Response to continuous and pulsatile PTH dosing: a mathematical model for parathyroid hormone receptor kinetics

A lipid-based delivery platform for thermo-responsive delivery of teriparatide

Teriparatide (and analogue peptides) are the only FDA approved anabolic treatments for osteoporosis. Current therapies are administered as a daily subcutaneous injection, which limits patient adherence and clinical efficacy. To achieve the desired anabolic effect, a controlled delivery system must ensure a pulsatile release profile over a prolonged period. Thermo-responsive formulations (e.g. liposomes) can undergo a temperature-related phase-transition which can allow active control of drug release. Herein, thermo-responsive liposomes were developed to permit control over teriparatide release rate through modulation of temperature. Entrapment of hydrophilic molecules, including peptides, within liposomes remains challenging due to the large volume of hydration. In this work, hydrophobic ion pairing was employed for the first time to enhance peptide entrapment within liposomes. The method resulted in a hydrophobic complex that achieved high teriparatide entrapment (>75 %) in sub-200 nm monodispersed liposomes. Hydrophobic ion pairing outperformed other entrapment approaches. Several liposomal formulations with transition temperatures between 38 and 50 °C were obtained by modulation of the phospholipid composition. In vitro assays demonstrated temperature-dependent release kinetics with faster rates of release observed at/above the transition temperature. The maintenance of biological activity of released teriparatide was demonstrated in a cell-based assay utilising the PTH1 receptor. Overall, this provides the first proof-of-concept of the suitability of thermo-responsive systems for pulsatile delivery of teriparatide and similar peptides.

Effects of PTH glandular and external dosing patterns on bone cell activity using a two-state receptor model-Implications for bone disease progression and treatment

Temporal aspects of ligand specificity have been shown to play a significant role in the case of pulsatile hormone secretion, as exemplified by parathyroid hormone (PTH) binding to its receptor (PTH1R), a G-protein-coupled receptor expressed on surfaces of osteoblasts and osteocytes. The latter binding reaction regulates intracellular signalling and subsequently modulates skeletal homeostasis via bone remodelling. PTH glandular secretion patterns dictate bone cellular activity. In healthy humans, 70% of PTH is secreted in a tonic fashion, whereas 30% is secreted in low-amplitude and high-frequency bursts occurring every 10-20 min, superimposed on the tonic secretion. Changes in the PTH secretion patterns have been associated with various bone diseases. In this paper, we analyse PTH glandular secretion patterns for healthy and pathological states and their link to bone cellular responsiveness (αR). We utilise a two-state receptor ligand binding model of PTH to PTH1R together with a cellular activity function which is able to distinguish various aspects of the stimulation signal including peak dose, time of ligand exposure, and exposure period. Formulating and solving several constrained optimisation problems, we investigate the potential of pharmacological manipulation of the diseased glandular secretion and via clinical approved external PTH injections to restore healthy bone cellular responsiveness. Based on the mean experimentally reported data, our simulation results indicate cellular responsiveness in healthy subjects is sensitive to the tonic baseline stimulus and it is 28% of the computed maximum responsiveness. Simulation results for pathological cases of glucocorticoid-induced osteoporosis, hyperparathyroidism, initial and steady state hypocalcemia clamp tests indicate αR values significantly larger than the healthy baseline (1.7, 2.2, 4.9 and 1.9-times, respectively). Manipulation of the pulsatile glandular secretion pattern, while keeping the mean PTH concentration constant, allowed restoration of healthy baseline values from these catabolic bone diseases. Conversely, PTH glandular diseases that led to maximum bone cellular responsiveness below the healthy baseline value can't be restored to baseline via glandular manipulation. However, external PTH injections allowed restoration of these latter cases.

The Interplay Between the Renin-Angiotensin-Aldosterone System and Parathyroid Hormone

The renin-angiotensin-aldosterone system (RAAS) is the regulatory system by which renin induces aldosterone production. Angiotensin II (Ang II) is the main effector substance of the RAAS. The RAAS regulates blood pressure and electrolyte balance by controlling blood volume and peripheral resistance. Excessive activation of the RAAS is an important factor in the onset of cardiovascular disease and the deterioration of this disease. The most common RAAS abnormality is primary aldosteronism (PA). Parathyroid hormone (PTH) is a peptide secreted by the main cells of the parathyroid gland, which promotes elevated blood calcium (Ca²⁺) levels and decreased blood phosphorus (Pi) levels. Excessive secretion of PTH can cause primary hyperparathyroidism (PHPT). Parathyroidism is highly prevalent in postmenopausal women and is often associated with secondary osteoporosis. PA and PHPT are common endocrine system diseases. However, studies have shown a link between the RAAS and PTH, indicating a positive relationship between them. In this review, we explore the complex bidirectional relationship between the RAAS and PTH. We also point out possible future treatment options for related diseases based on this relationship.

Computational model of the dual action of PTH - Application to a rat model of osteoporosis

This paper presents a pharmacokinetic/pharmacodynamic (PK/PD) model of the action of PTH(1-34) on bone modelling and remodelling, developed for quantitatively investigating the dose- and administration pattern-dependency of the bone tissue response to this drug. Firstly, a PK model of PTH(1-34) was developed, accounting for administration via subcutaneous injections. Subsequently, the PK model was coupled to a (mechanistic) bone cell population model of bone modelling and remodelling, taking into account the effects of PTH(1-34) on the differentiation of lining cells into active osteoblasts, on the apoptosis of active osteoblasts, and on proliferation of osteoblast precursors, as well as on the key regulatory pathways of bone cell activities. Numerical simulations show that the coupled PK/PD model is able to distinguish between continuous and intermittent administration patterns of PTH(1-34), in terms of yielding both catabolic bone responses (if drug administration is carried out continuously) and anabolic bone responses (if drug administration is carried out intermittently). The model also features a non-linear relation between bone gain and drug dose (as known from experiments); doubling the dose from 80 μg/kg/day to 160 μg/kg/day induced a 1.3-fold increase of the bone volume-to-total volume ratio. Furthermore, the model presented in this paper confirmed that bone modelling represents an essential mechanism of the anabolic response of bone to PTH(1-34) administration in rat models, and that the large amount of bone formation observed in such models cannot be explained via remodelling alone.

Dynamics of Bone Cell Interactions and Differential Responses to PTH and Antibody-Based Therapies

We propose a mathematical model describing the dynamics of osteoblasts and osteoclasts in bone remodeling. The goal of this work is to develop an integrated modeling framework for bone remodeling and bone cell signaling dynamics that could be used to explore qualitatively combination treatments for osteoporosis in humans. The model has been calibrated using 57 checks from the literature. Specific global optimization methods based on qualitative objectives have been developed to perform the model calibration. We also added pharmacokinetics representations of three drugs to the model, which are teriparatide (PTH(1-34)), denosumab (a RANKL antibody) and romosozumab (a sclerostin antibody), achieving excellent goodness-of-fit of human clinical data. The model reproduces the paradoxical effects of PTH on the bone mass, where continuous administration of PTH results in bone loss but intermittent administration of PTH leads to bone gain, thus proposing an explanation of this phenomenon. We used the model to simulate different categories of osteoporosis. The main attributes of each disease are qualitatively well captured by the model, for example changes in bone turnover in the disease states. We explored dosing regimens for each disease based on the combination of denosumab and romosozumab, identifying adequate ratios and doses of both drugs for subpopulations of patients in function of categories of osteoporosis and the degree of severity of the disease.

Regulatory Perspectives in Pharmacometric Models of Osteoporosis

Osteoporosis is a disorder of the bones in which they are weakened to the extent that they become more prone to fracture. There are various forms of osteoporosis: some of them are induced by drugs, and others occur as a chronic progressive disorder as an individual gets older. As the median age of the population rises across the world, the chronic form of the bone disease is drawing attention as an important worldwide health issue. Developing new treatments for osteoporosis and comparing them with existing treatments are complicated processes due to current acceptance by regulatory authorities of bone mineral density (BMD) and fracture risk as clinical end points, which require clinical trials to be large, prolonged, and expensive to determine clinically significant impacts in BMD and fracture risk. Moreover, changes in BMD and fracture risk are not always correlated, with some clinical trials showing BMD improvement without a reduction in fractures. More recently, bone turnover markers specific to bone formation and resorption have been recognized that reflect bone physiology at a cellular level. These bone turnover markers change faster than BMD and fracture risk, and mathematically linking the biomarkers via a computational model to BMD and/or fracture risk may help in predicting BMD and fracture risk changes over time during the progression of a disease or when under treatment. Here, we discuss important concepts of bone physiology, osteoporosis, treatment options, mathematical modeling of osteoporosis, and the use of these models by the pharmaceutical industry and the Food and Drug Administration.

Optimal dosing and delivery of parathyroid hormone and its analogues for osteoporosis and hypoparathyroidism - translating the pharmacology

In primary hyperparathyroidism (PHPT), bone loss results from the resorptive effects of excess parathyroid hormone (PTH). Under physiological conditions, PTH has actions that are more targeted to homeostasis and to bone accrual. The predominant action of PTH, either catabolic, anabolic or homeostatic, can be understood in molecular and pharmacokinetic terms. When administered intermittently, PTH increases bone mass, but when present continuously and in excess (e.g. PHPT), bone loss ensues. This dual effect of PTH depends not only on the dosing regimen, continuous or intermittent, but also on how the PTH molecule interacts with various states of its receptor (PTH/PTHrP receptor) influencing downstream signalling pathways differentially. Altering the amino-terminal end of PTH or PTHrP could emphasize the state of the receptor that is linked to an osteoanabolic outcome. This concept led to the development of a PTHrP analogue that interacts preferentially with the transiently linked state of the receptor, emphasizing an osteoanabolic effect. However, designing PTH or PTHrP analogues with prolonged state of binding to the receptor would be expected to be linked to a homeostatic action associated with the tonic secretory state of the parathyroid glands that is advantageous in treating hypoparathyroidism. Ideally, further development of a drug delivery system that mimics the physiological tonic, circadian, and pulsatile profile of PTH would be optimal. This review discusses basic, translational and clinical studies that may well lead to newer approaches to the treatment of osteoporosis as well as to different PTH molecules that could become more advantageous in treating hypoparathyroidism.

Pharmacokinetics and osteogenic potential of PEGylated NELL-1 in vivo after systemic administration

Osteoporosis is a skeletal disorder attributable to an imbalance in osteoblast and osteoclast activity. NELL-1, a secretory protein that promotes osteogenesis while suppressing osteoclastic activity, holds potential as an osteoporosis therapy. Recently, we demonstrated that PEGylation of NELL-1 significantly improves its thermostability while preserving its bioactivity in vitro. However, the effect of PEGylation on the pharmacokinetics and osteogenic potential of NELL-1 in vivo have yet to be investigated. The present study demonstrated that PEGylation of NELL-1 significantly increases the elimination half-life time of the protein from 5.5 h to 15.5 h while distributing more than 2-3 times the amount of protein to bone tissues (femur, tibia, vertebrae, calvaria) in vivo when compared to naked NELL-1. In addition, microCT and DXA analyses demonstrated that systemic NELL-PEG therapy administered every 4 or 7 days significantly increases not only femoral and lumbar BMD and percent bone volume, but also new bone formation throughout the overall skeleton after four weeks of treatment. Furthermore, immunohistochemistry revealed increased osteocalcin expression, while TRAP staining showed reduced osteoclast numbers in NELL-PEG groups. Our findings suggest that the PEGylation technique presents a viable and promising approach to further develop NELL-1 into an effective systemic therapeutic for the treatment of osteoporosis.

Regenerative orthopaedics: in vitro, in vivo...in silico

In silico, defined in analogy to in vitro and in vivo as those studies that are performed on a computer, is an essential step in problem-solving and product development in classical engineering fields. The use of in silico models is now slowly easing its way into medicine. In silico models are already used in orthopaedics for the planning of complicated surgeries, personalised implant design and the analysis of gait measurements. However, these in silico models often lack the simulation of the response of the biological system over time. In silico models focusing on the response of the biological systems are in full development. This review starts with an introduction into in silico models of orthopaedic processes. Special attention is paid to the classification of models according to their spatiotemporal scale (gene/protein to population) and the information they were built on (data vs hypotheses). Subsequently, the review focuses on the in silico models used in regenerative orthopaedics research. Contributions of in silico models to an enhanced understanding and optimisation of four key elements-cells, carriers, culture and clinics-are illustrated. Finally, a number of challenges are identified, related to the computational aspects but also to the integration of in silico tools into clinical practice.

A theoretical study of bone remodelling under PEMF at cellular level

Pulsed electromagnetic field (PEMF) devices have been used clinically to slow down osteoporosis and accelerate the healing of bone fractures for many years. However, the underlying mechanism by which bone remodelling under PEMF is regulated remains poorly understood. In this paper, a mathematical model of bone cell population of bone remodelling under PEMF at cellular level is developed to address this issue for the first time. On the basis of this model and control theory, parametric study of control mechanisms is carried out and a number of possible control mechanisms are identified. These findings will help further the understanding of bone remodelling under PEMF and advance therapies and pharmacological developments in clinical trials.

Cinacalcet treatment of primary hyperparathyroidism

Although parathyroidectomy remains the only curative approach to most primary hyperparathyroidism cases, medical treatment with cinacalcet HCl has been proven to be a reasonable alternative for several patient subgroups. Cinacalcet almost always controls hypercalcemia and hypophosphatemia sufficiently. PTH levels are lowered, and cognitive parameters improve. While an increase in bone mineral density DEXA scan scores was not demonstrated in cinacalcet trials, the same applies to more than half of patients after parathyroidectomy. Medical therapy should be first choice in patients with hyperplasia in all glands rather than an isolated adenoma (10-15%), patients with persisting HPT following unsuccessful surgery or inoperable cases due to comorbidities, and patients detected in lab screens for hypercalcemia before developing symptoms who should be treated early but are usually reluctant to undergo surgery. Nephrolithiasis was not found to occur more frequently in cinacalcet trial groups, but urine calcium excretion as one major risk factor of this complication of primary HPT may increase on cinacalcet. Patients carrying the rs1042636 polymorphism of the calcium-sensing receptor gene respond more sensitively to cinacalcet and have a higher risk of calcium stone formation. Cinacalcet is usually administered twice daily but three or four doses per day should be discussed to mimic the beneficial pulsatile PTH-pattern.

Mathematical modeling in bone biology: from intracellular signaling to tissue mechanics

Although conceptual and experimental models are historically well incorporated in bone biology studies, mathematical modeling has been much less-frequently utilized. This review aims to introduce mathematical modeling to readers who are not familiar with the concept underlying this methodology, to outline how mathematical models can help to improve current understanding of bone biology and to discuss examples where mathematical modeling was used to provide new insights into important questions of bone biology.

Parathyroid hormone (1-34)-coated microneedle patch system: clinical pharmacokinetics and pharmacodynamics for treatment of osteoporosis

OBJECTIVES

To evaluate the clinical PK/PD of PTH(1-34) delivered by a novel transdermal drug-coated microneedle patch system (ZP-PTH) for the treatment of osteoporosis.

METHODS

Phase 1 PK studies evaluated the effect of site of administration, patch wear time and dose in normal volunteers, ages 40-85 yrs. Phase 2 was conducted in post-menopausal women with osteoporosis to determine the patch dose response compared to placebo patch and FORTEO® injection.

RESULTS

Phase 1 ZP-PTH patch delivery demonstrated a rapid PTH plasma pulse profile with T(max) 3 times shorter and apparent T(1/2) 2 times shorter than FORTEO®. In Phase 2, ZP-PTH 20, 30 and 40 µg doses showed a proportional increase in plasma PTH AUC. Inter-subject and intra-subject AUC variability was similar for all patch doses and comparable to injection. All patch doses produced a significant increase in spine bone mineral density. Unexpectedly, ZP-PTH also produced an early increase in hip bone mineral density, an effect not observed with the injection.

CONCLUSIONS

These studies suggest that this novel ZP-PTH patch system can deliver a consistent and therapeutically relevant PTH PK profile. Based on encouraging Phase 2 safety and efficacy data, the program is advancing into a pivotal Phase 3 clinical study.

A physiologically based mathematical model of integrated calcium homeostasis and bone remodeling

Bone biology is physiologically complex and intimately linked to calcium homeostasis. The literature provides a wealth of qualitative and/or quantitative descriptions of cellular mechanisms, bone dynamics, associated organ dynamics, related disease sequela, and results of therapeutic interventions. We present a physiologically based mathematical model of integrated calcium homeostasis and bone biology constructed from literature data. The model includes relevant cellular aspects with major controlling mechanisms for bone remodeling and calcium homeostasis and appropriately describes a broad range of clinical and therapeutic conditions. These include changes in plasma parathyroid hormone (PTH), calcitriol, calcium and phosphate (PO4), and bone-remodeling markers as manifested by hypoparathyroidism and hyperparathyroidism, renal insufficiency, daily PTH 1-34 administration, and receptor activator of NF-kappaB ligand (RANKL) inhibition. This model highlights the utility of systems approaches to physiologic modeling in the bone field. The presented bone and calcium homeostasis model provides an integrated mathematical construct to conduct hypothesis testing of influential system aspects, to visualize elements of this complex endocrine system, and to continue to build upon iteratively with the results of ongoing scientific research.

Evaluation of the role of FGF23 in mineral metabolism

Fibroblast growth factor 23 (FGF23) has recently been identified as a critical regulatory factor in phosphate (P) metabolism. Although the exact molecular mechanism of FGF23 synthesis through sensing the concentration of P is yet to be determined, experimental and clinical data indicate the influential role of FGF23 in P and calcium (Ca) homeostasis. Here, we extended our previous mathematical model in calcium regulation and examined the conceivable roles of FGF23 in mineral metabolism. We assumed that the level of FGF23 was controlled through the concentrations of P and calcitriol in serum, and its actions such as lowering of the renal threshold for P, inhibition of the production of calcitriol in the kidney tubule, and inhibition of the production of parathyroid hormone (PTH) were included. Comparisons between the models with and without FGF23 demonstrate a complex interplay of FGF23 with calcitriol and PTH. In consistent with the model, our in vitro experimentation indicates that expression of FGF23 is activated in the presence of P though a G-protein linked receptor. We expect that further efforts on modeling and experimental evaluation would contribute to diagnosing patients with metabolic diseases such as osteoporosis and chronic kidney diseases, and developing FGF23-linked treatment strategies.

Motivations and methods for analyzing pulsatile hormone secretion

Endocrine glands communicate with remote target cells via a mixture of continuous and intermittent signal exchange. Continuous signaling allows slowly varying control, whereas intermittency permits large rapid adjustments. The control systems that mediate such homeostatic corrections operate in a species-, gender-, age-, and context-selective fashion. Significant progress has been made in understanding mechanisms of adaptive interglandular signaling in vivo. Principal goals are to understand the physiological origins, significance, and mechanisms of pulsatile hormone secretion. Key analytical issues are: 1) to quantify the number, size, shape, and uniformity of pulses, nonpulsatile (basal) secretion, and elimination kinetics; 2) to evaluate regulation of the axis as a whole; and 3) to reconstruct dose-response interactions without disrupting hormone connections. This review will focus on the motivations driving and the methodologies used for such analyses.