Osteoprotegerin in Bone Metastases: Mathematical Solution to the Puzzle

Biology of the RANKL–RANK–OPG System in Immunity, Bone, and Beyond

Discovery and characterization of the cytokine receptor-cytokine-decoy receptor triad formed by RANKL-RANK-OPG have led not only to immense advances in understanding the biology of bone homeostasis, but have also crystalized appreciation of the critical regulatory relationship that exists between bone and immunity, resulting in the emergence of the burgeoning field of osteoimmunology. RANKL-RANK-OPG are members of the tumor necrosis factor (TNF) and TNF receptor superfamilies, and share signaling characteristics common to many members of each. Developmentally regulated and cell-type specific expression patterns of each of these factors have revealed key regulatory functions for RANKL-RANK-OPG in bone homeostasis, organogenesis, immune tolerance and cancer. Successful efforts at designing and developing therapeutic agents targeting RANKL-RANK-OPG have been undertaken for osteoporosis, and additional efforts are underway for other conditions. In this review, we will summarize the basic biology of the RANKL-RANK-OPG system, relate its cell-type specific functions to system-wide mechanisms of development and homeostasis, and highlight emerging areas of interest for this cytokine group.

Mathematical Modeling of Spatio-Temporal Dynamics of a Single Bone Multicellular Unit

Abstract During bone remodeling, bone-resorbing osteoclasts and bone-forming osteoblasts are organized in bone multicellular units (BMUs), which travel at a rate of 20–40 μm/d for 6–12 mo, maintaining a cylindrical structure. However, the interplay of local BMU geometry with biochemical regulation is poorly understood. We developed a mathematical model of BMU describing changes in time and space of the concentrations of proresorptive cytokine RANKL and its inhibitor osteoprotegerin (OPG), in osteoclast and osteoblast numbers, and in bone mass. We assumed that osteocytes surrounding a microfracture produce RANKL, which attracted osteoclasts. OPG and RANKL were produced by osteoblasts and diffused through bone, RANKL was eliminated by binding to OPG and RANK. Osteoblasts were coupled to osteoclasts through paracrine factors. The evolution of the BMU arising from this model was studied using numerical simulations. Our model recapitulated the spatio-temporal dynamics observed in vivo in a cross-section of bone. In response to a RANKL field, osteoclasts moved as a well-confined cutting cone. The coupling of osteoclasts to osteoblasts allowed for sufficient recruitment of osteoblasts to the resorbed surfaces. The RANKL field was the highest at the microfracture in front of the BMU, whereas the OPG field peaked at the back of the BMU, resulting in the formation of a RANKL/OPG gradient, which strongly affected the rate of BMU progression and its size. Thus, the spatial organization of a BMU provides important constraints on the roles of RANKL and OPG as well as possibly other regulators in determining the outcome of remodeling in the BMU.

Dynamic Biochemical and Cellular Models of Bone Physiology: Integrating Remodeling Processes, Tumor Growth, and Therapy

Bone is an activeCoelho, Rui M.  Neto, Joana P. connective tissue composed of different types of cells. The dynamic behavior of bone remodeling processes is typically represented throughValério, Duarte differential equations, which represent the physiological phenomena occurring in this organ. These models takeVinga, Susana into account the tight biochemical regulation between osteoclasts and osteoblasts and have also been enriched with variables and parameters related to bone pathologies and treatment. This chapter reviews some of the more recent models describing bone physiology, focusing on those that include the main cellular processes, along the biochemical control, and also the pharmacokinetic/pharmacodynamic (PK/PD) of the most common treatments for diseases such as cancer. These models are then compared in terms of the simulations obtained and, finally, some highlights on integrating them with the biomechanical component of the system which will be given. These models are expected to provide a valuable insight into this complex system and to support the development of clinical decision systems for bone pathologies.

The Role of Osteocytes in Targeted Bone Remodeling: A Mathematical Model

Until recently many studies of bone remodeling at the cellular level have focused on the behavior of mature osteoblasts and osteoclasts, and their respective precursor cells, with the role of osteocytes and bone lining cells left largely unexplored. This is particularly true with respect to the mathematical modeling of bone remodeling. However, there is increasing evidence that osteocytes play important roles in the cycle of targeted bone remodeling, in serving as a significant source of RANKL to support osteoclastogenesis, and in secreting the bone formation inhibitor sclerostin. Moreover, there is also increasing interest in sclerostin, an osteocyte-secreted bone formation inhibitor, and its role in regulating local response to changes in the bone microenvironment. Here we develop a cell population model of bone remodeling that includes the role of osteocytes, sclerostin, and allows for the possibility of RANKL expression by osteocyte cell populations. We have aimed to give a simple, yet still tractable, model that remains faithful to the underlying system based on the known literature. This model extends and complements many of the existing mathematical models for bone remodeling, but can be used to explore aspects of the process of bone remodeling that were previously beyond the scope of prior modeling work. Through numerical simulations we demonstrate that our model can be used to explore theoretically many of the qualitative features of the role of osteocytes in bone biology as presented in recent literature.

Complex Dynamics of Osteoclast Formation and Death in Long-Term Cultures

BackgroundOsteoclasts, cells responsible for bone resorption, contribute to the development of degenerative, metabolic and neoplastic bone diseases, which are often characterized by persistent changes in bone microenvironment. We aimed to investigate the dynamics of osteoclast formation and death in cultures that considerably exceeded the length of standard protocol and to design a mathematical model describing osteoclastogenesis.Methodology/Principal FindingsRAW 264.7 monocytic cells fuse to form multinucleated osteoclasts upon treatment with pro-resorptive cytokine RANKL. We have found that in long-term experiments (15–26 days), the dynamics of changes in osteoclast numbers was remarkably complex and qualitatively variable in different experiments. Whereas 19 of 46 experiments exhibited single peak of osteoclast formation, in 27 experiments we observed development of successive waves of osteoclast formation and death. Periodic changes in osteoclast numbers were confirmed in long-term cultures of mouse bone marrow cells treated with M-CSF and RANKL. Because the dynamics of changes in osteoclast numbers was found to be largely independent of monocytes, a two-species model of ordinary differential equations describing the changes in osteoclasts and monocytes was ineffective in recapitulating the oscillations in osteoclast numbers. Following experimental observation that medium collected from mature osteoclasts inhibited osteoclastogenesis in fresh cultures, we introduced a third variable, factor f, to describe osteoclast-derived inhibitor. This model allowed us to simulate the oscillatory changes in osteoclasts, which were coupled to oscillatory changes in the factor f, whereas monocytes changed exponentially. Importantly, to achieve the experimentally observed oscillations with increasing amplitude, we also had to assume that osteoclast presence stimulates osteoclast formation.Conclusions/SignificanceThis study identifies the critical role for osteoclast autocrine regulation in controlling long-term dynamic of osteoclast formation and death and describes the complementary roles for negative and positive feedback mediators in determining the sharp dynamics of activation and inactivation of osteoclasts.

An Integrated Computational Model of the Bone Microenvironment in Bone-Metastatic Prostate Cancer

Abstract Bone metastasis will impact most men with advanced prostate cancer. The vicious cycle of bone degradation and formation driven by metastatic prostate cells in bone yields factors that drive cancer growth. Mechanistic insights into this vicious cycle have suggested new therapeutic opportunities, but complex temporal and cellular interactions in the bone microenvironment make drug development challenging. We have integrated biologic and computational approaches to generate a hybrid cellular automata model of normal bone matrix homeostasis and the prostate cancer-bone microenvironment. The model accurately reproduces the basic multicellular unit bone coupling process, such that introduction of a single prostate cancer cell yields a vicious cycle similar in cellular composition and pathophysiology to models of prostate-to-bone metastasis. Notably, the model revealed distinct phases of osteolytic and osteogenic activity, a critical role for mesenchymal stromal cells in osteogenesis, and temporal changes in cellular composition. To evaluate the robustness of the model, we assessed the effect of established bisphosphonate and anti-RANKL therapies on bone metastases. At approximately 100% efficacy, bisphosphonates inhibited cancer progression while, in contrast with clinical observations in humans, anti-RANKL therapy fully eradicated metastases. Reducing anti-RANKL yielded clinically similar results, suggesting that better targeting or dosing could improve patient survival. Our work establishes a computational model that can be tailored for rapid assessment of experimental therapies and delivery of precision medicine to patients with prostate cancer with bone metastases. Cancer Res; 74(9); 2391–401. ©2014 AACR.

Mathematical modelling of the pathogenesis of multiple myeloma‐induced bone disease

SUMMARY Multiple myeloma (MM) is the second most common haematological malignancy and results in destructive bone lesions. The interaction between MM cells and the bone microenvironment plays an important role in the development of the tumour cells and MM‐induced bone disease and forms a ‘vicious cycle’ of tumour development and bone destruction, intensified by suppression of osteoblast activity and promotion of osteoclast activity. In this paper, a mathematical model is proposed to simulate how the interaction between MM cells and the bone microenvironment facilitates the development of the tumour cells and the resultant bone destruction. It includes both the roles of inhibited osteoblast activity and stimulated osteoclast activity. The model is able to mimic the temporal variation of bone cell concentrations and resultant bone volume after the invasion and then removal of the tumour cells and explains why MM‐induced bone lesions rarely heal even after the complete removal of MM cells. The behaviour of the model compares well with published experimental data. The model serves as a first step to understand the development of MM‐induced bone disease and could be applied further to evaluate the current therapies against MM‐induced bone disease and even suggests new potential therapeutic targets. © 2014 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd

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.

Modelling osteomyelitis

This work focuses on the computational modelling of osteomyelitis, a bone pathology caused by bacteria infection (mostly Staphylococcus aureus). The infection alters the RANK/RANKL/OPG signalling dynamics that regulates osteoblasts and osteoclasts behaviour in bone remodelling, i.e. the resorption and mineralization activity. The infection rapidly leads to severe bone loss, necrosis of the affected portion, and it may even spread to other parts of the body. On the other hand, osteoporosis is not a bacterial infection but similarly is a defective bone pathology arising due to imbalances in the RANK/RANKL/OPG molecular pathway, and due to the progressive weakening of bone structure.

Bone metastases

Bone is the most frequent site for metastasis for many cancers, notably for tumours originating in the breast and the prostate. Tumour cells can escape from the primary tumour site and colonize the bone microenvironment. Within the bone, these disseminated tumour cells, as well as those arising in the context of multiple myeloma, may assume a state of dormancy, remaining quiescent for years before resuming proliferation and causing overt metastasis, which causes bone destruction via activation of osteoclast-mediated osteolysis. This structural damage can lead to considerable morbidity, including pain, fractures and impaired quality of life. Although treatment of bone metastases and myeloma bone disease is rarely curative, disease control is often possible for many years through the use of systemic anticancer treatments on a background of multidisciplinary supportive care. This care should include bone-targeted agents to inhibit tumour-associated osteolysis and prevent skeletal morbidity as well as use of appropriate local treatments such as radiation therapy, orthopaedic surgery and specialist palliative care to minimize the impact of metastatic bone disease on physical functioning. In this Primer, we provide an overview of the clinical features, the pathophysiology and the specific treatment approaches to prevent and treat bone metastases from solid tumours as well as myeloma bone disease.

A mathematical model for describing the metastasis of cancer in bone tissue

Metastasis is the rapid proliferation of cancer cells (secondary tumour) at a specific place, generally leading to death. This occurs at anatomical parts providing the necessary environment for vas...

Modeling the Human Bone–Tumor Niche: Reducing and Replacing the Need for Animal Data

ABSTRACT Bone is the most common site for cancer metastasis. Understanding the interactions within the complex, heterogeneous bone–tumor microenvironment is essential for the development of new therapeutics. Various animal models of tumor‐induced bone disease are routinely used to provide valuable information on the relationship between cancer cells and the skeleton. However, new model systems exist that offer an alternative approach to the use of animals and might more accurately reveal the cellular interactions occurring within the human bone–tumor niche. This review highlights replacement models that mimic the bone microenvironment and where cancer metastases and tumor growth might be assessed alongside bone turnover. Such culture models include the use of calcified regions of animal tissue and scaffolds made from bone mineral hydroxyapatite, synthetic polymers that can be manipulated during manufacture to create structures resembling trabecular bone surfaces, gel composites that can be modified for stiffness and porosity to resemble conditions in the tumor–bone microenvironment. Possibly the most accurate model system involves the use of fresh human bone samples, which can be cultured ex vivo in the presence of human tumor cells and demonstrate similar cancer cell–bone cell interactions as described in vivo. In addition, the use of mathematical modeling and computational biology approaches provide an alternative to preliminary animal testing. The use of such models offers the capacity to mimic significant elements of the human bone–tumor environment, and complement, refine, or replace the use of preclinical models. © 2020 The Authors. JBMR Plus published by Wiley Periodicals, Inc. on behalf of American Society for Bone and Mineral Research.

MODEL-BASED ANALYSIS OF IGF-1 EFFECT ON OSTEOBLAST AND OSTEOCLAST REGULATION IN BONE TURNOVER

The main determinant of bone Ca accretion is a bimolecular regulatory network on osteoblast (OB) and osteoclast (OC). Even though IGF-1 is known as an important regulator in bone cell cycle, little has been done to model IGF-1 action in bone cell regulation. Thus, the objective is to develop a mathematical model that depicts the regulatory action of IGF-1 onto the OB and OC interaction, and to evaluate adolescent and adult bone Ca accretion in response to differences in IGF-1 levels. As a result, a dynamic model of OB and OC with two main regulatory systems, i.e., Receptor Activator for Nuclear Factor [Formula: see text]B (RANK)-RANK Ligand (RANKL)-osteoprogerin (OPG) system, and TGF-[Formula: see text], was augmented with the IGF-1, and incorporated into Ca kinetic data to predict exchangeable bone Ca. The developed model could predict a change in OB and OC levels in response to perturbations in regulators, producing results consistent with bone physiology and published experimental data. The model also estimated parametric difference in regulators between adults and adolescents, suggesting that RANKL/OPG in adolescents was about 4 times higher than in adults, while adolescent serum PTH and IGF-1 concentrations were 60% and 220% of those of adults, respectively. This study highlighted the influence of IGF-1 on the regulation of bone cells in positively modulating bone Ca, suggesting that IGF-1 may be an effective target for reducing bone loss by promoting mature OB.

Osteocyte-Related Cytokines Regulate Osteoclast Formation and Bone Resorption

The process of bone remodeling is the result of the regulated balance between bone cell populations, namely bone-forming osteoblasts, bone-resorbing osteoclasts, and the osteocyte, the mechanosensory cell type. Osteoclasts derived from the hematopoietic stem cell lineage are the principal cells involved in bone resorption. In osteolytic diseases such as rheumatoid arthritis, periodontitis, and osteoporosis, the balance is lost and changes in favor of bone resorption. Therefore, it is vital to elucidate the mechanisms of osteoclast formation and bone resorption. It has been reported that osteocytes express Receptor activator of nuclear factor κΒ ligand (RANKL), an essential factor for osteoclast formation. RANKL secreted by osteocytes is the most important factor for physiologically supported osteoclast formation in the developing skeleton and in pathological bone resorption such as experimental periodontal bone loss. TNF-α directly enhances RANKL expression in osteocytes and promotes osteoclast formation. Moreover, TNF-α enhances sclerostin expression in osteocytes, which also increases osteoclast formation. These findings suggest that osteocyte-related cytokines act directly to enhance osteoclast formation and bone resorption. In this review, we outline the most recent knowledge concerning bone resorption-related cytokines and discuss the osteocyte as the master regulator of bone resorption and effector in osteoclast formation.

Osteoclast differentiation and activation

Osteoclasts are specialized cells derived from the monocyte/macrophage haematopoietic lineage that develop and adhere to bone matrix, then secrete acid and lytic enzymes that degrade it in a specialized, extracellular compartment. Discovery of the RANK signalling pathway in the osteoclast has provided insight into the mechanisms of osteoclastogenesis and activation of bone resorption, and how hormonal signals impact bone structure and mass. Further study of this pathway is providing the molecular basis for developing therapeutics to treat osteoporosis and other diseases of bone loss.

The Cellular Dynamics of Bone Remodeling: A Mathematical Model

The mechanical properties of vertebrate bone are largely determined by a process which involves the complex interplay of three different cell types. This process is called bone remodeling and occurs asynchronously at multiple sites in the mature skeleton. The cells involved are bone resorbing osteoclasts, bone matrix producing osteoblasts, and mechanosensing osteocytes. These cells communicate with each other by means of autocrine and paracrine signaling factors and operate in complex entities, the so-called bone multicellular units (BMUs). To investigate the BMU dynamics in silico, we develop a novel mathematical model resulting in a system of nonlinear partial differential equations (PDEs) with time delays. The model describes the osteoblast and osteoclast populations together with the dynamics of the key messenger molecule RANKL and its decoy receptor OPG. Scaling theory is used to address parameter sensitivity and predict the emergence of pathological remodeling regimes. The model is studied numerically in one and two space dimensions using finite difference schemes in space and explicit delay equation solvers in time. The computational results are in agreement with in vivo observations and provide new insights into the role of the RANKL/OPG pathway in the spatial regulation of bone remodeling.