Low frequency of CD4+CD25+ Treg in SLE patients: a heritable trait associated with CTLA4 and TGFβ gene variants
© Barreto et al; licensee BioMed Central Ltd. 2009
Received: 04 September 2008
Accepted: 27 January 2009
Published: 27 January 2009
CD4+CD25+ regulatory T cells play an essential role in maintaining immune homeostasis and preventing autoimmunity. Therefore, defects in Treg development, maintenance or function have been associated with several human autoimmune diseases including Systemic Lupus Erythematosus (SLE), a systemic autoimmune disease characterized by loss of tolerance to nuclear components and significantly more frequent in females.
To investigate the involvement of Treg in SLE pathogenesis, we determined the frequency of CD4+CD25+CD45RO+ T cells, which encompass the majority of Treg activity, in the PBMC of 148 SLE patients (76 patients were part of 54 families), 166 relatives and 117 controls. SLE patients and their relatives were recruited in several Portuguese hospitals and through the Portuguese Lupus Association. Control individuals were blood donors recruited from several regional blood donor centers. Treg frequency was significantly lower in SLE patients than healthy controls (z = -6.161, P < 0.00001) and intermediate in the relatives' group. Remarkably, this T cell subset was also lower in females, most strikingly in the control population (z = 4.121, P < 0.001). We further ascertained that the decreased frequency of Treg in SLE patients resulted from the specific reduction of bona fide FOXP3+CD4+CD25+ Treg. Treg frequency was negatively correlated with SLE activity index (SLEDAI) and titers of serum anti-dsDNA antibodies. Both Treg frequency and disease activity were modulated by IVIg treatment in a documented SLE case. The segregation of Treg frequency within the SLE families was indicative of a genetic trait. Candidate gene analysis revealed that specific variants of CTLA4 and TGFβ were associated with the decreased frequency of Treg in PBMC, while FOXP3 gene variants were associated with affection status, but not with Treg frequency.
SLE patients have impaired Treg production or maintenance, a trait strongly associated with SLE disease activity and autoantibody titers, and possibly resulting from the inability to convert FOXP3+CD25- into FOXP3+CD25+ T cells. Treg frequency is highly heritable within SLE families, with specific variants of the CTLA4 and TGFβ genes contributing to this trait, while FOXP3 contributes to SLE through mechanisms not involving a modulation of Treg frequency. These findings establish that the genetic components in SLE pathogenesis include genes related to Treg generation or maintenance.
Immunological tolerance is a key feature of the immune system that allows the organism to discriminate self from nonself, providing defense against foreign pathogens while preventing autoimmunity. This ability of the immune system is controlled by mechanisms of central and peripheral tolerance. Central tolerance involves deletion of self-reactive T cells in the thymus at an early stage of development . However, this mechanism alone is not sufficient for preventing autoimmunity, as autoreactive T cells are also detected in healthy individuals . A second mechanism involves the thymic selection of a population of regulatory T cells (Treg), which dominantly prevents both the activation and the effector function of autoreactive T cells that have eluded other mechanisms of tolerance . The depletion or inactivation of Treg leads to the development of a wide range of autoimmune and inflammatory manifestations such as gastritis, oophoritis, orchitis, thyroiditis, inflammatory bowel disease and spontaneous autoimmune diabetes, in animal models . In addition, reduced numbers of this cellular subset have been found in murine models of SLE .
T cells expressing the high affinity T Cell Receptor (TCR) for antigens expressed on the thymic epithelium  are selected in the thymus, originating Treg cells able to suppress both proliferation and cytokine production by effector cells in a cell-contact dependent manner. The mechanisms involved in Treg generation, maintenance or function have not been fully clarified. For instance, while CTLA-4-/- mice develop an early lymphoproliferative disease  and CTLA4 gene expression in the thymus appears instrumental for T cell selection , some regulatory T cells can be generated in the absence of CTLA-4 . Given its wide ranged immuno-suppressor activity, TGF-β was first thought to be a mediator of Treg activity , but is nowadays known to play a major role in Treg homeostasis by promoting their proliferation .
In humans, Treg are highly enriched in the cellular subset expressing CD4, the α chain of the IL-2 receptor (CD25) and the memory marker CD45RO . Low numbers or functional defects in CD4+CD25+ T cells have been found in patients with SLE [13, 14], immune-mediated diabetes , and multiple sclerosis . Natural CD4+CD25+ Treg express the transcription factor FOXP3, which controls their development and function . Functional defects in the FOXP3 gene lead to the absence of Treg production and to Immunodysregulation, Polyendocrinopathy and Enteropathy, X-linked Syndrome (IPEX) . The control of immune cell numbers and effector functions in response to lymphopenia, infection and autoimmune reactivity are also under the strict control of Treg .
SLE is a chronic systemic autoimmune disease with unknown etiology, and thought to result from the interplay between genetic and environmental factors . Multiple immune system defects have been described in patients with this condition, including B cell hyperactivity and increased antinuclear autoantibody production, defects in T cell activation and aberrant cytokine production [21, 22]. To establish the involvement of Treg in SLE pathogenesis, we compared the frequency of CD4+CD25+CD45RO+ T cells in SLE patients and controls and correlated it with disease activity and antinuclear autoantibody production. We also analyzed the frequency of CD4+FOXP3+ cells in a subset of patients and investigated Treg frequency variation with disease activity, severity and development and remission of symptoms in two SLE cases. Further, we analyzed the segregation of CD4+CD25+CD45RO+ frequency in SLE-affected families and tested the candidate genes CTLA4, TGFβ, FOXP3, IL2 and CD25 for association with Treg frequency distribution and with SLE.
SLE survey questionnaire and percentage of patients and relatives that gave a positive answer to each question.
SLE survey questionnaire
% of Patients
% of Relatives
1. Have you ever had painful swollen joints for more than three months?
2. Do your fingers ever change color, become numb or uncomfortable in the cold?
3. Have you ever had mouth ulcers for more than two weeks?
4. Have you ever been told that you have low blood counts (anemia, low white cell count or low platelet count)?
5. Have you ever had an obvious or prominent rash on your cheeks for more than a month?
6. Do you develop a distinct rash in the sun (not just sunburn)?
7. Has it ever been painful to take a deep breath for more than just a few days (pleurisy)?
8. Have you ever been told that you have protein in the urine?
9. Do you find a lot of hair on your pillow on waking?
10.Have you ever had a seizure, convulsion or fit?
Cell surface staining and flow cytometry
PBMC were isolated using Vacutainer CPT™ tubes (Becton Dickinson). For the CD4CD25CD45RO staining 1 × 106 cells were fixed in 2% PFA, washed twice in PBS 2% FCS and subsequently incubated for 20 min at 4°C with the optimal dilution of each conjugated anti-human mAb (CD4-FITC, CD25-Cy-chrome, CD31-PE and CD45RO-APC, Becton Dickinson). Cells were washed again and fluorescence intensity staining was analyzed using a FACScan flow cytometer (FACScalibur™ and CellQuest™ software, Becton Dickinson). CD4+CD25+ T cells were defined, for all the individuals, as the population of CD4 positive T cells whose CD25 expression exceeded the level of CD25 positivity seen in the CD4 negative T cells. The CD4-FITC, CD25-APC, FOXP3-PE staining was performed according to eBioscience manufacture protocol.
Anti-dsDNA autoantibody measurement by quantitative ELISA
Reacti-Bind™ EIA plates (Pierce) were coated overnight at 4°C with 1 mg/mL purified dsDNA (Sigma-Aldrich). The plates were blocked with a solution of 1% gelatin for 5 h at 4°C and incubated overnight at 4°C with test plasma (in triplicates) at a total protein concentration was 0.5 mg/mL. Plates were then incubated overnight at 4°C with 50 μL of alkaline phosphatase-conjugated anti-human IgG (Sigma-Aldrich) and bound IgG was revealed using 1 mg/mL p-nitrophenyl phosphate (Sigma-Aldrich). Absorbance at 405 nm was measured in an ELISA plate reader (BioRad). Quantification of each reactivity was obtained by fitting ODs to a standard curve present in duplicates on each plate, and consisting of 12 serial dilutions of respective positive control sera. In the readout, one unit was defined as the equivalent of the highest concentration used for the respective positive control serum, which was previously chosen to be below the saturation level. Fractions of one unit were consequently defined by the dilution factor of this standard, at which it yielded an OD equivalent to that obtained for a respective sample .
Genomic DNA was isolated from PBMC by standard methods. The polymorphic markers tested were selected for their putative role in gene expression or function. Within the CTLA4 gene, we genotyped a functional SNP involving a missense A>G transition at +49 exon 1 (rs231775) and a 3'UTR microsatelite marker proposed to influence mRNA stability and turnover . In the TGFβ gene, we genotyped a C>T transition in the promoter (rs1800469) and a G>C SNP in exon 1 (rs1800471), both known to be associated with the serum concentration of TGF-β [28, 29]. Within the FOXP3 gene two microsatelite markers were genotyped (one in intron 0, which has been described as having a promoter/enhancer function and other in intron 5) and a -1128 G>A SNP (rs12843496) . The IL2 gene, -384 G<T (rs2069762) and +114 G>T (rs3087209) in the promoter and in exon 1, respectively, were genotyped as previously described [30, 31]. Within the CD25 gene, we genotyped a (CA)n repeat 10 kb upstream of the gene (D10S189) and two SNPs, rs2274037 (a A>G transition in exon 4) and rs1570538 (a C>T transition in the 3'UTR region of CD25) as previously described . The D10S189 microsatelite marker was genotyped using the Applied Biosystems fluorescence based automated sequencer. Semi-automated fragment sizing was performed using GENESCAN® 3.1.
mRNA isolation and quantification
Total RNA was isolated from 5 × 106 PBMC using the RNeasy Mini Kit (QIAGEN). The first strand cDNA was generated by reverse transcription with oligo dT primer (Invitrogen). The CTLA-4, TGF-β, FOXP3, IL-2 and CD25 mRNA levels were quantified with the LightCycler (Roche Molecular Biochemicals) in 33 patients and 24 controls, which were representative of the total population sample. 50 ng of first-stranded cDNA were amplified and real-time fluorimetric intensity of SYBR green I was monitored. RT-PCR reactions consisted in an initial denaturation step at 95°C for 10 minutes followed by 45 cycles of denaturation at 95°C for 15 seconds, 56°C for 5 seconds and 72°C for 23 seconds. The individual samples were standardized by the amount of HPRT RNA. This RT-PCR reaction consisted on an initial denaturation step at 95°C for 10 minutes followed by 45 cycles of denaturation at 95°C for 15 seconds, 60°C for 5 seconds and 72°C for 23 seconds. Additionally, CTLA-4 and CD25 mRNA expression levels were normalized by the proportion of CD4+ cells, given that these molecules are mainly expressed by CD4+ T cells.
Nonparametric analysis of variance was performed using the Mann-Whitney U and Kruskal-Wallis tests to compare the distributions of T cell frequencies in patients and controls. Results were considered significant at the 0.05 level. Heritability estimation was performed by the SOLAR software . In this test the likelihood of the sporadic model of no inheritance is compared with the likelihood of a polygenic model of inheritance. The sporadic model constitutes our null hypothesis in which it is assumed that there is not a genetic component underlying the frequencies of Treg cells. The polygenic model constitutes our testing hypothesis, where the quantitative trait is considered to be determined by a large number of genetic loci acting independently and/or additively. The models are then compared to find the hypothesis that is better supported by the data. Hardy-Weinberg equilibrium (HWE) was analyzed by the HWE exact test. Linkage disequilibrium (LD) between two polymorphic markers was quantified as D' using the HAPLOXT program implemented in the GOLD software .
Lower frequency of CD4+CD25+ and CD4+CD25+CD45RO+ cells in SLE patients
SLE affects primarily women and consequently only about 10% of our patients are male, while our control population is balanced in terms of gender. We therefore tested whether this gender bias was not a confounding factor in our interpretation. CD4+CD25+CD45RO+ T cell frequency was significantly lower in healthy females than in males (Mann-Whitney U test: z = 4.121, P < 0.001). The CD4+CD25+CD45RO+ T cell frequency was also lower in females than in males in the patient and relative groups, although the difference did not reach statistical significance (Figure 1C). Separate analysis within each gender group shows that the CD4+CD25+CD45RO+ T cell frequency is always significantly lower in patients (Mann-Whitney U test, Males: z = -2.504, P = 0.012; females: z = -3.864, P < 0.001).
CD25 is a marker for both Treg and activated cells. To rule out the possibility that this T cell population is mainly constituted by activated cells we measured the frequency of the CD4+CD45RO+ T cells, since CD45RO expression is associated with early activation events. No difference was found in the frequency of CD4+CD45RO+ cells between patients and controls (Mann-Whitney U test: z = -1.724, P = 0.089), indicating that the CD25+ population was largely a regulatory population.
SLE patients display higher frequency of CD4+FOXP3+ cells which are mainly CD25-
CD4+CD25+CD45RO+ T cell frequency is negatively correlated with SLE-associated phenotypes
The CD4+CD25+CD45RO+ T cell frequency was inversely correlated with disease activity measured by the SLEDAI index (ρ = -0.502, P = 0.002) (Figure 4B). However, no correlation was found with the SLICC damage index (ρ = 0.071, P = 0.658). There was no significant difference between the frequency of CD4+CD25+CD45RO+ T cells in patients untreated or treated with corticosteroids (Kruskall-Wallis Test: z = 0.07, P = 0.94), antimalarial agents (Kruskall-Wallis Test: z = 1.41, P = 0.158), or both drugs (Kruskall-Wallis Test: z = -1.32, P = 0.132). Noteworthy, no correlation was found between total lymphocyte counts and the frequency of CD4+CD25+CD45RO+ T cell (ρ = 0.021, P = 0.758), excluding the possibility that lymphopenia led to this phenotype. There was also no correlation with age (ρ = 0.153, P = 0.100).
Variation of CD4+CD25+CD45RO+ T cell frequency with the development and remission of SLE-related symptoms
Peripheral CD4+CD25+CD45RO+ T cell frequency is highly heritable
Relatives of SLE patients presented intermediate CD4+CD25+CD45RO+ T cell frequencies between patients and controls (Figure 1B), suggesting that Treg frequency might represent a genetic trait. Any potential bias due to recruitment design was excluded based on the following observations: for each family all samples were collected and processed on the same day; there were no significant differences in Treg frequency between families collected in different days. Treg frequencies in genetically unrelated family members and in controls collected and processed on the same day are within the range of healthy controls analyzed during the whole period of the study.
Lower frequency of CD4+CD25+CD45RO+ T cells is associated with specific CTLA4 and TGFβ gene variants
Distribution of Treg frequency according to genotypes of the CTLA4, TGFβ FOXP3, IL2 and CD25 genes (non-parametric analysis of variance – Kruskall-Wallis test).
CTLA4 rs 231775 genotypes
Median % CD4+CD25+CD45RO+Cells
CTLA4 3'UTR microssatelite genotypes
TGFβ rs18000469 genotypes
TGFβ rs18000471 genotypes
FOXP3 FOX0 microssatelite genotypes
FOXP3 FOX5 microssatelite genotypes
IL2 rs20699762 genotypes
IL2 rs3087209 genotypes
CD25 D10S189 genotypes
CD25 rs2274037 genotypes
CD25 rs1570538 genotypes
Genetic association between FOXP3 markers and SLE.
rs 12843496 allele
Number of alleles (%)
Number of alleles (%)
rs 12843496 genotypes
Taken together these results indicate that CTLA4 and TGFβ gene variants contribute to the determination of CD4+CD25+CD45RO+ T cell frequency in PBMC, independently of disease activity, while the involvement of FOXP3 gene variants in SLE is likely not mediated by CD4+CD25+CD45RO+ T cell frequency.
No correlation was found between CTLA-4, TGF-β, IL-2 or CD25 expression levels and the frequency of CD4+CD25+CD45RO+ T cells, disease status or marker genotypes (data not shown). There was a trend towards higher levels of FOXP3 mRNA in SLE patients, although not significant (Mann-Whitney U-test: z = -1.78, P = 0.075), and in individuals carrying the A allele of FOXP3 rs12843496 (Mann-Whitney U-test: z = 4.95, P = 0.026). These results suggest that variability in CD4+CD25+CD45RO+ T cell frequency associated with SLE is not influenced by altered expression of any of the tested genes.
The present study supports and expands previous observations of decreased CD4+CD25+CD45RO+ T cell frequency in SLE patients. It further demonstrates a clear gender difference in the distribution of this regulatory T cell subset and provides evidence suggesting that CD4+CD25+CD45RO+ T cell frequency variation may result from a defect in the conversion of FOXP3+CD25- into FOXP3+CD25+cells. CD4+CD25+CD45RO+ T cell frequency is shown to be negatively correlated with disease activity and with anti-dsDNA antibodies in the patient and control groups, and to change with development and remission of SLE symptoms in two documented cases. The study also established that the frequency of CD4+CD25+CD45RO+ T cells is highly heritable in families affected with SLE, that it is negatively correlated with the severity of SLE-associated manifestations in patients and relatives, and that it is influenced by genetic variants in the CTLA4 and TGFβ genes.
We initially analyzed the frequency of Treg with the available anti-CD25 an CD45RO antibodies as described by Jonuleit et al. , who have demonstrated that human CD4+CD25+CD45RO+ T cells are highly enriched in T cells with suppressor properties. CD25 and CD45RO are also markers of activation and one could argue that our measurement concerned conventional activated cells. Several observations indicate that this is not the case. First, the total frequency of CD45RO+ cells was not significantly different between patients' and controls' PBMC, indicating that conventional activated cells are not enriched in SLE patients' PMBC. Second, once a FOXP3 antibody became available, we have tested this marker in a subset of patients. All together our analyses reveal that, when compared to controls, patients had a significantly decreased frequency of CD25+ cells of either the CD4+ CD45RO+ or the FOXP3+ phenotype, supporting the notion that the CD4+CD25+CD45RO+ T cell subset is enriched in Treg. Hence, the analyses we presented here most likely concern bona fide Treg. Furthermore, while the CD4+FOXP3+ cell subset was comparable between patients and controls, patients had a significantly higher frequency of FOXP3+ CD25- cells, suggesting that they are unable to convert FOXP3+ CD25- into FOXP3+ CD25+ cells. Previous observations endorse this hypothesis: SLE patients display multiple signaling defects leading to a defective IL-2 production , and CD4+FOXP3+ thymocytes from IL-2-/- mice have very few cells expressing CD25 when compared to wild type mice . In fact, IL-2 does not seem to be required for the induction of FOXP3 expression but is required for the survival and expansion of Treg cells in the periphery, leading to autoimmune manifestations.
The percentage of CD45RO-CD31+ RTE was not correlated with disease or with CD4+CD25+CD45RO+ T cell frequency, ruling out a defect in thymic export. The faster decrease rate of CD4+CD25+ CD31+ cells in SLE patients, however, is indicative of a specific thymic defect leading to a decreased Treg production and thus contributing to the lower frequency of these cells in the periphery. The observed decrease of CD4+CD25+CD45RO+ T cell frequency in patients might also result from cell migration to the sites of inflammation. However, this hypothesis seems unlikely because patients with rheumatoid arthritis display enriched CD4+CD25+CD45RO+ T cells not only in inflamed joints but also in peripheral blood .
The difference found in CD4+CD25+CD45RO+ T cell frequency between males and females is remarkable, given the much higher prevalence of SLE in females. This difference is very significant in the control population, suggesting this may be a gender specific trait that renders females more susceptible to SLE. The lack of significance in the patient group may be due to the very small number of males, while in the relatives' group this might be explained by the high heterogeneity of this population, where only some individuals carry the disease susceptibility factors.
The significant negative correlation of CD4+CD25+CD45RO+ T cell frequency with anti-dsDNA antibodies observed in the patients and in the relatives suggests that these cells may be able to inhibit antinuclear antibody production by B cells, and therefore an additional mechanism through which loss of immunological tolerance may be achieved in SLE. This phenomenon may also occur in the relatives, but the fact that they display a positive correlation between CD4+CD25+CD45RO+ T cell frequency and anti-dsDNA antibodies may represent a compensation effect in which the relatives' are able to overcome this pathogenic mechanism.
CD4+CD25+CD45RO+ T cell frequency was also associated with disease activity and with the extent of clinical manifestations. This suggests a direct involvement in disease development and prognosis, which is corroborated by the variation observed with onset and remission of symptoms in the two documented cases. The frequency of CD4+CD25+CD45RO+ T cells was not associated with the use of immunosuppressive drugs. Whether these therapies affect basal frequencies of Treg was not addressed in the present work as it would require longitudinal studies. Interestingly, in one case the clinical improvement that followed IVIg administration was associated with increased CD4+CD25+CD45RO+ T cell frequency, suggesting that this treatment may influence Treg generation or maintenance .
The CD4+CD25+CD45RO+ T cell frequency was highly heritable in the affected families and was also strongly correlated with the extent of autoimmune manifestations in patients and in affected and unaffected relatives, in concordance with the clustering of autoimmune diseases and/or autoimmune-related phenotypes observed in these families. These findings are of particular importance because they show a contribution of genetic factors to the decrease in CD4+CD25+CD45RO+ T cell frequency and thus substantiate a genetic basis for SLE. Although we still cannot establish whether the decrease in CD4+CD25+CD45RO+ T cells is a cause or a consequence of autoimmune manifestations in SLE, we show evidence for the existence of genetic factors that, by influencing this trait, may contribute to SLE.
The frequency of CD4+CD25+CD45RO+ T cells likely results from a combination of processes regulating their expansion and survival in the periphery, and therefore multiple genetic factors may contribute to this trait. This study provided evidence for an involvement of the CTLA4 and TGFβ genes. The specific polymorphisms associated with CD4+CD25+CD45RO+ cell frequency were not correlated with CTLA-4 and TGF-β mRNA expression level variation; expression levels in turn were not associated with cell variation or with disease status, indicating that a functional defect in these genes, rather than changes in expression levels, contributes to the observed CD4+CD25+CD45RO+ T cell phenotype in SLE patients.
In mouse models the generation and expansion of Treg are dependent on CTLA-4 and TGF-β respectively, [41–46]. CTLA-4-/- animals have reduced numbers of CD4+CD25+ T cells with reduced regulatory capacity, while TGF-β regulates the Treg cell pool size and expression of the Treg commitment factor Foxp3 . TGFβ has also been shown to induce CD4+CD25+ regulatory T cells in vitro, which were able to prevent a murine lupus-like syndrome and graft versus host disease . In humans, it was demonstrated that it has the capacity to expand CD4+CD25+ in normal subjects . Our results therefore extend the role of these genes in the regulation of Treg frequency and autoimmunity to humans.
Other Treg specific candidate genes that may contribute to the determination of the size of the Treg pool are the FOXP3 commitment factor and the IL2 and CD25 genes, which deliver crucial growth and/or survival signals to these cells. In the study population, a promoter polymorphism (rs12843496) in the FOXP3 gene was associated with SLE but not with the frequency of CD4+CD25+CD45RO+ T cells, indicating that susceptibility to the disease is mediated by mechanisms other than influencing Treg frequency. The rs12843496 allele A associated with SLE creates a putative binding site to the transcriptional activator PLAG1 in the FOXP3 promoter region, which may explain the slightly higher FOXP3 mRNA expression found in SLE patients. A compensatory mechanism can be hypothesized to account for the maintenance of a normal mean CD4+FOXP3+ cell frequency in patients even in the presence of increased frequency of this allele, and is plausible since FOXP3 can be upregulated by other cytokines.
The IL2 and CD25 genes were not associated with CD4+CD25+CD45RO+ T cell frequency or with SLE. It should be remarked that the study population sample is small and that we focused on genotyping known functional polymorphisms because of their previously reported relevance, but did not fully cover genetic variation in any of these genes. Our genetic results should therefore be considered preliminary.
In conclusion, we report that low peripheral CD4+CD25+CD45RO+ T cell frequency is a genetically determined predisposing factor for SLE development. Our results demonstrate the contribution of specific genes and suggest pathways involved in the establishment of CD4+CD25+CD45RO+ T cell frequency. Whether a defect in number or function is a prerequisite for SLE development remains to be understood. Most importantly, our findings open new perspectives for therapy for SLE patients based on the manipulation of Treg. Criteria for the selection of candidate patients for Treg based therapy remains to be fully established but likely should include evaluation of Treg frequency and analysis of genes involved in Treg generation or maintenance, strongly benefiting the management of this autoimmune disease.
The authors would like to thank Isabel Reis, Ana Tam, Maria João Antunes, the Associação dos Doentes com Lupus, and also Leonor Miranda, for their precious help in the recruitment of patients and collection of blood samples. We also thank the Serviço de Imunohemoterapia, Hospital Egas Moniz, as well as all the blood donors for their participation in this study. The authors thank Sofia Marques for her help in the mRNA experiments, Isabel Marques for her bioinformatics support and António Coutinho for advice and critical reading of the manuscript. M. Barreto was supported by Fundação para a Ciência e Tecnologia.
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