Modeling and Simulation of the Effect of Proton Pump Inhibitors on

Oct 11, 2012 - ∥Office of Generic Drugs, Office of Pharmaceutical Science, §Office of Pharmacovigilance and Epidemiology, Office of Surveillance an...
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Modeling and Simulation of the Effect of Proton Pump Inhibitors on Magnesium Homeostasis. 1. Oral Absorption of Magnesium Jane P. F. Bai,*,†,‡ Ethan Hausman,§ Robert Lionberger,∥ and Xinyuan Zhang‡,∥ ∥

Office of Generic Drugs, Office of Pharmaceutical Science, §Office of Pharmacovigilance and Epidemiology, Office of Surveillance and Epidemiology, and †Office of Clinical Pharmacology, Office of Translational Sciences, Center for Drug Evaluation, Food and Drug Administration, Rockville, Maryland, United States ABSTRACT: Prolonged use of proton pump inhibitors has reportedly caused rare clinically symptomatic hypomagnesemia. A review of the literature suggests PPI drugs may impair intestinal magnesium absorption. With the goal of preventing PPI-induced hypomagnesemia, an oral absorption-centric model was developed by referencing literature data. Our modeling with human data reveals that magnesium absorption is substantial in the distal intestine. We then perform simulations by referring to the reported reduction in mid to distal intestinal pH caused by one week of oral esomeprazole, and to reported reduction of the divalent cation-sensitive current when the carboxyl side chains of glutamic and aspartic residues in the binding channels of TRPM6/TRPM7 were neutralized. Our simulations reveal that short-term PPI therapy may cause a very small reduction (5%) in the serum magnesium level, which is qualitatively consistent with the reported 1% reduction in magnesium absorption following 1 week of omeprazole in humans. Simulations provide insight into the benefit of frequent but small dose of magnesium supplementation in maintaining the serum magnesium level when magnesium deficiency occurs. KEYWORDS: proton pump inhibitors, hypomagnesemia, TRPM6/TRPM7, oral absorption, solubility, balance of input and output, adverse reactions

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INTRODUCTION On March 2, 2011, the U.S. Food and Drug Administration (FDA) informed the public that prescription proton pump inhibitor (PPI) drugs may cause low serum magnesium levels (hypomagnesemia) if taken for prolonged periods of time (in most cases, longer than one year).1 Intravenous infusion of magnesium, though relieving symptoms and normalizing serum magnesium, is not a long-term solution.2,3 Oral magnesium supplementation did not improve low serum magnesium in most of the cases, and PPI drugs had to be discontinued. Occurrence of clinically symptomatic hypomagnesemia associated with PPI use is rare, with 30 cases reported in the literature between 2006 and 2011,4 and 38 cases in FDA’s Adverse Event Reporting System (AERS). Most cases were reported in older adult patients who had been on PPI drugs for several years. On initial presentation, serum magnesium ranged between 0.03 and 0.35 mM in severe cases,5 much lower than the normal lower limit of 0.76 mM.6,7 Severe hypomagnesemia may produce impaired parathyroid hormone secretion, which may lead to hypocalcemia. In cases where comprehensive clinical laboratory data were available, most patients had concomitant hypocalcemia and normal parathyroid hormone levels, suggesting that hypomagnesemia was the primary deficit. Six PPI drugs have been approved for marketing by the FDA.8 PPI drugs are widely prescribed; in the Unites States, approximately 70 million PPI prescriptions were filled in 2009.9 In addition, there are three PPI products available over the This article not subject to U.S. Copyright. Published 2012 by the American Chemical Society

counter. On average, therapy with prescription PPI drugs lasts for 6 months or longer. In addition to adult indications, five PPI drugs are approved for treating gastroesophageal reflux disease in children as young as 1 year of age.8 Magnesium is intricately linked to the homeostasis of calcium and potassium, and plays an important role in cardiovascular and neuromuscular functions.10−13 It has been proposed that magnesium deficit could reduce immune response, cause elevations of proinflammatory cytokines, and increase oxidative stress, thereby accelerating aging and causing age related diseases.14 Magnesium is associated with hypertension, diabetes, osteoporosis, and congestive heart failure.15 We posit that the clinical reports to date raise the possibility that subclinical magnesium deficiency among PPI users may be more common than suspected, in light of the volume of PPI prescriptions filled every year and the duration of prescription PPI therapy. Therefore, it would be useful to understand the underlying mechanism and to determine the usefulness of magnesium supplementation for correcting PPI-induced hypomagnesemia. Magnesium homeostasis is governed by a balance of input (intestinal absorption) and output (renal elimination).16 In this study, we mined the literature to Received: Revised: Accepted: Published: 3495

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distribution, clearance, and distribution constant among compartments) were obtained by fitting the reported intravenous plasma concentration/time profile from a study of 50 mg magnesium enriched with 25Mg,19 and the plotted data were extracted using g3data (http://www.frantz.fi/software/g3data. php). Compartmental models were fitted to data using PKPlus, and the Akaike Information Criterion (AIC) was used to select the best fitted compartmental model. Modeling Oral Absorption. The advanced compartmental absorption and transit model (ACAT) implemented in GastroPlus, which was developed based on Yu and Amidon’s compartmental absorption and transit (CAT) model,20 was used to simulate oral magnesium absorption. As shown in Figure 1A, the ACAT model mimics the human gastrointestinal

understand the clinical changes in magnesium input and output following a long-term PPI therapy, to gather published information related to possible underlying mechanisms, and then to construct a model accordingly to simulate the impact of short-term PPI therapy on serum magnesium. Finally, the constructed model was used to simulate what magnesium supplement dosing regimens could help to normalize serum magnesium during chronic PPI therapy.

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METHODS

Literature Mining. Clinical case reports of PPI-induced hypomagnesemia were identified in PubMed with keywords of hypomagnesemia in combination with “proton pump inhibitors” or with individual proton pump inhibitor names (i.e., drug name and commercial/trade name). Each case report was carefully reviewed to determine clinical plausibility. Thereafter, literature mining focused on absorption and elimination of magnesium in relation to magnesium homeostasis. Modeling Intestinal Magnesium Permeability by Leveraging Literature Data. Jejunal and ileal absorption of magnesium is nonlinear and concentration dependent.17 The reported data from an intestinal perfusion study in healthy volunteers were used to calculate intestinal permeability in each perfused region.17 The permeability at each concentration studied was calculated from the corresponding absorption rate (mmol/30 cm/h) over a 30 cm segment. In these calculation exercises, an intracellular free magnesium concentration of 0.5 mM18 was adopted to calculate the concentration gradient across the epithelial brush border membrane. Jejunal permeability coefficients at 1, 2.5, 5, 10, 15, and 20 mM were then fitted with a general equation shown below to obtain jejunal Michaelis−Menten parameters, Vmax,jej and Km. ⎛ V C ⎞ Jtot = Jcarrier + Jpassive = PtotC = ⎜ max ⎟ + PpassiveC ⎝ Km + C ⎠ Vmax ⇒ Ptot = + Ppassive Km + C (1)

Figure 1. Schematic details of magnesium absorption model: (A) Intestinal advanced compartmental absorption and transit (ACAT) model connected with a pharmacokinetic compartmental model. (B) Routes of magnesium absorption (paracellular and transportermediated, presumably via transient receptor potential melastin 6 (TRPM 6)), across intestinal epithelium.

where J is the flux, Ptot the total permeability consisting of both paracellular (Ppassive) and carrier-mediated components, C the lumenal concentration gradient across intestinal epithelium, Vmax the maximum transport coefficient per unit area, and Km the Michaelis−Menten constant. Km has the same unit as concentration, and Vmax the unit of mass per unit time per unit area. It is assumed that jejunum and ileum share the same magnesium transporter but may differ in its expression level; in other words, there may be regional differences in Vmax but not in Km. So, jejunal Km was applied to obtain ileal Vmax (Vmax,ile) by fitting eq 1 to ileal permeability coefficients at 1, 5, 10, 15, and 20 mM. Total jejunal and ileal carrier-mediated activities were estimated by multiplying Vmax,jej and Vmax,ile with their respective surface areas. Under the assumption of the same transporter with a same Km value being applicable to duodenal and colonic transporter-mediated absorption, simulated and reported oral plasma concentration/time profiles of magnesium19 were compared to optimally select duodenal and colonic Vmax values. To obtain duodenal and colonic absorption rates, parameter sensitivity analysis (PSA) was performed to scan a range of Vmax values for duodenum, cecum, and colon each. Intravenous Pharmacokinetic Modeling. The pharmacokinetic (PK) parameters of magnesium (volume of

tract, consisting of nine compartments (stomach, duodenum, jejunum 1, jejunum 2, ileum 1, ileum 2, ileum 3, cecum, and ascending colon). Each compartment is assumed to be a cylinder with a specific radius, length, transit time, and pH value. In the intestinal lumen, drug molecules can simultaneously exist in three forms as unreleased (in formulated particles), undissolved, and dissolved. All these three forms can transit along the GI tract in first order processes, but only dissolved drug molecules can be absorbed across enterocytes and into the systemic blood circulation. The epithelial absorption model of magnesium includes both paracellular and carrier-mediated routes (Figure 1B).21 There are phosphate, carbonate, bicarbonate, and hydroxide anions present in intestinal lumen, contributing to controlling the availability of magnesium ion for absorption. Therefore, Ksp values (solubility product constants) of Mg3(PO4)2, Mg(HPO4), Mg(H2PO4)2, Mg(CO3), Mg(HCO3)2, Mg(HSO4)2, Mg(SO4), and Mg(OH)2, Ka (acid dissociation constant) values of H3PO4, HPO4−2, H2PO4−1, CO3−2, HCO3−1, SO4−2, and HSO4−1, Kw (dissociation constant of H2O), and lumenal pH’s 3496

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along the small intestine were considered when calculating magnesium solubility in each intestinal segment. Calculations to realistically capture multiple processes simultaneously in dynamic equilibrium in the intestinal lumen are difficult exercises. It is the intestinal pH and hydroxide concentration, not the concentrations of various anions, that ultimately controlled the availability of lumenal magnesium for absorption, following several calculation exercises. Considering magnesium hydroxide solubility is 0.0098 g/L at 18 °C and 0.0042 g/L at 100 °C,22 a range of values were tested. The solubility of 0.0091 g/L for magnesium ion in the form of hydroxide salt throughout intestinal lumen was found to achieve a better fitting of the reported plasma concentration/time profile of an oral study with 360 mg of magnesium enriched with 26Mg.19 This solubility was used thereafter for modeling and simulation. Impact of Uncertainty in Solubility and in Transporter Activity on Oral Bioavailability. In vivo magnesium solubility and transporter activity are affected by many factors in the GI tract such as pH values, concentrations of various anions, available surface area, etc. These two parameters in the model are highly uncertain. PSA was performed, and twenty values were scanned for solubility ranging between 0.00091 and 0.091 mg/mL. For the transporter’s activity, twenty values of scale factor (SF) between 0.2 and 3 (i.e., change in maximum transport coefficient from 0.2- to 3-fold) were assessed. Thus, a total of 400 simulations were performed to assess how solubility and transporter activity each impact magnesium bioavailability. Simulation of the Effect of PPI Drugs on Serum Magnesium. A review of the literature23−25 suggests that the effect of PPI drugs on intestinal magnesium absorption could be indirectly attributed to the pharmacological effect of PPI drugs at off-target sites (see Results). Literature data support the assumption that PPI drugs could indirectly decrease the quantity of intestinal transporter binding sites available for magnesium absorption. These published data were referred to in our simulation exercises. Reduced dietary magnesium intake with or without magnesium supplementation was tested first to see how the model performed. Then the effect of omeprazole was introduced by referring to the reported intestinal pH changes following oral PPI drugs to investigate how the model responded. All simulations were performed on Gastroplus.

Table 1. Clinical Laboratory Values of 24 Patients with Hypomagnesemia and Proton Pump Inhibitor Usea initial presentation N = 24

mean SD min max

Mg

Ca

0.24 0.12 0.03 0.49

1.73 0.34 1.1 2.88

N = 11 PTH U Mg 3.8 1.3 0.9 5.7

0.27 0.25 0 0.8

Mg N = 23: dechallengeb

N = 4: rechallenge

0.8 0.09 0.62 1.6

0.45 0.1 0.4 0.6

a

Abbreviations: Mg = magnesium, Ca = calcium, PTH = parathyroid hormone, U Mg = urinary magnesium, SD = standard deviation, min = minimum reported value, max = maximum reported value, N = number of patients for whom an analyte was reported. Reference values: lower limit of normal for serum Mg = 0.7 mmol/L, 24 h U Mg = mmol/24 h, lower limit of normal serum Ca = 2.2 mmol/L, reference range for PTH = 1.5 to 7 pmol/L. mmol/L: millimoles/liter. pmol/L: picomol/liter. Reference ranges derived from mean of reported reference ranges reported in each clinical report. bWith magnesium supplementation.

Table 2. Contemporaneous Blood Magnesium and Urinary Magnesium Excretion at Presentationa

mean SD median

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blood Mg (mmol/L)

urine Mg excretion (mmol/24 h)

0.16 0.12 0.2 0.03 0.34 0.08 0.13 0.66b 0.74b 0.44b 0.57b 0.8b 0.49b 0.37 0.27 0.34

0.03 0.4 0.3 0.5 0.2 0.1 0.1 0.4b 0.71b 0.6b 0.61b 1.64b 0.8b 0.49 0.42 0.4

a

Clinical laboratory data from case reports found in the literature. First contemporaneous report occuring after partial magnesium correction.

RESULTS Literature Findings. Clinical Evidence Implicating PPI Therapy in Impairing Intestinal Intake. A review of literature of PPI-associated hypomagnesemia found 25 cases, 24 of which contained clinical laboratory data (Table 1).2,3,5,26−32 Nadir mean serum magnesium at presentation or prior to discontinuation of PPI drugs was 0.24 mM (SD 0.12, range 0.03 to 0.49), and mean serum calcium was 1.7 mM (SD 0.34, range 1.1 to 2.88). Normal serum magnesium levels are from 0.7 to 1.1 mM,7 and normal serum calcium 2.2−2.6 mM.33 Parathyroid hormone (PTH) was unexpectedly normal in 10 of 11 patients whose values were reported; mean PTH of all 11 patients was 3.8 pM (SD 1.3, range: 0.9 to 5.7). Normal serum PTH ranges from 1.5 to 6.8 pM,34 and 24 h urinary magnesium excretion ranges from 3 to 10 mmol.35 When contemporaneous blood magnesium and urinary magnesium excretion at presentation were reported (N = 13), mean urine magnesium excretion was 0.49 mmol/24 h (SD 0.42, range: 0.03 to 1.64) (Table 2). Urinary magnesium excretion on discontinuation of PPI and magnesium repletion was not systematically assessed. In patients whose urinary magnesium excretion was assessed on

b

contemporaneous PPI discontinuation/magnesium repletion, urinary magnesium excretion reportedly increased.3,5,26,31 Since homeostatic regulations of magnesium and calcium are intimately related to each other, lowering magnesium level may cause reduction of serum calcium. A variety of clinical symptoms associated with either hypomagnesemia or hypocalcemia were reported alone or in combination. A partial list of symptoms includes loss of consciousness,3 seizures,26 muscle spasm/cramp/tetany,29 recurrent atrial fibrillation,5 electrocardiographic disturbance [U wave5 and long QT3], paresthesias,29 “exacerbation” of chronic obstructive pulmonary disease,26 or laboratory finding with no symptoms reported.26 The durations of PPI use in these case reports were at least 5 years. Clinical cases of PPI-induced hypomagnesemia revealed no urinary wasting of magnesium, and urinary excretion of magnesium was in fact reduced in patients with PPI-induced hypomagnesemia,3,29,36 suggesting that PPI-induced hypomagnesemia result from reduction in magnesium input (intestinal 3497

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TRPM6 mRNA.47 This study suggests that TRPM6, not TRPM7, is a gatekeeper at both input and output sites of a human body for maintaining systemic magnesium homeostasis. In the respective putative pore-forming regions of TRPM6 and TRPM7, the ionized carboxyl side chains of both glutamic acid (E1024, E1029, E1047, E1052) and aspartic acid (D1031, D1054, D1059) residues were suggested to be important for the binding of divalent cations including magnesium and for electrical conductivity.48−51 Neutralization of both E1024 and D1031 resulted in nonfunctional channels.50 Proton reportedly reduced the affinity of TRPM7 for magnesium or decreased the divalent cation sensitive current via presumably TRPM6 and TRPM7 channels.25,52 It is, therefore, expected that the number of ionized carboxyl side chains of both amino acid residues on TRPM6/TRPM7 will impact intestinal absorption of magnesium. Modeling Characterization of Intestinal Magnesium Absorption. Fitting of Literature Data for Jejunal and Ileal Michaelis−Menten Parameters. Using the perfusion data in human subjects,17 the calculated jejunal permeability coefficients at 1, 2.5, 5, 10, 15, and 20 mM were 56.1 × 10−6, 28.06 × 10−6, 24.94 × 10−6, 15.75 × 10−6, 14.19 × 10−6, and 11.51 × 10−6 cm/s, respectively, while the calculated ileal permeability coefficients at 1, 5, 10, 15, and 20 mM were 165.84 × 10−6, 36.85 × 10−6, 29.09 × 10−6, 19.06 × 10−6, and 14.88 × 10−6 cm/s, respectively. Jejunal Michaelis−Menten parameters were obtained by fitting these permeability coefficients with eq 1. Jejunal Vmax and Km are 53.02 × 10−6 μmol/s/cm2 and 0.173 mM, respectively. Jejunal Km was used for ileal Km when fitting ileal data with eq 1; ileal Vmax was determined to be 156.9 × 10−6 μmol/s/cm2. Figure 1 shows both simulated and observed permeability versus concentration curves. The fitted jejunal and ileal fitted passive permeability coefficients are the same, 0.11 × 10−4 cm/s, which is lower than the human jejunal permeability of atenolol (0.2 ± 0.2 × 10−4 cm/s),53 a low permeability compound.54 Optimization of Oral Absorption Model. The data of an intravenous PK study using magnesium enriched with 25Mg were used for modeling.19 A 3-compartmental model was eventually selected based on the AIC value, and its fitted parameters are listed in Table 3. Figure 2 shows simulated vs observed plasma concentration/time profiles following intravenous magnesium. The final integrated model consisting of intravenous PK model plus the intestinal absorption model was fitted to the reported oral plasma concentration/time data.19

absorption) while the kidneys respond by upregulating its reabsorption as a means to conserve magnesium in the body. Intravenous infusion of magnesium in 2 patients with PPIinduced hypomagnesemia revealed that 24 h renal handling of infusion load, with renal creatinine clearance as the reference, was normal, and failure in intestinal absorption was suggested as the underlying mechanism.3 Taken together, impairment of intestinal absorption is the focus of our investigation into PPIinduced hypomagnesemia. Decrease of pH by Esomeprazole in Mid to Distal Intestine. In 20 healthy subjects, one week of esomeprazole 40 mg twice daily (bid) reportedly had no effect on intestinal motility but reduced luminal pH by 0.5 unit throughout the mid to distal intestine,23 which is equivalent to an increase of proton concentration by 3.2-fold. Clearly, PPI drugs have an effect external to their gastric target. PPI drugs are prodrugs known to be activated in the acidic environment inside the parietal cells prior to inhibiting their target, H(+)-K(+)ATPases (the gastric proton pumps). However, PPI drugs can be activated at pH 5.0, though at a slower rate,37 indicating that PPI drugs could be activated in tissues other than the parietal cells, and thereby cause off-target effects. RNAs and proteins of functional gastric and nongastric H(+)-K(+)-ATPases were reportedly expressed in the plasma membrane of the pancreatic duct, and gastric H(+)-K(+)-ATPases appeared to secrete proton into the interstitium to drive secretion of bicarbonate into the lumen of pancreatic duct.24 Novak et al. reported that omeprazole inhibited gastric H(+)-K(+)-ATPases in the plasma membrane of pancreatic duct, and reduced H+ secretion into the interstitium and secretion of bicarbonate into the pancreatic duct.24 This observation of reduced bicarbonate secretion caused by omeprazole seems to provide the pharmacological rationale for the observed reduction of intestinal pH following one week of oral esomeprazole.23 Magnesium Absorption Reduced by Omeprazole in Humans and Its Transcellular Transport Reduced by Neutralization of Glutamic and Aspartic Carboxyl Side Chains. In a whole-intestine lavage parallel study in healthy volunteers,38 administration of omeprazole (40 mg) once a day for 7 days reduced magnesium absorption by 1%, while lavage with 120 mL of 0.1 M hydrochloric acid caused a 2% reduction. Interestingly, lavage with 120 mL of 0.1 M hydrochloric acid reduced magnesium absorption by 2% while 120 mL of 0.1 M hydrochloric acid plus a 7-day pretreatment with omeprazole caused a synergistic reduction (4%). Transepithelial absorption of magnesium involves saturable ion channels. Transient receptor potential melastin 6 (TRPM6) is mainly present in intestinal and renal epithelia, and is involved in intestinal absorption and renal reabsorption of magnesium,39 whereas its close homologue TRPM7 also involved in magnesium absorption has a ubiquitous distribution.40,41 In cultured lymphocytes, both TRPM6 and TRPM7 were shown to be essential and functionally nonredundant in maintaining magnesium homeostasis,42 and TRPM6/TRPM7 complex also contributed to transepithelial magnesium absorption by TRPM6.43 Though familial hypomagnesemia with secondary hypocalcemia is only linked to loss-of-function mutations of TRPM6, not TRPM7,44,45 heterozygous TRPM7 deficiency caused mice to exhibit abnormal magnesium status.46 TRPM6 mRNA levels, but not TRPM7 mRNA expression, changed with magnesium intake; magnesium-restricted diet upregulated intestinal and renal TRPM6 mRNA while magnesium-enriched diet downregulated renal and intestinal

Table 3. Pharmacokinetic Parameters of Magnesium from Fitting Intravenous Plasma Concentration/Time at a Dose of 50 mg of Magnesium Enriched with 25Mg Isotope

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parameters

Mg2+

BW (kg) central compartment volume, Vc (L/kg) systemic clearance, CL (L/h) half-life, T1/2 (h) distribution constant from central to peripheral, K12 (1/h) distribution constant from peripheral to central, K21 (1/h) peripheral compartment volume, V2 (L/kg) (=K12/K21 × Vc) distribution constant from central to the third compartment, K13 (1/h) distribution constant from the third to central compartment, K31 (1/h) third compartment volume, V3 (L/kg) (=K13/K31 × Vc)

69.5 0.296 1.816 89.57 0.463 0.712 0.193 0.249 0.0332 2.214

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duodenal carrier-mediated permeability did not have much impact on the simulated plasma concentration/time profiles when the duodenum scale factor (Duo SF) relative to jejunal transporter activity was tested between 0 and 2. The effect of transporter activity in cecum and ascending colon each on the oral plasma concentration/time profile is shown in Figure 5. The transporter activity in the cecum and ascending colon each was expressed as a scale factor relative to the jejunal transporter activity. Cecum SF was fixed, but ascending colon was allowed to vary. Figure 5 shows that cecal transporter activity influenced the shape of plasma concentration/time profiles between 5 and 10 h postdose while the transporter activity in the ascending colon between 10 and 40 h postdose, suggesting that magnesium is continuously absorbed through the colon. When cecal SF was 0.5 and ascending colon SF between 0.5 and 1.0, the simulated profiles more closely resembled the observed one. Assuming that cecum and ascending colon have the same transporter activity per unit area as jejunum, optimal SF values in the cecum and ascending colon, after correcting for the surface area, were 0.48 and 0.72, respectively, judging from the overlapping of simulated profiles with the observed one following oral administration of 360 mg of magnesium enriched with 26Mg (Figure 6A). It is expected that availability of an optimization algorithm could help produce the simulation profiles that resemble the observed one more closely. Once the carrier-mediated permeability coefficients in various GI compartments were optimized, simulations were then performed to determine the impact of passive permeation, presumably via paracellular tight junctions. Figure 6A shows that the plasma concentration/time profiles of 360 mg of oral magnesium were superimposable regardless of Ppassive being 0.0 or 10.66 × 10−6 cm/s, indicating that passive permeability (P passive ) via tight junctions contributed minimally to magnesium absorption. This observation is contrary to a recent study that suggested omeprazole reduced paracellular transport of magnesium but not its transcellular carrier-mediated transport.55 To further explore why passive permeability was insignificant, the flux/time profile resulting from active transport and passive permeation each was simulated for each intestinal segment, as shown in Figure 6B. Active flux was calculated using VmaxC/(Km + C) and passive flux PpassiveC, where C is luminal concentration. Only in the duodenum, passive flux was higher than active flux while in every other compartment active flux was much higher than passive flux with jejunum 1 having active flux only slightly higher than passive flux. Solubility and transporter activity are two uncertain parameters that would impact Cmax and bioavailability, as shown in Figures 7A and 7C. Figures 7B and 7D are the contour plots of Cmax and bioavailability, respectively, as a function of solubility and transporter activity. Each contour line represents an identical Cmax or bioavailability value. The contour plots show that to obtain the target Cmax and bioavailability, there could be an infinite number of solubility−transporter activity combinations. Simulation of Serum Magnesium. To understand how the model performs in simulating a long-term effect of dietary magnesium deficiency, simulations of dietary magnesium depletion and repletion, of the impact of PPI drugs on magnesium absorption, and of various oral dosing regimens were conducted. The model was first forced to reach a steady state of serum magnesium within the normal range; magnesium

Figure 2. Fitted permeability/concentration curves vs calculated permeability coefficients. Abbreviations: obs.Jeg, calculated permeability using reported human jejunal absorption data; obs.Ile, calculated ileal permeability using reported human ileal absorption data.

A same transporter activity per unit surface area was assumed across duodenum, jejunum, ileum, and colon as shown in Figure 3A. That is, jejunum 1 and jejunum 2 shared a Vmax of

Figure 3. Observed vs simulated plasma concentration/time profiles of magnesium following intravenous administration of 50 mg of magnesium enriched with 25Mg isotope.

53.02 μmol/s/cm2, and ileum 1, ileum 2, and ileum 3 a Vmax of 156.9 μmol/s/cm2. With these Vmax values, the final integrated model took into account the absorptive surface area of each segment and both paracellular and transcellular carriermediated absorption (Figure 3B). Since duodenal and colonic magnesium absorption rates in humans are unknown, PSA was first performed to assess how the transport rates in duodenum and colon affect magnesium absorption. Then an optimal value in each segment was selected for simulation. The same passive permeability was applied throughout the intestine. In the base model, duodenum was assumed to have the same transporter activity per unit area as jejunum. As shown in Figure 4,

Figure 4. The effect of duodenal transporter activity on the plasma concentration/time profiles following oral administration of 360 mg of magnesium enriched with 26Mg isotope. Duo SF is the duodenal transporter activity scale factor relative to jejunal transporter activity. 3499

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Figure 5. The effect of transporter activity (expressed as SF) in the cecum and ascending colon on the pharmacokinetic profiles of magnesium following oral administration of 360 mg of magnesium enriched with 26Mg isotope. In each panel, cecum scaling factor (SF) was fixed and ascending colon SF varied.

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DISCUSSION Macroscopic magnesium homeostasis in a human body is maintained by a balance of input (gastrointestinal absorption) and output (urinary excretion). A comprehensive review of clinical case reports of severe PPI-induced hypomagnesemia reveals that prolonged periods of PPI use did not cause urinary wasting of magnesium, that is, the output component is not impaired. In fact, urinary secretion of magnesium in PPIinduced hypomagnesemia patients decreases, suggesting that renal reabsorption increases to conserve magnesium for maintaining the homeostatic status. In mice, similar renal conservation was observed in response to dietary magnesium deficiency.58 The conclusion of intestinal absorption being impaired by PPI drugs based on the observation of normal renal handling of intravenous load of magnesium in 2 PPIinduced hypomagnesemia patients3 is consistent with other observations of increased renal conversation (see Table 1). Though one week of omeprazole only reduced magnesium bioavailability by 1%,38 this observation seems to be in line with the clinical observations in PPI-induced hypomagnesemia patients. Assuming 1% reduction in absorption will cause a 0.01% depletion of magnesium store in the body (with renal reabsorption upregulated in an attempt to restoring homeostasis), 356 days (∼1 year) of PPI therapy could cause 80% magnesium depletion. It is not impossible 1% reduction in intestinal absorption resulting from a week of omeprazole eventually could lead to hypomagnesemia following prolonged use of PPI therapy. Considering magnesium absorption is dosedependent and involves both paracellular and transcellular

intake was then reduced to 100 mg/day (33.33 mg three times daily [tid]), which is supposed to reflect a state of magnesium deficiency. As shown in Figure 8A, prolonged magnesium deficiency caused average serum magnesium to decline from ∼0.85 mM to ∼0.8 mM, and subsequent increase of magnesium intake to 300 mg/day pushed serum magnesium to stay above 0.85 mM. This exercise was intended to simulate the study published by Nielsen et al.56 Then the treatment effect of PPI drugs was simulated by adopting a reduction of pH by 0.5 following oral PPI drugs, which could correspond to an increase of lumenal proton concentration by 3.5-fold. This proton concentration increase was assumed to reduce Vmax by 3.5-fold throughout the intestine (Figure 8B). Steady state serum magnesium following daily administration of 237 mg was reduced from ∼0.85 mM to 0.79 mM as a result of decreasing pH by 0.5 following an oral PPI. Bioavailability and AUC0−24 were correspondingly reduced by 5% and 6%, respectively. Referencing a recent estimate of daily magnesium requirement for men and women,57 daily intake of 199 mg of magnesium was used in later simulations. Simulation of 199 mg of magnesium daily for 40 days, either given once a day or 66.3 mg tid, was performed with the presence or absence of omeprazole. Daily 66.3 mg tid resulted in higher serum magnesium compared to 199 mg qd (Figure 8C). Omeprazole reduced serum magnesium when magnesium supplement was given 199 mg qd (Figure 8C). 3500

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Figure 6. (Top, A) Effect of passive permeability on the simulated plasma concentration/time profile of magnesium following oral administration of 360 mg of magnesium enriched with 26Mg isotope. (Bottom, B) Contributions of active flux and passive flux from the gastrointestinal lumen to the portal vein.

Our simulations utilized the reported data from both an oral bioavailability study with a radioactive magnesium isotope and a human perfusion study, whereas Fine et al. calculated the amount of magnesium unabsorbed by a 4 h gastrointestinal lavage at 10 h after a meal plus magnesium supplement. Current simulations reveal that significant magnesium absorption occurs in the distal intestine, which is consistent with what was reported in the literature.21 Comparison of jejunal and ileal Vmax values revealed that there may be a higher activity per unit area of transport protein (presumably TRPM6/TRPM7) in the distal intestine. Ileal pH is known to be higher than jejunal pH, with a difference of 0.6

processes, there may be a biological plausibility for PPI drugs to reduce transcelluar absorption of magnesium. Based on the totality of clinical evidence, we focused our efforts on modeling and simulating the effect of PPI drugs on the input component of magnesium homeostasis. Simulations revealed that carrier-mediated absorption dominated at a single dose of 360 mg (29.6 mequiv), and also at a daily dietary intake of 237 mg from 3 meals (data not shown). According to a study by Fine et al.,59 at 30 mequiv approximately 60% of absorption was mediated by a saturable process, which is lower than the >90% suggested by our results. The discrepancy could be explained by different methods used. 3501

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Figure 7. (A) 3D plot showing the effects of solubility and transporter activity (Vmax) on Cmax of magnesium following oral administration of 360 mg of Mg enriched with 26Mg isotope. (B) Contour plot of Cmax of Mg2+ as a function of solubility and Vmax. (C) 3D plot showing the effects of solubility and Vmax on bioavailability of magnesium following oral administration of 360 mg of Mg enriched with 26Mg isotope. (D) Contour plot of bioavailability of magnesium as a function of solubility and Vmax.

implemented in the software tool we used. If H+ concentration can affect magnesium binding to TRPM6/TRPM7, then a 0.6 higher pH can translate into a notable difference in the quantity of ionized glutamic acid and aspartic acid carboxylate side chains on TRPM6/TRPM7 available for magnesium transport, and thus in Vmax. Insignificant duodenal carrier-mediated absorption revealed by this study could be attributed to a short transit time and much lower lumenal pH as a result of being at the receiving end of gastric acidic content. Low duodenal pH means fewer ionized glutamic acid and aspartic acid side chains available to absorb magnesium. The Ka values of aspartic acid and glutamic acid carboxyl side chains are 3.9 and 4.07, respectively, which means that, at the same pH and molar quantity, the ratio of ionized Asp to Glu side chains would be approximately 1.48. It is not known whether this would amount to any significant in vivo differential contributions between these two amino acids since the relative numbers of these amino acids contributed to magnesium binding and absorption are not known. As reported by Michalek et al.,23 the pH values were reduced by one week of daily administration of 40 mg of omeprazole from 6.9 to 6.4,

from 7.5 to 7.0, and from 7.7 to 7.2, in the second, third, and fourth quarter of the intestine, respectively. Referring to the relative current equation by Gwanyanya et al.,52 these pH reductions could cause the relative divalent-cation-sensitive current to reduce by 0.26, 0.24, and 0.2, respectively. Though the TRPM6 or TRPM7 current obtained from in vitro cell line or protein construct studies could provide mechanistic insight, both channels are permeable to divalent and monovalent cations. So, the currents reported in the literature were the results of permeation of all the cationic species including H+ present in the in vitro system.25 It is not possible to obtain the current solely attributed to Mg+2, and therefore, the in vitro currents cannot be quantitatively converted for the estimation of intestinal magnesium membrane permeability via TRPM6/ TRPM7. Furthermore, the quantitative relationship between microscopic current and macroscopic bioavailability involves complex mathematical operations. Adequate translation of the in vitro non-magnesium-specific current reductions to the changes in in vivo magnesium permeability and absorption would not be straightforward. 3502

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and Glu for magnesium transport via TRPM6/TRPM7. Since hydrochloric acid reduces lumenal pH, higher lumenal acidity is expected to affect both membrane permeability and solubility of magnesium. Magnesium solubility in the intestinal lumen would actually increase with acidity considering the Ksp values of Mg(OH)2 and of various salts of magnesium phosphate and sulfate. So reduction of magnesium absorption by hydrochloric acid or by hydrochloric acid plus omeprazole pretreatment is very likely caused by lower membrane permeability. This study supports the notion that ionized glutamic and aspartic acid side chains on TRPM6/TRPM7 are critical for transmembrane permeation of magnesium and that reducing intestinal pH (increasing proton concentration) can jeopardize magnesium membrane permeability. Though our model is by no means perfect, a small reduction in magnesium bioavailability projected by our model may be in fact not far from what actually happened in real clinical cases where most cases of PPI-induced hypomagnesemia occurred only following prolonged periods of PPI use. Minute changes accumulated over a prolonged period of time could lead to a significant deviation eventually. As discussed earlier, the reported 1% reduction by a 7-day omeprazole administration supports that chronic use of PPI therapy may lead to clinically symptoms of disturbance of magnesium homeostasis. Our simulated reduction in serum magnesium, nonetheless, only reflects the impact of intestinal absorption caused by PPI drugs, but not the global change in magnesium homeostasis dynamics which is likely linked to clinical PPI-induced hypomagnesemia. Quantitative comparisons should not be made between current simulated results and reported clinical outcomes of magnesium depletion. Clinical case reports revealed that daily single dose of oral magnesium supplementation, compared to intravenous administration,2 did not resolve26 or only partially resolved3 clinical PPI-induced hypomagnesemia. Much less success of oral magnesium supplementation could be attributed to a not well-designed rescue treatment with a large dose of magnesium rendering an unfavorable dose/solubility ratio that is too high to allow complete dissolution of magnesium for absorption. Simulated results indicate that frequent dosing of magnesium supplementation in divided doses may help to maintain serum magnesium during PPI therapy. It appears that balancing dose and solubility ratio is critical. Nielsen et al. showed that serum magnesium in healthy subjects declined from 0.8 mM to 0.72 mM after about 20 days of depletion, and then returned to the normal range after about 60 days of repletion. Serum magnesium did not return to the normal range during the first 58 days of repletion.56 Fluctuation in serum magnesium during the repletion phase of their study might have reflected dynamic magnesium redistribution beyond the circulation and throughout the whole body, since the fraction of blood magnesium accounts for only about 1% of total body magnesium.16 Our model only captures the decrease in serum magnesium level, but not the fluctuated profiles of serum magnesium observed by Nielsen et al. (Figure 8A), because of the inherent simple empirical distribution structure implemented in the current model. In our current modeling, magnesium was treated as a drug and there was no magnesium present in the three PK compartments prior to dosing. Neither was there a dynamic regulation of magnesium homeostasis or a renal reabsorption mechanism implemented. This simple model, therefore, by no means represents our body where magnesium is distributed in various organs including bone and muscle, with tight dynamic regulations between the circulation

Figure 8. Simulations of serum magnesium levels: (Top, A) Steady state serum magnesium profiles after depletion (100 mg/day, tid) and repletion (300 mg/day, tid). (Middle, B) Steady state serum magnesium profiles given oral magnesium of 237 mg/day (tid) with or without a proton pump inhibitor (PPI). The PPI effect was simulated by reducing the transporter activity by 3.5-fold. (Bottom, C) Steady state serum magnesium profiles given oral magnesium of 199 mg (tid or qd) with or without a PPI. The PPI effect was simulated by reducing the transporter activity by 3.5-fold.

To simulate the reported 1% reduction in magnesium bioavailability by omeprazole,38 we referred to the Ka equation. The effect of PPI drugs on oral magnesium bioavailability was simulated under a literature-supported assumption that PPI drugs cause a reduction in lumenal pH by 0.5. A 0.5 reduction in pH following a week of esomeprazole23 is equivalent to a 3.5fold increase in intestinal proton concentration, which can presumably reduce the [ionized]/[un-ionized] ratio by 3.5-fold for glutamic and aspartic acid residues each. Since Vmax is proportional to the number of magnesium binding sites (ionized glutamic acid and aspartic acid residues) and the quantity of glutamic acid and aspartic acid residues throughout various intestinal regions is unknown, it is assumed that a 3.5fold decrease in the [ionized]/[un-ionized] ratio could translate into a 3.5-fold decrease in Vmax. This assumption implies that the pH change in the intestinal lumen unequivocally reflects that in the TRPM6/TRPM7 channels where magnesium binding and absorption takes place. With this applied, our simulation revealed that PPI therapy causes a 5% reduction in magnesium bioavailability, which is qualitatively consistent with, though quantitatively higher than, the observed 1% reduction of magnesium absorption from a test meal by omeprazole in a parallel comparison.38 It appeared that omeprazole actually worsened the effect of hydrochloric acid on magnesium availability, indicating that the synergistic effects are consistent with proton reducing the number of ionized Asp 3503

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(7) Schimatschek, H. F.; Rempis, R. Prevalence of hypomagnesemia in an unselected German population of 16,000 individuals. Magnesium Res. 2001, 14 (4), 283−90. (8) Drug@FDA. http://www.accessdata.fda.gov/scripts/cder/ drugsatfda/index.cfm, accessed January 2012. (9) The Burden of Digestive Diseases in the United States. NIH Publication 09-6443, 2009. (10) Romani, A. M. Cellular magnesium homeostasis. Arch. Biochem. Biophys. 2011, 512 (1), 1−23. (11) Altura, B. M.; Altura, B. T. Cardiovascular risk factors and magnesium: relationships to atherosclerosis, ischemic heart disease and hypertension. Magnesium Trace Elem. 1991, 10 (2−4), 182−92. (12) Altura, B. M.; Altura, B. T. New perspectives on the role of magnesium in the pathophysiology of the cardiovascular system. II. Experimental aspects. Magnesium 1985, 4 (5−6), 245−71. (13) Swaminathan, R. Magnesium metabolism and its disorders. Clin. Biochem. Rev. 2003, 24 (2), 47−66. (14) Barbagallo, M.; Belvedere, M.; Dominguez, L. J. Magnesium homeostasis and aging. Magnesium Res. 2009, 22 (4), 235−46. (15) Ueshima, K. Magnesium and ischemic heart disease: a review of epidemiological, experimental, and clinical evidences. Magnesium Res. 2005, 18 (4), 275−84. (16) Wallach, S. Availability of body magnesium during magnesium deficiency. Magnesium 1988, 7 (5−6), 262−70. (17) Brannan, P. G.; Vergne-Marini, P.; Pak, C. Y.; Hull, A. R.; Fordtran, J. S. Magnesium absorption in the human small intestine. Results in normal subjects, patients with chronic renal disease, and patients with absorptive hypercalciuria. J. Clin. Invest. 1976, 57 (6), 1412−8. (18) Asif, M. H.; Ali, S. M.; Nur, O.; Willander, M.; Englund, U. H.; Elinder, F. Functionalized ZnO nanorod-based selective magnesium ion sensor for intracellular measurements. Biosens. Bioelectron. 2010, 26 (3), 1118−23. (19) Benech, H.; Pruvost, A.; Batel, A.; Bourguignon, M.; Thomas, J. L.; Grognet, J. M. Use of the stable isotopes technique to evaluate the bioavailability of a pharmaceutical form of magnesium in man. Pharm. Res. 1998, 15 (2), 347−51. (20) Yu, L. X.; Amidon, G. L. A compartmental absorption and transit model for estimating oral drug absorption. Int. J. Pharm. 1999, 186 (2), 119−25. (21) Behar, J. Magnesium absorption by the rat ileum and colon. Am. J. Physiol. 1974, 227 (2), 334−40. (22) National Lime Association, F. S. PROPERTIES OF TYPICAL COMMERCIAL LIME PRODUCTS. http://www.lime.org/ documents/lime_basics/lime-physical-chemical.pdf, accessed January 2011. (23) Michalek, W.; Semler, J. R.; Kuo, B. Impact of acid suppression on upper gastrointestinal pH and motility. Dig. Dis. Sci. 2011, 56 (6), 1735−42. (24) Novak, I.; Wang, J.; Henriksen, K. L.; Haanes, K. A.; Krabbe, S.; Nitschke, R.; Hede, S. E. Pancreatic bicarbonate secretion involves two proton pumps. J. Biol. Chem. 2011, 286 (1), 280−9. (25) Jiang, J.; Li, M.; Yue, L. Potentiation of TRPM7 inward currents by protons. J. Gen. Physiol. 2005, 126 (2), 137−50. (26) Epstein, M.; McGrath, S.; Law, F. Proton-pump inhibitors and hypomagnesemic hypoparathyroidism. N. Engl. J. Med. 2006, 355 (17), 1834−6. (27) Furlanetto, T. W.; Faulhaber, G. A. Hypomagnesemia and proton pump inhibitors: below the tip of the iceberg. Arch. Intern. Med. 2011, 171 (15), 1391−2. (28) Hoorn, E. J.; van der Hoek, J.; de Man, R. A.; Kuipers, E. J.; Bolwerk, C.; Zietse, R. A case series of proton pump inhibitor-induced hypomagnesemia. Am. J. Kidney Dis. 2010, 56 (1), 112−6. (29) Kuipers, M. T.; Thang, H. D.; Arntzenius, A. B. Hypomagnesaemia due to use of proton pump inhibitors–a review. Neth. J. Med. 2009, 67 (5), 169−72. (30) Metz, D. C.; Sostek, M. B.; Ruszniewski, P.; Forsmark, C. E.; Monyak, J.; Pisegna, J. R. Effects of esomeprazole on acid output in

and individual organs to control and maintain its homeostasis. Nonetheless, our absorption-centric model has a unique characteristic of providing mechanistic insight. Future integration of a physiologically based distribution model which reflects multiple dynamic exchange processes between the blood circulation and key magnesium deposit organs will conceivably enable a better depiction of the dynamic details of magnesium homeostasis. Future works will include in silico clinical trial simulations for multiple years to determine how demographic factors, genetic factors, and dietary intake of magnesium impact the outcome of rare PPI-induced hypomagnesemia. This will be accomplished by developing a magnesium-homeostasis model that will be humanized with the data from clinical dietary magnesium balance studies to include dynamic adaptation to external disturbance caused by PPI therapy.

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CONCLUSION This study demonstrates that one can utilize the wealth of data in the literature to gain mechanistic insight into the physiological plausibility of PPI-induced hypomagnesemia. Literature mining allows us to gather sufficient data to construct an absorption centric model, and to conduct simulations to understand the impact of a short-term PPI therapy on the serum magnesium level, as well as to illustrate the usefulness of frequent dosing, in divided doses of magnesium supplementation for correcting low serum magnesium. The current results shed light on the plausible cause and suggest the path to overcome hypomagnesemia associated with PPI therapy.

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AUTHOR INFORMATION

Corresponding Author

*Office of Clinical Pharmacology, Office of Translational Sciences, CDER, FDA, Silver Spring, MD. Tel: 301-796-2473. E-mail: [email protected]. Author Contributions ‡

Equal contribution.

Notes

The views expressed in this article do not represent the views of the US Food and Drug Administration. The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank Dr. Darrell Abernethy for his helpful comments.

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REFERENCES

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