Defective circadian control in mesenchymal cells reduces adult bone mass in mice by promoting osteoclast function.

Serum bone turnover markers show diurnal variation in humans, suggesting that circadian rhythms contribute to normal bone physiology. This conclusion is corroborated by bone phenotypes in mice with genetic disruption of the circadian molecular clock mechanism, for instance via deletion of the transcription factor Brain and Muscle Arntl-like 1 (Bmal1). To dissect the contribution of circadian molecular clocks in individual bone cell types, we generated mice with conditional deletion of Bmal1 in osteoclasts (Ctsk-cre) and in mesenchymal cells of the limbs (Prx1-cre). We report that deletion of Bmal1 in osteoclasts had no effect on trabecular or cortical bone parameters in vivo or on osteoclast differentiation in vitro. In contrast, Bmal1f/f.Prx1-cre mice had significantly less trabecular and cortical bone than Bmal1f/f littermate controls, recapitulating the bone phenotype of Bmal1 germline deficient mice. The number of osteoblast precursors in the bone marrow of Bmal1f/f.Prx1-cre mice was similar to wild-type controls, while the in vitro differentiation capacity of Bmal1-deficient osteoblast precursors, measured as induction of alkaline phosphatase activity, was significantly lower. Despite this, serum procollagen type 1 N-terminal propeptide (P1NP), a measure of bone formation in vivo, was higher in Bmal1f/f.Prx1-cre mice than in Bmal1f/f mice. Consistent with a high bone turnover state in the mutant mice, the bone resorption marker serum C-terminal telopeptides of Type I collagen (CTX-I) was also elevated, and Bmal1f/f.Prx1-cre mice had a higher number of tartrate resistant acid phosphatase (TRAP) positive osteoclasts than Bmal1f/f controls. These results demonstrate that adult bone mass in mice is controlled by the intrinsic circadian molecular clock in mesenchymal cells but not osteoclasts. The effect of the mesenchymal cell clock on bone turnover appears to involve osteoblast-osteoclast cross-talk.

Utility of quantitative micro-computed tomographic analysis in zebrafish to define gene function during skeletogenesis.

The zebrafish is a powerful experimental model to investigate the genetic and morphologic basis of vertebrate development. Analysis of skeletogenesis in this fish is challenging as a result of the small size of the developing and adult zebrafish. Many of the bones of small fishes such as the zebrafish and medaka are quite thin, precluding many standard assays of bone quality and morphometrics commonly used on bones of larger animals. Microcomputed tomography (microCT) is a common imaging technique used for detailed analysis of the skeleton of the zebrafish and determination of mutant phenotypes. However, the utility of this modality for analysis of the zebrafish skeleton, and the effect of inherent variation among individual zebrafish, including variables such as sex, age and strain, is not well understood. Given the increased use and accessibility of microCT, we set out to define the sensitivity of microCT methods in developing and adult zebrafish. We assessed skeletal shape and density measures in the developing vertebrae and parasphenoid of the skull base. We found most skeletal variables are tightly correlated to standard length, but that at later growth stages (>3months) there are age dependent effects on some skeletal measures. Further we find modest strain but not sex differences in skeletal measures. These data suggest that the appropriate control for assessing mutant phenotypes should be age and strain matched, ideally a wild-type sibling. By analyzing two mutants exhibiting skeletal dysplasia, we show that microCT imaging can be a sensitive method to quantify distinct skeletal parameters of adults. Finally, as developing zebrafish skeletons remain difficult to resolve by radiographic means, we define a contrast agent specific for bone that enhances resolution at early stages, permitting detailed morphometric analysis of the forming skeleton. This increased capability for detection extends the use of this imaging modality to leverage the zebrafish model to understand the development causes of skeletal dysplasias.

Nonswelling Click-Cross-Linked Gelatin and PEG Hydrogels with Tunable Properties Using Pluronic Linkers.

Swelling of hydrogels leads to a decrease in mechanical performance coupled with complications in solute diffusion. In addition, hydrogel swelling affects patient safety in biomedical applications such as compression of tissue and fluid blockage. A conventional strategy for suppressing swelling is to introduce a thermoresponsive polymer with a lower critical solution temperature (LCST) within the network structure to counter the water uptake at elevated temperature. However, altering the gel's mechanical strength via modification of the network structure often affects the water uptake behavior and thus a nonswelling platform with tunable mechanical properties suitable for various biomedical applications is desirable. In this study we applied the commercially available triblock PEG-PPG-PEG (Pluronic) as a cross-linker for the preparation of nucleophilic thiol-yne click cross-linked hydrogels with suppressed swelling at physiologically relevant temperature. The mechanical properties and degradation rate of these nonswelling hydrogels can be tuned by judicious combinations of the available linkers. The Pluronic linkers can be applied to prepare biologically relevant gelatin based hydrogels with suppressed swelling under physiological conditions that support attachment of fibroblast cells in 2D culture and controlled release of albumin, paving the way for the development of reliable and better performing soft biomaterials.

Gut microbiota induce IGF-1 and promote bone formation and growth.

Appreciation of the role of the gut microbiome in regulating vertebrate metabolism has exploded recently. However, the effects of gut microbiota on skeletal growth and homeostasis have only recently begun to be explored. Here, we report that colonization of sexually mature germ-free (GF) mice with conventional specific pathogen-free (SPF) gut microbiota increases both bone formation and resorption, with the net effect of colonization varying with the duration of colonization. Although colonization of adult mice acutely reduces bone mass, in long-term colonized mice, an increase in bone formation and growth plate activity predominates, resulting in equalization of bone mass and increased longitudinal and radial bone growth. Serum levels of insulin-like growth factor 1 (IGF-1), a hormone with known actions on skeletal growth, are substantially increased in response to microbial colonization, with significant increases in liver and adipose tissue IGF-1 production. Antibiotic treatment of conventional mice, in contrast, decreases serum IGF-1 and inhibits bone formation. Supplementation of antibiotic-treated mice with short-chain fatty acids (SCFAs), products of microbial metabolism, restores IGF-1 and bone mass to levels seen in nonantibiotic-treated mice. Thus, SCFA production may be one mechanism by which microbiota increase serum IGF-1. Our study demonstrates that gut microbiota provide a net anabolic stimulus to the skeleton, which is likely mediated by IGF-1. Manipulation of the microbiome or its metabolites may afford opportunities to optimize bone health and growth.

IL4RA on lymphatic endothelial cells promotes T cell egress during sclerodermatous graft versus host disease.

Systemic sclerosis (SSc) is a potentially fatal autoimmune disorder with limited therapeutic options. Sclerodermatous graft versus host disease (sclGvHD), induced by transfer of B10.D2 splenocytes into BALB/c Rag2-/- mice, models an inflammatory subset of SSc characterized by a prominent IL13-induced gene expression signature in the skin. Host mice deficient in IL4RA, a subunit of the type II IL4/IL13 receptor, are protected from sclGvHD. While IL4RA has a well-established role in Th2 differentiation and alternative macrophage activation, we report here a previously unappreciated function for IL4RA in lymphatic endothelial cells (LECs): regulation of activated T cell egress. Seven days after splenocyte transfer, Il4ra-/- hosts had increased numbers of activated graft CD4+ T cells in skin draining lymph nodes (dLNs) but fewer T cells in efferent lymph, blood, and skin. Sphingosine-1 phosphate (S1P), master regulator of lymphocyte egress from LNs, was lower in dLNs of Il4ra-/- hosts with a corresponding decrease of S1P kinase 1 (Sphk1) expression in LECs. Bypassing the efferent lymphatics via i.v. injection of CD4+ T cells from dLNs of Il4ra-/- sclGvHD mice restored clinical GvHD in secondary Il4ra-/- recipients. These results identify a role for IL4RA and suggest that modulation of lymphocyte egress from LNs may be effective in SSc and GvHD.

Sex-Specific Protection of Osteoarthritis by Deleting Cartilage Acid Protein 1.

Cartilage acidic protein 1 (CRTAC1) was recently identified as an elevated protein in the synovial fluid of patients with osteoarthritis (OA) by a proteomic analysis. This gene is also upregulated in both human and mouse OA by transcriptomic analysis. The objective of this study was to characterize the expression and function of CRTAC1 in OA. Here, we first confirm the increase of CRTAC1 in cartilage biopsies from OA patients undergoing joint replacement by real-time PCR and immunohistochemistry. Furthermore, we report that proinflammatory cytokines interleukin-1beta and tumor necrosis factor alpha upregulate CRTAC1 expression in primary human articular chondrocytes and synovial fibroblasts. Genetic deletion of Crtac1 in mice significantly inhibited cartilage degradation, osteophyte formation and gait abnormalities of post-traumatic OA in female, but not male, animals undergoing the destabilization of medial meniscus (DMM) surgery. Taken together, CRTAC1 is upregulated in the osteoarthritic joint and directly induced in chondrocytes and synovial fibroblasts by pro-inflammatory cytokines. This molecule is necessary for the progression of OA in female mice after DMM surgery and thus represents a potential therapy for this prevalent disease, especially for women who demonstrate higher rates and more severe OA.

NFAT restricts osteochondroma formation from entheseal progenitors.

Osteochondromas are common benign osteocartilaginous tumors in children and adolescents characterized by cartilage-capped bony projections on the surface of bones. These tumors often cause pain, deformity, fracture, and musculoskeletal dysfunction, and they occasionally undergo malignant transformation. The pathogenesis of osteochondromas remains poorly understood. Here, we demonstrate that nuclear factor of activated T cells c1 and c2 (NFATc1 and NFATc2) suppress osteochondromagenesis through individual and combinatorial mechanisms. In mice, conditional deletion of NFATc1 in mesenchymal limb progenitors, Scleraxis-expressing (Scx-expressing) tendoligamentous cells, or postnatally in Aggrecan-expressing cells resulted in osteochondroma formation at entheses, the insertion sites of ligaments and tendons onto bone. Combinatorial deletion of NFATc1 and NFATc2 gave rise to larger and more numerous osteochondromas in inverse proportion to gene dosage. A population of entheseal NFATc1- and Aggrecan-expressing cells was identified as the osteochondroma precursor, previously believed to be growth plate derived or perichondrium derived. Mechanistically, we show that NFATc1 restricts the proliferation and chondrogenesis of osteochondroma precursors. In contrast, NFATc2 preferentially inhibits chondrocyte hypertrophy and osteogenesis. Together, our findings identify and characterize a mechanism of osteochondroma formation and suggest that regulating NFAT activity is a new therapeutic approach for skeletal diseases characterized by defective or exaggerated osteochondral growth.

Facile One-step Micropatterning Using Photodegradable Methacrylated Gelatin Hydrogels for Improved Cardiomyocyte Organization and Alignment.

Hydrogels are often employed as temporary platforms for cell proliferation and tissue organization in vitro. Researchers have incorporated photodegradable moieties into synthetic polymeric hydrogels as a means of achieving spatiotemporal control over material properties. In this study protein-based photodegradable hydrogels composed of methacrylated gelatin (GelMA) and a crosslinker containing o-nitrobenzyl ester groups have been developed. The hydrogels are able to degrade rapidly and specifically in response to UV light and can be photopatterned to a variety of shapes and dimensions in a one-step process. Micropatterned photodegradable hydrogels are shown to improve cell distribution, alignment and beating regularity of cultured neonatal rat cardiomyocytes. Overall this work introduces a new class of photodegradable hydrogel based on natural and biofunctional polymers as cell culture substrates for improving cellular organization and function.

Photodegradable Gelatin-Based Hydrogels Prepared by Bioorthogonal Click Chemistry for Cell Encapsulation and Release.

In this study, we present a method for the fabrication of in situ forming gelatin and poly(ethylene glycol)-based hydrogels utilizing bioorthogonal, strain-promoted alkyne-azide cycloaddition as the cross-linking reaction. By incorporating nitrobenzyl moieties within the network structure, these hydrogels can be designed to be degradable upon irradiation with low intensity UV light, allowing precise photopatterning. Fibroblast cells encapsulated within these hydrogels were viable at 14 days and could be readily harvested using a light trigger. Potential applications of this new class of injectable hydrogel include its use as a 3D culturing platform that allows the capture and release of cells, as well as light-triggered cell delivery in regenerative medicine.

Highly Elastic Micropatterned Hydrogel for Engineering Functional Cardiac Tissue.

Heart failure is a major international health issue. Myocardial mass loss and lack of contractility are precursors to heart failure. Surgical demand for effective myocardial repair is tempered by a paucity of appropriate biological materials. These materials should conveniently replicate natural human tissue components, convey persistent elasticity, promote cell attachment, growth and conformability to direct cell orientation and functional performance. Here, microfabrication techniques are applied to recombinant human tropoelastin, the resilience-imparting protein found in all elastic human tissues, to generate photocrosslinked biological materials containing well-defined micropatterns. These highly elastic substrates are then used to engineer biomimetic cardiac tissue constructs. The micropatterned hydrogels, produced through photocrosslinking of methacrylated tropoelastin (MeTro), promote the attachment, spreading, alignment, function, and intercellular communication of cardiomyocytes by providing an elastic mechanical support that mimics their dynamic mechanical properties in vivo. The fabricated MeTro hydrogels also support the synchronous beating of cardiomyocytes in response to electrical field stimulation. These novel engineered micropatterned elastic gels are designed to be amenable to 3D modular assembly and establish a versatile, adaptable foundation for the modeling and regeneration of functional cardiac tissue with potential for application to other elastic tissues.

NFATc1 and NFATc2 repress spontaneous osteoarthritis.

Osteoarthritis (OA) was once viewed originally as a mechanical disease of "wear and tear," but advances made during the past two decades suggest that abnormal biomechanics contribute to active dysregulation of chondrocyte biology, leading to catabolism of the cartilage matrix. A number of signaling and transcriptional mechanisms have been studied in relation to the regulation of this catabolic program, but how they specifically regulate the initiation or progression of the disease is poorly understood. Here, we demonstrate that cartilage-specific ablation of Nuclear factor of activated T cells c1 (Nfatc1) in Nfatc2(-/-) mice leads to early onset, aggressive OA affecting multiple joints. This model recapitulates features of human OA, including loss of proteoglycans, collagen and aggrecan degradation, osteophyte formation, changes to subchondral bone architecture, and eventual progression to cartilage effacement and joint instability. Consistent with the notion that NFATC1 is an OA-suppressor gene, NFATC1 expression was significantly down-regulated in paired lesional vs. macroscopically normal cartilage samples from OA patients. The highly penetrant, early onset, and severe nature of this model make it an attractive platform for the preclinical development of treatments to alter the course of OA. Furthermore, these findings indicate that NFATs are key suppressors of OA, and regulating NFATs or their transcriptional targets in chondrocytes may lead to novel disease-modifying OA therapies.

SLC4A2-mediated Cl-/HCO3- exchange activity is essential for calpain-dependent regulation of the actin cytoskeleton in osteoclasts.

Bone remodeling requires osteoclasts to generate and maintain an acidified resorption compartment between the apical membrane and the bone surface to solubilize hydroxyapatite crystals within the bone matrix. This acidification process requires (i) apical proton secretion by a vacuolar H(+)-ATPase, (ii) actin cytoskeleton reorganization into a podosome belt that forms a gasket to restrict lacunar acid leakage, and (iii) basolateral chloride uptake and bicarbonate extrusion by an anion exchanger to provide Cl(-) permissive for apical acid secretion while preventing cytoplasmic alkalinization. Here we show that osteoclast-targeted deletion in mice of solute carrier family 4 anion exchanger member 2 (Slc4a2) results in osteopetrosis. We further demonstrate a previously unrecognized consequence of SLC4A2 loss of function in the osteoclast: dysregulation of calpain-dependent podosome disassembly, leading to abnormal actin belt formation, cell spreading, and migration. Rescue of SLC4A2-deficient osteoclasts with functionally defined mutants of SLC4A2 indicates regulation of actin cytoskeletal reorganization by anion-exchange activity and intracellular pH, independent of SLC4A2's long N-terminal cytoplasmic domain. These data suggest that maintenance of intracellular pH in osteoclasts through anion exchange regulates the actin superstructures required for bone resorption.

Surface grafting of electrospun fibers using ATRP and RAFT for the control of biointerfacial interactions.

BACKGROUND: The ability to present signalling molecules within a low fouling 3D environment that mimics the extracellular matrix is an important goal for a range of biomedical applications, both in vitro and in vivo. Cell responses can be triggered by non-specific protein interactions occurring on the surface of a biomaterial, which is an undesirable process when studying specific receptor-ligand interactions. It is therefore useful to present specific ligands of interest to cell surface receptors in a 3D environment that minimizes non-specific interactions with biomolecules, such as proteins. METHOD: In this study, surface-initiated atom transfer radical polymerization (SI-ATRP) of poly(ethylene glycol)-based monomers was carried out from the surface of electrospun fibers composed of a styrene/vinylbenzyl chloride copolymer. Surface initiated radical addition-fragmentation chain transfer (SI-RAFT) polymerisation was also carried out to generate bottle brush copolymer coatings consisting of poly(acrylic acid) and poly(acrylamide). These were grown from surface trithiocarbonate groups generated from the chloromethyl styrene moieties existing in the original synthesised polymer. XPS was used to characterise the surface composition of the fibers after grafting and after coupling with fluorine functional XPS labels. RESULTS: Bottle brush type coatings were able to be produced by ATRP which consisted of poly(ethylene glycol) methacrylate and a terminal alkyne-functionalised monomer. The ATRP coatings showed reduced non-specific protein adsorption, as a result of effective PEG incorporation and pendant alkynes groups existing as part of the brushes allowed for further conjugation of via azide-alkyne Huisgen 1,3-dipolar cycloaddition. In the case of RAFT, carboxylic acid moieties were effectively coupled to an amine label via amide bond formation. In each case XPS analysis demonstrated that covalent immobilisation had effectively taken place. CONCLUSION: Overall, the studies presented an effective platform for the preparation of 3D scaffolds which contain effective conjugation sites for attachment of specific bioactive signals of interest, as well as actively reducing non-specific protein interactions.

Graft versus host disease in the bone marrow, liver and thymus humanized mouse model.

Mice bearing a "humanized" immune system are valuable tools to experimentally manipulate human cells in vivo and facilitate disease models not normally possible in laboratory animals. Here we describe a form of GVHD that develops in NOD/SCID mice reconstituted with human fetal bone marrow, liver and thymus (NS BLT mice). The skin, lungs, gastrointestinal tract and parotid glands are affected with progressive inflammation and sclerosis. Although all mice showed involvement of at least one organ site, the incidence of overt clinical disease was approximately 35% by 22 weeks after reconstitution. The use of hosts lacking the IL2 common gamma chain (NOD/SCID/γc(-/-)) delayed the onset of disease, but ultimately did not affect incidence. Genetic analysis revealed that particular donor HLA class I alleles influenced the risk for the development of GVHD. At a cellular level, GVHD is associated with the infiltration of human CD4+ T cells into the skin and a shift towards Th1 cytokine production. GVHD also induced a mixed M1/M2 polarization phenotype in a dermal murine CD11b+, MHC class II+ macrophage population. The presence of xenogenic GVHD in BLT mice both presents a major obstacle in the use of humanized mice and an opportunity to conduct preclinical studies on GVHD in a humanized model.

The collection of NFATc1-dependent transcripts in the osteoclast includes numerous genes non-essential to physiologic bone resorption.

Osteoclasts are specialized secretory cells of the myeloid lineage important for normal skeletal homeostasis as well as pathologic conditions of bone including osteoporosis, inflammatory arthritis and cancer metastasis. Differentiation of these multinucleated giant cells from precursors is controlled by the cytokine RANKL, which through its receptor RANK initiates a signaling cascade culminating in the activation of transcriptional regulators which induce the expression of the bone degradation machinery. The transcription factor nuclear factor of activated T-cells c1 (NFATc1) is the master regulator of this process and in its absence osteoclast differentiation is aborted both in vitro and in vivo. Differential mRNA expression analysis by microarray is used to identify genes of potential physiologic relevance across nearly all biologic systems. We compared the gene expression profile of murine wild-type and NFATc1-deficient osteoclast precursors stimulated with RANKL and identified that the majority of the known genes important for osteoclastic bone resorption require NFATc1 for induction. Here, five novel RANKL-induced, NFATc1-dependent transcripts in the osteoclast are described: Nhedc2, Rhoc, Serpind1, Adcy3 and Rab38. Despite reasonable hypotheses for the importance of these molecules in the bone resorption pathway and their dramatic induction during differentiation, the analysis of mice with mutations in these genes failed to reveal a function in osteoclast biology. Compared to littermate controls, none of these mutants demonstrated a skeletal phenotype in vivo or alterations in osteoclast differentiation or function in vitro. These data highlight the need for rigorous validation studies to complement expression profiling results before functional importance can be assigned to highly regulated genes in any biologic process.

Interspecies comparison of human and murine scleroderma reveals IL-13 and CCL2 as disease subset-specific targets.

Development of personalized treatment regimens is hampered by lack of insight into how individual animal models reflect subsets of human disease, and autoimmune and inflammatory conditions have proven resistant to such efforts. Scleroderma is a lethal autoimmune disease characterized by fibrosis, with no effective therapy. Comparative gene expression profiling showed that murine sclerodermatous graft-versus-host disease (sclGVHD) approximates an inflammatory subset of scleroderma estimated at 17% to 36% of patients analyzed with diffuse, 28% with limited, and 100% with localized scleroderma. Both sclGVHD and the inflammatory subset demonstrated IL-13 cytokine pathway activation. Host dermal myeloid cells and graft T cells were identified as sources of IL-13 in the model, and genetic deficiency of either IL-13 or IL-4Rα, an IL-13 signal transducer, protected the host from disease. To identify therapeutic targets, we explored the intersection of genes coordinately up-regulated in sclGVHD, the human inflammatory subset, and IL-13-treated fibroblasts; we identified chemokine CCL2 as a potential target. Treatment with anti-CCL2 antibodies prevented sclGVHD. Last, we showed that IL-13 pathway activation in scleroderma patients correlated with clinical skin scores, a marker of disease severity. Thus, an inflammatory subset of scleroderma is driven by IL-13 and may benefit from IL-13 or CCL2 blockade. This approach serves as a model for personalized translational medicine, in which well-characterized animal models are matched to molecularly stratified patient subsets.

Polymorphisms in the interleukin 4, interleukin 13, and corresponding receptor genes are not associated with systemic sclerosis and do not influence gene expression.

OBJECTIVE: Polymorphisms in the genes encoding interleukin 4 (IL4), interleukin 13 (IL13), and their corresponding receptors have been associated with multiple immune-mediated diseases. Our aim was to validate these previous observations in patients with systemic sclerosis (SSc) and scrutinize the effect of the polymorphisms on gene expression in various populations of peripheral blood leukocytes. METHODS: We genotyped a cohort of 2488 patients with SSc and 2246 healthy controls from The Netherlands, Spain, United Kingdom, Italy, Germany, and France. Taqman assays were used to genotype single-nucleotide polymorphisms (SNP) in the following genes: (1) IL4 (-590C>T/rs2243250); (2) IL4 receptor alpha (IL4RA) (Q576R/rs1801275); (3) IL13 (R130Q/rs20541 and -1112C>T/rs1800925); and (4) IL13RA1 (43163G>A/rs6646259). The effect of these polymorphisms on expression of the corresponding genes was assessed using quantitative RT-PCR on RNA derived from peripheral blood B cells, T cells, plasmacytoid dendritic cells, monocytes, and myeloid dendritic cells. We investigated whether these polymorphisms influenced development of pulmonary complications over 15 years in patients with SSc. RESULTS: None of the investigated polymorphisms was associated with SSc or any SSc clinical subtype. We did not observe any effect on transcript levels in the cell subtypes or on development of pulmonary complications. CONCLUSION: Our data showed that polymorphisms in IL4, IL13, and their receptors do not play a role in SSc and do not influence the expression of their corresponding transcript in peripheral blood cells.

Biomaterials for spinal cord regeneration: outgrowth of presumptive neuronal precursors on electrospun poly(epsilon)-caprolactone scaffolds microlayered with alternating polyelectrolytes.

The aim of this study was to assess the feasibility of electrospun poly(epsilon)-caprolactone (PCL) scaffolds treated with alternating paly-electrolytes as a controllable three-dimensional adhesive substrate for neuronal progenitors. Unmodified PCL surfaces were generally not supportive of mouse embryonic stem cell (mESC) colony adhesion. However, scaffolds surfaced using layer-by-layer (LbL) deposition of heparin/poly-L-lysine encouraged better local adhesion of mESC colonies, and networking of monolayers containing nestin-positive presumptive neurons, similar to laminin coated controls, as observed by immuno-fluorescence microscopy. Confocal microscopy further revealed depth-wise penetration of mESC nestin-positive cell populations, and orientation along grass topographical features in the LbL scaffolds. LbL deposition therefore appears to provide a satisfactory adhesive substrate for contact and mechanical guidance of neuronal outgrowth in three-dimensions.