A reaction–diffusion model for long bones growth

Bone development is characterized by differentiation and growth of chondrocytes from the proliferation zone to the hypertrophying one. These two cellular processes are controlled by a complex signalling regulatory loop between different biochemical signals, whose production depends on the current cell density, constituting a coupled cell-chemical system. In this work, a mathematical model of the process of early bone growth is presented, extending and generalizing other earlier approaches on the same topic. A reaction–diffusion regulatory loop between two chemical factors: parathyroid hormone-related peptide (PTHrP) and Indian hedgehog (Ihh) is hypothesized, where PTHrP is activated by Ihh and inhibits Ihh production. Chondrocytes proliferation and hypertrophy are described by means of population equations being both regulated by the PTHrP and Ihh concentrations. In the initial stage of bone growth, these two cellular proceses are considered to be directionally dependent, modelling the well known column cell formation, characteristic of endochondral ossification. This coupled set of equations is solved within a finite element framework, getting an estimation of the chondrocytes spatial distribution, growth of the diaphysis and formation of the epiphysis of a long bone. The results obtained are qualitatively similar to the actual physiological ones and quantitatively close to some available experimental data. Finally, this extended approach allows finding important relations between the model parameters to get stability of the physiological process and getting additional insight on the spatial and directional distribution of cells and paracrine factors.     

Can the growth factors PTHrP,Ihh and VEGF,together regulate the development of a long bone?

Endochondral ossification is the process of differentiation of cartilaginous into osseous tissue. Parathyroid hormone related protein (PTHrP), Indian hedgehog (Ihh) and vascular endothelial growth factor (VEGF), which are synthesized in different zones of the growth plate, were found to have crucial roles in regulating endochondral ossification. The aim of this study was to evaluate whether the three growth factors PTHrP, Ihh and VEGF, together, could regulate longitudinal growth in a normal human, fetal femur. For this purpose, a one-dimensional finite element (FE) model, incorporating growth factor signaling, was developed of the human, distal, femoral growth plate. It included growth factor synthesis in the relevant zones, their transport and degradation and their effects. Simulations ran from initial hypertrophy in the center of the bone until secondary ossification starts at approximately 3.5 months postnatal. For clarity, we emphasize that no mechanical stresses were considered. The FE model showed a stable growth plate in which the bone growth rate was constant and the number of cells per zone oscillated around an equilibrium. Simulations incorporating increased and decreased PTHrP and Ihh synthesis rates resulted, respectively, in more and less cells per zone and in increased and decreased bone growth rates. The FE model correctly reflected the development of a growth plate and the rate of bone growth in the femur. Simulations incorporating increased and decreased PTHrP and Ihh synthesis rates reflected growth plate pathologies and growth plates in PTHrP-/- and Ihh-/- mice. The three growth factors, PTHrP, Ihh and VEGF, could potentially together regulate tissue differentiation.     

Indian hedgehog signals independently of PTHrP to promote chondrocyte hypertrophy

Chondrocyte hypertrophy is an essential process required for endochondral bone formation. Proper regulation of chondrocyte hypertrophy is also required in postnatal cartilage homeostasis. Indian hedgehog (Ihh) and PTHrP signaling play crucial roles in regulating the onset of chondrocyte hypertrophy by forming a negative feedback loop, in which Ihh signaling regulates chondrocyte hypertrophy by controlling PTHrP expression. To understand whether there is a PTHrP-independent role of Ihh signaling in regulating chondrocyte hypertrophy, we have both activated and inactivated Ihh signaling in the absence of PTHrP during endochondral skeletal development. We found that upregulating Ihh signaling in the developing cartilage by treating PTHrP(-/-) limb explants with sonic hedgehog (Shh) protein in vitro, or overexpressing Ihh in the cartilage of PTHrP(-/-) embryos or inactivating patched 1 (Ptch1), a negative regulator of hedgehog (Hh) signaling, accelerated chondrocyte hypertrophy in the PTHrP(-/-) embryos. Conversely, when Hh signaling was blocked by cyclopamine or by removing Smoothened (Smo), a positive regulator of Hh signaling, chondrocyte hypertrophy was delayed in the PTHrP(-/-) embryo. Furthermore, we show that upregulated Hh signaling in the postnatal cartilage led to accelerated chondrocyte hypertrophy during secondary ossification, which in turn caused reduction of joint cartilage. Our results revealed a novel role of Ihh signaling in promoting chondrocyte hypertrophy independently of PTHrP, which is particularly important in postnatal cartilage development and homeostasis. In addition, we found that bone morphogenetic protein (Bmp) and Wnt/beta-catenin signaling in the cartilage may both mediate the effect of upregulated Ihh signaling in promoting chondrocyte hypertrophy.     

The PTHrP–Ihh Feedback Loop in the Embryonic Growth Plate Allows PTHrP to Control Hypertrophy and Ihh to Regulate Proliferation

Growth plate and long bone development is governed by biochemical signaling pathways of which the PTHrP–Ihh system is the best known. Other factors, such as BMPs, FGFs and mechanical loading, may interact with this system. This study aims at elucidating the relative importance of PTHrP and Ihh for controlling proliferation, and hypertrophy in fetal growth plate cartilage. We assessed the question why reduced Ihh expression leads to more pronounced effects on the number of non-hypertrophic cells and total bone formation, compared to PTHrP down-regulation.Using few basic equations, constituted from literature data, this paper shows how the PTHrP–Ihh feedback system can control different aspects of tissue differentiation at distinct locations. In particular, it is shown that (mechanical or biochemical) perturbations will affect proliferation via Ihh-related parameters, whereas changes in PTHrP-related parameters selectively interact with hypertrophy. This is contra-intuitive, since PTHrP acts to keep cells proliferating. In this context, the critical PTHrP level for keeping cells proliferating has been reconsidered. In addition, an explanation is provided for the aforementioned difference in effect between reduced Ihh and PTHrP expression.     

BMP and Ihh/PTHrP signaling interact to coordinate chondrocyte proliferation and differentiation.

During endochondral ossification, two secreted signals, Indian hedgehog (Ihh) and parathyroid hormone-related protein (PTHrP), have been shown to form a negative feedback loop regulating the onset of hypertrophic differentiation of chondrocytes. Bone morphogenetic proteins (BMPs), another family of secreted factors regulating bone formation, have been implicated as potential interactors of the Ihh/PTHrP feedback loop. To analyze the relationship between the two signaling pathways, we used an organ culture system for limb explants of mouse and chick embryos. We manipulated chondrocyte differentiation by supplementing these cultures either with BMP2, PTHrP and Sonic hedgehog as activators or with Noggin and cyclopamine as inhibitors of the BMP and Ihh/PTHrP signaling systems. Overexpression of Ihh in the cartilage elements of transgenic mice results in an upregulation of PTHrP expression and a delayed onset of hypertrophic differentiation. Noggin treatment of limbs from these mice did not antagonize the effects of Ihh overexpression. Conversely, the promotion of chondrocyte maturation induced by cyclopamine, which blocks Ihh signaling, could not be rescued with BMP2. Thus BMP signaling does not act as a secondary signal of Ihh to induce PTHrP expression or to delay the onset of hypertrophic differentiation. Similar results were obtained using cultures of chick limbs. We further investigated the role of BMP signaling in regulating proliferation and hypertrophic differentiation of chondrocytes and identified three functions of BMP signaling in this process. First we found that maintaining a normal proliferation rate requires BMP and Ihh signaling acting in parallel. We further identified a role for BMP signaling in modulating the expression of IHH: Finally, the application of Noggin to mouse limb explants resulted in advanced differentiation of terminally hypertrophic cells, implicating BMP signaling in delaying the process of hypertrophic differentiation itself. This role of BMP signaling is independent of the Ihh/PTHrP pathway.     

L-Maf,a downstream target of Pax6, is essential for chick lens development

Vascular endothelial growth factor (VEGF)-mediated angiogenesis is an important part of bone formation. To clarify the role of VEGF isoforms in endochondral bone formation, we examined long bone development in mice expressing exclusively the VEGF120 isoform (VEGF120/120 mice). Neonatal VEGF120/120 long bones showed a completely disturbed vascular pattern, concomitant with a 35% decrease in trabecular bone volume, reduced bone growth and a 34% enlargement of the hypertrophic chondrocyte zone of the growth plate. Surprisingly, embryonic hindlimbs at a stage preceding capillary invasion exhibited a delay in bone collar formation and hypertrophic cartilage calcification. Expression levels of marker genes of osteoblast and hypertrophic chondrocyte differentiation were significantly decreased in VEGF120/120 bones. Furthermore, inhibition of all VEGF isoforms in cultures of embryonic cartilaginous metatarsals, through the administration of a soluble receptor chimeric protein (mFlt-1/Fc), retarded the onset and progression of ossification, suggesting that osteoblast and/or hypertrophic chondrocyte development were impaired. The initial invasion by osteoclasts and endothelial cells into VEGF120/120 bones was retarded, associated with decreased expression of matrix metalloproteinase-9. Our findings indicate that expression of VEGF164 and/or VEGF188 is important for normal endochondral bone development, not only to mediate bone vascularization but also to allow normal differentiation of hypertrophic chondrocytes, osteoblasts, endothelial cells and osteoclasts.     

Expression profile of Xenopus banded hedgehog, a homolog of mouse Indian hedgehog, is related to the late development of endochondral ossification in Xenopus laevis

Late development of endochondral ossification occurs at the boundary between the growth cartilage and bone marrow during the formation of long bones in Xenopus laevis. Since the Indian hedgehog (Ihh) is involved in endochondral ossification in mouse, we investigated the expression of Xenopus banded hedgehog (X-bhh), which is a homolog of mouse Ihh. RT-PCR analysis demonstrated that the X-bhh mRNA was detected from an early stage of limb formation to formation of femurs in mature frogs, and it was associated with the expression of Xenopus-ptc1 (X-ptc1), Xenopus-gli1 (X-gli1), Xenopus-type II collagen (X-col II), Xenopus-runx2 (X-runx2), and Xenopus-osteocalcin (X-ocn) mRNAs. In situ hybridization revealed that chondrogenic cells observed at early limb development expressed X-bhh and X-gli1. At later stages of limb development, chondrocytes, located slightly away from the boundary between the cartilage and bone marrow, expressed the X-bhh, X-ptc1, and X-gli1 mRNAs; however, the mesenchymal cells at the boundary failed to express these mRNAs. The X-bhh, X-ptc1, and X-gli1 mRNAs as well as those of X-runx2 and X-ocn were expressed by the mesenchymal cells in the periosteal region at the tip of the cortical bone, indicating an intimate relationship between X-bhh expression and bone formation in this region. Considered collectively, the present study suggests that X-bhh evolutionally acquired the function to induce osteogenesis; however, the expression profile of X-bhh in epiphysis is closely related to the late development of endochondral ossification in X. laevis.     

Epigenetic mechanical factors in the evolution of long bone epiphyses

In developing vertebrate long bones in which endochondral ossification occurs, it is preceded or accompanied by perichondral ossification. The speed and extent of perichondral apposition relative to endochondral ossification varies in different taxa. Perichondral ossification dominates early long bone development in extinct basal tetrapods and dinosaurs, extant bony fish, amphibians, and birds. In mammals and lizards, perichondral and endochondral ossification proceed more synchronously. One of the most important epigenetic factors in skeletogenesis is mechanical loading caused by muscle contractions which begin in utero or in ovo . It has been previously shown that the stress distributions created perinatally in the chondroepiphysis during human skeletal development can influence the appearance of secondary ossification centres. Using finite element computer models representing bones near birth or hatching, we demonstrate that in vertebrates in which perichondral ossification significantly precedes endochondral ossification, the distribution of mechanical stresses in the ossifying cartilage anlagen tends to inhibit the appearance of secondary ossification centres in the ends of long bones. In models representing vertebrates in which endochondral ossification keeps pace with perichondral apposition, the appearance of secondary centres is promoted. The appearance of secondary centres leads to the formation of bony epiphyses and growth plates, which are most common in mammals and extant lizards. We postulate that genotypic factors influencing the relative speed and extent of perichondral and endochondral ossification interact with mechanical epigenetic factors early in development to account for many of the morphological differences observed in vertebrate skeletons.     

Wnt/beta-catenin signaling interacts differentially with Ihh signaling in controlling endochondral bone and synovial joint formation

Both the Wnt/beta-catenin and Ihh signaling pathways play essential roles in crucial aspects of endochondral ossification: osteoblast differentiation, chondrocyte proliferation and hypertrophy. To understand the genetic interaction between these two signaling pathways, we have inactivated the beta-catenin gene and upregulated Ihh signaling simultaneously in the same cells during endochondral skeletal development using beta-catenin and patched 1 floxed alleles. We uncovered previously unexpected roles of Ihh signaling in synovial joint formation and the essential function of Wnt/beta-catenin signaling in regulating chondrocyte survival. More importantly, we found that Wnt and Ihh signaling interact with each other in distinct ways to control osteoblast differentiation, chondrocyte proliferation, hypertrophy, survival and synovial joint formation in the developing endochondral bone. Beta-catenin is required downstream of Ihh signaling and osterix expression for osteoblast differentiation. But in chondrocyte survival, beta-catenin is required upstream of Ihh signaling to inhibit chondrocyte apoptosis. In addition, Ihh signaling can inhibit chondrocyte hypertrophy and synovial joint formation independently of beta-catenin. However, there is a strong synergistic interaction between Wnt/beta-catenin and Ihh signaling in regulating synovial joint formation.     

Regulation of skeletogenic differentiation in cranial dermal bone

Although endochondral ossification of the limb and axial skeleton is relatively well-understood, the development of dermal (intramembranous) bone featured by many craniofacial skeletal elements is not nearly as well-characterized. We analyzed the expression domains of a number of markers that have previously been associated with endochondral skeleton development to define the cellular transitions involved in the dermal ossification process in both chick and mouse. This led to the recognition of a series of distinct steps in the dermal differentiation pathways, including a unique cell type characterized by the expression of both osteogenic and chondrogenic markers. Several signaling molecules previously implicated in endochondrial development were found to be expressed during specific stages of dermal bone formation. Three of these were studied functionally using retroviral misexpression. We found that activity of bone morphogenic proteins (BMPs) is required for neural crest-derived mesenchyme to commit to the osteogenic pathway and that both Indian hedgehog (IHH) and parathyroid hormone-related protein (PTHrP, PTHLH) negatively regulate the transition from preosteoblastic progenitors to osteoblasts. These results provide a framework for understanding dermal bone development with an aim of bringing it closer to the molecular and cellular resolution available for the endochondral bone development.     

Indian hedgehog: its roles and regulation in endochondral bone development

Normal endochondral bone development requires the coordination of chondrocyte proliferation and differentiation. Indian hedgehog (Ihh) is a morphogen produced by chondrocytes in the early stage of terminal differentiation and plays several key roles in this process. Ihh regulates growth of adjacent proliferative chondrocytes and can also regulate the rate of differentiation of chondrocytes indirectly through its stimulation of parathyroid hormone-related protein (PTHrP). In this review, we focus on recent studies that have identified new functions of Ihh and how Ihh itself is being regulated.     

Influence of electromagnetic fields on endochondral bone formation

Endochondral ossification is a basic physiological process in limb development and is central to bone repair and linear growth. Factors which regulate endochondral ossification include several biophysical and biochemical agents and are of interest from clinical and biological perspectives. One of these agents, electric stimulation, has been shown to result in enhanced synthesis of extracellular matrix, calcification, and bone formation in a number of experimental systems and is the subject of this review. The effects of electric stimulation have been studied in embryonic limb rudiments, growth plates, and experimental endochondral ossification induced with decalcified bone matrix and, in all these models, endochondral ossification has been enhanced. It is not known definitively whether electric fields stimulate cell differentiation or modulate an increased number of molecules synthesized by committed cell population and this is a fertile area of current study.     

The turnover of mineralized growth plate cartilage into bone may be regulated by osteocytes

During endochondral ossification, growth plate cartilage is replaced with bone. Mineralized cartilage matrix is resorbed by osteoclasts, and new bone tissue is formed by osteoblasts. As mineralized cartilage does not contain any cells, it is unclear how this process is regulated. We hypothesize that, in analogy with bone remodeling, osteoclast and osteoblast activity are regulated by osteocytes, in response to mechanical loading. Since the cartilage does not contain osteocytes, this means that cartilage turnover during endochondral ossification would be regulated by the adjacent bone tissue. We investigated this hypothesis with an established computational bone adaptation model. In this model, osteocytes stimulate osteoblastic bone formation in response to the mechanical bone tissue loading. Osteoclasts resorb bone near randomly occurring microcracks that are assumed to block osteocyte signals. We used finite element modeling to evaluate our hypothesis in a 2D-domain representing part of the growth plate and adjacent bone. Cartilage was added at a constant physiological rate to simulate growth. Simulations showed that osteocyte signals from neighboring bone were sufficient for successful cartilage turnover, since equilibrium between cartilage remodeling and growth was obtained. Furthermore, there was good agreement between simulated bone structures and rat tibia histology, and the development of the trabecular architecture resembled that of infant long bones. Additionally, prohibiting osteoclast invasion resulted in thickened mineralized cartilage, similar to observations in a knock-out mouse model. We therefore conclude that it is well possible that osteocytes regulate the turnover of mineralized growth plate cartilage.     

Ihh signaling is directly required for the osteoblast lineage in the endochondral skeleton

Indian hedgehog (Ihh) is indispensable for development of the osteoblast lineage in the endochondral skeleton. In order to determine whether Ihh is directly required for osteoblast differentiation, we have genetically manipulated smoothened (Smo), which encodes a transmembrane protein that is essential for transducing all Hedgehog (Hh) signals. Removal of Smo from perichondrial cells by the Cre-LoxP approach prevents formation of a normal bone collar and also abolishes development of the primary spongiosa. Analysis of chimeric embryos composed of wild-type and Smo(n/n) cells indicates that Smo(n/n) cells fail to contribute to osteoblasts in either the bone collar or the primary spongiosa but generate ectopic chondrocytes. In order to assess whether Ihh is sufficient to induce bone formation in vivo, we have analyzed the bone collar in the long bones of embryos in which Ihh was artificially expressed in all chondrocytes by the UAS-GAL4 bigenic system. Although ectopic Ihh does not induce overt ossification along the entire cartilage anlage, it promotes progression of the bone collar toward the epiphysis, suggesting a synergistic effect between ectopic Ihh and endogenous factors such as the bone morphogenetic proteins (BMPs). In keeping with this model, Hh signaling is further found to be required in BMP-induced osteogenesis in cultures of a limb-bud cell line. Taken together, these results demonstrate that Ihh signaling is directly required for the osteoblast lineage in the developing long bones and that Ihh functions in conjunction with other factors such as BMPs to induce osteoblast differentiation. We suggest that Ihh acts in vivo on a potential progenitor cell to promote osteoblast and prevent chondrocyte differentiation.     

Involvement of the MAP kinase pathways in induction of GADD45 following UV radiation

Indian hedgehog (Ihh) is highly expressed in prehypertrophic chondrocytes in vivo and has been proposed to regulate the proliferation and maturation of chondrocytes and bone collar formation in the growth plate. In high-density cultures of rabbit growth-plate chondrocytes, Ihh mRNA was also expressed at the highest level in the prehypertrophic stage. To explore endogenous factors that regulate Ihh expression in chondrocytes, we examined the effects of various growth factors on Ihh mRNA expression in this system. Retinoic acid (RA) and bone morphogenetic protein-2 enhanced Ihh mRNA expression, whereas PTH/PTH-related peptide (PTHrP) markedly suppressed Ihh expression. RA at more than 10(-8) M induced the expression of Ihh and Patched 1 (Ptc1) within 3 h, before it increased the type X collagen mRNA level at 6-24 h. Cycloheximide blocked the up-regulation of Ihh by RA, indicating the requirement of de novo protein synthesis for this stimulation. These findings suggest that RA is involved in the up-regulation of Ihh during endochondral bone formation. In contrast to RA, PTH (1-84) at 10(-7) M abolished the mRNA expression of Ihh and Ptc1 within 2-4 h, before it suppressed the expression of type X collagen at 12-24 h. The inhibition of Ihh expression by PTH (1-84) did not require de novo protein synthesis. PTH (1-34), PTHrP (1-34), and (Bu)(2)cAMP also suppressed Ihh expression. On the other hand, Ihh has been reported to induce PTHrP synthesis in the perichondrium. Consequently, the direct inhibitory action of PTH/PTHrP on Ihh appears to be a negative feedback mechanism that prevents excess PTHrP accumulation in cartilage.     

Site specific effects of zoledronic acid during tibial and mandibular fracture repair

Numerous factors can affect skeletal regeneration, including the extent of bone injury, mechanical loading, inflammation and exogenous molecules. Bisphosphonates are anticatabolic agents that have been widely used to treat a variety of metabolic bone diseases. Zoledronate (ZA), a nitrogen-containing bisphosphonate (N-BP), is the most potent bisphosphonate among the clinically approved bisphosphonates. Cases of bisphosphonate-induced osteonecrosis of the jaw have been reported in patients receiving long term N-BP treatment. Yet, osteonecrosis does not occur in long bones. The aim of this study was to compare the effects of zoledronate on long bone and cranial bone regeneration using a previously established model of non-stabilized tibial fractures and a new model of mandibular fracture repair. Contrary to tibial fractures, which heal mainly through endochondral ossification, mandibular fractures healed via endochondral and intramembranous ossification with a lesser degree of endochondral ossification compared to tibial fractures. In the tibia, ZA reduced callus and cartilage formation during the early stages of repair. In parallel, we found a delay in cartilage hypertrophy and a decrease in angiogenesis during the soft callus phase of repair. During later stages of repair, ZA delayed callus, cartilage and bone remodeling. In the mandible, ZA delayed callus, cartilage and bone remodeling in correlation with a decrease in osteoclast number during the soft and hard callus phases of repair. These results reveal a more profound impact of ZA on cartilage and bone remodeling in the mandible compared to the tibia. This may predispose mandible bone to adverse effects of ZA in disease conditions. These results also imply that therapeutic effects of ZA may need to be optimized using time and dose-specific treatments in cranial versus long bones.     

Impaired endochondral bone development and osteopenia in Gli2-deficient mice

Mice homozygous for targeted disruption of the zinc finger domain of Gli2 (Gli2(zfd/zfd)) die at birth with developmental defects in several organ systems including the skeleton. The current studies were undertaken to define the role of Gli2 in endochondral bone development by characterizing the molecular defects in the limbs and vertebrae of Gli2(zfd/zfd) mice. The bones of mutant mice removed by cesarian section at E16.5 and E18.5 demonstrated delayed endochondral ossification. This was accompanied by an increase in the length of cartilaginous growth plates, reduced bone tissue in the femur and tibia and by failure to develop the primary ossification centre in vertebral bodies. The growth plates of tibiae and vertebrae exhibited increased numbers of proliferating and hypertrophic chondrocytes with no apparent alteration in matrix mineralisation. The changes in growth plate morphology were accompanied by an increase in expression of FGF2 in proliferating chondrocytes and decreased expression of Indian hedgehog (Ihh), patched (Ptc) and parathyroid-hormone-related protein (PTHrP) in prehypertrophic cells. Furthermore, there was a reduction in expression of angiogenic molecules in hypertrophic chondrocytes, which was accompanied by a decrease in chondroclasts at the cartilage bone interface, fewer osteoblasts lining trabecular surfaces and a reduced volume of metaphyseal bone. These results indicate that functional Gli2 is necessary for normal endochondral bone development and that its absence results in increased proliferation of immature chondrocytes and decreased resorption of mineralised cartilage and bone formation.