Elsevier

Journal of Theoretical Biology

Volume 473, 21 July 2019, Pages 67-79
Journal of Theoretical Biology

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

https://doi.org/10.1016/j.jtbi.2019.04.020Get rights and content

Highlights

  • The novel PK/PD model is able to distinguish between bone anabolic and catabolic bone tissue response to PTH administration.

  • The anabolic effect of PTH is modelled via osteoblast apoptosis reduction, increased osteoblast precursor proliferation and lining cell differentiation.

  • Intermittent administration of PTH induces bone modelling responses, essential for the substantial bone gain observed in rats.

  • The model is able to reproduce experimentally observed key features of PTH administration.

Abstract

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.

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/β-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/β-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, β-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 β-catenin. As a result, β-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 μg/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.

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