RESUMEN
During lung inflation, airspace dimensions are affected nonlinearly by both alveolar expansion and recruitment, potentially confounding the identification of emphysematous lung by hyperpolarized helium-3 diffusion magnetic resonance imaging (HP MRI). This study aimed to characterize lung inflation over a broad range of inflation volume and pressure values in two different models of emphysema, as well as in normal lungs. Elastase-treated rats (n = 7) and healthy controls (n = 7) were imaged with HP MRI. Gradual inflation was achieved by incremental changes to both inflation volume and airway pressure. The apparent diffusion coefficient (ADC) was measured at each level of inflation and fitted to the corresponding airway pressures as the second-order response equation, with minimizing residue (χ2 < 0.001). A biphasic ADC response was detected, with an initial ADC increase followed by a decrease at airway pressures >18 cmH2O. Discrimination between treated and control rats was optimal when airway pressure was intermediate (between 10 and 11 cmH2O). Similar findings were confirmed in mice following long-term exposure to cigarette smoke, where optimal discrimination between treated and healthy mice occurred at a similar airway pressure as in the rats. We subsequently explored the evolution of ADC measured at the intermediate inflation level in mice after prolonged smoke exposure and found a significant increase (P < 0.01) in ADC over time. Our results demonstrate that measuring ADC at intermediate inflation enhances the distinction between healthy and diseased lungs, thereby establishing a model that may improve the diagnostic accuracy of future HP gas diffusion studies.
Asunto(s)
Pulmón/patología , Enfisema Pulmonar/patología , Animales , Imagen de Difusión por Resonancia Magnética/métodos , Modelos Animales de Enfermedad , Helio/química , Ratones , Ratones Endogámicos C57BL , Elastasa Pancreática/administración & dosificación , Presión , Ratas , Ratas Sprague-Dawley , Humo/efectos adversosRESUMEN
Nuclear factor (erythroid-derived 2)-like 2 (Nrf2) is a key regulator of oxidative stress and cellular repair and can be activated through inhibition of its cytoplasmic repressor, Kelch-like ECH-associated protein 1 (Keap1). Several small molecule disrupters of the Nrf2-Keap1 complex have recently been tested and/or approved for human therapeutic use but lack either potency or selectivity. The main goal of our work was to develop a potent, selective activator of NRF2 as protection against oxidative stress. In human bronchial epithelial cells, our Nrf2 activator, 3-(pyridin-3-ylsulfonyl)-5-(trifluoromethyl)-2H-chromen-2-one (PSTC), induced Nrf2 nuclear translocation, Nrf2-regulated gene expression, and downstream signaling events, including induction of NAD(P)H:quinone oxidoreductase 1 (NQO1) enzyme activity and heme oxygenase-1 protein expression, in an Nrf2-dependent manner. As a marker of subsequent functional activity, PSTC restored oxidant (tert-butyl hydroperoxide)-induced glutathione depletion. The compound's engagement of the Nrf2 signaling pathway translated to an in vivo setting, with induction of Nrf2-regulated gene expression and NQO1 enzyme activity, as well as restoration of oxidant (ozone)-induced glutathione depletion, occurring in the lungs of PSTC-treated rodents. Under disease conditions, PSTC engaged its target, inducing the expression of Nrf2-regulated genes in human bronchial epithelial cells derived from patients with chronic obstructive pulmonary disease, as well as in the lungs of cigarette smoke-exposed mice. Subsequent to the latter, a dose-dependent inhibition of cigarette smoke-induced pulmonary inflammation was observed. Finally, in contrast with bardoxolone methyl and sulforaphane, PSTC did not inhibit interleukin-1ß-induced nuclear factor-κB translocation or insulin-induced S6 phosphorylation in human cells, emphasizing the on-target activity of this compound. In summary, we characterize a potent, selective Nrf2 activator that offers protection against pulmonary oxidative stress in several cellular and in vivo models.
Asunto(s)
Cumarinas/uso terapéutico , Células Epiteliales/efectos de los fármacos , Pulmón/efectos de los fármacos , Factor 2 Relacionado con NF-E2/agonistas , Estrés Oxidativo/efectos de los fármacos , Neumonía/prevención & control , Enfermedad Pulmonar Obstructiva Crónica/metabolismo , Sulfonas/uso terapéutico , Animales , Western Blotting , Línea Celular , Núcleo Celular/metabolismo , Cumarinas/administración & dosificación , Cumarinas/sangre , Modelos Animales de Enfermedad , Descubrimiento de Drogas , Células Epiteliales/metabolismo , Expresión Génica/efectos de los fármacos , Glutatión/metabolismo , Células HEK293 , Humanos , Pulmón/metabolismo , Ratones Endogámicos C57BL , NAD(P)H Deshidrogenasa (Quinona)/genética , Factor 2 Relacionado con NF-E2/genética , Ozono/toxicidad , Neumonía/etiología , Neumonía/metabolismo , Transporte de Proteínas , ARN Interferente Pequeño/genética , Ratas Wistar , Fumar/efectos adversos , Sulfonas/administración & dosificación , Sulfonas/sangre , TransfecciónRESUMEN
Inhalation of airborne toxicants such as cigarette smoke and ozone is a shared health risk among the world's populations. The use of toxic herbicides like paraquat (PQ) is restricted by many countries, yet in the developing world PQ has demonstrable ill effects. The present study examined changes in pulmonary function, mitochondrial DNA (mtDNA) integrity and markers of DNA repair induced by acute or repeated exposure of PQ to rats. Similar to cigarette smoke and ozone, PQ promotes oxidative stress, and the impact of PQ on mtDNA was compared with that obtained with these agents. Tracheal instillation (i.t.) of PQ (0.01-0.075 mg/kg) dose dependently increased Penh (dyspnoea) by 48 h while body weight and temperature declined. Lung wet weight and the wet/dry weight ratio rose; for the latter, by as much as 52%. At low doses (0.02 and 0.03 mg/kg), PQ increased Penh by about 7.5-fold at 72 h. It quickly waned to near baseline levels. The lung wet/dry weight ratio remained elevated 7 days after administration coincident with marked inflammatory cell infiltrate. Repeated administration of PQ (1 per week for 8 weeks) resulted in a similar rise in Penh on the first instillation, but the magnitude of this response was markedly attenuated upon subsequent exposures. Pulmonary [lactate] and catalase activity, [8-oxodG] and histone fragmentation (cell death) were significantly increased. Repeated PQ instillation downregulated the expression of the mitochondrial-encoded genes, mtATP8, mtNd2 and mtcyB and nuclear ones for the DNA glycosylases, Ogg1, Neil1, Neil2 and Neil3. Ogg1 protein content decreased after acute and repeated PQ administration. mtDNA damage or changes in mtDNA copy number were evident in lungs of PQ-, cigarette smoke- and ozone-exposed animals. Taken together, these data indicate that loss of pulmonary function and inflammation are coupled to the loss of mtDNA integrity and DNA repair capability following exposure to airborne toxicants.
Asunto(s)
Daño del ADN , ADN Glicosilasas/efectos de los fármacos , Reparación del ADN/efectos de los fármacos , ADN Mitocondrial/efectos de los fármacos , Pulmón/efectos de los fármacos , Paraquat/toxicidad , 8-Hidroxi-2'-Desoxicoguanosina , Animales , ADN Glicosilasas/genética , ADN Mitocondrial/metabolismo , Desoxiguanosina/análogos & derivados , Regulación hacia Abajo , Femenino , Herbicidas/administración & dosificación , Herbicidas/farmacología , Herbicidas/toxicidad , Instilación de Medicamentos , Pulmón/metabolismo , Pulmón/fisiopatología , Masculino , Ratones , Estrés Oxidativo , Paraquat/administración & dosificación , Paraquat/farmacología , Ratas , TráqueaRESUMEN
The innate immune system protects the host from bacterial and viral invasion. Surfactant protein A (SPA), a lung-specific collectin, stimulates macrophage chemotaxis. However, the mechanisms regulating this function are unknown. Hyaluronan (HA) and its receptors RHAMM (receptor for HA-mediated motility, CD168) and CD44 also regulate cell migration and inflammation. We therefore examined the role of HA, RHAMM, and CD44 in SPA-stimulated macrophage chemotaxis. Using antibody blockade and murine macrophages, SPA-stimulated macrophage chemotaxis was dependent on TLR2 but not the other SPA receptors examined. Anti-TLR2 blocked SPA-induced production of TGFß. In turn, TGFß1-stimulated chemotaxis was inhibited by HA-binding peptide and anti-RHAMM antibody but not anti-TLR2 antibody. Macrophages from TLR2(-/-) mice failed to migrate in response to SPA but responded normally to TGFß1 and HA, effects that were blocked by anti-RHAMM antibody. Macrophages from WT and CD44(-/-) mice had similar responses to SPA, whereas those from RHAMM(-/-) mice had decreased chemotaxis to SPA, TGFß1, and HA. In primary macrophages, SPA-stimulated TGFß production was dependent on TLR2, JNK, and ERK but not p38. Pam3Cys, a specific TLR2 agonist, stimulated phosphorylation of JNK, ERK, and p38, but only JNK and ERK inhibition blocked Pam3Cys-stimulated chemotaxis. We have uncovered a novel pathway for SPA-stimulated macrophage chemotaxis where SPA stimulation via TLR2 drives JNK- and ERK-dependent TGFß production. TGFß1, in turn, stimulates macrophage chemotaxis in a RHAMM and HA-dependent manner. These findings are highly relevant to the regulation of innate immune responses by SPA with key roles for specific components of the extracellular matrix.
Asunto(s)
Quimiotaxis , Proteínas de la Matriz Extracelular/metabolismo , Receptores de Hialuranos/metabolismo , Ácido Hialurónico/fisiología , Macrófagos/fisiología , Proteína A Asociada a Surfactante Pulmonar/fisiología , Receptor Toll-Like 2/metabolismo , Factor de Crecimiento Transformador beta1/fisiología , Animales , Línea Celular , Citoesqueleto/metabolismo , Proteínas de la Matriz Extracelular/genética , Técnicas de Inactivación de Genes , Receptores de Hialuranos/genética , Ácido Hialurónico/metabolismo , Lipoproteínas/farmacología , Sistema de Señalización de MAP Quinasas , Macrófagos/metabolismo , Ratones , Visón , Proteínas Quinasas Activadas por Mitógenos/metabolismo , Seudópodos/metabolismo , Seudópodos/fisiología , Receptor Toll-Like 2/agonistas , Receptor Toll-Like 2/genética , Factor de Crecimiento Transformador beta1/metabolismoRESUMEN
The role of T cells in chronic obstructive pulmonary disease (COPD) is not well understood. We have previously demonstrated that chronic cigarette smoke exposure can lead to the accumulation of CD4(+) and CD8(+) T cells in the alveolar airspaces in a mouse model of COPD, implicating these cells in disease pathogenesis. However, whether specific inhibition of T cell responses represents a therapeutic strategy has not been fully investigated. In this study inhibition of T cell responses through specific depleting antibodies, or the T cell immunosuppressant drug cyclosporin A, prevented airspace enlargement and neutrophil infiltration in a mouse model of chronic cigarette smoke exposure. Furthermore, individual inhibition of either CD4(+) T helper or CD8(+) T cytotoxic cells prevented airspace enlargement to a similar degree, implicating both T cell subsets as critical mediators of the adaptive immune response induced by cigarette smoke exposure. Importantly, T cell depletion resulted in significantly decreased levels of the Th17-associated cytokine IL-17A, and of caspase 3 and caspase 7 gene expression and activity, induced by cigarette smoke exposure. Finally, inhibition of T cell responses in a therapeutic manner also inhibited cigarette smoke-induced airspace enlargement, IL-17A expression, and neutrophil influx in mice. Together these data demonstrate for the first time that therapeutic inhibition of T cell responses may be efficacious in the treatment of COPD. Given that broad immunosuppression may be undesirable in COPD patients, this study provides proof-of-concept for more targeted approaches to inhibiting the role of T cells in emphysema development.
Asunto(s)
Linfocitos T CD4-Positivos/inmunología , Linfocitos T CD8-positivos/inmunología , Alveolos Pulmonares/patología , Enfermedad Pulmonar Obstructiva Crónica/inmunología , Fumar , Animales , Caspasa 3/sangre , Caspasa 7/biosíntesis , Caspasa 7/genética , Ciclosporina , Modelos Animales de Enfermedad , Femenino , Expresión Génica , Terapia de Inmunosupresión , Interleucina-17/sangre , Mediciones del Volumen Pulmonar , Activación de Linfocitos , Depleción Linfocítica , Ratones , Ratones Endogámicos C57BL , Infiltración Neutrófila/inmunología , Alveolos Pulmonares/inmunología , Enfermedad Pulmonar Obstructiva Crónica/patología , Contaminación por Humo de TabacoRESUMEN
The pulmonary collectins, surfactant proteins A and D (SP-A and SP-D) have been implicated in the regulation of the innate immune system within the lung. In particular, SP-D appears to have both pro- and anti-inflammatory signaling functions. At present, the molecular mechanisms involved in switching between these functions remain unclear. SP-D differs in its quaternary structure from SP-A and the other members of the collectin family, such as C1q, in that it forms large multimers held together by the N-terminal domain, rather than aligning the triple helix domains in the traditional "bunch of flowers" arrangement. There are two cysteine residues within the hydrophobic N terminus of SP-D that are critical for multimer assembly and have been proposed to be involved in stabilizing disulfide bonds. Here we show that these cysteines exist within the reduced state in dodecameric SP-D and form a specific target for S-nitrosylation both in vitro and by endogenous, pulmonary derived nitric oxide (NO) within a rodent acute lung injury model. S-nitrosylation is becoming increasingly recognized as an important post-translational modification with signaling consequences. The formation of S-nitrosothiol (SNO)-SP-D both in vivo and in vitro results in a disruption of SP-D multimers such that trimers become evident. SNO-SP-D but not SP-D, either dodecameric or trimeric, is chemoattractive for macrophages and induces p38 MAPK phosphorylation. The signaling capacity of SNO-SP-D appears to be mediated by binding to calreticulin/CD91. We propose that NO controls the dichotomous nature of this pulmonary collectin and that posttranslational modification by S-nitrosylation causes quaternary structural alterations in SP-D, causing it to switch its inflammatory signaling role. This represents new insight into both the regulation of protein function by S-nitrosylation and NO's role in innate immunity.
Asunto(s)
Lesión Pulmonar Aguda/inmunología , Inflamación/inmunología , Óxido Nítrico/metabolismo , Proteína D Asociada a Surfactante Pulmonar/metabolismo , S-Nitrosotioles/metabolismo , Transducción de Señal , Animales , Cisteína/química , Cisteína/metabolismo , Dimerización , Regulación de la Expresión Génica , Humanos , Inmunidad Innata , Inflamación/metabolismo , Pulmón/inmunología , Pulmón/metabolismo , Macrófagos , Masculino , Ratones , Proteína D Asociada a Surfactante Pulmonar/química , Proteína D Asociada a Surfactante Pulmonar/genética , Proteína D Asociada a Surfactante Pulmonar/inmunología , Ratas , Ratas Sprague-Dawley , Mucosa Respiratoria/inmunologíaRESUMEN
BACKGROUND: A precise balance exists between the actions of endogenous glucocorticoids (GC) and retinoids to promote normal lung development, in particular during alveolarization. The mechanisms controlling this balance are largely unknown, but recent evidence suggests that midkine (MK), a retinoic acid-regulated, pro-angiogenic growth factor, may function as a critical regulator. The purpose of this study was to examine regulation of MK by GC and RA during postnatal alveolar formation in rats. METHODS: Newborn rats were treated with dexamethasone (DEX) and/or all-trans-retinoic acid (RA) during the first two weeks of life. Lung morphology was assessed by light microscopy and radial alveolar counts. MK mRNA and protein expression in response to different treatment were determined by Northern and Western blots. In addition, MK protein expression in cultured human alveolar type 2-like cells treated with DEX and RA was also determined. RESULTS: Lung histology confirmed that DEX treatment inhibited and RA treatment stimulated alveolar formation, whereas concurrent administration of RA with DEX prevented the DEX effects. During normal development, MK expression was maximal during the period of alveolarization from postnatal day 5 (PN5) to PN15. DEX treatment of rat pups decreased, and RA treatment increased lung MK expression, whereas concurrent DEX+RA treatment prevented the DEX-induced decrease in MK expression. Using human alveolar type 2 (AT2)-like cells differentiated in culture, we confirmed that DEX and cAMP decreased, and RA increased MK expression. CONCLUSION: We conclude that MK is expressed by AT2 cells, and is differentially regulated by corticosteroid and retinoid treatment in a manner consistent with hormonal effects on alveolarization during postnatal lung development.
Asunto(s)
Proteínas Angiogénicas/metabolismo , Citocinas/metabolismo , Dexametasona/farmacología , Células Epiteliales/efectos de los fármacos , Alveolos Pulmonares/efectos de los fármacos , Tretinoina/farmacología , Factores de Edad , Proteínas Angiogénicas/genética , Animales , Animales Recién Nacidos , Northern Blotting , Western Blotting , Diferenciación Celular/efectos de los fármacos , Células Cultivadas , AMP Cíclico/metabolismo , Citocinas/genética , Células Epiteliales/metabolismo , Humanos , Midkina , Alveolos Pulmonares/crecimiento & desarrollo , Alveolos Pulmonares/metabolismo , ARN Mensajero/metabolismo , Ratas , Ratas Sprague-Dawley , Factores de TiempoRESUMEN
BACKGROUND: Dexamethasone (Dex) limits and all-trans-retinoic acid (RA) promotes alveolarization. While structural changes resulting from such hormonal exposures are known, their functional consequences are unclear. METHODS: Neonatal rats were treated with Dex and/or RA during the first two weeks of life or were given RA after previous exposure to Dex. Morphology was assessed by light microscopy and radial alveolar counts. Function was evaluated by plethysmography at d13, pressure volume curves at d30, and exercise swim testing and arterial blood gases at both d15 and d30. RESULTS: Dex-treated animals had simplified lung architecture without secondary septation. Animals given RA alone had smaller, more numerous alveoli. Concomitant treatment with Dex + RA prevented the Dex-induced changes in septation. While the results of exposure to Dex + RA were sustained, the effects of RA alone were reversed two weeks after treatment was stopped. At d13, Dex-treated animals had increased lung volume, respiratory rate, tidal volume, and minute ventilation. On d15, both RA- and Dex-treated animals had hypercarbia and low arterial pH. By d30, the RA-treated animals resolved this respiratory acidosis, but Dex-treated animals continued to demonstrate blood gas and lung volume abnormalities. Concomitant RA treatment improved respiratory acidosis, but failed to normalize Dex-induced changes in pulmonary function and lung volumes. No differences in exercise tolerance were noted at either d15 or d30. RA treatment after the period of alveolarization also corrected the effects of earlier Dex exposure, but the structural changes due to RA alone were again lost two weeks after treatment. CONCLUSION: We conclude that both RA- and corticosteroid-treatments are associated with respiratory acidosis at d15. While RA alone-induced changes in structure andrespiratory function are reversed, Dex-treated animals continue to demonstrate increased respiratory rate, minute ventilation, tidal and total lung volumes at d30. Concomitant treatment with Dex + RA prevents decreased septation induced by Dex alone and results in correction of hypercarbia. However, these animals continue to have abnormal pulmonary function and lung volumes. Increased septation as a result of RA treatment alone is reversed upon discontinuation of treatment. These data suggest that Dex + RA treatment results in improved gas exchange likely secondary to normalized septation.
Asunto(s)
Dexametasona/farmacología , Alveolos Pulmonares/crecimiento & desarrollo , Alveolos Pulmonares/fisiopatología , Tretinoina/farmacología , Acidosis Respiratoria/inducido químicamente , Acidosis Respiratoria/patología , Animales , Animales Recién Nacidos , Dexametasona/efectos adversos , Femenino , Pulmón/efectos de los fármacos , Pulmón/crecimiento & desarrollo , Pulmón/fisiopatología , Masculino , Embarazo , Alveolos Pulmonares/efectos de los fármacos , Ratas , Ratas Sprague-Dawley , Pruebas de Función Respiratoria , Tretinoina/efectos adversosRESUMEN
KEAP1 is the key regulator of the NRF2-mediated cytoprotective response, and increasingly recognized as a target for diseases involving oxidative stress. Pharmacological intervention has focused on molecules that decrease NRF2-ubiquitination through covalent modification of KEAP1 cysteine residues, but such electrophilic compounds lack selectivity and may be associated with off-target toxicity. We report here the first use of a fragment-based approach to directly target the KEAP1 Kelch-NRF2 interaction. X-ray crystallographic screening identified three distinct "hot-spots" for fragment binding within the NRF2 binding pocket of KEAP1, allowing progression of a weak fragment hit to molecules with nanomolar affinity for KEAP1 while maintaining drug-like properties. This work resulted in a promising lead compound which exhibits tight and selective binding to KEAP1, and activates the NRF2 antioxidant response in cellular and in vivo models, thereby providing a high quality chemical probe to explore the therapeutic potential of disrupting the KEAP1-NRF2 interaction.
Asunto(s)
Proteína 1 Asociada A ECH Tipo Kelch/metabolismo , Factor 2 Relacionado con NF-E2/metabolismo , Animales , Células Cultivadas , Cristalografía por Rayos X , Descubrimiento de Drogas , Humanos , Proteína 1 Asociada A ECH Tipo Kelch/química , Ratones , Factor 2 Relacionado con NF-E2/química , Unión ProteicaRESUMEN
Lung injury is associated with increased concentrations of hyaluronan (hyaluronic acid, HA). HA modifies cell behavior through interaction with cell-associated receptors such as receptor for HA-mediated motility (RHAMM, CD168). Using a function blocking anti-RHAMM antibody (R36), we investigated the expression and role of RHAMM in the inflammatory response to intratracheal bleomycin in rats. Immunostaining showed increased expression of RHAMM in macrophages 4-7 d after injury. Surface biotin labeling of cells isolated by lavage confirmed increased surface expression of a 70-kD RHAMM after lung injury, and in situ hybridization demonstrated increased RHAMM mRNA in macrophages responding to injury. Time-lapse cinemicrography demonstrated a 5-fold increase in motility of alveolar macrophages from bleomycin-treated animals that was completely blocked by R36 in vitro. Further, HA-stimulated macrophage chemotaxis was also inhibited by R36. Daily administration of R36 to injured animals resulted in a 40% decrease in macrophage accumulation 7 d after injury. Further, H&E staining of tissue sections showed that bleomycin-mediated changes in lung architecture were improved with R36 treatment. Taken together with previous results showing the inhibitory effects of HA-binding peptide on inflammation and fibrosis, we conclude that the interaction of RHAMM with HA is a critical component of the recruitment of inflammatory cells to the lung after injury.
Asunto(s)
Quimiotaxis , Proteínas de la Matriz Extracelular/metabolismo , Receptores de Hialuranos/metabolismo , Macrófagos/inmunología , Macrófagos/metabolismo , Neumonía/inmunología , Animales , Anticuerpos Bloqueadores/farmacología , Bleomicina/toxicidad , Membrana Celular/química , Proteínas de la Matriz Extracelular/análisis , Proteínas de la Matriz Extracelular/antagonistas & inhibidores , Receptores de Hialuranos/análisis , Ácido Hialurónico/metabolismo , Ácido Hialurónico/farmacología , Pulmón/efectos de los fármacos , Pulmón/patología , Macrófagos/química , Masculino , Neumonía/inducido químicamente , Ratas , Ratas Sprague-DawleyRESUMEN
Claudins are proteins that participate in epithelial barrier function and regulate paracellular permeability. By immunohistochemistry of adult rat lung sections, claudin-3, claudin-4, and claudin-5 were found to be co-expressed by type II alveolar epithelial cells. Claudin-3 and claudin-4 were also co-expressed by some alveolar epithelial cells adjacent to type II cells. In contrast, claudin-5 was expressed throughout the alveolus. Isolated primary rat alveolar epithelial cells in culture also expressed claudin-3, claudin-4, and claudin-5, but showed little claudin-1 and claudin-2 expression. Claudin expression by isolated cells at both the mRNA and protein level varied with time in culture. In particular, claudin-3 and claudin-5 co-localized and were distributed around the alveolar cell periphery, but claudin-4 expression was heterogeneous. We also found that paracellular permeability was increased when cultured alveolar epithelial cells were treated with a fatty acid amide, methanandamide. Methanandamide did not alter cell viability. Claudin-3, claudin-4, claudin-5, occludin, and zona occludens 1 remained localized to cell-cell contact sites at the plasma membrane in methanandamide-treated cells, suggesting that plasma membrane localization of these junction proteins is not sufficient for maintaining barrier function. However, methanandamide-treated cells showed a 12-fold increase in claudin-5 expression and a 2- to 3-fold increase in claudin-3, consistent with the notion that specific changes in claudin expression levels may correlate with changes in alveolar epithelial barrier function.