Osteocytes as a record of bone formation dynamics: A mathematical model of osteocyte generation in bone matrix

The formation of new bone involves both the deposition of bone matrix, and the formation of a network of cells embedded within the bone matrix, called osteocytes. Osteocytes derive from bone-synthesising cells (osteoblasts) that become buried in bone matrix during bone deposition. The generation of osteocytes is a complex process that remains incompletely understood. Whilst osteoblast burial determines the density of osteocytes, the expanding network of osteocytes regulates in turn osteoblast activity and osteoblast burial. In this paper, a spatiotemporal continuous model is proposed to investigate the osteoblast-to-osteocyte transition. The aims of the model are (i) to link dynamic properties of osteocyte generation with properties of the osteocyte network imprinted in bone, and (ii) to investigate Marotti's hypothesis that osteocytes prompt the burial of osteoblasts when they become covered with sufficient bone matrix. Osteocyte density is assumed in the model to be generated at the moving bone surface by a combination of osteoblast density, matrix secretory rate, rate of entrapment, and curvature of the bone substrate, but is found to be determined solely by the ratio of the instantaneous burial rate and matrix secretory rate. Osteocyte density does not explicitly depend on osteoblast density nor curvature. Osteocyte apoptosis is also included to distinguish between the density of osteocyte lacuna and the density of live osteocytes. Experimental measurements of osteocyte lacuna densities are used to estimate the rate of burial of osteoblasts in bone matrix. These results suggest that: (i) burial rate decreases during osteonal infilling, and (ii) the control of osteoblast burial by osteocytes is likely to emanate as a collective signal from a large group of osteocytes, rather than from the osteocytes closest to the bone deposition front.Comment: 11 pages, 6 figures. V2: substantially augmented version. Addition of Section 4 (osteocyte apoptosis

Reduced order modelling of bone resorption and formation.

The bone remodelling process, performed by the Bone Multicellular Unit (BMU) is a key multi-hierarchically regulated process, which provides and supports various functionality of bone tissue. It is also plays a critical role in bone disorders, as well as bone tissue healing following damage. Improved modelling of bone turnover processes could play a significant role in helping to understand the underlying cause of bone disorders and thus develop more effective treatment methods. Moreover, despite extensive research in the field of bone tissue engineering, bonescaffold development is still very empirical. The development of improved methods of modelling the bone remodelling process should help to develop new implant designs which encourage rapid osteointegration. There are a number of limitations with respect to previous research in the field of mathematical modelling of the bone remodelling process, including the absence of an osteocyte loop of regulation. It is within this context that this research presented in this thesis utilises a range of modelling methods to develop a framework for bone remodelling which can be used to improve treatment methods for bone disorders. The study concentrated on dynamic and steady state variables that in perspective can be used as constraints for optimisation problem considering bone remodelling or tissue remodelling with the help of the grafts/scaffolds.The cellular and combined allosteric-regulation approaches to modelling of bone turnover, based on the osteocyte loop of regulation, have been studied. Both approaches have been studied different within wide range of rate parameters. The approach to the model validation has been considered, including a statistical approach and parameter reduction approach. From a validation perspective the cellular class of modes is preferable since it has fewer parameters to validate. The optimal control framework for regulation of remodelling has been studied. Future work in to improve the models and their application to bone scaffold design applications have been considered. The study illustrates the complexity of formalisation of the metabolic processes and the relations between hierarchical subsystems in hard tissue where a relatively small number of cells are active. Different types/modes of behaviour have been found in the study: relaxational, periodical and chaotic modes. All of these types of behaviour can be found, in bone tissue. However, a chaotic or periodic modes are ones of the hardest to verify although a number of periodical phenomena have been observed empirically in bone and skeletal development. Implementation of the allosteric loop into cellular model damps other types of behaviour/modes. In this sense it improves the robustness, predictability and control of the system. The developed models represent a first step in a hierarchical model of bone tissue (system versus local effects). The limited autonomy of any organ or tissue implies differentiation on a regulatory level as well as physiological functions and metabolic differences. Implementation into the cellular phenomenological model of allosteric-like loop of regulation has been performed. The results show that the robustness of regulation can be inherited from the phenomenological model. An attempt to correlate the main bone disorders with different modes of behaviour has been undertaken using Paget’s disorder in bone, osteoporosis and some more general skeleton disorders which lead to periodical changes in bone mass, reported by some authors. However, additional studies are needed to make this hypothesis significant. The study has revealed a few interesting techniques. When studying a multidimensional phenomenon, as a bone tissue is, the visualisation and data reduction is important for analysis and interpretation of results. In the study two novel technical methods have been proposed. The first is the graphical matrix method to visualise/project the multidimensional phase space of variables into diagonal matrix of regular combination of two-dimensional graphs. This significantly simplifies the analysis and, in principle, makes it possible to visualise the phase space higher than three-dimensional. The second important technical development is the application of the Monte-Carlo method in combination with the regression method to study the character and stability of the equilibrium points of a dynamic system. The advantage of this method is that it enables the most influential parameters that affect the character and stability of the equilibrium point to be identified from a large number of the rate parameters/constants of the dynamic system. This makes the interpretation of parameters and conceptual verification of the model much easier

Estudio de las alteraciones del metabolismo mineral y de los trastornos óseos asociados a la enfermedad renal crónica

Chronic Kidney Disease (CKD) affects million people worldwide and is a risk factor for morbidity and mortality. CKD patients have poor bone mineral density due to mineral metabolism imbalance and secondary hyperparathyroidism resulting in an increased fracture incidence. Bone, despite its well-known function on mineral storage and organ protection, plays an important role as endocrine organ controlling several system functions and metabolic pathways. In this respect, bone status have been associated with cardiovascular diseases and mortality in both, the general and CKD populations. Moreover, Fibroblast Growth Factor 23 (FGF23), a phosphaturic hormone secreted by osteocytes and mature osteoblasts has been associated with increased mortality and left ventricular hypertrophy. In clinical practice, mineral abnormalities are commonly treated with calcitriol, phosphate binders and calcimimetics, to maintain plasma parathyroid hormone (PTH) and phosphate levels within the normal range. Among the distinct types of phosphate binders available, those based on magnesium have additional benefits, preventing vascular smooth muscle cells calcification. As bone disorders are involved in adverse outcomes, we consider of interest the study of the abnormalities of mineral and bone disorders associated with CKD and how calcitriol, magnesium, calcimimetic and FGF23 affect bone cells and bone homeostasis in the context of renal insufficiency. To address this issue we used animal models of renal insuficiency and in vitro models of osteoblasts and osteoclasts and we found that 1) moderate doses of calcitriol decrease osteoblast acitivity and increase mineralization in vivo whereas high doses of calcitriol impair osteogenic differentiation in vitro; 2) dietary magnesium supplementation increases osteoblast activity and may impair mineralization in vivo and magnesium supplementation promotes osteogenic differentiation in vitro through Notch signaling activation; 3) treatment with calcimimetic maintains bone turnover despite the concomitant decrease in PTH concentration in vivo and increased steogenesis and mineralization in vitro and 4) high FGF23 concentrations produce bone changes in a model of uni-nefrectomized rats and impair osteocyte maturation whereas promote osteoclast differentiation in vitro. Altogether, our results demonstrate a potential role of these molecules on bone homeostasis in CKD by targeting directly bone cells.La Enfermedad Renal Crónica (ERC) afecta a millones de personas mundialmente y es un factor de riesgo para morbilidad y mortalidad. Los pacientes con ERC tienen pérdida de densidad mineral ósea debido al desequilibrio del metabolismo mineral y al hiperparatiroidismo secundario que resulta en un incremento del índice de fracturas. El hueso, además de sus conocidas funciones como almacén de minerales y soporte y protección de órganos, juega un importante papel como órgano endocrino controlando el funcionamiento de varios sistemas y procesos metabólicos. En este sentido, el estado del hueso ha sido asociado con enfermedades cardiovasculares y mortalidad tanto en la población general como en pacientes con ERC. Además, el Factor de Crecimiento Fibroblástico 23 (FGF23), una hormona fosfatúrica secretada por osteocitos y osteoblastos maduros ha sido asociada con el incremento de mortalidad y la hipertrofia de ventrículo izquierdo. En la clínica, el tratamiento con calcitriol, quelantes de fósforo y calcimiméticos es a menudo usado para controlar los niveles plasmáticos de hormona paratiroidea (PTH) y fósforo. Entre los distintos quelantes de fósforo, los que contienen magnesio ofrecen beneficios adicionales, previniendo la calcificación de células de músculo liso vascular. Ya que los trastornos óseos están implicados en eventos adversos, consideramos de interés el estudio de las alteraciones del metabolismo mineral y los trastornos óseos asociados con la ERC y como el calcitriol, magnesio, calcimimético y FGF23 afectan las células del hueso y la homeostasis ósea en el contexto de la insuficiencia renal. Para abordar este trabajo usamos modelos animales de insuficiencia renal y modelos in vitro de osteoblastos y osteoclastos y encontramos que 1) dosis moderadas de calcitriol mejoran la mineralización y disminuyen la actividad osteoblástica in vivo mientras altas dosis bloquean la diferenciación osteogénica in vitro; 2) el alto magnesio en la dieta incrementa la actividad osteoblástica y puede afectar la mineralización in vivo, mientras que in vitro el suplemento con magnesio promueve la diferenciación osteogénica a tráves de la activación de la ruta Notch; 3) el tratamiento con calcimimético mantiene el remodelado óseo a pesar de la consecuente disminución de los nivels de PTH in vivo e incrementa la osteogénesis y la mineralización in vitro y 4) altas concentraciones de FGF23 provocan cambios en el hueso en un modelo de ratas uninefrectomizadas mientras que in vitro inhiben la maduración de los osteocitos y promueven la diferenciación osteoclástica. En general, nuestros resultados demuestran el potencial papel de estas moléculas en la homeostasis del hueso en la ERC, afectando directamente las células del hueso

Simulating Bone Loss in Microgravity Using Mathematical Formulations of Bone Remodeling

Most mathematical models of bone remodeling are used to simulate a specific bone disease, by disrupting the steady state or balance in the normal remodeling process, and to simulate a therapeutic strategy. In this work, the ability of a mathematical model of bone remodeling to simulate bone loss as a function of time under the conditions of microgravity is investigated. The model is formed by combining a previously developed set of biochemical, cellular dynamics, and mechanical stimulus equations in the literature with two newly proposed equations; one governing the rate of change of the area of cortical bone tissue in a cross section of a cylindrical section of bone and one governing the rate of change of calcium in the bone fluid. The mechanical stimulus comes from a simple model of stress due to a compressive force on a cylindrical section of bone which can be reduced to zero to mimic the effects of skeletal unloading in microgravity. The complete set of equations formed is a system of first order ordinary differential equations. The results of selected simulations are displayed and discussed. Limitations and deficiencies of the model are also discussed as well as suggestions for further research

Oestrogen and thyroid hormone interactions in the regulation of bone mass

Osteoporosis is characterised by low bone mass, reduced bone mineral density and a deterioration of bone microarchitecture, resulting in increased susceptibility to fragility fractures. Oestrogen deficiency and thyrotoxicosis are established risk factors for osteoporosis. Oestrogen and thyroid hormone have opposing actions on adult bone and I hypothesise that accelerated bone loss at the menopause is due to unopposed actions of thyroid hormone on the skeleton. To test this hypothesis, I investigated the effect of altered thyroid status on the skeleton in adult sham-operated and ovariectomised wild type and thyroid hormone receptor (TR) α and β knockout mice (TRα0/0 and TRβ-/-). Skeletal phenotype analysis included determination of structural, densitometric, histomorphometric and biomechanical parameters. Skeletal phenotypes of euthyroid wild type mice were compared to hypothyroid and thyrotoxic wild type as well as TRα0/0and TRβ-/- mice. Bone mass was elevated in TRα0/0and reduced in TRβ-/- mice despite similar bone formation rates. These data suggest that the differences in bone mass are due to differing osteoclast activity. The skeletal phenotypes of TRα0/0 and TRβ-/- mice following manipulation of thyroid status were then described in detail. TRβ-/- and wild type mice rendered hypothyroid, had significantly lower bone formation than hypothyroid TRα0/0 mice suggesting that, in the absence of thyroid hormone, TRα may inhibit bone formation. Finally, the effect of oestrogen withdrawal in each of these groups of mice was also investigated. These studies demonstrate oestrogen deficiency bone loss was greater in hypothyroid compared to hyperthyroid mice, indicating that accelerated bone loss following oestrogen withdrawal cannot result from unopposed actions of thyroid hormones. Nevertheless, the studies contained in this thesis provide new insight regarding the roles of TRα and TRβ in bone maintenance and the effects of interactions between oestrogen and thyroid hormones on the regulation of bone mass.Open Acces

Nutrient supply impacts osteocytic specification by regulating a nuclear transcription program

[spa] El hueso es un órgano con múltiples funciones. No sólo actúa como elemento de soporte, protección y locomoción, sino que también resulta indispensable en el mantenimiento del equilibrio mineral y ácido/base, conforma un nicho adecuado para el desarrollo de la hematopoyesis, y mantiene la homeostasis energética del organismo. En estos procesos, los osteocitos tienen un papel especialmente relevante, ya que actúan transduciendo estímulos mecánicos en señales bioquímicas. Los osteocitos constituyen el principal componente celular óseo. Derivan de osteoblastos, los cuales a su vez proceden de células madre mensenquimales (MSC). Los osteoblastos pueden seguir tres destinos alternativos: entrar en apoptosis, originar células de revestimiento óseo o progresar en la diferenciación hacia osteocitos. Actualmente, los estímulos y vías de señalización que regulan cada uno de estos procesos son desconocidos. Por ello, y teniendo en cuenta la importancia de los osteocitos en la homeostasis del organismo, consideramos necesario profundizar en su investigación. Durante el proceso de diferenciación ósea, los osteoblastos quedan embebidos en una matriz mineralizada que limita su disponibilidad de nutrientes, estando expuestos a un ambiente hipoglucémico al cual deben adaptarse. En este contexto Wei et al. demostraron que la glucosa juega un papel importante en la regulación de la diferenciación osteoblástica. Por otro lado, se ha observado que, en ambientes hiperglucémicos, típicos de pacientes diabéticos, se produce una reducción del número y función osteoblástica, así como una disminución de la densidad mineral ósea y alteración de la microarquitectura ósea. Teniendo en cuenta todo lo expuesto, estudiamos la capacidad de diferenciación de las IDG-SW3 en condiciones de hipoglucemia (1mM glucosa), normoglucemia (5mM glucosa) o hiperglucemia (25mM glucosa). Las condiciones de hipoglucemia promueven la diferenciación osteocitica, mientras que altas concentraciones de glucosa dificultan este proceso. A nivel metabólico, las condiciones de baja glucosa aumentan la cantidad de mitocondrias y su agrupación en forma de redes. Por otro lado, los ambientes hipoglucémicos, promueven los eventos de fisión mitocondrial. En este contexto PGC1α podría desempeñar un papel crucial como nexo entre el estrés metabólico y la reprogramación génica de los osteoblastos. PGC1α es un coactivador transcripcional que responde a diferentes tipos de estrés. Aunque sus dianas son múltiples, afectan principalmente a la expresión de genes implicados en el metabolismo, así como la biogénesis y función mitocondrial. PGC1 se activa a través de fosforilación y acetilación mediadas por AMPK y SIRT1. La activación de PGC1α, podría iniciar una reprogramación metabólica y génica que culminaría en una inducción de la diferenciación osteocítica

Modulation of parathyroid hormone 1 receptor signaling by extracellular nucleotides

Parathyroid hormone (PTH) activates the PTH/PTH-related peptide receptor (PTH1R) on osteoblasts and other target cells. Mechanical stimulation of cells, including osteoblasts, causes release of nucleotides such as ATP into the extracellular fluid. In addition to its role as an energy source, ATP serves as an agonist at P2 receptors and an allosteric regulator of many proteins. We investigated the effects of concentrations of extracellular ATP, comparable to those that activate low affinity P2X7 receptors, on PTH1R signaling. Cyclic AMP levels were monitored in real-time using a bioluminescence reporter and β-arrestin recruitment to PTH1R was followed using a complementation-based luminescence assay. ATP markedly enhanced cyclic AMP and β-arrestin signaling as well as downstream activation of CREB. CMP – a nucleotide that lacks a high energy bond and does not activate P2 receptors – mimicked this effect of ATP. Moreover, potentiation was not inhibited by P2 receptor antagonists, including a specific blocker of P2X7. Thus, nucleotide-induced potentiation of signaling pathways was independent of P2 receptor signaling. ATP and CMP reduced the concentration of PTH (1-34) required to produce a half-maximal cyclic AMP or β-arrestin response, with no evident change in maximal receptor activity. Increased potency was similarly apparent with PTH1R agonists PTH (1-14) and PTH-related peptide (1-34). These observations suggest that extracellular nucleotides increase agonist affinity, efficacy or both, and are consistent with modulation of signaling at the level of the receptor or a closely associated protein. Taken together, our findings establish that ATP enhances PTH1R signaling through a heretofore unrecognized allosteric mechanism

Discovery of First-in-Class Small Molecule Agonists of the RXFP2 Receptor as Therapeutic Candidates for Osteoporosis

Osteoporosis is a chronic bone disease characterized by decreased bone mass and increased risk of developing fractures, predominantly observed in the elderly. The pathophysiological cause of the disease is a decrease in the activity of the bone-forming cells (osteoblasts) that alters bone remodeling in favor of bone resorption, leading to a decrease in bone mass. Recent studies identified the relaxin family peptide receptor 2 (RXFP2), the G protein-coupled receptor (GPCR) for insulin-like 3 peptide (INSL3), as an attractive target expressed in osteoblast cells to increase bone formation. The goal of this dissertation is to discover and characterize small molecule agonists of RXFP2 that are stable and can be delivered orally to promote bone growth. Several low molecular weight compounds were identified as agonists of the RXFP2 receptor using a cAMP high-throughput screen of the NCATS small molecule library. An extensive structure-activity relationship campaign resulted in highly potent and efficient full RXFP2 agonists. The selectivity and specificity of these compounds for human and mouse RXFP2 was shown in counter-screens against the related relaxin receptor RXFP1 and other GPCRs. Using a series of RXFP2/RXFP1 chimeric receptors, in silico modeling and RXFP2 point mutants, we established that the compounds are allosteric agonists of the RXFP2 receptor and identified the GPCR transmembrane domains as the specific region for compound interaction. We also showed that the candidate compounds promoted mineralization in primary human osteoblasts and had low cytotoxicity in various cell types. The compound with the highest activity in vitro was selected for pharmacokinetics profiling in mice, showing oral bioavailability and bone exposure. Moreover, an efficacy study in wild-type female mice treated orally with the lead compound showed a significant increase of the vertebral trabecular number and thickness compared to vehicle treated controls. Overall, our study has successfully identified and characterized the first-in-class small molecule series of RXFP2 agonists, which may lead to the development of a new class of orally bioavailable drugs for the treatment of diseases associated with bone loss

Emerging Paradigms in Insulin Resistance

This book provides a resource for the scientist or medical professional interested in the topic of insulin resistance. With a mix of review and primary data articles, emerging paradigms in insulin resistance are highlighted. The topics are succinctly presented, and distinct viewpoints are represented. An introduction to the Special Issue that provides summaries of the studies included, is provided by the Guest Editor, Dr. Susan Burke, and her colleague at the Pennington Biomedical Research Center, Dr. Jason Collier