Retraction Note: miR-34a blocks osteoporosis and bone metastasis by inhibiting osteoclastogenesis and Tgif2.

A Retraction to this paper has been published and can be accessed via a link at the top of the paper.

Author Correction: miR-34a blocks osteoporosis and bone metastasis by inhibiting osteoclastogenesis and Tgif2.

Change history: In this Letter, the citation to 'Fig. 4e, f' in the main text should be 'Fig. 3e, f'. This has not been corrected online.

Sickle cell allele HBB-rs334(T) is associated with decreased risk of childhood Burkitt lymphoma in East Africa.

Burkitt lymphoma (BL) is an aggressive B-cell lymphoma that significantly contributes to childhood cancer burden in sub-Saharan Africa. Plasmodium falciparum, which causes malaria, is geographically associated with BL, but the evidence remains insufficient for causal inference. Inference could be strengthened by demonstrating that mendelian genes known to protect against malaria-such as the sickle cell trait variant, HBB-rs334(T)-also protect against BL. We investigated this hypothesis among 800 BL cases and 3845 controls in four East African countries using genome-scan data to detect polymorphisms in 22 genes known to affect malaria risk. We fit generalized linear mixed models to estimate odds ratios (OR) and 95% confidence intervals (95% CI), controlling for age, sex, country, and ancestry. The ORs of the loci with BL and P. falciparum infection among controls were correlated (Spearman's ρ = 0.37, p = .039). HBB-rs334(T) was associated with lower P. falciparum infection risk among controls (OR = 0.752, 95% CI 0.628-0.9; p = .00189) and BL risk (OR = 0.687, 95% CI 0.533-0.885; p = .0037). ABO-rs8176703(T) was associated with decreased risk of BL (OR = 0.591, 95% CI 0.379-0.992; p = .00271), but not of P. falciparum infection. Our results increase support for the etiological correlation between P. falciparum and BL risk.

Mitapivat increases ATP and decreases oxidative stress and erythrocyte mitochondria retention in a SCD mouse model.

Polymerization of deoxygenated sickle hemoglobin (HbS) leads to erythrocyte sickling. Enhancing activity of the erythrocyte glycolytic pathway has anti-sickling potential as this reduces 2,3-diphosphoglycerate (2,3-DPG) and increases ATP, factors that decrease HbS polymerization and improve erythrocyte membrane integrity. These factors can be modulated by mitapivat, which activates erythrocyte pyruvate kinase (PKR) and improves sickling kinetics in SCD patients. We investigated mechanisms by which mitapivat may impact SCD by examining its effects in the Townes SCD mouse model. Control (HbAA) and sickle (HbSS) mice were treated with mitapivat or vehicle. Surprisingly, HbSS had higher PKR protein, higher ATP, and lower 2,3-DPG levels, compared to HbAA mice, in contrast with humans with SCD, in whom 2,3-DPG is elevated compared to healthy subjects. Despite our inability to investigate 2,3-DPG-mediated sickling and hemoglobin effects, mitapivat yielded potential benefits in HbSS mice. Mitapivat further increased ATP without significantly changing 2,3-DPG or hemoglobin levels, and decreased levels of leukocytosis, erythrocyte oxidative stress, and the percentage of erythrocytes that retained mitochondria in HbSS mice. These data suggest that, even though Townes HbSS mice have increased PKR activity, further activation of PKR with mitapivat yields potentially beneficial effects that are independent of changes in sickling or hemoglobin levels.

Whole genome sequence-based haplotypes reveal a single origin of the 1393 bp HBB deletion.

BACKGROUND: Mutations of HBB give rise to two prevalent haemoglobin disorders-sickle cell disease (SCD) and ß-thalassaemia. While SCD is caused by a single base substitution, nearly 300 mutations that downregulate expression of HBB have been described. The vast majority of ß-thalassaemia alleles are point mutations or small insertion/deletions within the HBB gene; deletions causing ß-thalassaemia are very rare. We have identified three individuals with haemoglobin Sß0-thalassaemia in which the ß0-thalassaemia mutation is caused by a large deletion. OBJECTIVE: To use whole genome sequence data to determine whether these deletions arose from a single origin. METHODS: We used two approaches to confirm unrelatedness: pairwise comparison of SNPs and identity by descent analysis. Eagle, V.2.4, was used to generate phased haplotypes for the 683 individuals. The Neighbor-Net method implemented in SplitsTree V.4.13.1 was used to construct the network of haplotypes. RESULTS: All three deletions involved 1393 bp, encompassing the ß-promoter, exons 1 and 2, and part of intron 2, with identical breakpoints. The cases were confirmed to be unrelated. Haplotypes based on 29 SNPs in the HBB cluster showed that the three individuals harboured different ßS haplotypes. In contrast, the haplotype harbouring the 1393 bp deletion was the same in all three individuals. CONCLUSION: We suggest that all the reported cases of the 1393 bp HBB deletion, including the three cases here, are likely to be of the same ancestral origin.

miR-34a blocks osteoporosis and bone metastasis by inhibiting osteoclastogenesis and Tgif2.

Bone-resorbing osteoclasts significantly contribute to osteoporosis and bone metastases of cancer. MicroRNAs play important roles in physiology and disease, and present tremendous therapeutic potential. Nonetheless, how microRNAs regulate skeletal biology is underexplored. Here we identify miR-34a as a novel and critical suppressor of osteoclastogenesis, bone resorption and the bone metastatic niche. miR-34a is downregulated during osteoclast differentiation. Osteoclastic miR-34a-overexpressing transgenic mice exhibit lower bone resorption and higher bone mass. Conversely, miR-34a knockout and heterozygous mice exhibit elevated bone resorption and reduced bone mass. Consequently, ovariectomy-induced osteoporosis, as well as bone metastasis of breast and skin cancers, are diminished in osteoclastic miR-34a transgenic mice, and can be effectively attenuated by miR-34a nanoparticle treatment. Mechanistically, we identify transforming growth factor-ß-induced factor 2 (Tgif2) as an essential direct miR-34a target that is pro-osteoclastogenic. Tgif2 deletion reduces bone resorption and abolishes miR-34a regulation. Together, using mouse genetic, pharmacological and disease models, we reveal miR-34a as a key osteoclast suppressor and a potential therapeutic strategy to confer skeletal protection and ameliorate bone metastasis of cancers.

Analgesia by Deletion of Spinal Neurokinin 1 Receptor Expressing Neurons Using a Bioengineered Substance P-Pseudomonas Exotoxin Conjugate.

Abstract: Cell deletion approaches to pain directed at either the primary nociceptive afferents or second-order neurons are highly effective analgesic manipulations. Second-order spinal neurons expressing the neurokinin 1 (NK1) receptor are required for the perception of many types of pain. To delete NK1+ neurons for the purpose of pain control, we generated a toxin­peptide conjugate using DTNB-derivatized (Cys0) substance P (SP) and a N-terminally truncated Pseudomonas exotoxin (PE35) that retains the endosome-release and ADP-ribosylation enzymatic domains but with only one free sulfhydryl side chain for conjugation. This allowed generation of a one-to-one product linked by a disulfide bond (SP-PE35). In vitro, Chinese hamster ovary cells stably transfected with the NK1 receptor exhibited specific cytotoxicity when exposed to SP-PE35 (IC50 = 5 × 10−11 M), whereas the conjugate was nontoxic to NK2 and NK3 receptor-bearing cell lines. In vivo studies showed that, after infusion into the spinal subarachnoid space, the toxin was extremely effective in deleting NK1 receptor-expressing cells from the dorsal horn of the spinal cord. The specific cell deletion robustly attenuated thermal and mechanical pain sensations and inflammatory hyperalgesia but did not affect motoric capabilities. NK1 receptor cell deletion and antinociception occurred without obvious lesion of non­receptor-expressing cells or apparent reorganization of primary afferent innervation. These data demonstrate the extraordinary selectivity and broad-spectrum antinociceptive efficacy of this ligand-directed protein therapeutic acting via receptor-mediated endocytosis. The loss of multiple pain modalities including heat and mechanical pinch, transduced by different populations of primary afferents, shows that spinal NK1 receptor-expressing neurons are critical points of convergence in the nociceptive transmission circuit. We further suggest that therapeutic end points can be effectively and safely achieved when SP-PE35 is locally infused, thereby producing a regionally defined analgesia.

Heme-bound iron activates placenta growth factor in erythroid cells via erythroid Krüppel-like factor.

In adults with sickle cell disease (SCD), markers of iron burden are associated with excessive production of the angiogenic protein placenta growth factor (PlGF) and high estimated pulmonary artery pressure. Enforced PlGF expression in mice stimulates production of the potent vasoconstrictor endothelin-1, producing pulmonary hypertension. We now demonstrate heme-bound iron (hemin) induces PlGF mRNA >200-fold in a dose- and time-dependent fashion. In murine and human erythroid cells, expression of erythroid Krüppel-like factor (EKLF) precedes PlGF, and its enforced expression in human erythroid progenitor cells induces PlGF mRNA. Hemin-induced expression of PlGF is abolished in EKLF-deficient murine erythroid cells but rescued by conditional expression of EKLF. Chromatin immunoprecipitation reveals that EKLF binds to the PlGF promoter region. SCD patients show higher level expression of both EKLF and PlGF mRNA in circulating blood cells, and markers of iron overload are associated with high PlGF and early mortality. Finally, PlGF association with iron burden generalizes to other human diseases of iron overload. Our results demonstrate a specific mechanistic pathway induced by excess iron that is linked in humans with SCD and in mice to markers of vasculopathy and pulmonary hypertension. These trials were registered at www.clinicaltrials.gov as #NCT00007150, #NCT00023296, #NCT00081523, and #NCT00352430.

Fibroblast growth factor 21 promotes bone loss by potentiating the effects of peroxisome proliferator-activated receptor γ.

The endocrine hormone fibroblast growth factor 21 (FGF21) is a powerful modulator of glucose and lipid metabolism and a promising drug for type 2 diabetes. Here we identify FGF21 as a potent regulator of skeletal homeostasis. Both genetic and pharmacologic FGF21 gain of function lead to a striking decrease in bone mass. In contrast, FGF21 loss of function leads to a reciprocal high-bone-mass phenotype. Mechanistically, FGF21 inhibits osteoblastogenesis and stimulates adipogenesis from bone marrow mesenchymal stem cells by potentiating the activity of peroxisome proliferator-activated receptor γ (PPAR-γ). Consequently, FGF21 deletion prevents the deleterious bone loss side effect of the PPAR-γ agonist rosiglitazone. Therefore, FGF21 is a critical rheostat for bone turnover and a key integrator of bone and energy metabolism. These results reveal that skeletal fragility may be an undesirable consequence of chronic FGF21 administration.

Circulating blood endothelial nitric oxide synthase contributes to the regulation of systemic blood pressure and nitrite homeostasis.

OBJECTIVE: Mice genetically deficient in endothelial nitric oxide synthase (eNOS(-/-)) are hypertensive with lower circulating nitrite levels, indicating the importance of constitutively produced nitric oxide (NO•) to blood pressure regulation and vascular homeostasis. Although the current paradigm holds that this bioactivity derives specifically from the expression of eNOS in endothelium, circulating blood cells also express eNOS protein. A functional red cell eNOS that modulates vascular NO• signaling has been proposed. APPROACH AND RESULTS: To test the hypothesis that blood cells contribute to mammalian blood pressure regulation via eNOS-dependent NO• generation, we cross-transplanted wild-type and eNOS(-/-) mice, producing chimeras competent or deficient for eNOS expression in circulating blood cells. Surprisingly, we observed a significant contribution of both endothelial and circulating blood cell eNOS to blood pressure and systemic nitrite levels, the latter being a major component of the circulating NO• reservoir. These effects were abolished by the NOS inhibitor L-NG-nitroarginine methyl ester and repristinated by the NOS substrate L-arginine and were independent of platelet or leukocyte depletion. Mouse erythrocytes were also found to carry an eNOS protein and convert (14)C-arginine into (14)C-citrulline in NOS-dependent fashion. CONCLUSIONS: These are the first studies to definitively establish a role for a blood-borne eNOS, using cross-transplant chimera models, that contributes to the regulation of blood pressure and nitrite homeostasis. This work provides evidence suggesting that erythrocyte eNOS may mediate this effect.

Activating pyruvate kinase improves red blood cell integrity by reducing band 3 tyrosine phosphorylation.

ABSTRACT: In a phase 1 study (NCT04000165), we established proof of concept for activating pyruvate kinase (PK) in sickle cell disease (SCD) as a viable antisickling therapy. AG-348 (mitapivat), a PK activator, increased adenosine triphosphate (ATP) and decreased 2,3-diphosphoglycerate levels while patients were on treatment, in line with the mechanism of the drug. We noted that the increased hemoglobin (Hb) persisted for 4 weeks after stopping AG-348 until the end of study (EOS). Here, we investigated the pathways modulated by activating PK that may contribute to the improved red blood cell (RBC) survival after AG-348 cessation. We evaluated frozen whole blood samples taken at multiple time points from patients in the phase 1 study, from which RBC ghosts were isolated and analyzed by western blotting for tyrosine phosphorylation of band 3 (Tyr-p-bd3), ankyrin-1, and intact (active) protein tyrosine phosphatase 1B (PTP1B) levels. We observed a significant dose-dependent decrease in mean Tyr-p-bd3 from baseline in the patients, accompanied by an increase in the levels of membrane-associated ankyrin-1 and intact PTP1B, all of which returned to near baseline by EOS. Because PTP1B is cleaved (inactivated) by intracellular Ca2+-dependent calpain, we next measured the effect of AG-348 on ATP production and calpain activity and the plasma membrane Ca2+ ATPase pump-mediated efflux kinetics in HbAA and HbSS erythrocytes. AG-348 treatment increased ATP levels, decreased calpain activity, and increased Ca2+ efflux. Altogether, our data indicate that ATP increase is a key mechanism underlying the increase in hemoglobin levels upon PK activation in SCD. This trial was registered at www.clinicaltrials.gov as #NCT04000165.

In vivo measurement of RBC survival in patients with sickle cell disease before or after hematopoietic stem cell transplantation.

ABSTRACT: Stable, mixed-donor-recipient chimerism after allogeneic hematopoietic stem cell transplantation (HSCT) for patients with sickle cell disease (SCD) is sufficient for phenotypic disease reversal, and results from differences in donor/recipient-red blood cell (RBC) survival. Understanding variability and predictors of RBC survival among patients with SCD before and after HSCT is critical for gene therapy research which seeks to generate sufficient corrected hemoglobin to reduce polymerization thereby overcoming the red cell pathology of SCD. This study used biotin labeling of RBCs to determine the lifespan of RBCs in patients with SCD compared with patients who have successfully undergone curative HSCT, participants with sickle cell trait (HbAS), and healthy (HbAA) donors. Twenty participants were included in the analysis (SCD pre-HSCT: N = 6, SCD post-HSCT: N = 5, HbAS: N = 6, and HbAA: N = 3). The average RBC lifespan was significantly shorter for participants with SCD pre-HSCT (64.1 days; range, 35-91) compared with those with SCD post-HSCT (113.4 days; range, 105-119), HbAS (126.0 days; range, 119-147), and HbAA (123.7 days; range, 91-147) (P<.001). RBC lifespan correlated with various hematologic parameters and strongly correlated with the average final fraction of sickled RBCs after deoxygenation (P<.001). No adverse events were attributable to the use of biotin and related procedures. Biotin labeling of RBCs is a safe and feasible methodology to evaluate RBC survival in patients with SCD before and after HSCT. Understanding differences in RBC survival may ultimately guide gene therapy protocols to determine hemoglobin composition required to reverse the SCD phenotype as it relates directly to RBC survival. This trial was registered at www.clinicaltrials.gov as #NCT04476277.

Nitrite augments tolerance to ischemia/reperfusion injury via the modulation of mitochondrial electron transfer.

Nitrite (NO(2)(-)) is an intrinsic signaling molecule that is reduced to NO during ischemia and limits apoptosis and cytotoxicity at reperfusion in the mammalian heart, liver, and brain. Although the mechanism of nitrite-mediated cytoprotection is unknown, NO is a mediator of the ischemic preconditioning cell-survival program. Analogous to the temporally distinct acute and delayed ischemic preconditioning cytoprotective phenotypes, we report that both acute and delayed (24 h before ischemia) exposure to physiological concentrations of nitrite, given both systemically or orally, potently limits cardiac and hepatic reperfusion injury. This cytoprotection is associated with increases in mitochondrial oxidative phosphorylation. Remarkably, isolated mitochondria subjected to 30 min of anoxia followed by reoxygenation were directly protected by nitrite administered both in vitro during anoxia or in vivo 24 h before mitochondrial isolation. Mechanistically, nitrite dose-dependently modifies and inhibits complex I by posttranslational S-nitrosation; this dampens electron transfer and effectively reduces reperfusion reactive oxygen species generation and ameliorates oxidative inactivation of complexes II-IV and aconitase, thus preventing mitochondrial permeability transition pore opening and cytochrome c release. These data suggest that nitrite dynamically modulates mitochondrial resilience to reperfusion injury and may represent an effector of the cell-survival program of ischemic preconditioning and the Mediterranean diet.

Defibrotide interferes with several steps of the coagulation-inflammation cycle and exhibits therapeutic potential to treat severe malaria.

OBJECTIVE: The coagulation-inflammation cycle has been implicated as a critical component in malaria pathogenesis. Defibrotide (DF), a mixture of DNA aptamers, displays anticoagulant, anti-inflammatory, and endothelial cell (EC)-protective activities and has been successfully used to treat comatose children with veno-occlusive disease. DF was investigated here as a drug to treat cerebral malaria. METHODS AND RESULTS: DF blocks tissue factor expression by ECs incubated with parasitized red blood cells and attenuates prothrombinase activity, platelet aggregation, and complement activation. In contrast, it does not affect nitric oxide bioavailability. We also demonstrated that Plasmodium falciparum glycosylphosphatidylinositol (Pf-GPI) induces tissue factor expression in ECs and cytokine production by dendritic cells. Notably, dendritic cells, known to modulate coagulation and inflammation systemically, were identified as a novel target for DF. Accordingly, DF inhibits Toll-like receptor ligand-dependent dendritic cells activation by a mechanism that is blocked by adenosine receptor antagonist (8-p-sulfophenyltheophylline) but not reproduced by synthetic poly-A, -C, -T, and -G. These results imply that aptameric sequences and adenosine receptor mediate dendritic cells responses to the drug. DF also prevents rosetting formation, red blood cells invasion by P. falciparum and abolishes oocysts development in Anopheles gambiae. In a murine model of cerebral malaria, DF affected parasitemia, decreased IFN-γ levels, and ameliorated clinical score (day 5) with a trend for increased survival. CONCLUSION: Therapeutic use of DF in malaria is proposed.

Random forest classifiers trained on simulated data enable accurate short read-based genotyping of structural variants in the alpha globin region at Chr16p13.3.

In regions where reads don't align well to a reference, it is generally difficult to characterize structural variation using short read sequencing. Here, we utilize machine learning classifiers and short sequence reads to genotype structural variants in the alpha globin locus on chromosome 16, a medically-relevant region that is challenging to genotype in individuals. Using models trained only with simulated data, we accurately genotype two hard-to-distinguish deletions in two separate human cohorts. Furthermore, population allele frequencies produced by our methods across a wide set of ancestries agree more closely with previously-determined frequencies than those obtained using currently available genotyping software.

14-3-3 binding and phosphorylation of neuroglobin during hypoxia modulate six-to-five heme pocket coordination and rate of nitrite reduction to nitric oxide.

Neuroglobin protects neurons from hypoxia in vitro and in vivo; however, the underlying mechanisms for this effect remain poorly understood. Most of the neuroglobin is present in a hexacoordinate state with proximal and distal histidines in the heme pocket directly bound to the heme iron. At equilibrium, the concentration of the five-coordinate neuroglobin remains very low (0.1-5%). Recent studies have shown that post-translational redox regulation of neuroglobin surface thiol disulfide formation increases the open probability of the heme pocket and allows nitrite binding and reaction to form NO. We hypothesized that the equilibrium between the six- and five-coordinate states and secondary reactions with nitrite to form NO could be regulated by other hypoxia-dependent post-translational modification(s). Protein sequence models identified candidate sites for both 14-3-3 binding and phosphorylation. In both in vitro experiments and human SH-SY5Y neuronal cells exposed to hypoxia and glucose deprivation, we observed that 1) neuroglobin phosphorylation and protein-protein interactions with 14-3-3 increase during hypoxic and metabolic stress; 2) neuroglobin binding to 14-3-3 stabilizes and increases the half-life of phosphorylation; and 3) phosphorylation increases the open probability of the heme pocket, which increases ligand binding (CO and nitrite) and accelerates the rate of anaerobic nitrite reduction to form NO. These data reveal a series of hypoxia-dependent post-translational modifications to neuroglobin that regulate the six-to-five heme pocket equilibrium and heme access to ligands. Hypoxia-regulated reactions of nitrite and neuroglobin may contribute to the cellular adaptation to hypoxia.

Human neuroglobin functions as a redox-regulated nitrite reductase.

Neuroglobin is a highly conserved hemoprotein of uncertain physiological function that evolved from a common ancestor to hemoglobin and myoglobin. It possesses a six-coordinate heme geometry with proximal and distal histidines directly bound to the heme iron, although coordination of the sixth ligand is reversible. We show that deoxygenated human neuroglobin reacts with nitrite to form nitric oxide (NO). This reaction is regulated by redox-sensitive surface thiols, cysteine 55 and 46, which regulate the fraction of the five-coordinated heme, nitrite binding, and NO formation. Replacement of the distal histidine by leucine or glutamine leads to a stable five-coordinated geometry; these neuroglobin mutants reduce nitrite to NO ∼2000 times faster than the wild type, whereas mutation of either Cys-55 or Cys-46 to alanine stabilizes the six-coordinate structure and slows the reaction. Using lentivirus expression systems, we show that the nitrite reductase activity of neuroglobin inhibits cellular respiration via NO binding to cytochrome c oxidase and confirm that the six-to-five-coordinate status of neuroglobin regulates intracellular hypoxic NO-signaling pathways. These studies suggest that neuroglobin may function as a physiological oxidative stress sensor and a post-translationally redox-regulated nitrite reductase that generates NO under six-to-five-coordinate heme pocket control. We hypothesize that the six-coordinate heme globin superfamily may subserve a function as primordial hypoxic and redox-regulated NO-signaling proteins.

High levels of placenta growth factor in sickle cell disease promote pulmonary hypertension.

Pulmonary hypertension is associated with reduced nitric oxide bioavailability and early mortality in sickle cell disease (SCD). We previously demonstrated that placenta growth factor (PlGF), an angiogenic factor produced by erythroid cells, induces hypoxia-independent expression of the pulmonary vasoconstrictor endothelin-1 in pulmonary endothelial cells. Using a lentivirus vector, we simulated erythroid expression of PlGF in normal mice up to the levels seen in sickle mice. Consequently, endothelin-1 production increased, right ventricle pressures increased, and right ventricle hypertrophy and pulmonary changes occurred in the mice within 8 weeks. These findings were corroborated in 123 patients with SCD, in whom plasma PlGF levels were significantly associated with anemia, endothelin-1, and tricuspid regurgitant velocity; the latter is reflective of peak pulmonary artery pressure. These results illuminate a novel mechanistic pathway linking hemolysis and erythroid hyperplasia to increased PlGF, endothelin-1, and pulmonary hypertension in SCD, and suggest that strategies that block PlGF signaling may be therapeutically beneficial.

Genetic variants of PKLR are associated with acute pain in sickle cell disease.

Acute pain, the most prominent complication of sickle cell disease (SCD), results from vaso-occlusion triggered by sickling of deoxygenated red blood cells (RBCs). Concentration of 2,3-diphosphoglycerate (2,3-DPG) in RBCs promotes deoxygenation by preferentially binding to the low-affinity T conformation of HbS. 2,3-DPG is an intermediate substrate in the glycolytic pathway in which pyruvate kinase (gene PKLR, protein PKR) is a rate-limiting enzyme; variants in PKLR may affect PKR activity, 2,3-DPG levels in RBCs, RBC sickling, and acute pain episodes (APEs). We performed a candidate gene association study using 2 cohorts: 242 adult SCD-HbSS patients and 977 children with SCD-HbSS or SCD-HbSß0 thalassemia. Seven of 47 PKLR variants evaluated in the adult cohort were associated with hospitalization: intron 4, rs2071053; intron 2, rs8177970, rs116244351, rs114455416, rs12741350, rs3020781, and rs8177964. All 7 variants showed consistent effect directions in both cohorts and remained significant in weighted Fisher's meta-analyses of the adult and pediatric cohorts using P < .0071 as threshold to correct for multiple testing. Allele-specific expression analyses in an independent cohort of 52 SCD adults showed that the intronic variants are likely to influence APE by affecting expression of PKLR, although the causal variant and mechanism are not defined.