The purpose of this study was to develop a mechanism-based pharmacokinetic/pharmacodynamic model that describes the regulation of the parathyroid hormone (PTH)-Ca2+ system in rats and humans. Temporal concentration data for endogenous PTH and Ca2+ were extracted from literature for rats (normal adult males) and humans. In addition, exogenous PTH was administered subcutaneously to male Sprague-Dawley rats with jugular vein catheters, and plasma concentrations were measured over time. A mathematical model was developed and fitted simultaneously to endogenous PTH, Ca2+, and exogenous PTH concentrations in rats. Ca2+ concentrations were described using a turnover model, with its depletion being induced by a chelating agent, and PTH concentrations were characterized using a precursor-dependent indirect response model. The same structural model was used for fitting data obtained in humans. PTH stimulation was driven by occupancy of the Ca2+ sensing receptor, and lowering of physiological Ca2+ concentrations increased PTH secretion, with PTH profiles being adequately described by the model. PTH stimulatory capacity was baseline-dependent in rats [Smax_rats = 34.8 × PTH0] and humans [Smax_humans = 392/PTH0]. Modeling results suggest that normal rats are twice as sensitive to Ca2+-induced PTH stimulation compared with humans. In conclusion, the developed model adequately characterizes the PTH-Ca2+ regulation across species and may be useful in the development of therapeutic drugs targeting this system.
The translation of molecular and preclinical models to successful treatments of bone-related disorders (e.g., osteoporosis, rheumatoid and osteoarthritis, and multiple myeloma) is a formidable challenge, due in part to an as yet incomplete understanding of the homeostatic mechanisms in the bone microenvironment. Major research efforts are focused on understanding the complexities of bone regulation, thus enabling the development of newer treatments or optimization of current therapies. A principle regulatory mechanism maintaining bone homeostasis involves the interplay of parathyroid hormone (PTH) and ionized calcium (Ca2+) (Juppner et al., 2001; Friedman, 2006). Secretion of PTH in response to signaling from calcium-sensing receptors (CaSR), located on the parathyroid cell surface, is one of the key endocrine regulators of Ca2+ (Nemeth, 2002; Friedman and Goodman, 2006), and this relationship is characterized by a very steep dose-response curve (Chen and Goodman, 2004). Slight perturbations in blood Ca2+ concentrations elicit PTH secretory responses that are disproportionate in magnitude. Resultant PTH secretion or inhibition also mediates the regulation of Ca2+ concentrations in blood. Elevated extracellular Ca2+ detected by the CaSR results in inhibition of PTH secretion, whereas lowering of Ca2+ concentrations cause an increase in serum PTH. Serum PTH in turn affects renal Ca2+ excretion and reabsorption, and bone resorption/formation to maintain concentrations at the normal physiological range (approximately 1.2 mM).
Pharmacological agents targeting the PTH-Ca2+ system represent an important therapeutic class of drugs in osteoporosis. Teriparatide is a 34-amino acid N-terminal PTH fragment currently approved for therapy (Body et al., 2002; Brixen et al., 2004). Trials investigating the efficacy of the full-length human PTH(1-84) hormone have also been conducted and have demonstrated comparative short-term success (Hodsman et al., 2003; Greenspan et al., 2007). Interest in the full-length recombinant hormone emanates from the fact that it may also exert antiapoptotic activity on osteoblasts (Jilka et al., 1999).
Clinical trials for intact PTH and its fragment have been reviewed previously (Hamann and Lane, 2006). These trials have focused on the clinical endpoint—improvement of bone mineral density. Analyses of results from these clinical trials are empirical, and assessments of improved efficacy in osteoporotic conditions are qualitative or semiquantitative. Model-based analysis of concentration-response relationships is increasingly being used in drug discovery and development (Lalonde et al., 2007), for which a diverse array of mechanism-based models are available (Mager et al., 2003). Cross talk between PTH and Ca2+ has also been examined using modeling techniques. Brown (1983) proposed a four-parameter logistic model to characterize the steep relationship between PTH release and extracellular Ca2+. This empirical model permits data from an in vitro system to be analyzed using a continuous function describing PTH responses to perturbations in extracellular Ca2+. Momsen and Schwarz (1997) derived a simple biexponential model, based on simplifying assumptions of biochemical processes controlling PTH release and elimination, to describe induced PTH secretion by rapid lowering of blood Ca2+. However, the explicit function excludes the time course of Ca2+ concentrations, which may limit the utility of the model under different experimental conditions. Another model for Ca2+ homeostasis has been reported, which accounts for serum concentrations of PTH, Ca2+, and calcitriol (Raposo et al., 2002). The mechanistic aspects of the model may enhance predictive capabilities through simulations; however, the complex model structure precludes its use for fitting routine pharmacokinetic/pharmacodynamic (PK/PD) data from animals and humans.
In this current study, PTH-Ca2+ homeostasis has been quantified using an integrated mechanism-based PK/PD model and is applicable to both rats and humans. This model could be used to design informative preclinical studies for investigational compounds affecting the PTH-Ca2+ system. It also enables the estimation of physiological parameters in rats and humans, thus facilitating the translational potential of predictions of PTH responses in humans upon perturbation of Ca2+.
Materials and Methods
Data for model development were extracted from the literature. Serum Ca2+ and PTH concentrations were digitized for rats (Fox, 1991; Fox et al., 1997) and humans (Schmitt et al., 1996; Cosman et al., 1998, 1999).
Rat Literature Data. In one study, Ca2+ and PTH concentrations were measured in adult male Sprague-Dawley rats (6 months old; n = 6) that were catheterized at the femoral artery and vein (Fox, 1991). An arterial blood sample was withdrawn for measuring baseline concentrations of Ca2+ and PTH followed by reconstitution of lost blood volume. Lowering of Ca2+ was achieved using a calcium-clamp technique (Fox and Heath, 1981). EGTA at a concentration of 250 mM was infused intravenously at varying rates to induce rapid lowering of Ca2+. Subsequent maintenance of Ca2+ concentrations, approximately 0.3 mM below baseline, was achieved by continuously adjusting infusion rates of EGTA. A second study was conducted in normal male Sprague-Dawley rats (age not specified) that were catheterized via the abdominal aorta and inferior vena cava for sampling and infusions, respectively (Fox et al., 1997). The purpose of this study was to examine the maximum PTH secretory response upon stimulation. EGTA solutions with concentrations of 60, 90, and 120 mM at pH 7.4 were infused intravenously at 0.167 ml/min for 2 min. Blood sampling was carried out at 2, 5, 10, and 15 min after start of the infusion. Plasma Ca2+ concentrations were obtained from heparinized blood using a Ca2+ analyzer (model 634; Ciba Corning, Medford, MA), and PTH concentrations were measured using a rat PTH(1-34) immunoradiometric assay.
Human Literature Data. Seven healthy volunteers (21–30 years old; six males and one female) were cannulated through the contralateral cubital vein (Schmitt et al., 1996). Each participant underwent a hypocalcemic and hypercalcemic clamp study in a randomized sequence separated by 7 days. For the purposes of this analysis, only the hypocalcemic clamp data were analyzed. The steady-state baseline for plasma Ca2+ was monitored for 75 min with blood samples withdrawn every 10 min. A hypocalcemic clamp using a 0.2 mM solution of sodium citrate was initiated at the end of the baseline assessment. A step-down protocol for rates of sodium citrate infusion was followed to maintain plasma Ca2+ at lower steady-state concentrations for the duration of the study. Blood samples were withdrawn at 5-min intervals after the start of infusion. An ion-selective electrode system (Ionometer EH-F; Fresenius, Oberursel, Germany) was used for Ca2+ measurements, and a two-site immunoradiometric assay (Nichols Institute, San Juan Capistrano, CA) was used for measuring intact PTH. A second study was conducted in healthy premenopausal white female volunteers (age 25–40; n = 17) (Cosman et al., 1999). Two samples for baseline characterization were obtained, and sampling was conducted over a period of 5 h after initiation of a 2-h sodium EDTA infusion (0.1 mg/ml/kg) at 250 ml/h. The above-mentioned protocol was also used for a study that was conducted in postmenopausal women (age 47–71; n = 3) (Cosman et al., 1998). The patients were selected from a pool of patients undergoing hormonal replacement therapy for 1 year and having a stable bone mass baseline. In these studies, PTH was measured using the same two-site immunoradiometric assay. Serum Ca2+ was measured using the NOVA 8 ionized Ca2+ analyzer (Nova Biomedicals, Newton, MA).
Rat Pharmacokinetic Study. Sixteen male Sprague-Dawley rats (11–13 weeks old; Taconic Farms, Spafas, NY) with surgically implanted jugular vein catheters were assigned (n = 4) to four dosing arms (0, 1500, 5000, and 15,000 ng/kg). Intact rat PTH(1-84) was injected subcutaneously, and the vehicle used was 0.001 N HCl with 2% heat-inactivated normal rat serum collected from age-, sex-, and strain-matched animals. Blood samples were collected via the catheters at 0 (baseline), 2, 5, 15, 30, 60, 120, 240, and 360 min postdosing time. The catheters were flushed with saline with 10 IU/ml sodium heparin between samples. The initial portion of each blood draw for each series time point sample was not collected in order to eliminate any heparinized saline that resided in the catheter. Blood samples were allowed to remain at room temperature in plasma microcentrifuge tubes and were then centrifuged at 14,000 rpm for 10 min in an Eppendorf microcentrifuge (Eppendorf North America, New York, NY). Plasma was drawn off the samples and placed in Eppendorf tubes and frozen until PTH(1-84) was assayed at a later date.
PTH Assay. Plasma samples were analyzed for PTH concentrations by use of a commercially available enzyme-linked immunosorbent assay kit (Rat Intact PTH ELISA; Immutopics, San Clemente, CA) according to kit instructions.
PK/PD Model. Mean data were digitized using a data digitization tool (Graph Digitizer, version 1.9) and used for model development. A schematic representation of the model structure is shown in Fig. 1. Chelating agent sodium citrate/sodium EDTA/EGTA was assumed to follow a standard one compartment linear disposition model and is described by the following differential equation: where Cchel(0) = 0, and R0 and kel_chel are the zero-order input and first-order elimination rate constants, respectively, of the chelating agent. The elimination rate was inferred from subsequent model fitting of Ca2+ concentrations and fixed in the final parameter estimation procedure.
The in vivo turnover of Ca2+ concentrations was modeled using the following differential equation: where kin_Ca2+ is the zero-order production rate constant of Ca2+ and kout_Ca2+ is the first-order loss rate constant of Ca2+ from the body. The initial condition for the above system is defined as the measured baseline endogenous concentration of Ca2+. Chelating agents stimulate the loss of Ca2+ and was achieved by incorporating a stimulatory function influencing kout_Ca2+. The stimulatory function in rats is the standard nonlinear Hill equation: and a linear stimulatory coefficient, S_Chel, was sufficient to describe the data in humans: H(Cchel) = S_Chel × CChel.
A precursor-dependent indirect response model (Sharma et al., 1998) was proposed to characterize PTH turnover. Differential equations describing this system are as follows (rats and humans): where ρ′ is the change from baseline of the Ca2+/CaSR complex, S is a linear stimulation function, PP is the PTH precursor concentration, and the initial condition for each equation is given as PP(0) and PTH(0). The choice of a precursor-dependent model was based on the underlying physiology of PTH production and loss. PTH is synthesized as a 115-amino acid translation product (preproparathyroid hormone), which upon cleavage forms the proparathyroid hormone. Proparathyroid hormone is transported to the Golgi complex for further processing to form intact PTH, which is stored in secretory granules within the gland (Friedman, 2006). The precursor compartment is representative of a composite measure of preproparathyroid hormone, proparathyroid hormone, and stored intact PTH. To account for the constant production of these precursors within gland, a zero-order production rate, kin_PP, is assumed. Release of intact PTH or the degraded product into blood circulation is mediated through PTH cells in the gland (Lewin et al., 1995). This observation is supported by in vitro studies using bovine PTH gland slices incubated in a hypocalcemic or hypercalcemic medium (Habener et al., 1975). Newly synthesized PTH degradation within cells was regulated by extracellular calcium. In vitro exposure to a hypocalcemic solution induced the release of intact PTH from the gland, whereas a hypercalcemic solution resulted in an almost 50% degradation of PTH. Similar findings were seen in vivo for calves (Mayer et al., 1979). The proposed model accounts for these processes with a first-order degradation rate, ks, and first-order PTH production rate, kp. Subsequent loss of PTH from the circulation is defined as a first-order rate constant, kout_PTH. A basic assumption for the model is that ks, kp, kout_PTH, and PP fully account for the production and loss of PTH.
Modulation of PTH exocytosis is mediated through the actions of extracellular Ca2+ on the CaSR (Nemeth, 2002). Activation of the CaSR induces a complex network of signal transduction cascades that includes moieties such as diacyl glycerol, G proteins, and inositol triphosphate among many others (Hofer and Brown, 2003). However, the precise mechanism of control of PTH secretion from the glands through the Ca2+/CaSR interaction is not completely understood. The PK/PD model links Ca2+ and PTH interaction through the Ca2+/CaSR receptor binding phenomenon: and where KD is the equilibrium dissociation constant of Ca2+ with CaSR (KD = 1.1–1.3 mM) (Chattopadhyay, 2000), ρ is the calcium-receptor occupancy at any time (t), and ρ(0) is the calcium-receptor occupancy at baseline. Initial modeling efforts suggested that the extent of PTH stimulation was dependent on PTH baseline concentrations. To better characterize this phenomenon, the linear term in the stimulation function was further qualified: where m is a linear slope parameter for PTH stimulation in response to lowering of Ca2+ and n equals 1 (rats) or -1 (humans).
An added component in the model specific to rats was the analysis of in vivo concentrations of PTH after exogenous administration (Fig. 1). A dual-absorption kinetic model developed by Ramakrishnan et al. (2003) was used for input of subcutaneously administered PTH. The model includes a rapid zero-order absorption of a fractional dose (1 - fr) up to time interval, τ, and a slow first-order absorption of the remaining fraction. Data for placebo and three subcutaneous doses were fitted simultaneously to estimate model parameters. The differential equations for this model are as follows: where and ka is a first-order absorption rate constant. Based on initial model fitting, the time parameter (τ) was fixed to 5 min.
Data Analysis. Initial model runs were carried out in a sequential manner for parameter optimization of each submodel. The final analysis involved simultaneous fitting of all the data in each species as per the model scheme shown in Fig. 1. Assessment of model predictions across the two species was conducted by simulating PTH profiles in rats and humans. PTH stimulation achieved in rats and humans were compared.
Parameter estimation was conducted using nonlinear regression analysis with the ADAPT II program (D'Argenio and Schumitzky, 1997) by the maximum likelihood method. The variance model was defined as follows: where σ1 and σ2 are the variance model parameters and M(θ,ti) is the ith predicted value from the PK/PD model. Distinct variance parameters were used for the Ca2+ and PTH models. Model selection was based on goodness-of-fit criterion, which included convergence criterion, Akaike information criterion, estimation criterion value for the maximum likelihood method, and visual inspection of predicted versus observed and residual plots.
Rat PK/PD Profiles. PK/PD data and model-predicted profiles in rats are shown in Figs. 2 and 3. Final model parameter estimates are reported in Table 1 and were estimated with good precision (low CV%). For ease of interpretation, parameters specific to the Fox (1991) and Fox and Heath (1981) studies are reported with suffixes “1” and “2,” respectively. The elimination rate (kel_EGTA) for EGTA in rats was fixed to the estimate obtained from initial model runs. All parameters in the Ca2+ turnover model were estimated, with the exception of KD and SC50_EGTA_2. The PK/PD model predicted profiles for Ca2+ are shown in Fig. 2 (left). The KD was fixed to an in vitro value (1.2 mM) and is physiologically relevant (Chattopadhyay, 2000). A nonlinear function was required to stimulate the loss of Ca2+. The SC50_EGTA_2 parameter also could not be estimated with low error and had to be fixed to 349 mM, a value obtained from initial runs. Examination of model-predicted time course profiles for loss of Ca2+ demonstrates that the proposed model is able to well characterize observed data from both studies. There seems to be some slight deviation in the recession phase in Fig. 2B, which could be an artifact of using mean data for the analysis. Baseline Ca2+ for both studies in normal rats were comparable and initial conditions, Ca2+(0), were reasonably estimated. The observed mean and model predicted concentration-time profiles for PTH is shown in Fig. 2 (right). All parameters for the PTH model were estimated and are listed in Table 1. The need for a distinct PTH degradation pathway (ks) was supported by model-fitting criteria. Baseline PTH concentrations were different between the two studies. This necessitated the estimation of PTH baselines for optimal fitting. A higher PTH baseline resulted in greater stimulation of secretion upon reduction in Ca2+ (see eq. 8). The linear parameter, m, accounted for this baseline dependence and was estimated to have a magnitude of 34.8. Overall, the predictions are in agreement with observed concentration-time profiles of in vivo PTH.
Figure 3A shows the model prediction and mean concentration-time profiles after subcutaneous administration of PTH. PK parameter estimates for exogenously administered PTH are reported in Table 2. Initially, a standard one-compartment model with a first-order rate of absorption (ka) was evaluated. However, it was unable to simultaneously characterize data from the higher dose levels. With the exception of the lowest dose (1500 ng/kg), the higher doses were characterized well by the proposed dual-absorption model. The gradual return to baseline for the lowest dose does not seem to mimic the mean observed data. However, analysis of the individual observed data in Fig. 3B for the lowest dose suggests high variability in PTH measurements and lack of a clear trend. There does not seem to be a clear delineation between observed PTH concentrations for the placebo and low-dose PTH arms. The zero-order absorption of PTH is rapid and accounts for a very small fraction of the total dose (1 - fr = 6.9%).
Human PK/PD Profiles. Mean observed concentration-time and model predicted profiles for humans are shown in Fig. 4. The structural model for humans is similar to that implemented for rats. To account for potential differences between sodium citrate and sodium EDTA, individual first-order elimination rates (kel_Citrate and kel_EDTA) were assigned for optimization. Model fittings for loss of Ca2+ after administration of a chelating agent are shown in Fig. 4 (left). Despite the use of mean data, model predicted profiles are in good agreement with observed data. All parameters for the Ca2+ turnover model were estimated and are presented in Table 1. A simple linear term for the stimulation of removal of Ca2+ by the chelating agent was adequate for describing mean Ca2+ concentrations. The estimate for KD is 1.25 mM, which is in close agreement with the in vitro value of 1.2 mM. Baseline Ca2+ was estimated for each study, and the data are reported in Table 1.
A 6-fold stimulation in PTH concentrations relative to baseline is observed after a rapid drop in Ca2+ (Fig. 4A) (Schmitt et al., 1996). When steady-state Ca2+ is further maintained by adjusting the rate of infusion, PTH concentrations decline to a new steady state, which is approximately 2-fold higher than the original baseline. In studies by Cosman et al. (1998, 1999), females seem to have a higher PTH baseline compared with the subjects (predominantly males) in Schmitt et al. (1996), and the extent of stimulation for PTH is approximately 3-fold relative to baseline. As a result, baseline and maximum PTH concentrations suggested an inverse relationship for the extent of stimulation achieved in response to hypocalcemia. Incorporation of this baseline dependence (see eq. 8) allowed for improved model performance. However, the linear slope term (m) had to be fixed due to the large error associated with it. The value chosen for the final estimation was based on initial runs. Figure 4 (right) shows model-predicted profiles for mean PTH concentrations in the three studies, and the proposed PK/PD model well describes the data. The model estimated in vivo half-life for PTH is 0.63 min. This is in concordance with the literature reported half-life for PTH, which ranges between 0.5 and 5 min (Kao et al., 1992; Libutti et al., 1999; Bieglmayer et al., 2002).
Model Prediction across Species. Resultant profiles from simulations of the structural model for rats and humans are shown in Fig. 5. For a given rate of decrease in Ca2+, humans seem to be more sensitive to changes in Ca2+ for reaching peak concentrations of PTH, compared with normal rats. A 0.1 mM change in Ca2+ results in a 4- to 5-fold change in PTH concentrations. A 6- to 8-fold stimulation of PTH is achieved in normal adult rats, which results from a 0.2 mM change in Ca2+. The extent of PTH stimulation achieved by a hypocalcemic stimulus seems to be greater in rats than in humans.
A PK/PD model was developed that attempts to codify potential underlying mechanisms for observed secretory effects of PTH in response to hypocalcemia (Fig. 1). The final model was used to simultaneously characterize Ca2+ and PTH data across different studies in rats and humans. Mean concentrations for Ca2+ and PTH after different doses of chelating agents were well captured across studies for both species. The binding kinetics of Ca2+ with its receptor were accounted for, which to our knowledge, is unique to our model. This approach allows for adapting the proposed structural model to therapeutic agents targeting the CaSR and thus holds great potential in its application toward achieving desirable PTH stimulation profiles for new therapeutic agents targeting this system.
The secretory response of PTH to hypocalcemia is multifactorial (Juppner et al., 2001). The principle mechanism is release of PTH from stored reserves in secretory vesicles. It is reported that enough PTH is stored lasting up to 60 to 90 min for a low sustained hypocalcemic stimulus. In addition, the net synthesis rate would be greater due to decreased intracellular degradation of PTH. Prolonged hypocalcemia for hours or days may also stimulate PTH gene expression and proliferation of PTH cells, thus further increasing capacity. Whereas the model does not account for several of these complex mechanisms, it does provide for continuous synthesis of PTH, stimulatory PTH release from stores, and degradation of PTH to fragments (predominantly 7–84 amino acids in length) (Friedman and Goodman, 2006) within the vesicles. The present model is flexible and such mechanisms may be incorporated in future presentations once data are available.
The elimination rates estimated for the chelating agents are hybrid parameters encompassing distribution and elimination properties. The lack of concentration data required the PK to be inferred from the input rate of the agent and observed decrease in Ca2+ concentrations. A standard one-compartment linear model was sufficient for modeling the data. All parameters for the Ca2+ turnover model were estimated, with the exception of SC50_EGTA_2 in rats. A possible explanation for the poor identifiability of SC50_EGTA_2 could be the constraint imposed on this parameter by the use of a single elimination rate, kel_EGTA, across the two studies in rats. Attempts to use a linear function for stimulation of kout_Ca2+ were evaluated but were unsuccessful (data not shown). Smax_EGTA is the maximum increase in kout_Ca2+ that can be achieved. Although these were reasonably estimated, SC50_EGTA was relatively high and was fixed based on initial runs. A linear function for stimulation of kout_Ca2+ was successful for the human data. This might result from the chelating agent concentrations being restricted to the linear portion of a hyperbolic function. The rate of loss for Ca2+ in rats (kout_Ca2+ = 0.236 min-1) was predicted to be greater than that in humans (kout_Ca2+ = 0.0477 min-1), which was anticipated based on allometric principles. The traditional allometric equation used to scale rate constants across species. where W is the body weight and α is a coefficient term. Accordingly, the kout_Ca2+ in human is predicted to be 0.0603 min-1. Bone tissue is the major store of Ca2+ and turnover rates for bone in small animals are faster compared with those of higher organisms. In addition, the KD value in humans was estimated to be 1.25 mM and is in agreement with in vitro values for Ca2+ interacting with the CaSR. Data in rats were not sufficient to accurately estimate the KD and hence was fixed to the known in vitro value (Chattopadhyay, 2000). The Ca2+ turnover model does not include any feedback from PTH. It is known that PTH affects Ca2+ concentrations, and this effect is most evident for long-term elevation of PTH. Constant increase in PTH concentrations results in net bone resorption leading to increases in Ca2+ concentrations. However, for the current analysis, the chelating agents may partially override this homeostatic mechanism. In addition, the selected studies do not address long-term increases in PTH concentrations nor do the data suggest increases in Ca2+ concentrations.
Mean PTH concentrations in response to hypocalcemia were also well characterized for rats and humans. In rats, all parameters including maximum stimulation were estimated. Model predicted profiles suggest that the true peak (Cmax_PTH) and extent of stimulation of PTH might have been underestimated owing to the previous study designs. To further enhance model parameter estimability, PTH concentrations after subcutaneous administration in rats were included in the analysis. The proposed dual-absorption model well characterized the PTH PK data. A standard first-order absorption model was not adequate to capture PTH PK peak concentration, especially for the 15,000-ng/kg dose (data not shown). This empirical model has been applied elsewhere to recombinant human erythropoietin (Ramakrishnan et al., 2003), and allowed for an initial rapid rise in PTH concentrations governed by the zero-order input for a relatively small fraction of the dose (7% of the dose) for up to 5 min, and a slow first-order rate governing the terminal disposition. PTH concentrations after placebo and the lowest PTH dose were indistinguishable due to high assay variability. Bioavailability was not modeled due to the lack of intravenous dosing data. However, a noncompartmental analysis shows a less than proportional area under the curve, suggesting incomplete bioavailability at the higher doses (data not shown). Given its large molecular mass (9500 Da), PTH may undergo lymphatic uptake before entering the systemic circulation (Porter and Charman, 2000). Lymphatic transport coupled with incomplete bioavailability could explain rapid absorption and less than proportional exposure for higher doses. Another, albeit less likely explanation, might include feedback to the PTH-Ca2+ system resulting in slightly elevated concentrations of endogenous PTH due to lowering of Ca2+ in response to PTH administration. Although plausible, it is difficult to verify this possibility as existing assays do not distinguish between exogenous and endogenous PTH.
In humans, the degradation rate of PTH from the precursor compartment, ks, was roughly twice that of the PTH secretion rate, kp. The estimated value of ks (0.0172 min-1) is in agreement with the estimated value of 0.0169 min-1 reported by Momsen and Schwarz (1997). Our estimate of the steady-state basal PTH production rate constant (kp of 0.0107 min-1) is also similar to their reported estimate of 0.011 min-1 (Momsen and Schwarz, 1997). This is consistent with the literature, in which the concentration of late carboxyl-terminal PTH(39-84) fragment as roughly twice that of intact PTH(1-84) in normocalcemic volunteers (D'Amour et al., 1992). Hypocalcemia shifts this balance in favor of intact PTH. The model in its current form does not account for inhibition of PTH degradation within the precursor pool. Additional studies are needed to evaluate the relative proportion of intact and inactive PTH. The model describes emptying of PTH stores in response to hypocalcemia; however, it is possible that maximal stimulation or complete emptying may not have been achieved in these studies. Maximal stimulation is expected to be regulated by multiple factors apart from Ca2+ (Lewin et al., 1995). Mean PTH concentrations exhibited a baseline dependence for maximum stimulation in response to lowering of Ca2+, which was incorporated into the model (see eq. 8). There was a linear dependence in rats for maximum stimulation; however, the converse was observed in humans, where a greater PTH baseline resulted in less stimulation. For the different baselines (Fig. 4, A–C), the absolute concentrations after stimulation of PTH were roughly similar. The reasons for such an observation are not clearly apparent. One possibility could be the use of mean data, which does not account for interindividual variability. If the baseline dependence does exist in humans, then it probably represents a threshold for maximum PTH stimulation achieved in humans. The differences in baseline for humans may be attributed to several factors, including gender differences, but larger population studies are needed to ascertain model covariates.
Pharmacodynamic models that seem to be consistent across species may prove useful in translational medicine (Mager and Jusko, 2008). Given the good predictive performance of our model in rats and humans, we compared predictions of interspecies differences in Ca2+-PTH regulation. Normal adult rats seem to exhibit approximately a 2-fold greater stimulation of PTH compared with humans (Fig. 5). This prediction is only valid given the model assumptions are correct. This model provides a means for interpreting preclinical experimental outcomes and may prove useful in the development of future experimental therapeutics for this system.
In conclusion, a comprehensive mechanism-based PK/PD model was developed to describe in vivo PTH-Ca2+ homeostatic regulation and accounts for the underlying physiology regulating PTH secretion. A major advantage of this model is the use of Ca2+-CaSR receptor binding as a driving factor for stimulation of PTH. Such an approach may extend the application of the model to data resulting from the in vivo administration of CaSR antagonists in rats. The applicability of this model for predicting human data after exposure to such agents could enhance the decision-making process in a drug discovery and development setting. Furthermore, the proposed model may eventually be used to incorporate PD clinical endpoint data such as increase in bone mineral density in response to pulsatile PTH stimulation.
This study was funded in part by the University at Buffalo–Pfizer Strategic Alliance.
Article, publication date, and citation information can be found at http://jpet.aspetjournals.org.
ABBREVIATIONS: PTH, parathyroid hormone; CaSR, calcium-sensing receptor; PK, pharmacokinetics; PD, pharmacodynamics; CV, coefficient of variation.
- Received February 6, 2009.
- Accepted April 9, 2009.
- The American Society for Pharmacology and Experimental Therapeutics