ABSTRACT
Appropriate classification of fusion-driven bone and soft tissue neoplasms continues to evolve, often relying on the careful integration of morphologic findings with immunohistochemical, molecular, and clinical data. Herein, we present 3 cases of a morphologically distinct myxoid mesenchymal neoplasm with myogenic differentiation and novel CRTC1::MRTFB (formerly MKL2) gene fusion. Three tumors occurred in 1 male and 2 female patients with a median age of 72 years (range: 28-78). Tumors involved the left iliac bone, the right thigh, and the left perianal region with a median size of 4.0 cm (4.0-7.6 cm). Although 1 tumor presented as an incidental finding, the other 2 tumors were noted, given their persistent growth. At the time of the last follow-up, 1 patient was alive with unresected disease at 6 months, 1 patient was alive without evidence of disease at 12 months after surgery, and 1 patient died of disease 24 months after diagnosis. On histologic sections, the tumors showed multinodular growth and were composed of variably cellular spindle to round-shaped cells with distinct brightly eosinophilic cytoplasm embedded within a myxoid stroma. One tumor showed overt smooth muscle differentiation. Cytologic atypia and mitotic activity ranged from minimal (2 cases) to high (1 case). By immunohistochemistry, the neoplastic cells expressed focal smooth muscle actin, h-caldesmon, and desmin in all tested cases. Skeletal muscle markers were negative. Next-generation sequencing detected nearly identical CRTC1::MRTFB gene fusions in all cases. We suggest that myxoid mesenchymal tumors with myogenic differentiation harboring a CRTC1::MRTFB fusion may represent a previously unrecognized, distinctive entity that involves soft tissue and bone. Continued identification of these novel myxoid neoplasms with myogenic differentiation will be important in determining appropriate classification, understanding biologic potential, and creating treatment paradigms.
Subject(s)
Bone Neoplasms , Cell Differentiation , Soft Tissue Neoplasms , Transcription Factors , Humans , Male , Female , Aged , Transcription Factors/genetics , Soft Tissue Neoplasms/genetics , Soft Tissue Neoplasms/pathology , Adult , Bone Neoplasms/genetics , Bone Neoplasms/pathology , Biomarkers, Tumor/genetics , Biomarkers, Tumor/analysis , Oncogene Proteins, Fusion/genetics , Gene Fusion , Trans-Activators/genetics , Muscle Development/geneticsABSTRACT
OBJECTIVE: To characterize relationships between quantitative computed tomography bone mineral density measurements and other qualitative and quantitative imaging measures, as well as clinical metrics, in patients with autosomal dominant osteopetrosis type 2 (ADO2). MATERIALS AND METHODS: Clinical and radiologic parameters of 9 adults and 3 children with autosomal dominant osteopetrosis type 2 were assessed including lumbar spine quantitative computed tomography (QCT), radiographic skeletal survey (skull base thickening; Erlenmeyer flask deformity; endobone pattern; and spine density pattern (endplate sclerosis, "anvil" appearance, or diffuse sclerosis)), dual-energy x-ray absorptiometry (DXA), tibial peripheral quantitative computed tomography (pQCT) volumetric bone mineral density (vBMD), bone turnover markers, and bone marrow failure or visual impairment. RESULTS: The skeletal parameter most divergent from normal was lumbar spine QCT Z-score (+ 3.6 to + 38.7). Lumbar QCT Z-score correlated positively with pQCT tibial diaphysis vBMD (Pearson correlation r = 0.73, p = 0.02) and pQCT tibial metaphysis vBMD (r = 0.87, p < 0.01). A trend towards positive lumbar QCT Z-score correlation with serum P1NP/CTX ratio (r = 0.54, p = 0.10) and lumbar DXA Z-score (r = 0.55, p = 0.10) were observed. Bone marrow failure and vision impairment occurred in those with most severe quantitative and qualitative measures, while those with less severe radiographic features had the lowest QCT Z-scores. CONCLUSION: Lumbar spine QCT provided the most extreme skeletal assessment in ADO2, which correlated positively with other radiologic and clinical markers of disease severity. Given the quantification of trabecular bone and greater variation from normal with wider range of values, lumbar QCT Z-scores may be useful to determine or detect impact of future treatments.
Subject(s)
Osteopetrosis , Absorptiometry, Photon , Adult , Bone Density , Bone and Bones , Child , Humans , Lumbar Vertebrae/diagnostic imaging , Osteopetrosis/diagnostic imaging , Osteopetrosis/genetics , Severity of Illness IndexABSTRACT
PURPOSE: Reformatting computed tomography (CT) scans along the scaphoid longitudinal axis improves the ability to detect scaphoid fractures compared with reformats along the wrist axis. However, it remains unclear whether scaphoid axis reformats affect measurements of displacement or deformity, which are factors that drive the clinical decision to perform open reduction internal fixation. Our null hypothesis was that reformatting CT scans along the scaphoid axis does not affect measurements of fracture displacement and deformity. METHODS: Thirty patients with CT scans demonstrating scaphoid fractures (4 proximal pole, 17 midwaist fractures, and 9 distal) were identified and reformatted along 2 axes: the longitudinal axis of the scaphoid and the longitudinal axis of the wrist. The reformatted scans were sent to 2 musculoskeletal radiologists and 2 orthopedic hand surgeons who made the following measurements: (1) fracture gap, (2) displacement of the articular surface, (3) intrascaphoid angle, and (4) height to length (H:L) ratio. RESULTS: The reliability of each of the measurements cited above was compared for all raters between the 2 axes using intraclass correlation coefficients. Measurement of fracture gap and articular displacement trended toward more reliability in the wrist axis, whereas measurement of H:L ratio and intrascaphoid angle trended toward more reliability in the scaphoid axis. However, no differences in measurements between the 2 axes were statistically significant. CONCLUSIONS: This study demonstrates that reformatting CT scans in line with the axis of the scaphoid does not result in more reliable measurements of displacement or deformity. CLINICAL RELEVANCE: Measurements of displacement and deformity in scaphoid fractures can be made in the wrist axis with comparative reliability to those in the longitudinal scaphoid axis.
Subject(s)
Fractures, Bone/diagnostic imaging , Scaphoid Bone/diagnostic imaging , Tomography, X-Ray Computed/methods , Humans , Reproducibility of Results , Retrospective StudiesABSTRACT
Chronic kidney disease (CKD) is characterized by secondary hyperparathyroidism and an increased risk of hip fractures predominantly related to cortical porosity. Unfortunately, bone mineral density measurements and high-resolution peripheral computed tomography (HR-pQCT) imaging have shortcomings that limit their utility in these patients. Ultrashort echo time magnetic resonance imaging (UTE-MRI) has the potential to overcome these limitations by providing an alternative assessment of cortical porosity. The goal of the current study was to determine if UTE-MRI could detect changes in porosity in an established rat model of CKD. Cy/+ rats (n = 11), an established animal model of CKD-MBD, and their normal littermates (n = 12) were imaged using microcomputed tomography (microCT) and UTE-MRI at 30 and 35 weeks of age (which approximates late-stage kidney disease in humans). Images were obtained at the distal tibia and the proximal femur. Cortical porosity was assessed using the percent porosity (Pore%) calculated from microCT imaging and the porosity index (PI) calculated from UTE-MRI. Correlations between Pore% and PI were also calculated. Cy/+ rats had higher Pore% than normal rats at both skeletal sites at 35 weeks (tibia = 7.13 % +/- 5.59 % vs. 0.51 % +/- 0.09 %, femur = 19.99 % +/- 7.72 % vs. 2.72 % +/- 0.32 %). They also had greater PI at the distal tibia at 30 weeks of age (0.47 +/- 0.06 vs. 0.40 +/- 0.08). However, Pore% and PI were only correlated in the proximal femur at 35 weeks of age (ρ = 0.929, Spearman). These microCT results are consistent with prior studies in this animal model utilizing microCT imaging. The UTE-MRI results were inconsistent, resulting in variable correlations with microCT imaging, which may be related to suboptimal bound and pore water discrimination at higher magnetic field strengths. Nevertheless, UTE-MRI may still provide an additional clinical tool to assess fracture risk without using ionizing radiation in CKD patients.
Subject(s)
Hip Fractures , Renal Insufficiency, Chronic , Humans , Animals , Rats , X-Ray Microtomography , Porosity , Cortical Bone/diagnostic imaging , Magnetic Resonance Imaging/methods , Bone Density , Models, Animal , Renal Insufficiency, Chronic/diagnostic imagingABSTRACT
Mechanical loading and intermittent parathyroid (iPTH) treatment are both osteoanabolic stimuli and are regulated by partially overlapping cellular signaling pathways. iPTH has been shown clinically to be effective in increasing bone mass and reducing fracture risk. Likewise, mechanical stimulation can significantly enhance bone apposition and prevent bone loss, but its clinical effects on fracture susceptibility are less certain. Many of the osteogenic effects of iPTH are localized to biomechanically suboptimal bone surfaces, whereas mechanical loading directs new bone formation to high-stress areas and not to strain-neutral areas. These differences in localization in new tissue, resulting from load-induced versus iPTH-induced bone accumulation, should affect the relation between bone mass and bone strength, or "tissue economy." We investigated the changes in bone mass and strength induced by 6 weeks of mechanical loading and compared them to changes induced by 6 weeks of iPTH treatment. Loading and iPTH both increased ulnar bone accrual, as measured by bone mineral density and content, and fluorochrome-derived bone formation. iPTH induced a significantly greater increase in bone mass than loading, but ulnar bone strength was increased approximately the same amount by both treatments. Mechanical loading during growth can spatially optimize new bone formation to improve structural integrity with a minimal increase in mass, thereby increasing tissue economy, i.e., the amount of strength returned per unit bone mass added. Furthermore, exercise studies in which only small changes in bone mass are detected might be more beneficial to bone health and fracture resistance than has commonly been presumed.
Subject(s)
Bone and Bones/drug effects , Osteogenesis/drug effects , Parathyroid Hormone/pharmacology , Absorptiometry, Photon , Animals , Bone Density/drug effects , Bone and Bones/physiology , Female , Injections, Subcutaneous , Mechanotransduction, Cellular , Mice , Mice, Inbred C57BL , Osteogenesis/physiology , Stress, Mechanical , Ulna/drug effects , Ulna/growth & development , Ulna/metabolism , Weight-BearingABSTRACT
The low density lipoprotein receptor-related protein-5 (LRP5), a co-receptor in the Wnt signaling pathway, modulates bone mass in humans and in mice. Lrp5 knock-out mice have severely impaired responsiveness to mechanical stimulation whereas Lrp5 gain-of-function knock-in and transgenic mice have enhanced responsiveness to mechanical stimulation. Those observations highlight the importance of Lrp5 protein in bone cell mechanotransduction. It is unclear if and how high bone mass-causing (HBM) point mutations in Lrp5 alter the bone-wasting effects of mechanical disuse. To address this issue we explored the skeletal effects of mechanical disuse using two models, tail suspension and Botulinum toxin-induced muscle paralysis, in two different Lrp5 HBM knock-in mouse models. A separate experiment employing estrogen withdrawal-induced bone loss by ovariectomy was also conducted as a control. Both disuse stimuli induced significant bone loss in WT mice, but Lrp5 A214V and G171V were partially or fully protected from the bone loss that normally results from disuse. Trabecular bone parameters among HBM mice were significantly affected by disuse in both models, but these data are consistent with DEXA data showing a failure to continue growing in HBM mice, rather than a loss of pre-existing bone. Ovariectomy in Lrp5 HBM mice resulted in similar protection from catabolism as was observed for the disuse experiments. In conclusion, the Lrp5 HBM alleles offer significant protection from the resorptive effects of disuse and from estrogen withdrawal, and consequently, present a potential mechanism to mimic with pharmaceutical intervention to protect against various bone-wasting stimuli.
Subject(s)
Bone Density/physiology , Bone Diseases, Metabolic/prevention & control , Low Density Lipoprotein Receptor-Related Protein-5/physiology , Mutation, Missense , Point Mutation , Animals , Bone Density/genetics , Bone Diseases, Metabolic/etiology , Bone Diseases, Metabolic/pathology , Botulinum Toxins/toxicity , Disease Models, Animal , Estrogens/deficiency , Estrogens/physiology , Female , Femur/pathology , Gene Knock-In Techniques , Humans , Immobilization/adverse effects , Low Density Lipoprotein Receptor-Related Protein-5/genetics , Mechanotransduction, Cellular/genetics , Mechanotransduction, Cellular/physiology , Mice , Osteoporosis, Postmenopausal/pathology , Osteoporosis, Postmenopausal/prevention & control , Ovariectomy/adverse effects , Paralysis/chemically induced , Paralysis/complications , Paralysis/pathology , Stress, Mechanical , Weight-BearingABSTRACT
Certain missense mutations affecting LRP5 cause high bone mass (HBM) in humans. Based on in vitro evidence, HBM LRP5 receptors are thought to exert their effects by providing resistance to binding/inhibition of secreted LRP5 inhibitors such as sclerostin (SOST) and Dickkopf homolog-1 (DKK1). We previously reported the creation of two Lrp5 HBM knock-in mouse models, in which the human p.A214V or p.G171V missense mutations were knocked into the endogenous Lrp5 locus. To determine whether HBM knock-in mice are resistant to SOST- or DKK1-induced osteopenia, we bred Lrp5 HBM mice with transgenic mice that overexpress human SOST in osteocytes ((8kb) Dmp1-SOST) or mouse DKK1 in osteoblasts and osteocytes ((2.3kb) Col1a1-Dkk1). We observed that the (8kb) Dmp1-SOST transgene significantly lowered whole-body bone mineral density (BMD), bone mineral content (BMC), femoral and vertebral trabecular bone volume fraction (BV/TV), and periosteal bone-formation rate (BFR) in wild-type mice but not in mice with Lrp5 p.G171V and p.A214V alleles. The (2.3kb) Col1a1-Dkk1 transgene significantly lowered whole-body BMD, BMC, and vertebral BV/TV in wild-type mice and affected p.A214V mice more than p.G171V mice. These in vivo data support in vitro studies regarding the mechanism of HBM-causing mutations, and imply that HBM LRP5 receptors differ in their relative sensitivity to inhibition by SOST and DKK1.
Subject(s)
Bone Density/genetics , Femur/metabolism , Glycoproteins/metabolism , Intercellular Signaling Peptides and Proteins/metabolism , Low Density Lipoprotein Receptor-Related Protein-5 , Mutation, Missense , Osteocytes/metabolism , Adaptor Proteins, Signal Transducing , Amino Acid Substitution , Animals , Collagen Type I/genetics , Collagen Type I/metabolism , Collagen Type I, alpha 1 Chain , Femur/pathology , Gene Knock-In Techniques , Genetic Loci , Glycoproteins/genetics , Humans , Intercellular Signaling Peptides and Proteins/genetics , Low Density Lipoprotein Receptor-Related Protein-5/genetics , Low Density Lipoprotein Receptor-Related Protein-5/metabolism , Mice , Organ Size/genetics , Osteocytes/pathologyABSTRACT
Mechanotransduction in bone requires components of the Wnt signaling pathway to produce structurally adapted bone elements. In particular, the Wnt co-receptor LDL-receptor-related protein 5 (LRP5) appears to be a crucial protein in the mechanotransduction cascades that translate physical tissue deformation into new bone formation. Recently discovered missense mutations in LRP5 are associated with high bone mass (HBM), and the altered function of these proteins provide insight into LRP5 function in many skeletal processes, including mechanotransduction. We further investigated the role of LRP5 in bone cell mechanotransduction by applying mechanical stimulation in vivo to two different mutant mouse lines, which harbor HBM-causing missense mutations in Lrp5. Axial tibia loading was applied to mature male Lrp5 G171V and Lrp5 A214V knock-in mice, and to their wild type controls. Fluorochrome labeling revealed that 3 days of loading resulted in a significantly enhanced periosteal response in the A214V knock in mice, whereas the G171V mice exhibited a lowered osteogenic threshold on the endocortical surface. In summary, our data further highlight the importance of Lrp5 in bone cell mechanotransduction, and indicate that the HBM-causing mutations in Lrp5 can alter the anabolic response to mechanical stimulation in favor of increased bone gain.
Subject(s)
Amino Acid Substitution/genetics , Low Density Lipoprotein Receptor-Related Protein-5/genetics , Mechanotransduction, Cellular , Mutation/genetics , Osteogenesis/physiology , Tibia/physiology , Animals , Low Density Lipoprotein Receptor-Related Protein-5/metabolism , Male , Mice , Mice, Transgenic , Periosteum/growth & development , Periosteum/metabolism , Radiography , Surface Properties , Tibia/diagnostic imaging , Tibia/metabolism , Weight-Bearing/physiologyABSTRACT
Mutations among genes that participate in the canonical Wnt signaling pathway can lead to drastically different skeletal phenotypes, ranging from severe osteoporosis to severe osteosclerosis. Many high-bone-mass (HBM) causing mutations that occur in the LRP5 gene appear to impart the HBM phenotype, in part, by increasing resistance to soluble Wnt signaling inhibitors, including sclerostin. Sost loss-of-function mutant mice (Sost knock-out) and Lrp5 gain-of-function mutant mice (Lrp5 HBM knock-in) have high bone mass. These mutants potentially would be predicted to be phenocopies of one another, because in both cases, the sclerostin-Lrp5 interaction is disrupted. We measured bone mass, size, geometry, architecture, and strength in bones from three different genetic mouse models (Sost knock-out, Lrp5 A214V knock-in, and Lrp5 G171V knock-in) of HBM. We found that all three mouse lines had significantly elevated bone mass in the appendicular skeleton and in the cranium. Sost mutants and Lrp5 A214V mutants were statistically indistinguishable from one another in most endpoints, whereas both were largely different from the Lrp5 G171V mutants. Lrp5 G171V mutants preferentially added bone endocortically, whereas Lrp5 A214V and Sost mutants preferentially added bone periosteally. Cranial thickness and cranial nerve openings were similarly altered in all three HBM models. We also assessed serum serotonin levels as a possible mechanism accounting for the observed changes in bone mass, but no differences in serum serotonin were found in any of the three HBM mouse lines. The skeletal dissimilarities of the Lrp5 G171V mutant to the other mutants suggest that other, non-sclerostin-associated mechanisms might account for the changes in bone mass resulting from this mutation.
Subject(s)
Bone Development , Mutation , Organ Size , Signal Transduction/genetics , Wnt Proteins/metabolism , Animals , Biomechanical Phenomena , Male , Mice , Mice, Mutant Strains , Phenotype , Serotonin/blood , Tomography, X-Ray Computed/methodsABSTRACT
The human skeleton is affected by mutations in low-density lipoprotein receptor-related protein 5 (LRP5). To understand how LRP5 influences bone properties, we generated mice with osteocyte-specific expression of inducible Lrp5 mutations that cause high and low bone mass phenotypes in humans. We found that bone properties in these mice were comparable to bone properties in mice with inherited mutations. We also induced an Lrp5 mutation in cells that form the appendicular skeleton but not in cells that form the axial skeleton; we observed that bone properties were altered in the limb but not in the spine. These data indicate that Lrp5 signaling functions locally, and they suggest that increasing LRP5 signaling in mature bone cells may be a strategy for treating human disorders associated with low bone mass, such as osteoporosis.
Subject(s)
Bone Density/genetics , LDL-Receptor Related Proteins/physiology , Alleles , Animals , Bone Density/physiology , Bone and Bones/metabolism , Bone and Bones/physiology , Female , Gene Knock-In Techniques , Gene Knockout Techniques , Genotype , LDL-Receptor Related Proteins/genetics , Low Density Lipoprotein Receptor-Related Protein-5 , Male , Mice , Mice, Knockout , Mice, Mutant Strains , Osteocytes/metabolism , Osteocytes/physiology , Serotonin/biosynthesis , Spine/metabolism , Spine/physiology , Tryptophan Hydroxylase/physiologySubject(s)
Bone Density/genetics , LDL-Receptor Related Proteins/physiology , Animals , Female , MaleABSTRACT
Sclerostin, the protein product of the Sost gene, is a potent inhibitor of bone formation. Among bone cells, sclerostin is found nearly exclusively in the osteocytes, the cell type that historically has been implicated in sensing and initiating mechanical signaling. The recent discovery of the antagonistic effects of sclerostin on Lrp5 receptor signaling, a crucial mediator of skeletal mechanotransduction, provides a potential mechanism for the osteocytes to control mechanotransduction, by adjusting their sclerostin (Wnt inhibitory) signal output to modulate Wnt signaling in the effector cell population. We investigated the mechanoregulation of Sost and sclerostin under enhanced (ulnar loading) and reduced (hindlimb unloading) loading conditions. Sost transcripts and sclerostin protein levels were dramatically reduced by ulnar loading. Portions of the ulnar cortex receiving a greater strain stimulus were associated with a greater reduction in Sost staining intensity and sclerostin-positive osteocytes (revealed via in situ hybridization and immunohistochemistry, respectively) than were lower strain portions of the tissue. Hindlimb unloading yielded a significant increase in Sost expression in the tibia. Modulation of sclerostin levels appears to be a finely tuned mechanism by which osteocytes coordinate regional and local osteogenesis in response to increased mechanical stimulation, perhaps via releasing the local inhibition of Wnt/Lrp5 signaling.
Subject(s)
Bone Morphogenetic Proteins/biosynthesis , Mechanotransduction, Cellular/physiology , Osteocytes/metabolism , Osteogenesis/physiology , Tibia/metabolism , Ulna/metabolism , Adaptor Proteins, Signal Transducing , Animals , Female , Genetic Markers , Glycoproteins , In Situ Hybridization , Intercellular Signaling Peptides and Proteins , LDL-Receptor Related Proteins/metabolism , Low Density Lipoprotein Receptor-Related Protein-5 , Male , Mice , Osteocytes/cytology , Rats , Rats, Inbred Lew , Tibia/cytology , Ulna/cytology , Weight-Bearing/physiology , Weightlessness Simulation/methods , Wnt Proteins/metabolismABSTRACT
Intracellular signals involved in the maturation and function of osteoclasts are poorly understood. Here, we demonstrate that osteoclasts express multiple regulatory subunits of class I(A) phosphatidylinositol 3-kinase (PI3-K) although the expression of the full-length form of p85alpha is most abundant. In vivo, deficiency of p85alpha results in a significantly greater number of trabeculae and significantly lower spacing between trabeculae as well as increased bone mass in both males and females compared to their sex-matched wild-type controls. Consistently, p85alpha(-/-) osteoclast progenitors show impaired growth and differentiation, which is associated with reduced activation of Akt and mitogen-activated protein kinase extracellular signal-regulated kinase 1 (Erk1)/Erk2 in vitro. Furthermore, a significant reduction in the ability of p85alpha(-/-) osteoclasts to adhere to as well as to migrate via integrin alphavbeta3 was observed, which was associated with reduced bone resorption. Microarray as well as quantitative real-time PCR analysis of p85alpha(-/-) osteoclasts revealed a significant reduction in the expression of several genes associated with the maturation and migration of osteoclasts, including microphathalmia-associated transcription factor, tartrate-resistant acid phosphatase, cathepsin K, and beta3 integrin. Restoring the expression of the full-length form of p85alpha but not the version with a deletion of the Src homology-3 domain restored the maturation of p85alpha(-/-) osteoclasts to wild-type levels. These results highlight the importance of the full-length version of the p85alpha subunit of class I(A) PI3-K in controlling multiple aspects of osteoclast functions.
Subject(s)
Cell Differentiation , Cell Movement , Osteoclasts/cytology , Osteoclasts/enzymology , Phosphatidylinositol 3-Kinases/physiology , Animals , Bone Resorption , Cell Adhesion , Cell Proliferation , Female , Gene Expression Profiling , Gene Expression Regulation , Male , Mice , Mice, Knockout , Phosphatidylinositol 3-Kinases/deficiency , Protein SubunitsABSTRACT
To facilitate locomotion and support the body, the skeleton relies on the transmission of forces between muscles and bones through complex junctions called entheses. The varying mechanical and biological properties of the enthesis make healing this avascular tissue difficult; hence the need for an engineered alternative. Cells in situ interact with their environment on the nano-scale which suggests that engineered approaches to enthesis regeneration should include such biologically-inspired nano-scale surface features. The present in vitro study investigated the effects of etching poly-lactic-co-glycolic acid (PLGA) scaffolds to produce nano-topography on the adhesion of fibroblasts and osteoblasts, two integral enthesis cell types. Nano-topography was produced on PLGA by etching the scaffolds in NaOH. Results showed that etching PLGA with NaOH to create nano-scale surface features decreased fibroblast adhesion while it increased osteoblast adhesion; criteria critical for the spatial control of osteoblast and fibroblast adhesion for a successful enthesis tissue engineering material. Thus, the results of this study showed for the first time collective evidence that PLGA can be either treated with NaOH or not on ends of an enthesis tissue engineering construct to spatially increase osteoblast and fibroblast adhesion, respectively.