at each time point using GraphPad Prism Software (version 6; GraphPad Software Inc., La Jolla, California, USA). The goodness of fit was appraised by the weighted sum of square residuals (WSSR), Akaike information criterion (AIC), and SD of the parameter estimate, while the F-test was used for comparing the models. Significance was defined as P < 0.05.

Materials

1,25(OH)₂D₃ in powder form was obtained from Sigma-Aldrich. The EIA kit (Cat# AC-62F1) for 1,25(OH)₂D₃ measurements was manufactured by Immunodiagnostics Systems Inc. (Scottsdale, Arizona, USA) and purchased from Inter Medico (Markham, Ontario, Canada). All other reagents were obtained from Sigma-Aldrich and Fisher Scientific (Mississauga, Ontario, Canada).

Results

Dose-dependent PK of 1,25(OH)₂D₃

1,25(OH)₂D₃ concentrations for the 60 and 120 pmol doses fell below basal values (187 ± 48.5 pM) by 24 h whereas those for the 2 pmol dose remained relatively unchanged. Plasma 1,25(OH)₂D₃ concentrations decayed biexponentially at each dose level (Figure 2). There was a prolonged t_1/2β (36.7 h) for the lowest dose and a dramatically shorter t_1/2β (∼6 h) for higher doses (Table 1). Non-compartmental values of AUC_∞/dose decreased with increasing dose, yielding greater clearance values at higher doses. CL_total increased from 0.1 to 2.0 mL·min⁻¹·kg⁻¹ (Table 1), an observation compatible with induction of CYP24A1 for the metabolism of 1,25(OH)₂D₃.

Figure 2.

Plasma 1,25(OH)₂D₃ concentrations after i.v. administration of 2, 60 and 120 pmol doses versus basal levels. The two-compartment model was used to fit the 1,25(OH)₂D₃ data for each single 2, 60 or 120 pmol dose (A) individually, (B) combined fit of data for the first doses, with unscaled or scaled k₁₂, and (C) combined fit of data for all doses, with unscaled or scaled k₁₂. Observed plasma 1,25(OH)₂D₃ concentrations are shown as mean ± SEM (n = 3–4 different mice) with fitted values shown as a solid line. Data for vehicle-treated mice (basal level) were averaged and joined by the dashed line (n = 9).

Non-compartmental pharmacokinetic parameters following administration of first doses of 1,25(OH)₂D₃ to mice

	Dose (pmol)
	2	60	120
t1/2β (h)a	36.7	6.6	6.0
AUC∞ (pM·h)b	14 900	24 500	57 200
AUC∞/dose (h·L−1)	7 460	409	477
CLtotal (mL·min−1·kg−1)c	0.112	2.04	1.75

^at_1/2β was calculated as 0.693/β, where β is the terminal slope of ln(concentration) versus time data between 6 and 48 h.

^bAUC_∞ was determined as (AUC_0→48 + C_last/β) and AUC_0→48 was estimated by the trapezoidal rule.

^cCL_total was estimated as dose/AUC_∞.

For the simple two-compartment model that contained R_syn for 1,25(OH)₂D₃ formation from its vitamin D precursors, fits to the single dose data individually revealed a decreasing R_syn and an increasing k₁₀ with increasing dose (Figure A; Table 2). Furthermore, fitted values of k₁₂ and V_ss increased with dose, suggesting a larger distribution volume with increasing dose levels. These distributional changes could not be explained by a saturation of protein binding sites as the 5 μM concentration of DBP in plasma (Chun, 2012) greatly exceeds the plasma 1,25(OH)₂D₃ concentrations from i.v. dosing. We then performed combined fitting of all data from the first doses and compared the parameter estimates obtained to those from individual fits. Accommodation of the changing k₁₂ was accomplished by scaling k₁₂ with dose (Table 2; Appendix A). The model predicted the data for the first dose well, whether or not k₁₂ was scaled (Figure 2B). For the two-compartment model, the fitted k₁₂ value for the 2 pmol dose (2.77 ± 1.42 h⁻¹), obtained from the individual fit of the 2 pmol data (Figure 2A), was about half that from forced fitting of data from the first doses (4.15 ± 1.23 h⁻¹) and with scaling of k₁₂ (Table 2). For fitting of the first and repeated doses, the fit to the third 120 pmol dose was better than the fit to the first dose, with or without k₁₂ scaled (Figure 2C). For the forced fit to all data from single and repeated dosing, the averaged value of the fitted k₁₂ was halved when k₁₂ was scaled, k₂₁ and k₁₀ were lower and V₁ and V_ss were higher (Table 2). The WSSR was smaller with scaled k₁₂ (although the AICs were similar), suggesting that scaling of k₁₂ was an improvement (Table 2). The lack of a significant improvement in the forced fit for scaled k₁₂ versus unscaled k₁₂ was likely due to the inability of this model to account for the dose-dependent nature of R_syn and k₁₀.

Table 2.

Fitted pharmacokinetic parameters for first doses of 1,25(OH)₂D₃ according to the simple two-compartment model

	Individual fitting to first dose			Forced fitting to first doses
	2 pmol	60 pmol	120 pmol	2, 60 and 120 pmol k12 unscaled	2, 60 and 120 pmol k12 scaled
k12 (h−1)	2.77 ± 1.42c	4.17 ± 3.57	15.8 ± 4.36	10.8 ± 4.67	4.15 ± 1.23
k21 (h−1)	2.15 ± 1.14	1.41 ± 0.74	2.09 ± 0.40	2.93 ± 0.10	1.89 ± 0.49
k10 (h−1)	0.27 ± 1.10	0.93 ± 0.44	2.21 ± 0.71	1.11 ± 0.71	0.75 ± 0.37
V1 (mL·kg−1)	112 ± 17.0	167 ± 81.5	61.5 ± 21.0	72.0 ± 1.6	117 ± 10.5
Vss (mL·kg−1)a	255	659	526	337	409
Rsyn (fmol·h−1)b	71.9 ± 39.8	31.1 ± 10.8	32.6 ± 5.91	85.5 ± 4.78	81.6 ± 16.4
WSSR				9.05	5.73
AIC				494	523

^aV_ss was calculated as V₁ + V₂, where V₂, peripheral compartment = V₁ (k₁₂/k₂₁).

^bR_syn initial estimate (49.6 fmol·h⁻¹) was obtained from Hsu et al. (1987).

^cSD of parameter estimate.

CYP27B1 and CYP24A1 mRNA expression

The mRNA expression of the synthetic enzyme in kidney and degradation enzyme in intestine and kidney also displayed dose-dependent changes (Figure 3). For the 2 pmol single dose, there was an absence of any notable trend for the mRNA expression of renal CYP27B1 or renal and ileal CYP24A1, as levels remained relatively unchanged in relation to basal values (Figure 3, left panel). Furthermore, hypercalcaemia was not observed for the low dose (data not shown). Thus, the R_syn value obtained for the 2 pmol dose should represent the net synthesis rate of endogenous 1,25(OH)₂D₃ formation from its vitamin D precursors. In contrast, markedly lower CYP27B1 mRNA expression at 9 h after 1,25(OH)₂D₃ administration was noted with higher doses, wherein levels fell and remained below basal levels. Maximal induction of renal CYP24A1 expression occurred at 6–9 h and was sustained until 48 h. In ileum, maximal induction of CYP24A1 mRNA expression occurred at 3 h following the 60 pmol dose and at 6 h following the 120 pmol dose (Figure 3, left panel). Repeated administration of 120 pmol 1,25(OH)₂D₃ led to a greater down-regulation (CYP27B1) and induction (CYP24A1) of renal mRNA levels when compared with the single dose and a similar pattern was observed for ileal CYP24A1 mRNA expression (Figure 3, right panel).

Figure 3.

Relative mRNA expression for synthesis and degradation enzymes following single or repeated i.v. administration of 1,25(OH)₂D₃. (A) Renal CYP27B1 mRNA expression is reduced by both single and repeated administration of 60 and 120 pmol 1,25(OH)₂D₃. (B) Renal and (C) ileal CYP24A1 mRNA expression are induced by 1,25(OH)₂D₃ in a dose-dependent manner for single and repeated dosing. Data for vehicle-treated mice (basal level) were averaged and joined by the dashed line (n = 9), whereas data for treated mice are mean ± SEM and joined by a solid line (n = 3–4 different mice). Significant differences between groups were denoted by: ^abasal level versus 2 pmol; ^bbasal level versus 60 pmol; ^cbasal level versus 120 pmol; ^†2 pmol versus 60 pmol; ^‡2 pmol versus 120 pmol; ^#60 pmol versus 120 pmol; *all groups except basal level versus 2 pmol.

PD response versus concentration curves

Figure 4 shows the concentration-response relationship for FC of renal CYP27B1 and CYP24A1 and intestinal CYP24A1 mRNA expression in mice receiving single (2, 60 and 120 pmol) and repeated (2 and 120 pmol) doses of 1,25(OH)₂D₃. A plateau was reached for CYP27B1 and CYP24A1 within the dose range and FC for CYP27B1 down-regulation or CYP24A1 induction remained constant at 1,25(OH)₂D₃ concentrations >5000 pM. Upon fitting of Equation 1994, a threefold increase in I_max was observed after repeated dosing (Table 3; Figure 4A), although the fitted IC₅₀ values were similar for the single and repeated doses. Composite I_max and IC₅₀ values were also obtained upon regression of pooled data from the first and repeated doses with Equation 1994 and these values were similar to those obtained for the repeated third dose (Table 3). Estimated E_max values (expressed over basal level) obtained for CYP24A1 (Equation 2013a) for the first and the third doses were virtually identical (Figure 4B,C), whereas EC₅₀ values for both renal and intestinal CYP24A1 increased significantly upon repeated dosing compared with that for the first dose (Table 3). Values for E_max and EC₅₀ for the pooled data were similar to those for the third dose. For fitting of Equation 1974 of Appendix B, the E_max values obtained from the pooled data for renal and ileal CYP24A1 were summed to provide the total E_max; the EC₅₀ was estimated as the average of the EC₅₀ values for renal and intestinal CYP24A1.

Figure 4.

Inhibition of CYP27B1 and induction of CYP24A1 by 1,25(OH)₂D₃. Plots of renal CYP27B1 and renal and intestinal CYP24A1 mRNA FC versus plasma concentration of 1,25(OH)₂D₃ following first or third dose of 2, 60 and 120 pmol, with equations for inhibition and induction .

Fitting of the PD-linked model to 1,25(OH)₂D₃ concentrations

Owing to the dose discrepancy and progressive changes that occur for R_syn and k₁₀ with dose (Table 2), there was a need to incorporate the PD changes of CYP27B1 and CYP24A1 into the two-compartment model shown in Figure A (Appendix B). Hence, a PD-linked model (Figure 1B) was developed using scaled k₁₂ values for greater doses. From fitting with data from the first doses, the EC₅₀ (average of renal and ileal CYP24A1 EC₅₀) and the summed E_max for the kidney and intestine were used as initial estimates. Additionally, scaling factors and Hill coefficients for the inhibition and induction functions were added stepwise to monitor improvement of fit in order to determine the best predictive model. For data from the single doses, forced fitting with the PD-linked model showed significant improvement compared with the simple two-compartment model (Figure 5A and Table 4). The best outcome was obtained when all of these modifications were incorporated into the model (Table 4). Values of the Hill coefficients were close to unity, R_syn was 61.5 ± 5.24 fmol·h⁻¹ (a value lower than that estimated from the two-compartment model), V₁ was similar to plasma volume and k₁₀ [representing the basal elimination rate constant of 1,25(OH)₂D₃] was 0.128 ± 0.021 h⁻¹, a value lower than but reasonable to that estimated from the simple two-compartment model.

Figure 5.

Fitting of single and repeated dose plasma 1,25(OH)₂D₃ data using a PD-linked model. (A) Simultaneous fitting of single dose plasma 1,25(OH)₂D₃ data. Simultaneous fitting of combined single and repeated dose plasma 1,25(OH)₂D₃ using (B) one EC₅₀ and (C) simulations to predict data for higher doses using parameters from the 2 pmol dose. Simultaneous fitting with (D) different EC₅₀s and (E) simulations to predict data for higher doses. Observed plasma 1,25(OH)₂D₃ concentrations are shown as mean ± SEM (n = 3–4 different mice) with fitted values shown as a solid line and simulated values shown as a dashed line. Data for vehicle-treated mice (basal level) were averaged and joined by the dashed line (n = 9).

Table 4.

Simultaneous fitting of first dose or pooled first and third dose data to different models with k₁₂ scaled

	Combined fit to data of first dose			Combined fit to data of all doses (first and repeated third dose)
Fitted parameters	Two-compartment model	PD-linked model	Indirect response model	Two-compartment model	PD-linked model (one EC50)	PD-linked model (different EC50)	Indirect response model
k12 (h−1)a	4.15 ± 1.23d	4.71 ± 2.22	3.88 ± 3.52	3.23 ± 0.77	2.75 ± 1.42	2.74 ± 1.34	6.17 ± 4.81
k21 (h−1)	1.89 ± 0.49	3.01 ± 0.24	1.70 ± 1.21	2.22 ± 0.55	2.83 ± 1.40	3.25 ± 1.42	3.75 ± 2.68
k10 (h−1)	0.75 ± 0.37	0.128 ± 0.021	0.349 ± 0.096	0.55 ± 0.27	0.091 ± 0.034	0.092 ± 0.007	0.133 ± 0.118
V1 (mL)	2.33 ± 0.21	1.38 ± 0.30	1.79 ± 0.55	2.43 ± 0.31	1.86 ± 0.49	1.86 ± 0.49	1.43 ± 0.83
Rsyn (fmol·h−1)	81.6 ± 16.4	61.5 ± 5.24	49.1 ± 9.2	78.9 ± 42.8	47.2 ± 16.1	44.5 ± 6.47	29.4 ± 19.0
Emax		398 ± 54.6	802 ± 175		404 ± 80.7	407 ± 47.4	1050 ± 515
EC50(1) (pM)		713 ± 137	1530 ± 1280		790 ± 248	616 ± 296	3110 ± 2990
EC50(2) (pM)						3810 ± 326	4640 ± 6110
Imax		11.3 ± 3.30	23.4 ± 5.41		11.6 ± 2.56	10.0 ± 3.07	45.2 ± 14.6
IC50 (pM)		276 ± 91.0	143 ± 218		306 ± 49.7	310 ± 74.8	388 ± 701
SM1		4.24 ± 0.42	4.47 ± 0.87		5.41 ± 0.81	7.15 ± 1.38	0.81 ± 0.52
SM2		25.8 ± 2.87	75.4 ± 16.6		25.9 ± 4.66	26.8 ± 6.20	9.64 ± 10.4
γ1		1.25 ± 0.44	2.80 ± 0.96		1.85 ± 1.82	0.783 ± 0.391	2.12 ± 0.49
γ2		0.983 ± 0.249	2.14 ± 0.21		1.33 ± 0.16	1.15 ± 0.154	2.50 ± 0.53
kin1 (h−1)bc			0.390 ± 0.163				0.343 ± 0.083
kin2 (h−1)bc			0.195 ± 0.110				0.362 ± 0.175
τ (h)			0.809 ± 0.114				1.36 ± 1.07
WSSR	5.73	0.47	709	30.2	23.6	11.8	676
AIC	523	649	982	913	1067	1086	1547
F-test value		28.3*	−1.53		1.48	7.09*	−1.32
Fcritical (df1, df2)		2.45 (8, 20)	2.41 (11, 17)		2.17 (8, 42)	2.12 (9, 41)	2.43 (12, 16)

^aValues of k₁₂ for the 60 and 120 pmol doses were assigned as 1.5× and 5.7× the value of k₁₂ for the 2 pmol dose.

^bk_in1 and k_in2 are the zero-order synthesis rate constants for CYP27B1 and CYP24A1, respectively.

^ck_out1 and k_out2 are the first-order degradation rate constants for CYP27B1 and CYP24A1, respectively, and are equal to k_in1 × baseline or k_in2 × baseline, where baseline is 1.

^dSD of parameter estimate.

^*Significant difference between PD-linked versus two-compartment model at P < 0.05 compared with F_critical.

For fitting of data from all doses (Table 4), we further adopted a second strategy as there were changes in the EC₅₀ upon repeated dosing. We used one EC₅₀ [obtained from regression of FC vs. 1,25(OH)₂D₃ plasma concentrations from the first dose] or two different EC₅₀ values [EC₅₀₍₁₎ from regression of data from first dose and EC₅₀₍₂₎ from pooled data]. When using one EC₅₀, it was assumed that the EC₅₀ for the first dose was identical to that for the second and third doses and the regressed value from data from the first dose was used as the initial estimate. When using different EC₅₀ values, EC₅₀₍₁₎ obtained from the first dose and EC₅₀₍₂₎ from pooled data were used as initial estimates. These EC₅₀ values, together with scaled k₁₂ functions, scaling factors and/or Hill coefficients in the PD-linked model, were incorporated in a stepwise manner for fitting (data not shown). From fits based on one or two EC₅₀ values, we found that the parameters (k₁₂, k₂₁, k₁₀, V₁ and R_syn) and the scaling factors remained similar. The Hill coefficients using two EC₅₀ values remained similar to unity, whereas those for the one EC₅₀ model were greater (Table 4). Overall, it was concluded that the best fit was attained when all of these modifications, including different EC₅₀ values, were added to the PD-linked model (Table 4). We also used parameters obtained from the 2 pmol first dose to simulate plasma 1,25(OH)₂D₃ concentration time data for other single and repeated dosing regimens, with use of one EC₅₀ (Figure 5C) or two different EC₅₀s (Figure 5E). The simulations predicted the first dose reasonably well, but were unable to fully capture the later concentrations upon repeated dosing, presumably due to tolerance.

Indirect response model with inhibition and induction functions to explain 1,25(OH)₂D₃ PK

The PD components of the indirect response model incorporate both an indirect inhibitory (CYP27B1) and stimulatory (CYP24A1) response model. We added transit compartments with lag time (τ) to explain the time delay for CYP27B1 effects, as CYP27B1 was indirectly affected by vitamin D receptor activation by PTH (Figure C). A zero-order rate constant for formation (k_in), a first-order decay rate constant (k_out) and the appropriate inhibition and induction functions were added to account for decreased CYP27B1 and increased CYP24A1 production (Appendix C; Dayneka et al., 1993; Sharma and Jusko, 1996). Preliminary fits showed that two additional transit compartments were needed to improve model fitting (data not shown). Improved fits were obtained when scaling factors and Hill coefficients were incorporated into the model. For the single dose data, the fitted parameter values for k₁₂, k₂₁, k₁₀, V₁ and R_syn were usually within twofold (Table 4). For the pooled data, when different EC₅₀ values were used, greater values for k₁₂ and EC₅₀₍₁₎ values were obtained, whereas R_syn and the scaling factors were smaller (Table 4). Model fitting criteria were not statistically improved compared with the two-compartment model, although the indirect response model was able to reveal correlations between PD responses to 1,25(OH)₂D₃ concentrations in a temporal fashion (Figure 6).

Figure 6.

The indirect response model for simultaneous fitting of all data on plasma 1,25(OH)₂D₃ and FC of vitamin D receptor target genes, CYP27B1 and CYP24A1. (A) Simultaneous fitting of single dose (left) and single and repeated dose (right) plasma 1,25(OH)₂D₃ concentration. Simultaneous fitting for (B) inhibition of CYP27B1 FC and (C) stimulation of CYP24A1 FC. Observed plasma 1,25(OH)₂D₃ concentrations and CYP27B1 and CYP24A1 FC are shown as mean ± SEM (n = 3–4 different mice) with fitted values shown as a solid line. Data for vehicle-treated mice (basal level) were averaged and joined by the dashed line (n = 9).

Comparison of the two-compartment, PD-linked and indirect response models

Fitting of the two-compartment model to individual data sets revealed dose-dependent kinetics and reasonably good fits (Figure 2). However, fitting with the PD-linked model for the single dose data proved to be superior (Figure 5; Table 2013c). For repeated dosing, we found that the PD-linked model with different EC₅₀ values was associated with smaller WSSR values with a significant F-value compared with the two-compartment model (P < 0.05), despite the larger AIC (Figure 5D; Table 4). Furthermore, incorporation of scaled k₁₂ constants, scaling factors and Hill coefficients into the PD-linked model improved model performance (data not shown). Although the indirect response model did not improve the fit statistically compared with the two-compartment model, the model showed reasonable utility and was adequate in predicting changes in the temporal PD profiles against 1,25(OH)₂D₃ concentrations at the different administered dose levels (Figure 6).

Discussion and conclusions

1,25(OH)₂D₃ is used extensively for the treatment of secondary hyperparathyroidism in uraemic patients (Slatopolsky et al., 1984; Kimura et al., 1991; Brandi et al., 2002) and has demonstrated therapeutic potential for anticancer therapy (Hershberger et al., 2002; Rassnick et al., 2008; Ramnath et al., 2013). The therapeutic use of 1,25(OH)₂D₃ is often limited by the propensity of 1,25(OH)₂D₃ to cause hypercalcaemia and adverse effects. Recent studies have suggested that 1,25(OH)₂D₃ may also play a beneficial role in lowering cholesterol (Chow et al., 2014) as well as enhancement of amyloid-β efflux and reduction of cerebral plaque in transgenic mice expressing the human amyloid-β precursor protein (Durk et al., 2014). Thus, an understanding of the PK and PD of 1,25(OH)₂D₃ is critical for the prediction of a proper dose and dosing regimen for potential therapeutic uses.

Information on the PK of 1,25(OH)₂D₃ is equivocal. Some of the discrepancies in the reported PK parameters of 1,25(OH)₂D₃ may exist due to species differences, inadequate sampling or dose-dependent PK and altered PD with dose and route. An examination of available literature regarding the PK properties of 1,25(OH)₂D₃ shows substantially different t_1/2 values with respect to dose and route of administration among species. In humans, a 4 μg dose of 1,25(OH)₂D₃ administered i.v. or p.o. resulted in a t_1/2 of 25.9 and 28.2 h, respectively (Brandi et al., 2002), whereas a similar i.v. dose of 0.06 μg·kg⁻¹ led to a shorter t_1/2 of 16.5 h (Salusky et al., 1990). An equal dose of 20 μg·kg⁻¹ administered i.p. and p.o. to the rat resulted in different t_1/2 values of 5.0 and 10.4 h (Vieth et al., 1990). Administration of 10 and 50 μg·kg⁻¹ of 1,25(OH)₂D₃ i.v. resulted in t_1/2 of 3.8 and 2.3 h respectively (Kissmeyer and Binderup, 1991). These shorter t_1/2 values are due to greater clearances and are the consequence of a greater induction of CYP24A1. In contrast, mice treated with single doses of 0.125 or 0.5 μg of 1,25(OH)₂D₃/mouse i.p. did not exhibit a clear dose-dependency, with t_1/2 of 7.6 and 7.8 h (Muindi et al., 2004). Chow et al. (2013) also reported a t_1/2 of 6.8 h in mice treated i.p. with repeated doses of 0.05 μg per mouse 1,25(OH)₂D₃.

Our present study with 2, 60 and 120 pmol (0.00083, 0.025 and 0.05 μg per mouse) 1,25(OH)₂D₃ doses revealed dose-dependent t_1/2β values ranging from 36.7 to 6.6 h (Table 1). Accordingly, CL_total values of 0.1, 2.0 and 1.8 mL·min⁻¹·kg⁻¹ for 2, 60 and 120 pmol doses of 1,25(OH)₂D₃ were found (Table 1). Changes in enzymes were virtually absent for the 2 pmol dose, rendering the fitted parameters according to the two-compartment model pertinent to basal conditions, whereas maximal inhibitory (CYP27B1) and stimulatory (CYP24A1) responses were observed for the higher doses. Important information was revealed from fitted results from the lowest dose. For example, the volume of distribution of 1,25(OH)₂D₃ was low and R_syn was 71.9 ± 39.8 fmol·h⁻¹, a basal value that is higher than that (49.6 fmol·h⁻¹) previously reported by Hsu et al. (1987). Both the 60 and 120 pmol doses produced greater CL_total values (2.0 and 1.8 mL·min⁻¹·kg⁻¹) that were similar to i.p. mouse studies, with apparent CL_total values (CL_total/F where F is bioavailability of i.p. dose) of 1.2 and 2.8 mL·min⁻¹·kg⁻¹, estimated graphically from the data of Muindi et al. (2004), for doses of 0.125 and 0.5 μg per mouse.

Gene profiling of CYP27B1 and CYP24A1 in the kidney and intestine, two major vitamin D receptor-containing tissues, confirmed the inhibition and induction associated with 1,25(OH)₂D₃ administration (Figure 3). The dose-dependent down-regulation of renal CYP27B1 mRNA expression readily explains the decreased R_syn of 1,25(OH)₂D₃ for higher doses. Moreover, a dose-dependent induction of renal and ileal CYP24A1 mRNA expression further explains the increased CL_total and decreased t_1/2 with increasing dose. Interestingly, the concentration-response curve for CYP24A1 suggests tolerance as EC₅₀ values were increased in mice given repeated doses of 1,25(OH)₂D₃ without a change in E_max (Figure 4). The observed tolerance may be attributed to a decreased binding affinity of 1,25(OH)₂D₃ to the vitamin D receptor. We also observed a sustained induction of renal CYP24A1 mRNA expression at 48 h, whereas ileal CYP24A1 expression returned to basal levels by 24 h post-injection for both single and repeated dosing. Long-term treatment with 1,25(OH)₂D₃ has been shown to lower CYP24A1 mRNA expression, suggesting a lack of activation of vitamin D receptor upon repeated dosing (unpublished data). Accordingly, the change in intestinal CYP24A1 mRNA level in response to 1,25(OH)₂D₃ has been described to be more short-lived than in kidney and becomes refractory to the continued administration of 1,25(OH)₂D₃, suggesting the presence of intestinal adaptation mechanisms which down-regulate the responsiveness of the enzyme (Lemay et al., 1995). The sustained induction of renal, and not intestinal CYP24A1, and the fact that little to no intestinal removal occurs for systemically administered compounds (due to shunting of intestinal flow away from the enterocyte region) (Doherty and Pang, 1997; Cong et al., 2000) suggest that renal CYP24A1 is the major enzyme for the catabolism of 1,25(OH)₂D₃ given i.v. Collectively, tolerance of CYP24A1 to repeated 1,25(OH)₂D₃ administration explains the inconsistency of the parameters derived from the PD-linked model for the 2 pmol dose in predicting 1,25(OH)₂D₃ profiles for higher doses and upon repeated dosing.

The present comprehensive analysis of 1,25(OH)₂D₃ quantification, together with gene profiling and data fitting using PD-linked and indirect response models, brings a new perspective as to how 1,25(OH)₂D₃ levels affect vitamin D receptor target genes and how these PD changes affect the PK of exogenously administered 1,25(OH)₂D₃. We recommend that PK studies involving 1,25(OH)₂D₃ incorporate PD effects and R_syn in order to fully capture the disposition of 1,25(OH)₂D₃. Changes in CYP27B1 and CYP24A1 expression alter the synthesis and degradation of 1,25(OH)₂D₃, and these events can be explained with appropriate PKPD models. By incorporating the PD changes, we were able to integrate the gene changes that affect 1,25(OH)₂D₃ concentrations, showing the mutual interaction of kinetics and dynamics. With our findings, we caution against merely reporting t_1/2, especially when the data do not cover the time course describing the decay. Our findings could explain the array of reported t_1/2 with different doses in the literature, as we show that clearance is dose-dependent and that CYP27B1 and CYP24A1 work closely to affect 1,25(OH)₂D₃ levels and vice versa. Clearly, the simple two-compartment model, although adequately showing dose-dependency for k₁₂, V_ss, R_syn and CL_total, could not fully explain the intricacies of the dose-dependent PK of 1,25(OH)₂D₃. Using the derived parameters of E_max, EC₅₀, I_max and IC₅₀, with or without incorporating changes in EC₅₀ for single and repeated doses, we could adequately predict the dose-dependent PKPD profiles of 1,25(OH)₂D₃. Further modifications to the model, including scaled k₁₂, scaling factors and Hill coefficients significantly improved model performance. Although there is no apparent improvement with the indirect response model statistically, we could demonstrate the direct correlation between 1,25(OH)₂D₃ and vitamin D receptor target genes and essential time delays using transit compartments in the model (Mager and Jusko, 2001; Mager et al., 2003).

The unique PK of exogenously administered 1,25(OH)₂D₃ rests on the inhibition and induction of its own synthesis and metabolism, although there has been other evidence for altered 1,25(OH)₂D₃ efficacy due to single nucleotide polymorphisms in the CYP24A1 gene (Chen et al., 2011; Ramnath et al., 2013). We have demonstrated that future studies involving the administration of 1,25(OH)₂D₃ as a therapeutic agent should incorporate R_syn and PD effects of CYP27B1 and CYP24A1 in order to fully explain the disposition of 1,25(OH)₂D₃ in the body. This present investigation on the PKPD relationships with respect to renal and intestinal handling of synthesis and metabolism via down-regulation of CYP27B1 and induction of CYP24A1 has expanded ways to view changes of other vitamin D receptor target genes and their PD effects. A physiologically based PKPD model could extend this model to different routes of administration to describe the regulatory effects of the vitamin D receptor on vitamin D receptor target genes in other tissues in the body.

Glossary

AIC

Akaike information criterion

AUC

area under the plasma concentration time curve

CL

clearance

DBP

vitamin D binding protein

k

rate constant

PD

pharmacodynamic

PK

pharmacokinetic

PTH

parathyroid hormone

qPCR

quantitative real-time PCR

R_syn

net rate of synthesis

V_1,

volume of central compartment

V_ss

volume of distribution at steady state

WSSR

weighted sum of square residuals

1,25(OH)₂D₃

1α,25-dihydroxyvitamin D₃

25(OH)D₃

25-hydroxyvitamin D₃

Appendix A

For the simple two-compartment model (Figure 1A):

A1

A2

Note: k₁₂ for the 60 pmol dose is 1.5× k₁₂ of the 2 pmol dose; k₁₂ for the 120 pmol dose is 5.7× k₁₂ of the 2 pmol dose.

Appendix B

For PD-linked model with scaling factors (SM₁ and SM₂) and Hill coefficients (γ₁ and γ₂) (Figure 1B)

B1

Appendix C

For the indirect response model, with scaling factors (SM₁ and SM₂) to adjust for fold changes (FC) (Figure 1C)

C1

The rates of change in PD responses (CYP27B1 or CYP24A1) can be described as

C2

where k_in is the zero-order rate constant for production of the response and k_out is the first-order rate constant for loss of the response. The response variable, R, in this study is the same as the FC of vitamin D receptor target gene mRNA expression. The inhibition (Equation 1994) and induction (Equation 2013a) functions were included, respectively, to account for the inhibition of CYP27B1 and induction of CYP24A1. Inhibition of the CYP27B1 response variable () and induction of the CYP24A1 response variable () were described as

C3

C4

where C_p is the plasma 1,25(OH)2D3 concentration; k_in = k_out × baseline, with baseline = 1; I_max and E_max are the maximal FC for inhibition and induction factors; and IC₅₀ and EC₅₀ are the plasma concentrations that result in 50% of I_max and E_max. The E_max is the sum of the E_max from the intestine and kidney.

A time-delay function was required to provide a better fit for CYP27B1 expression, where τ is the time delay in h and A_transit1 and A_transit2 are the amounts in transit compartments 1 and 2 respectively:

C5

C6

Author contributions

H. P. Q., E. C. C. and S. Y. H. performed the experiments. H. P. Q., E. C. C. and K. S. P. designed the research study. H. P. Q., Q. J. Y., D. E. M. and K. S. P. analysed the data and wrote the manuscript. H. P. Q., E. C. C. and K. S. P. revised the manuscript.

Conflicts of interest

None.