Mechanism-based pharmacokinetic/pharmacodynamic model of parathyroid hormone-calcium homeostasis in rats and humans

Dose Predictions for Drug Design

The efficacious dose of a drug is perhaps the most holistic metric reflecting its therapeutic potential. Dose is predicted at many stages in drug discovery and development. Prior to the 1990s, dose prediction was limited to the drug "working" at a reasonable dose and dose regimen in an animal model. Through the early 2000s, dose predictions were generated at candidate nomination and then refined during clinical development. Currently, dose predictions can be made early in drug discovery to enable drug design. Dose predictions at this stage can identify critical drug properties for a viable dose regimen and provide clinically relevant context to lead optimization. In this paper, we give an overview of the opportunities and challenges associated with dose prediction for drug design. A number of general considerations, approaches, and case examples are discussed.

Bridging adults and paediatrics with secondary hyperparathyroidism receiving haemodialysis: a pharmacokinetic-pharmacodynamic analysis of cinacalcet

Aims

The aims of this study were to develop a pharmacokinetic (PK) and PK‐pharmacodynamic (PK/PD) model of cinacalcet in adults and paediatrics with secondary hyperparathyroidism (SHPT) on dialysis, to test covariates of interest, and to perform simulations to inform dosing in paediatrics with SHPT.

Methods

Cinacalcet PK, intact parathyroid hormone (iPTH) and corrected calcium (cCa) time courses following multiple daily oral doses (1–300 mg) were modelled using a nonlinear mixed effects modelling approach using data from eight clinical studies. Model‐based trial simulations, using adult or paediatric titration schemas, predicted efficacy (iPTH change from baseline and proportion achieving iPTH decrease ≥30%) and safety (cCa change from baseline and proportion achieving cCa ≤8.4 mg/dL) endpoints at 24 weeks.

Results

Cinacalcet PK parameters were described by a two‐compartment linear model with delayed first‐order absorption‐elimination (apparent clearance = 287.74 L h⁻¹). Simulations suggested that paediatric starting doses (1, 2.5, 5, 10 and 15 mg) would provide PK exposures less than or similar to a 30 mg adult dose. The titrated dose simulations suggested that the mean (prediction interval) proportion of paediatric and adult subjects achieving ≥30% reduction in iPTH from baseline at Week 24 was 49% (36%, 62%), and 70.1% (62.5%, 77%), respectively. Additionally, the mean (confidence interval) proportion of paediatric and adult subjects achieving cCa ≤8.4 mg dL⁻¹ at Week 24 was 8% (2%, 18%) and 23.6% (17.5%, 30.5%), respectively.

Conclusions

Model‐based simulations showed that the paediatric cinacalcet starting dose (0.2 mg kg⁻¹), titrated to effect, would provide the desired PD efficacy (PTH suppression <30%) while minimizing safety concerns (hypocalcaemia).

Highlighting Vitamin D Receptor-Targeted Activities of 1α,25-Dihydroxyvitamin D3 in Mice via Physiologically Based Pharmacokinetic-Pharmacodynamic Modeling

We expanded our published physiologically based pharmacokinetic model (PBPK) on 1α,25-dihydroxyvitamin D₃ [1,25(OH)₂D₃], ligand of the vitamin D receptor (VDR), to appraise VDR-mediated pharmacodynamics in mice. Since 1,25(OH)₂D₃ kinetics was best described by a segregated-flow intestinal model (SFM) that described a low/partial intestinal (blood/plasma) flow to enterocytes, with feedback regulation of its synthesis (Cyp27b1) and degradation (Cyp24a1) enzymes, this PBPK(SFM) model was expanded to describe the VDR-mediated changes (altered/basal mRNA expression) of target genes/responses with the indirect response model. We examined data on 1) renal Trpv5 (transient receptor potential cation channel, subfamily V member 5) and Trpv6 and intestinal Trpv6 (calcium channels) for calcium absorption; 2) liver 3-hydroxy-3-methyl-glutaryl-coenzyme A reductase (Hmgcr) and cytochrome 7α-hydroxylase (Cyp7a1) for cholesterol synthesis and degradation, respectively; and 3) renal and brain Mdr1 (multidrug-resistance protein that encodes the P-glycoprotein) for digoxin disposition after repetitive intraperitoneal doses of 120 pmol 1,25(OH)₂D₃ Fitting, performed with modeling software, yielded reasonable prediction of a dominant role of intestinal Trpv6 in calcium absorption, circadian rhythm that is characterized by simple cosine models for Hmgcr and Cyp7a1 on liver cholesterol, and brain and renal Mdr1 on tissue efflux of digoxin. Fitted parameters on the E_max, EC₅₀, and turnover rate constants of VDR-target genes [zero-order production (k_in) and first-order degradation (k_out) rate constants] showed low coefficients of variation and acceptable median prediction errors (4.5%-40.6%). Sensitivity analyses showed that the E_max and EC₅₀ values are key parameters that could influence the pharmacodynamic responses. In conclusion, the PBPK(SFM)-pharmacodynamic model successfully characterized VDR gene activation and serves as a useful tool to predict the therapeutic effects of 1,25(OH)₂D₃.

Coupling between phosphate and calcium homeostasis: a mathematical model

We developed a mathematical model of calcium (Ca) and phosphate (PO₄) homeostasis in the rat to elucidate the hormonal mechanisms that underlie the regulation of Ca and PO₄ balance. The model represents the exchanges of Ca and PO₄ between the intestine, plasma, kidneys, bone, and the intracellular compartment, and the formation of Ca-PO₄-fetuin-A complexes. It accounts for the regulation of these fluxes by parathyroid hormone (PTH), vitamin D₃, fibroblast growth factor 23, and Ca²⁺-sensing receptors. Our results suggest that the Ca and PO₄ homeostatic systems are robust enough to handle small perturbations in the production rate of either PTH or vitamin D₃ The model predicts that large perturbations in PTH or vitamin D₃ synthesis have a greater impact on the plasma concentration of Ca²⁺ ([Ca²⁺]_p) than on that of PO₄ ([PO₄]_p); due to negative feedback loops, [PO₄]_p does not consistently increase when the production rate of PTH or vitamin D₃ is decreased. Our results also suggest that, following a large PO₄ infusion, the rapidly exchangeable pool in bone acts as a fast, transient storage PO₄ compartment (on the order of minutes), whereas the intracellular pool is able to store greater amounts of PO₄ over several hours. Moreover, a large PO₄ infusion rapidly lowers [Ca²⁺]_p owing to the formation of CaPO₄ complexes. A large Ca infusion, however, has a small impact on [PO₄]_p, since a significant fraction of Ca binds to albumin. This mathematical model is the first to include all major regulatory factors of Ca and PO₄ homeostasis.

Population Pharmacokinetics and Pharmacodynamics of the Calcimimetic Etelcalcetide in Chronic Kidney Disease and Secondary Hyperparathyroidism Receiving Hemodialysis

Etelcalcetide is a novel calcimimetic in development for the treatment of secondary hyperparathyroidism (SHPT). A population pharmacokinetic/pharmacodynamic (PK/PD) model was developed relating etelcalcetide exposures to markers of efficacy (parathyroid hormone [PTH]) and safety (calcium) using data from three clinical studies. The semimechanistic model was developed that included allosteric activation pharmacology and understanding of calcium homeostasis. The temporal profiles for all biomarkers were well described by the model. The cooperativity constant was 4.94, confirming allosteric activation mechanism. Subjects with more severe disease (higher PTH baseline) were predicted to experience less pronounced reduction in PTH (percentage change from baseline), but more reduction in calcium (Ca; percentage change from baseline). There was no evidence that dose adjustment by any covariate was needed. Model‐based simulations provided quantitative support to several elements of dosing, such as starting dose, monitoring, and titration timing for registration trials.

A model of calcium homeostasis in the rat

We developed a model of calcium homeostasis in the rat to better understand the impact of dysfunctions such as primary hyperparathyroidism and vitamin D deficiency on calcium balance. The model accounts for the regulation of calcium intestinal uptake, bone resorption, and renal reabsorption by parathyroid hormone (PTH), vitamin D₃, and Ca²⁺ itself. It is the first such model to incorporate recent findings regarding the role of the calcium-sensing receptor (CaSR) in the kidney, the presence of a rapidly exchangeable pool in bone, and the delayed response of vitamin D₃ synthesis. Accounting for two (fast and slow) calcium storage compartments in bone allows the model to properly predict the effects of bisphophonates on the plasma levels of Ca²⁺ ([Ca²⁺]_p), PTH, and vitamin D₃ Our model also suggests that Ca²⁺ exchange rates between plasma and the fast pool vary with both sex and age, allowing [Ca²⁺]_p to remain constant in spite of sex- and age-based hormonal and other differences. Our results suggest that the inconstant hypercalciuria that is observed in primary hyperparathyroidism can be attributed in part to counterbalancing effects of PTH and CaSR in the kidney. Our model also correctly predicts that calcimimetic agents such as cinacalcet bring down [Ca²⁺]_p to within its normal range in primary hyperparathyroidism. In addition, the model provides a simulation of CYP24A1 inactivation that leads to a situation reminiscent of infantile hypercalcemia. In summary, our model of calcium handling can be used to decipher the complex regulation of calcium homeostasis.

Modeling of the parathyroid hormone response after calcium intake in healthy subjects

Plasma ionized calcium (Ca²⁺) concentrations are tightly regulated in the body and maintained within a narrow range; thus it is challenging to quantify calcium absorption under normal physiologic conditions. This study aimed to develop a mechanistic model for the parathyroid hormone (PTH) response after calcium intake and indirectly compare the difference in oral calcium absorption from PTH responses. PTH and Ca²⁺ concentrations were collected from 24 subjects from a clinical trial performed to evaluate the safety and calcium absorption of Geumjin Thermal Water in comparison with calcium carbonate tablets in healthy subjects. Indirect response models (NONMEM Ver. 7.2.0) were fitted to observed Ca²⁺ and PTH data, respectively, in a manner that absorbed but unobserved Ca²⁺ inhibits the secretion of PTH. Without notable changes in Ca²⁺ levels, PTH responses were modeled and used as a marker for the extent of calcium absorption.

Pharmacokinetics in rats of a long-acting human parathyroid hormone-collagen binding domain peptide construct

The pharmacokinetics of a hybrid peptide consisting of the N-terminal biologically active region of human parathyroid hormone (PTH) linked to a collagen-binding domain (CBD) were evaluated in female Sprague-Dawley rats. The peptide, PTH-CBD, consists of the first 33 amino acids of PTH linked as an extension of the amino acid chain to the CBD peptide derived from ColH collagenase of Clostridium histolyticum. Serum concentrations arising from single dose administration by the subcutaneous and intravenous routes were compared with those measured following route-specific mole equivalent doses of PTH(1-34). Population-based modeling demonstrated similar systemic absorption kinetics and bioavailability for both peptides. Exposure to PTH-CBD was sixfold higher because of a systemic clearance of approximately 20% relative to PTH(1-34); however, these kinetics were consistent with more than 95% of a dose being eliminated from serum within 24 h. Results obtained support continued investigation of PTH-CBD as a bone-targeted anabolic agent for the treatment of postmenopausal osteoporosis.

A semimechanistic model of the time-course of release of PTH into plasma following administration of the calcilytic JTT-305/MK-5442 in humans

JTT-305/MK-5442 is a calcium-sensing receptor (CaSR) allosteric antagonist being investigated for the treatment of osteoporosis. JTT-305/MK-5442 binds to CaSRs, thus preventing receptor activation by Ca(2+) . In the parathyroid gland, this results in the release of parathyroid hormone (PTH). Sharp spikes in PTH secretion followed by rapid returns to baseline are associated with bone formation, whereas sustained elevation in PTH is associated with bone resorption. We have developed a semimechanistic, nonpopulation model of the time-course relationship between JTT-305/MK-5442 and whole plasma PTH concentrations to describe both the secretion of PTH and the kinetics of its return to baseline levels. We obtained mean concentration data for JTT-305/MK-5442 and whole PTH from a multiple dose study in U.S. postmenopausal women at doses of 5, 10, 15, and 20 mg. We hypothesized that PTH is released from two separate sources: a reservoir that is released rapidly (within minutes) in response to reduction in Ca(2+) binding, and a second source released more slowly following hours of reduced Ca(2+) binding. We modeled the release rates of these reservoirs as maximum pharmacologic effect (Emax ) functions of JTT-305/MK-5442 concentration. Our model describes both the dose-dependence of PTH time of occurrence for maximum drug concentration (Tmax ) and maximum concentration of drug (Cmax ), and the extent and duration of the observed nonmonotonic return of PTH to baseline levels following JTT-305/MK-5442 administration.

A semi-mechanistic integrated toxicokinetic-toxicodynamic (TK/TD) model for arsenic(III) in hepatocytes

BACKGROUND

A systems engineering approach is presented for describing the kinetics and dynamics that are elicited upon arsenic exposure of human hepatocytes. The mathematical model proposed here tracks the cellular reaction network of inorganic and organic arsenic compounds present in the hepatocyte and analyzes the production of toxicologically potent by-products and the signaling they induce in hepatocytes.

METHODS AND RESULTS

The present modeling effort integrates for the first time a cellular-level semi-mechanistic toxicokinetic (TK) model of arsenic in human hepatocytes with a cellular-level toxicodynamic (TD) model describing the arsenic-induced reactive oxygen species (ROS) burst, the antioxidant response, and the oxidative DNA damage repair process. The antioxidant response mechanism is described based on the Keap1-independent Nuclear Factor-erythroid 2-related factor 2 (Nrf2) signaling cascade and accounts for the upregulation of detoxifying enzymes. The ROS-induced DNA damage is simulated by coupling the TK/TD formulation with a model describing the multistep pathway of oxidative DNA repair. The predictions of the model are assessed against experimental data of arsenite-induced genotoxic damage to human hepatocytes; thereby capturing in silico the mode of the experimental dose-response curve.

CONCLUSIONS

The integrated cellular-level TK/TD model presented here provides significant insight into the underlying regulatory mechanism of Nrf2-regulated antioxidant response due to arsenic exposure. While computational simulations are in a fair good agreement with relevant experimental data, further analysis of the system unravels the role of a dynamic interplay among the feedback loops of the system in controlling the ROS upregulation and DNA damage response. This TK/TD framework that uses arsenic as an example can be further extended to other toxic or pharmaceutical agents.

Engineering of therapeutic polypeptides through chemical synthesis: early lessons from human parathyroid hormone and analogues

Application of chemical synthesis to gain access to high purity hPTH as well as more stable analogues was accomplished through a menu of extended NCL followed by metal free dethiylation.

Intraoperative parathyroid hormone concentration to confirm removal of hypersecretory parathyroid tissue and time to postoperative normocalcaemia in nine dogs with primary hyperparathyroidism

OBJECTIVE

To determine (1) whether the intraoperative parathyroid hormone concentration ([PTH]) during parathyroidectomy (PTX) can be used to indicate cure in dogs with primary hyperparathyroidism and (2) the time taken for postoperative serum calcium concentration to normalise.

DESIGN

Retrospective study (2005-10) from a private referral hospital in Sydney, New South Wales, Australia.

PROCEDURE

Nine client-owned dogs underwent surgical PTX for naturally occurring primary hyperparathyroidism. [PTH] was measured from serum samples taken immediately post-induction (pre-PTX]) and at least 20 min after adenoma removal (post-PTX) for all dogs, and during parathyroid gland manipulation (intra-PTX) for six dogs. The concentration of ionised calcium (iCa) was measured at various time points postoperatively until it normalised, then stabilised or decreased below reference ranges. Statistical analysis compared the mean pre-, intra- and post-PTX [PTH] and the average rate of decline of iCa concentration postoperatively.

RESULTS

All dogs demonstrated a significant decrease from mean pre-PTX [PTH] (168.51 pg/mL) to mean post-PTX [PTH] (29.20 pg/mL). There was a significant increase in mean intra-PTX [PTH] (279.78 pg/mL). The average rate of decline of iCa concentration postoperatively to within the reference range (1.12-1.40 mmol/L) occurred after 24 h.

CONCLUSION

Intraoperative measurements of [PTH] can be used clinically to determine cure of primary hyperparathyroidism. Parathyroid hormone increases significantly during parathyroid gland manipulation. Plasma iCa concentration returns to within the reference range on average 24 h after successful PTX. Not all dogs require vitamin D or calcium supplementation pre- or postoperatively.

Application of the logic of cysteine-free native chemical ligation to the synthesis of Human Parathyroid Hormone (hPTH)

The power of chemical synthesis of large cysteine-free polypeptides has been significantly enhanced through the use of nonproteogenic constructs which bear strategically placed thiol groups, enabling native chemical ligation. Central to these much expanded capabilities is the specific, radical-induced, metal-free dethiolation, which can be accomplished in aqueous medium.

Pharmacodynamic model of parathyroid hormone modulation by a negative allosteric modulator of the calcium-sensing receptor

In this study, a pharmacodynamic model is developed, based on calcium-parathyroid hormone (PTH) homeostasis, which describes the concentration-effect relationship of a negative allosteric modulator of the calcium-sensing receptor (CaR) in rats. Plasma concentrations of drug and PTH were determined from plasma samples obtained via serial jugular vein sampling following single subcutaneous doses of 1, 5, 45, and 150 mg/kg to male Sprague-Dawley rats (n = 5/dose). Drug pharmacokinetics was described by a one-compartment model with first-order absorption and linear elimination. Concentration-time profiles of PTH were characterized using a model in which the compound allosterically modulates Ca(+2) binding to the CaR that, in turn, modulates PTH through a precursor-pool indirect response model. Additionally, negative feedback was incorporated to account for tolerance observed at higher dose levels. Model fitting and parameter estimation were conducted using the maximum likelihood algorithm. The proposed model well characterized the data and provided compound specific estimates of the K(i) and cooperativity constant (α) of 1.47 ng/mL and 0.406, respectively. In addition, the estimated model parameters for PTH turnover were comparable to that previously reported. The final generalized model is capable of characterizing both PTH-Ca(+2) homeostasis and the pharmacokinetics and pharmacodynamics associated with the negative allosteric CaR modulator. As such, the model provides a simple platform for analysis of drugs targeting the PTH-Ca(+2) system.

Mathematical model of uptake and metabolism of arsenic(III) in human hepatocytes - Incorporation of cellular antioxidant response and threshold-dependent behavior

Background

Arsenic is an environmental pollutant, potent human toxicant, and oxidative stress agent with a multiplicity of health effects associated with both acute and chronic exposures. A semi-mechanistic cellular-level toxicokinetic (TK) model was developed in order to describe the uptake, biotransformation and clearance of arsenical species in human hepatocytes. Notable features of this model are the incorporation of arsenic-glutathione complex formation and a "switch-like" formulation to describe the antioxidant response of hepatocytes to arsenic exposure.

Results

The cellular-level TK model applies mass action kinetics in order to predict the concentrations of trivalent and pentavalent arsenicals in hepatocytes. The model simulates uptake of arsenite (iAs^III) via aquaporin isozymes 9 (AQP9s), glutathione (GSH) conjugation, methylation by arsenic methyltransferase (AS3MT), efflux through multidrug resistant proteins (MRPs) and the induced antioxidant response via thioredoxin reductase (TR) activity. The model was parameterized by optimization of model estimates for arsenite (iAs^III), monomethylated (MMA) and dimethylated (DMA) arsenicals concentrations with time-course experimental data in human hepatocytes for a time span of 48 hours, and dose-response data at 24 hours for a range of arsenite concentrations from 0.1 to 10 μM. Global sensitivity analysis of the model showed that at low doses the transport parameters had a dominant role, whereas at higher doses the biotransformation parameters were the most significant. A parametric comparison of the TK model with an analogous model developed for rat hepatocytes from the literature demonstrated that the biotransformation of arsenite (e.g. GSH conjugation) has a large role in explaining the variation in methylation between rats and humans.

Conclusions

The cellular-level TK model captures the temporal modes of arsenical accumulation in human hepatocytes. It highlighted the key biological processes that influence arsenic metabolism by explicitly modelling the metabolic network of GSH-adducts formation. The parametric comparison with the TK model developed for rats suggests that the variability in GSH conjugation could have an important role in inter-species variability of arsenical methylation. The TK model can be incorporated into larger-scale physiologically based toxicokinetic (PBTK) models of arsenic for improving the estimates of PBTK model parameters.