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 Ca2+. 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 Ca2+ binding, and a second source released more slowly following hours of reduced Ca2+ 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.
Japan Tobacco Inc. developed JTT-305/MK-5442, an orally bioavailable, high-affinity calcium-sensing receptor (CaSR) allosteric antagonist that is being investigated for the treatment of osteoporosis.[1-5] JTT-305/MK-5442 binds reversibly to CaSR and does not share binding sites with Ca2+. The binding ability of 3H-labeled JTT-305/MK-5442 was studied using a cell membrane fraction of African green monkey kidney-derived cells (COS-7) expressing the human CaSR. We can express the propensity of 3H-labeled JTT-305/MK-5442 to bind to human CaSR as the dissociation constant (Kd) in the presence of excessive unlabeled JTT-305/MK-5442. This dissociation constant is 6.2 ± 0.5 nmol/L (mean ± SE, n = 3; Merck unpublished data). In response to this perceived hypocalcemia, the parathyroid gland releases parathyroid hormone (PTH) to trigger release of calcium from bone. Although sustained elevation of PTH has long been associated with bone loss, cyclical administration of short bursts of PTH has been found to stimulate bone formation.[6-8] Although the optimal duration and magnitude of elevated PTH levels to stimulate maximal bone density increases has not been quantified in humans, studies indicate that a profile with a rapid and high Cmax followed by a rapid return to baseline is preferred. Data are available for injectable synthetic PTH such as PTH(1-84), with a t1/2 of approximately 2.5 hours, for the treatment of osteoporosis. One study focusing on the shape of the PTH concentration-curve in relation to change in bone mass indicated that the duration of the elevation of PTH is likely the primary factor in determining whether net bone formation results from PTH administration, with Cmax and the area under the plasma level-time curve (AUC) of PTH being secondary. A study in humans comparing PTH(1-34) injections with a transdermal patch found that greater increases in bone mineral density (BMD) resulted from a PTH(1-34) profile with a higher Cmax and more rapid return to baseline. In order to develop optimal PTH-based therapies for osteoporosis, it is important to characterize the kinetics of PTH. Furthermore, for PTH therapies that are based on endogenous stores of PTH rather than on exogenous administration, gaining an understanding of the relationship between the pharmacokinetics (PK) of the CaSR allosteric antagonist and the resulting PTH release profile is critical to designing an optimal molecule, understanding both the absorption and elimination kinetics, and selecting the correct dose.
Single-dose and multiple-dose phase I studies showed that JTT-305/MK-5442 exhibits dose-proportional kinetics, and that PTH concentration-time profiles are dose-dependent. The Cmax of PTH increases with the dose of JTT-305/MK-5442, but at a rate that diminishes with dose, reaching a plateau between doses of 50 and 100 mg., the doses that were used in the single-dose Japanese study. PTH is initially released in a rapid burst, reaching a peak concentration followed by a return toward baseline. Initially, PTH levels decline rapidly, on the order of those reported for PTH(1-84). Approximately 4 hours after dosing, plasma PTH levels stop declining for some time, which produces a “shoulder,” and in some cases a small secondary peak, in the PTH concentration-time profiles. The duration of this PTH shoulder, and the magnitude of the secondary peak, when it exists, increases with the dose of JTT-305/MK-5442. At doses of 5 mg, little or no shoulder is apparent, whereas at 100 mg, this shoulder results in PTH levels above baseline throughout the 24-hour dosing interval, and can also appear as a secondary peak.
We developed a semimechanistic, nonpopulation model that describes the time-course of the relationship between JTT-305/MK-5442 and plasma PTH concentration. The parathyroid gland is known to respond rapidly—within seconds—to decreases in serum Ca2+ levels with rapid release of preformed PTH from secretory vesicles in the gland's chief cells.[12, 13] These stores are exhausted in 60 to 90 minutes. Following this initial fast response of the PTH gland, if periods of hypocalcemia persist beyond 30 minutes, the body begins to reduce the fraction of PTH that is degraded intracellularly, resulting in an increase in secretion of bioactive PTH into plasma, and after several hours begins to increase gene transcription and synthesis of PTH precursor.[8, 14] Following extended periods of hypocalcemia, lasting days or longer, the parathyroid gland eventually increases its production capacity through an increase in gland mass. In order to describe the initial sharp PTH peak following JTT-305/MK-5442 administration and the later PTH shoulder, we included in the model a rapid secretory vesicle source of PTH as well as the slower secretion resulting from decreased intracellular PTH degradation.
Subjects and Methods
Mean concentration data for JTT-305/MK-5442 and PTH were obtained from a multiple-dose study in healthy U.S. postmenopausal women (PMW). JTT-305/MK-5442 was administered at doses of 5, 10, 15, or 20 mg with or without vitamin D and calcium supplements for 14 days. Serial plasma samples were drawn at predose (0 hour), and at 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 6, 8, and 12 hours postdose on days 1, 3, and 14 for assessment of JTT-305/MK-5442 and PTH concentrations; additional samples were drawn prior to dosing on day 2, and on days 4 through 13 (ie, trough concentrations), and at 24, 36, and 48 hours following the final day 14 dose. In this work we used mean values of the day 14—steady-state—data.
The PK of JTT-305/MK-5442 was described adequately by a one-compartment model with first-order absorption and first-order elimination (see Fig. 1A). The concentration of JTT-305/MK-5442 in the plasma, M(t), was modeled by Eq. (1):
where F is bioavailability, V is the volume of distribution, D is the dose in nanomoles, k1 is the absorption rate constant, and k2 is the elimination rate constant. Table 1 presents the fitted model parameters. Although the concentration-time profiles for JTT-305/MK-5442 indicate the presence of one or more peripheral compartments, to facilitate fitting of the parameters with the simplest model, we did not include these in the model. To test the impact of the one-compartment simplification on the PK model, we used the observed JTT-305/MK-5442 concentration values as model inputs and compared predicted PTH values with those predicted when the PK model was used. We found no substantial differences in the fits of PTH data.
|k1||1.31||hour−1||JTT-305/MK-5442 absorption rate constant|
|k2||0.29||hour−1||JTT-305/MK-5442 clearance rate constant|
|F/V||38.19||nM/mg||Bioavailability/JTT-305/MK-5442 volume of distribution|
|k3||0.45||hour−1||Rate constant for transfer of JTT-305/MK-5442 between plasma and the effect compartment|
|k6||0.05||hour−1||Rate constant for refill of the PTH rapid reservoir|
|KR,Max||0.922||hour−1||Maximum PTH secretion rate from the rapid reservoir|
|KR,50||230||nM||EC50 for the secretion rate from the rapid reservoir|
|γR||2||–||Hill coefficient for secretion rate from rapid reservoir|
|KS,Max||72||pM||Maximum PTH secretion rate (zero order) from slow reservoir|
|KS,50||270||nM||EC50 for the filling rate of the slow reservoir|
|γS||5||–||Hill coefficient the filling rate of the slow reservoir|
|k4||0.4174||hour−1||Rate constant for PTH secretion from the slow reservoir|
|k5||8.316||hour−1||First-order rate of elimination of PTH from plasma|
|R0||212.8||pM||Baseline plasma equivalent concentration of PTH in rapid reservoir|
|S0||46.75||pM||Baseline plasma equivalent concentration of PTH in slow reservoir|
The dynamics of PTH release and reservoir maintenance are depicted in Fig. 1B.
In order to account for the two characteristic PTH decay times that are present in the data we introduced an effect compartment, into which JTT-305/MK-5442 partitions in a first-order transfer. The amount of drug that partitions is assumed to be a small fraction of the JTT-305/MK-5442 in the central compartment and is therefore neglected in the mass balance of the drug in plasma. The drug in this effect compartment determines the refill rate of the slow PTH reservoir, and introduces a time delay in the drug's effect on this reservoir. We let E(t) be the plasma equivalent concentration of the drug in the effect compartment, and we let k3 be the first-order rate at which the drug enters the effect compartment from plasma. We obtain the equation:
For this model we assumed that the binding of JTT-305/MK-5442 to CaSR equilibrates rapidly. We also neglected fluctuations in Ca2+ concentrations; these were too small and the data on them too sparse for us to incorporate them in the model fit. We hypothesized that PTH or its precursor, is produced and stored in two intracellular reservoirs. One reservoir is able to respond rapidly to large changes in CaSR binding, either by endogenous calcium or, in this case, by JTT-305/MK-5442. This rapid reservoir is depleted at a rate that, in order to account for the reservoir's limited capacity, is a nonlinear sigmoidal function of the plasma concentration of JTT-305/MK-5442:
Here, KR,Max is the Emax with units of reciprocal hours, KR,50 is the half maximal effective concentration (EC50), with units of nM, and γR is the Hill exponent. The second, slow reservoir releases PTH to the plasma compartment with first-order kinetics. The slow reservoir is filled with zero-order kinetics at a baseline rate that is independent of JTT-305/MK-5442 concentration, and with zero-order kinetics at a rate that is a nonlinear sigmoid function of the concentration of JTT-305/MK-5442 in the effect compartment:
Here, KS,Max is the Emax with units of reciprocal hours, KS,50 is the EC50, with units of nM, and γs is the Hill exponent.
We let P(t) in pg/ml be the rise in plasma PTH concentration above baseline. We let R(t) and S(t), both in pg/mL, be the plasma equivalent concentrations of PTH in the rapid and slow reservoirs, respectively.
The mass balance of PTH in our model is determined by six interactions:
- PTH is transferred from the rapid reservoir to plasma at a rate ρ(M)R.
- PTH is transferred to plasma from the slow reservoir in a first-order transfer with rate constant k4.
- Plasma PTH is cleared in a first-order clearance reaction with rate constant k5.
- The rapid release reservoir is driven toward its baseline level, R0, at the rate k6 (R0 − R), which is proportional to the difference between its PTH content and its baseline.
- The slow release reservoir is driven toward its baseline level, S0, at the rate k4 (S0 − S), which is proportional to the difference between its PTH content and its baseline.
- The slow release reservoir is replenished at an additional rate σ(E) because of JTT-305/MK-5442 in the effect compartment.
These interactions are expressed in the following equations:
The differential equations, Eqs. (1), (2), (5), (6), and (7), along with the Hill function definitions of Eqs. (3) and (4), and with the initial conditions, M(0) = E(0) = 0, P(0) = P0, R(0) = R0, S(0) = S0, define our model. Note that the initial values of plasma PTH, P0, and the concentration of the slow reservoir, S0, are constrained by the steady-state condition k4S0 − k5P0 = 0, which follows from Eq. (5) in the absence of the drug.
We have not accounted for diurnal variations in baseline PTH levels in the model. We did not have sufficient data to characterize these variations, and the drug-induced changes in PTH, which exceed 300%, are much greater than the diurnal fluctuations of about 10% around the baseline observed in endogenous PTH levels.
We fit the differential equations simultaneously to mean JTT-305/MK-5442 and PTH plasma concentrations using a gradient-based nonlinear least squares approach. To fit the data we calculated mean data as arithmetic mean concentrations at a nominal postdose sampling times across all subjects.
We then used the model parameters that were fit to observed data from U.S. PMW at doses ranging from 5 to 20 mg to predict PTH profile following doses of 50 and 100 mg. We compared these results with observed data at these higher doses in healthy Japanese males.
Figures 2 and 3 show actual and computed population mean steady-state JTT-305/MK-5442 plasma concentrations for doses of 5, 10, 15, and 20 mg in U.S. PMW. The one-compartmental approximation of JTT-305/MK-5442 PK tends to fit better at early times, ie, times less than 8 hours, which corresponds with the most dynamic portion of the PTH curve. We observed no significant effect on PTH predictions when we substituted PK concentration data for the PK parameters in the PTH model. Thus we decided that a one-compartmental model was adequate to capture the critical portion of the PK profile of JTT-305/MK-5442 although the terminal half-life is not well described.
Figure 4 shows actual and computed mean plasma PTH concentration-time profiles in response to JTT-305/MK-5442 doses of 5, 10, 15, and 20 mg in U.S. PMW. Figure 5 shows dose-dependent changes in the behavior of the dose-response curves in both observed data and our model's predictions. One interesting aspect of the data is the appearance of the secondary peak. This peak is particularly pronounced at doses greater than 15 mg. The appearance of the secondary peak in the PTH response makes the PTH profiles shown in Fig. 4 interesting and nonstandard. Furthermore, we see that the PTH response depends not only on the drug concentration but also on whether the drug concentration is increasing or decreasing; the response is affected by the time history of the drug concentration, especially at higher doses. Also, we see that the PTH peak precedes the drug concentration peak (see Fig. 5). Our model is able to accurately predict the dose-dependence in both PTH Tmax and Cmax, and it also predicts the extent and duration of the PTH shoulder.
Figure 6 shows actual and predicted mean PTH plasma concentration-time profiles in response to JTT-305/MK-5442 doses of 50 and 100 mg. The model prediction is based on fit of U.S. PMW, whereas the observed data are in healthy Japanese males, whose PTH levels tended to be somewhat higher than those in the U.S. study of PMW. Regardless, the model predicts the PTH peak (Fig. 7) and shoulder behavior at these higher doses well. It appears that the model may under predict the time above the upper level of normal at higher doses, resulting in underprediction of 24-hour PTH levels. Additional data between 12 and 24 hours could improve the model fit to these later time points.
The two-reservoir semimechanistic model of PTH appears to predict the key dynamic features and dose-response of observed PTH levels. There is biological evidence both specifically in the parathyroid gland and other hormonal-control systems in general to support this model structure.
Our observations of PTH concentration-time profiles relative to JTT-305/MK-5442 concentration-time profiles in clinical studies indicated the presence of a dose-dependent time-lapse between cause and effect (see Fig. 5). Although JTT-305/MK-5442 Tmax remains constant across doses, PTH levels peak at progressively earlier times as JTT-305/MK-5442 dose increases. This results in the increasingly large dose-dependent loops observed in Fig. 5, which warrants an indirect response model that incorporates a drug concentration effect. Furthermore, a dose-dependent shoulder in PTH levels was also observed, with an initial rapid decline from peak followed by a pause in decline or even a small secondary peak before PTH levels returned to baseline.
Abraham and colleagues proposed a single precursor-dependent indirect response model to characterize PTH-calcium homeostasis in rats and humans. That model does not account for the storage capacity of the PTH gland and the delay caused by PTH synthesis after a rapid depletion of the PTH reservoir. Ritchie and colleagues investigated the secretory patterns of PTH using a sequential reverse hemolytic plaque assay. They found that parathyroid cells cycled between two phases, a resting (nonsecretory) phase and a secretory phase. In developing our model we searched for mechanisms that could account for the nonmonotonic behavior of the PTH response, in which a shoulder appears in the PTH profiles for the higher JTT-305/MK-5442 doses (15 and 20 mg in Fig. 4; 50 and 100 mg in Fig. 6). The two-stage synthesis process of PTH we propose in this model includes dose-dependent reservoir depletion that captures the average PTH shoulder for the higher doses, as we show in Figs. 4 and 6.
In order to capture both the time history of the drug concentration and the dose-dependent shoulder in PTH levels in our model, we included features that fit the classification of a precursor-dependent indirect response model with two precursors responding at different speeds, one fast and one slow. The fast precursor adds a stimulatory Emax sigmoidal model with a Hill exponent of five to the PTH response (model type VI according to the classification scheme of Mager and colleagues). The slow precursor contributes to the PTH response with first-order kinetics; ie, a monoexponential model.
Our model is consistent with the data, and has a dose-dependent effect on the loop as seen by the PTH profiles in Fig. 5. Furthermore, we simulated the data for higher drug concentrations (50 and 100 mg), using the parameters obtained from the lower-dose data (5, 10, 15, and 20 mg), and compared it with available clinical observations. The observed clinical data were consistent with the model. They also supported the hypothesis of a limited capacity reservoir that is exhausted at moderate doses of JTT-305/MK-5442, thus accounting for the absence of a significant increase in the PTH concentration even when the drug dose is increased to 100 mg from 50 mg. The PTH shoulder that occurs at higher doses is undesirable—PTH elevation above baseline for longer durations at higher doses results in elevations in serum calcium with repeated dosing (a safety parameter assessed in the trial in U.S. PMW); the shoulder promotes bone resorption.[8, 21, 22] This suggests that if the absolute Cmax of PTH is critical to bone formation, therapy via the CaSR mechanism may be limited by endogenous stores of PTH; that the potency of such a drug, and the rates at which it absorbs and binds to the CaSR, may be irrelevant.
The dynamic relationship between CaSR antagonism and the resulting profile of PTH concentrations in blood is influential for both the efficacy and also tolerability of JTT-305/MK-5442, and, we presume, other CaSR antagonists. Regarding efficacy, the ability of increased PTH levels to have either an anabolic effect or a catabolic effect on bone metabolism needs to be accounted for. If, as suggested by data in rats, the Cmax of PTH is less important than time above the upper limit of normal for optimizing bone formation, then molecules with faster elimination rate constants that do not stimulate the secondary sources of PTH production could improve efficacy. This observation could be important for dose selection. For JTT-305/MK-5442, a small but significant increase in mean lumbar spine BMD was observed following 3 months of treatment in Japanese PMW at a daily dose of 10 mg, whereas at a 20-mg dose the mean BMD increase was numerically lower and not significant, suggesting a U-shaped dose-response curve. The observations of a lower response at a higher dose could be caused by the longer duration of PTH above the upper limit of normal. Longer-duration clinical studies have resulted in BMD gains that are minimal and specific to some but not all common sites of BMD measurement. Specifically, a 1-year study in Japanese PMW showed only small gains in lumbar spine BMD and no significant gains at other sites, whereas a Phase II trial of the CaSR antagonist ronacaleret demonstrated only small gains at the lumbar spine and loss of BMD at hip sites. These results with CaSR antagonist molecules contrast with those observed with exogenously administered PTH in which substantial gains of BMD are observed, and in which the PTH concentration-time profile consists of a rapid, sharp Cmax and then a rapid return to the normal range. These examples illustrate the importance of PK/PTH modeling for the development of CaSR antagonists.
The impact of the PTH profile is not limited to efficacy. A common, mechanism-based side effect of CaSR stimulation is hypercalcemia. This is caused in part by PTH secretion, which under normal physiologic conditions occurs in response to low serum Ca2+ in order to raise serum Ca2+ back to the normal range. Examination of the time above the upper limit of normal and serum calcium values from early clinical trials for JTT-305/MK-5442 suggests a causal relationship. In order to minimize this adverse effect, it will be desirable to shorten the time for which PTH is greater than the upper limit of normal via either dose selection or molecular properties of the antagonist. The results in this study show the applicability of the predictions to optimize JTT-305/MK-5442 dose with respect to PTH peak/shoulder, to optimize therapeutic benefit.
In conclusion, we have described a model of the dynamic pharmacokinetic/pharmacodynamic (PK/PD) relationship between the CaSR antagonist JTT-305/MK-5442 and PTH. This model will help us select dosing regimens and strategies to maximize the capacity of JTT-305/MK5442 to increase bone mass. It will thus aid in the development of this potential anabolic treatment for postmenopausal osteoporosis.
AC, KM, WC, RPS, and AD are employees of Merck Sharp & Dohme Corp. and may own stock options in the company. DSR has received consultancy fees from Merck Sharp & Dohme Corp. TI is an employee of Japan Tobacco. SMP has no conflicts of interest.
We thank Drs. Aubrey Stoch, Boyd B. Scott, and Sandy Allerheiligen for their careful review of this manuscript and for their assistance in preparing it.
Authors' roles: Study design: WC, AD, SMP, TI. Study conduct: WC, AD, SMP, TI. Data interpretation: AC, KM, DSR, RPS, WC. Drafting manuscript: AC, KM, DSR, WC. Revising manuscript content: AC, KM, DSR, RPS, WC, AD, SMP, TI. Approving final version of manuscript: AC, KM, DSR, RPS, WC, AD, SMP, TI. AC takes responsibility for the integrity of the data analysis.