Computational model of the dual action of PTH — Application to a rat model of osteoporosis
Introduction
The hormone secreted by the parathyroid glands, usually referred to as parathyroid hormone, or, in short, PTH, is known to be essential for calcium homeostasis. In particular, it is able to stimulate increased osteoclast activity, which, in turn, leads to the release of calcium ions stored in the bone matrix (Mundy and Guise, 1999). On the other hand, PTH has also been identified as a key substance in pharmacological applications. PTH peptides, namely PTH(1-34), also known as teriparatide, and PTH(1-84), were the first anabolic agents approved by drug administration agencies for the treatment of degenerative bone diseases (such as osteoporosis), see, e.g., (U.S. Food and Drug Administration, Drug, 2019, European Medicines Agency, 2019). However, depending on the applied administration pattern (i.e., on the periodicity of its exposure onto the body), PTH may induce fundamentally opposed bone responses (Silva and Bilezikian, 2015).
Continuous infusion of PTH and conditions such as hyperparathyroidism lead to catabolic responses, hence to increased bone resorption (Potts, 2005). In more detail, it is known from both in vitro and in vivo studies that PTH does not directly activate osteoclasts, but it enhances bone resorption indirectly, via the RANK-RANKL-OPG pathway (McSheehy, Chambers, 1986, Xiong, O’Brien, 2012, Hofbauer, Schoppet, 2004). In this context, it should be mentioned that receptors of PTH were found on osteoblast precursor cells, active osteoblasts, lining cells and osteocytes (Bringhurst et al., 2016). Continuous infusion of PTH actually leads to modulation of the RANK-RANKL-OPG pathway towards an increased RANKL/OPG ratio, thereby promoting osteoclastogenesis and inducing, in further consequence, increased bone resorption (Lee, Lorenzo, 1999, Huang, Sakata, Pfleger, Bencsik, Halloran, Bikle, Nissenson, 2004).
In contrast, daily subcutaneous injections of PTH are known to lead to anabolic responses in bone tissue, hence to increased bone formation (Dempster, Cosman, Parisien, Shen, Lindsay, 1993, Jilka, 2007). Similar to continuous PTH exposure, intermittent administration of PTH causes an increased bone turnover. However, in the latter case, PTH acts directly on osteoblasts to promote osteoblastogenesis. Namely, the anti-apoptotic action of PTH involves the phosphorylation and deactivation of the pro-apoptotic protein Bad, increased expression of survival genes like B-cell lymphoma 2 (Bcl-2), increased expression of Runt-related transcriptor factor 2 (Runx2), downregulation of the apoptosis inducer cell cycle and apoptosis regulatory protein (CARP-1) and increased DNA repair (Bellido, Ali, Plotkin, Fu, Gubrij, Roberson, Weinstein, O’Brien, Manolagas, Jilka, 2003, Jilka, 2007, Schnoke, Midura, Midura, 2009, Sharma, Mahalingam, Das, Jamal, Levi, Rishi, Datta, 2013). Furthermore, studies performed on rats treated with intermittent PTH showed an increased number of osteoblasts on bone surfaces associated with a decreased fraction of lining cells, without indication of increased osteoblast proliferation (Leaffer, Sweeney, Kellerman, Avnur, Krstenansky, Vickery, Caulfield, 1995, Dobnig, Turner, 1995, Kim, Pajevic, Selig, Barry, Yang, Shin, Baek, Kim, Kronenberg, 2012). In addition, recent studies have identified effects of PTH on the canonical Wnt/-catenin signalling pathway via sclerostin, a secreted glycoprotein primarily produced by osteocytes and acting as bone formation inhibitor (Poole, van Bezooijen, Loveridge, Hamersma, Papapoulos, Löwik, Reeve, 2005, Costa, Bilezikian, 2012). Sclerostin inhibits bone formation by antagonising the Wnt/-catenin anabolic signalling pathway, which modulates osteoblast proliferation, differentiation and survival (Kramer, Halleux, Keller, Pegurri, Gooi, Weber, Feng, Bonewald, Kneissel, 2010, Glass, Bialek, Ahn, Starbuck, Patel, Clevers, Taketo, Long, McMahon, Lang, Karsenty, 2005). PTH is believed to reduce sclerostin concentration and consequently reduce its inhibiting effect on bone formation (Canalis, Giustina, Bilezikian, 2007, Ogura, Iimura, Makino, Sugie-Oya, Takakura, Takao-Kawabata, Ishizuya, Moriyama, Yamaguchi, 2016). In the absence of Wnt signalling, -catenin is phosphorylated by the protein complex formed by Axin, adenomatous polyposis coli (APC) and glycogen synthase kinase 3 (GSK-3). If, however, Wnt signalling is present, the cytoplasmic protein disheveled (Dvl) is activated, disrupting the Axin-APC-GSK-3 complex from phosphorylating -catenin. As a result, -catenin translocates to the nucleus, regulating the transcription of Wnt target genes (Costa, Bilezikian, 2012, Cadigan, Liu, 2006).
While the dual action of PTH is well-known (as documented by the above-mentioned studies), the exact underlying molecular and intercellular mechanisms are still unclear, at least in quantitative terms. Thus, no comprehensive picture of the mechanisms responsible for this clinical paradox has been drawn yet (Qin, Raggatt, Partridge, 2004, Poole, Reeve, 2005). Attempting to remedy this unsatisfactory situation, a number of mathematical models were proposed, in order to better understand and even quantitatively predict the effects of PTH administration on bone cells, see, e.g., (Rattanakul, Lenbury, Krishnamara, Wollkind, 2003, Komarova, 2005, Potter, Greller, Cho, Nuttall, Stroup, Suva, Tobin, 2005) and similar works. Despite the progress achieved in the past 15 or so years, most of those models neither consider the involved biochemical pathways in appropriate detail, nor were they validated through comparison of model predictions to experimental data. In this paper, we attempt to fill both gaps.
In particular, a new mathematical model is presented which allows for shedding light on the intercellular and tissue-scale mechanisms contributing to the dual action of PTH, and its effects on the bone tissue development in rat models of osteoporosis. Thereby, the focus is on teriparatide, or recombinant human PTH(1-34), which is the first anabolic drug in a new class of agents inducing bone formation (Eli Lilly, 2014). PTH(1-34) is administered to patients suffering from severe osteoporosis, particularly to women with postmenopausal osteoporosis (PMO), who are believed to be at high risk of fracture. In clinical practice, it is administered daily, based on single subcutaneous injections (at a dose of 20 g/day). In terms of the modelling strategy, two concepts are combined. On the one hand, focussing on PTH(1-34), a one-compartment PK model was considered, allowing for (predictively) estimating the availability of PTH(1-34) in the blood serum if administration occurs in the form of intermittent injections, described in Section 2.1. Then, the effect of administering PTH(1-34) on the overall PTH serum concentration is described, in Section 2.2, after which a so-called bone cell population model (BCPM), adapted from previous works (Pivonka, Zimak, Smith, Gardiner, Dunstan, Sims, Martin, Mundy, 2008, Pivonka, Zimak, Smith, Gardiner, Dunstan, Sims, Martin, Mundy, 2010), is introduced. In more detail, those works were extended in order to account for both bone modelling and remodelling responses, and to take into account the differentiated effects of PTH(1-34) on those two processes, see Section 2.3. Emulating osteoporosis in rat models is standardly done through ovariectomy, and Section 2.4 describes how ovariectomy is considered in our model. Our new model, hereafter optionally referred to as mechanistic pharmacokinetic/pharmacodynamic (PK/PD) model (Danhof et al., 2007), is calibrated and validated based on experimental data on intermittent and continuous administration of PTH(1-34) in healthy and ovariectomized (OVX) rats, involving different doses and different starting points of drug administration; the considered data is presented in Section 2.5. Numerical studies are presented in Section 3, and all results are discussed in reasonable detail in Section 4. Conclusions and a brief outlook to possible future research directions end the paper, see Section 5.
Section snippets
Pharmacokinetics model for intermittent administration of PTH(1-34)
Following the results of previous works showing no significant difference between the use of a one-compartment and a two-compartment PK model for PTH(1-34) (Satterwhite, Heathman, Miller, Marín, Glass, Dobnig, 2010, Stratford, Vu, Sakon, Katikaneni, Gensure, Ponnapakkam, 2014), a one-compartment representation is considered in this paper, see Fig. 1. This one compartment, also referred to as central compartment, represents the blood and all highly perfused tissues that rapidly equilibrate with
Results
First, calibration of the mechanistic PK/PD model needed to be performed. As for the model parameters related to administration of PTH(1-34), the experimental results published by Li et al. (2007), see Section 2.5, were considered for that purpose. Thereby, the focus was on intermittent administration of PTH(1-34), in terms of achieving the best-possible agreement between model predictions and experimental data. When simulating intermittent administration of PTH(1-34) for 14 days, the increase
Discussion
The results presented in Section 3 clearly show that the new mechanistic PK/PD model proposed in this paper is indeed able to reproduce both anabolic and catabolic responses bone cell responses, depending on whether PTH(1-34) is administered intermittently or continuously. It should be noted that to that end, the (anabolic) osteoblast proliferation-related term of the model needs to be sufficiently small (in magnitude), in order to ensure that the dual action of PTH(1-34) can be reproduced (
Conclusions and outlook
The aim of the study presented in this paper was to accurately predict the development of bone tissue upon administration of PTH(1-34). For that purpose, a mathematical model was developed taking into account the dual action of PTH(1-34), differing fundamentally between intermittent and continuous administration of this drug. Considering the substantial variations in the corresponding experimental data, the model can be considered as successfully validated, see Sections 3 and 4 for presentation
Acknowledgement
Miss Silvia Trichilo acknowledges the support by The University of Melbourne, in the framework of the International PhD Scholarship Program.
References (56)
- et al.
Proteasomal degradation of Runx2 shortens parathyroid hormone-induced anti-apoptotic signaling in osteoblasts — a putative explanation for why intermittent administration is needed for bone anabolism
J. Biol. Chem.
(2003) - et al.
Wnt signaling: complexity at the surface
J. Cell Sci.
(2006) - et al.
Clinical implications of the osteoprotegerin/RANKL/RANK system for bone
J. Am. Med. Assoc.
(2004) Mathematical model of paracrine interactions between osteoclasts and osteoblasts predicts anabolic action of parathyroid hormone on bone
Endocrinology
(2005)- et al.
Determination of dual effects of parathyroid hormone on skeletal gene expression in vivo by microarray and network analysis
J. Biol. Chem.
(2007) - et al.
Osteoblastic cells mediate osteoclastic responsiveness to parathyroid hormone
Endocrinology
(1986) - et al.
A physiologically based mathematical model of integrated calcium homeostasis and bone remodeling
Bone
(2010) - et al.
The influence of bone surface availability in bone remodelling – a mathematical model including coupled geometrical and biomechanical regulations of bone cells
Eng. Struct.
(2013) - et al.
A systems approach to understanding bone cell interactions in health and disease
- et al.
Model structure and control of bone remodeling: a theoretical study
Bone
(2008)
Sclerostin is a delayed secreted product of osteocytes that inhibits bone formation
FASEB J.
Parathyroid hormone — a bone anabolic and catabolic agent
Curr. Opin. Pharmacol.
Parathyroid hormone: past and present
J. Endocrinol.
Parathyroid hormone: a double-edged sword for bone metabolism
Trends Endocrinol. Metab.
Pharmacokinetics of teriparatide (rhPTH[1-34]) and calcium pharmacodynamics in postmenopausal women with osteoporosis
Calcif. Tissue Int.
Coupling systems biology with multiscale mechanics, for computer simulations of bone remodeling
Comput. Methods Appl. Mech. Eng.
Cell cycle and apoptosis regulatory protein (CARP)-1 is expressed in osteoblasts and regulated by PTH
Biochem. Biophys. Res. Commun.
Parathyroid hormone: anabolic and catabolic actions on the skeleton
Curr. Opin. Pharmacol.
Pharmacokinetics in rats of a long-acting human parathyroid hormone-collagen binding domain peptide construct
J. Pharm. Sci.
Application of disease system analysis to osteoporosis: From temporal to spatio-temporal assessment of disease progression and intervention
Comparative effects of teriparatide, denosumab, and combination therapy on peripheral compartmental bone density, microarchitecture, and estimated strength: the DATA HR-pQCT study
J. Bone Miner. Res.
Hormones and disorders of mineral metabolism
Modelling the anabolic response of bone using a cell population model
J. Theor. Biol.
Mechanisms of anabolic therapies for osteoporosis
N. Engl. J. Med.
Sclerostin: therapeutic horizons based upon its actions
Curr. Osteoporos. Rep.
Mechanism-based pharmacokinetic-pharmacodynamic modeling: biophase distribution, receptor theory, and dynamical systems analysis
Annu. Rev. Pharmacol. Toxicol.
Anabolic actions of parathyroid hormone on bone
Endocr. Rev.
Evidence that intermittent treatment with parathyroid hormone increases bone formation in adult rats by activation of bone lining cells
Endocrinology
Cited by (12)
Modeling and simulation of bone cells dynamic behavior under the late effect of breast cancer treatments
2023, Medical Engineering and PhysicsOptimum parameters for each subject in bone remodeling models: A new methodology using surrogate and clinical data
2022, European Journal of Mechanics, A/SolidsCitation Excerpt :These signals are transmitted to other cells (mechanotransduction) to start the BR process (Adachi and Kameo, 2006; Scheiner et al., 2013; Avval et al., 2014; Hambli, 2014; Klika et al., 2014; Mercuri et al., 2016; Pastrama et al., 2018; Cerrolaza et al., 2019; Martin et al., 2019; Ashrafi et al., 2020). Finally, some models simulate bone tissue behavior using pharmacokinetic–pharmacodynamic models that include the effect of drugs (Trichilo et al., 2019; Bahia et al., 2020; Ashrafi et al., 2021). The coupling between the phenomenological models and Finite Element Method (FEM) allows the simulation of the tissue behavior regarding the applied load (see, e.g., Weinans et al. (1992), Jacobs et al. (1995, 1997), Doblaré and García (2001)).
Parameter reduction, sensitivity studies, and correlation analyses applied to a mechanobiologically regulated bone cell population model of the bone metabolism
2021, Computers in Biology and MedicineCitation Excerpt :However, the studied parameters could be extended to the mechanoregulatory parameters. Furthermore, it appears to be indeed relevant to also look into other simulation scenarios, possibly related to pharmacokinetics and pharmacodynamics [39–44], or to apply the same mode of analysis to alternative model formulations [38]. In this paper, we have demonstrated various ways how complex mathematical models can be analyzed.
Bone Remodeling Process: Mechanics, Biology, and Numerical Modeling
2021, Bone Remodeling Process: Mechanics, Biology, and Numerical ModelingSimulation of bone remodeling around a femoral prosthesis using a model that accounts for biological and mechanical interactions
2020, Medical Engineering and PhysicsCitation Excerpt :This continues until the system of differential equations returns to the equilibrium state. Despite the solid biological theory presented in the works cited above [1–4, 9–11], none of the models were applied to a three-dimensional, heterogeneous initial density distribution with the objective to simulate the BR process from interactions between mechanical and biological phenomena. Such a model establishes that the behavior of cell populations is associated with a certain level of the applied stimulus.