In vivo biochemical 7.0 Tesla magnetic resonance: preliminary results of dGEMRIC, zonal T2, and T2* mapping of articular cartilage

INTRODUCTION: Ultra-high-field whole-body systems (7.0 T) have a high potential for future human in vivo magnetic resonance imaging (MRI). In musculoskeletal MRI, biochemical imaging of articular cartilage may benefit, in particular. Delayed gadolinium-enhanced MRI of cartilage (dGEMRIC) and T2 mapping have shown potential at 3.0 T. Although dGEMRIC, allows the determination of the glycosaminoglycan content of articular cartilage, T2 mapping is a promising tool for the evaluation of water and collagen content. In addition, the evaluation of zonal variation, based on tissue anisotropy, provides an indicator of the nature of cartilage ie, hyaline or hyaline-like articular cartilage.Thus, the aim of our study was to show the feasibility of in vivo dGEMRIC, and T2 and T2* relaxation measurements, at 7.0 T MRI; and to evaluate the potential of T2 and T2* measurements in an initial patient study after matrix-associated autologous chondrocyte transplantation (MACT) in the knee. MATERIALS AND METHODS: MRI was performed on a whole-body 7.0 T MR scanner using a dedicated circular polarization knee coil. The protocol consisted of an inversion recovery sequence for dGEMRIC, a multiecho spin-echo sequence for standard T2 mapping, a gradient-echo sequence for T2* mapping and a morphologic PD SPACE sequence. Twelve healthy volunteers (mean age, 26.7 +/- 3.4 years) and 4 patients (mean age, 38.0 +/- 14.0 years) were enrolled 29.5 +/- 15.1 months after MACT. For dGEMRIC, 5 healthy volunteers (mean age, 32.4 +/- 11.2 years) were included. T1 maps were calculated using a nonlinear, 2-parameter, least squares fit analysis. Using a region-of-interest analysis, mean cartilage relaxation rate was determined as T1 (0) for precontrast measurements and T1 (Gd) for postcontrast gadopentate dimeglumine [Gd-DTPA(2-)] measurements. T2 and T2* maps were obtained using a pixelwise, monoexponential, non-negative least squares fit analysis; region-of-interest analysis was carried out for deep and superficial cartilage aspects. Statistical evaluation was performed by analyses of variance. RESULTS: Mean T1 (dGEMRIC) values for healthy volunteers showed slightly different results for femoral [T1 (0): 1259 +/- 277 ms; T1 (Gd): 683 +/- 141 ms] compared with tibial cartilage [T1 (0): 1093 +/- 281 ms; T1 (Gd): 769 +/- 150 ms]. Global mean T2 relaxation for healthy volunteers showed comparable results for femoral (T2: 56.3 +/- 15.2 ms; T2*: 19.7 +/- 6.4 ms) and patellar (T2: 54.6 +/- 13.0 ms; T2*: 19.6 +/- 5.2 ms) cartilage, but lower values for tibial cartilage (T2: 43.6 +/- 8.5 ms; T2*: 16.6 +/- 5.6 ms). All healthy cartilage sites showed a significant increase from deep to superficial cartilage (P < 0.001). Within healthy cartilage sites in MACT patients, adequate values could be found for T2 (56.6 +/- 13.2 ms) and T2* (18.6 +/- 5.3 ms), which also showed a significant stratification. Within cartilage repair tissue, global mean values showed no difference, with 55.9 +/- 4.9 ms for T2 and 16.2 +/- 6.3 ms for T2*. However, zonal assessment showed only a slight and not significant increase from deep to superficial cartilage (T2: P = 0.174; T2*: P = 0.150). CONCLUSION: In vivo T1 dGEMRIC assessment in healthy cartilage, and T2 and T2* mapping in healthy and reparative articular cartilage, seems to be possible at 7.0 T MRI. For T2 and T2*, zonal variation of articular cartilage could also be evaluated at 7.0 T. This zonal assessment of deep and superficial cartilage aspects shows promising results for the differentiation of healthy and affected articular cartilage. In future studies, optimized protocol selection, and sophisticated coil technology, together with increased signal at ultra-high-field MRI, may lead to advanced biochemical cartilage imaging.

Genetic association studies under the population stratification, family pedigree and application to genome-wide association studies

This dissertation has three separate parts: the first part deals with the general pedigree association testing incorporating continuous covariates; the second part deals with the association tests under population stratification using the conditional likelihood tests; the third part deals with the genome-wide association studies based on the real rheumatoid arthritis (RA) disease data sets from Genetic Analysis Workshop 16 (GAW16) problem 1. Many statistical tests are developed to test the linkage and association using either case-control status or phenotype covariates for family data structure, separately. Those univariate analyses might not use all the information coming from the family members in practical studies. On the other hand, the human complex disease do not have a clear inheritance pattern, there might exist the gene interactions or act independently. In part I, the new proposed approach MPDT is focused on how to use both the case control information as well as the phenotype covariates. This approach can be applied to detect multiple marker effects. Based on the two existing popular statistics in family studies for case-control and quantitative traits respectively, the new approach could be used in the simple family structure data set as well as general pedigree structure. The combined statistics are calculated using the two statistics; A permutation procedure is applied for assessing the p-value with adjustment from the Bonferroni for the multiple markers. We use simulation studies to evaluate the type I error rates and the powers of the proposed approach. Our results show that the combined test using both case-control information and phenotype covariates not only has the correct type I error rates but also is more powerful than the other existing methods. For multiple marker interactions, our proposed method is also very powerful. Selective genotyping is an economical strategy in detecting and mapping quantitative trait loci in the genetic dissection of complex disease. When the samples arise from different ethnic groups or an admixture population, all the existing selective genotyping methods may result in spurious association due to different ancestry distributions. The problem can be more serious when the sample size is large, a general requirement to obtain sufficient power to detect modest genetic effects for most complex traits. In part II, I describe a useful strategy in selective genotyping while population stratification is present. Our procedure used a principal component based approach to eliminate any effect of population stratification. The paper evaluates the performance of our procedure using both simulated data from an early study data sets and also the HapMap data sets in a variety of population admixture models generated from empirical data. There are one binary trait and two continuous traits in the rheumatoid arthritis dataset of Problem 1 in the Genetic Analysis Workshop 16 (GAW16): RA status, AntiCCP and IgM. To allow multiple traits, we suggest a set of SNP-level F statistics by the concept of multiple-correlation to measure the genetic association between multiple trait values and SNP-specific genotypic scores and obtain their null distributions. Hereby, we perform 6 genome-wide association analyses using the novel one- and two-stage approaches which are based on single, double and triple traits. Incorporating all these 6 analyses, we successfully validate the SNPs which have been identified to be responsible for rheumatoid arthritis in the literature and detect more disease susceptibility SNPs for follow-up studies in the future. Except for chromosome 13 and 18, each of the others is found to harbour susceptible genetic regions for rheumatoid arthritis or related diseases, i.e., lupus erythematosus. This topic is discussed in part III.

Molecular cytogenetics and gene mapping in sheep (Ovis aries, 2n = 54)

The development of a completely annotated sheep genome sequence is a key need for understanding the phylogenetic relationships and genetic diversity among the many different sheep breeds worldwide and for identifying genes controlling economically and physiologically important traits. The ovine genome sequence assembly will be crucial for developing optimized breeding programs based on highly productive, healthy sheep phenotypes that are adapted to modern breeding and production conditions. Scientists and breeders around the globe have been contributing to this goal by generating genomic and cDNA libraries, performing genome-wide and trait-associated analyses of polymorphism, expression analysis, genome sequencing, and by developing virtual and physical comparative maps. The International Sheep Genomics Consortium (ISGC), an informal network of sheep genomics researchers, is playing a major role in coordinating many of these activities. In addition to serving as an essential tool for monitoring chromosome abnormalities in specific sheep populations, ovine molecular cytogenetics provides physical anchors which link and order genome regions, such as sequence contigs, genes and polymorphic DNA markers to ovine chromosomes. Likewise, molecular cytogenetics can contribute to the process of defining evolutionary breakpoints between related species. The selective expansion of the sheep cytogenetic map, using loci to connect maps and identify chromosome bands, can substantially contribute to improving the quality of the annotated sheep genome sequence and will also accelerate its assembly. Furthermore, identifying major morphological chromosome anomalies and micro-rearrangements, such as gene duplications or deletions, that might occur between different sheep breeds and other Ovis species will also be important to understand the diversity of sheep chromosome structure and its implications for cross-breeding. To date, 566 loci have been assigned to specific chromosome regions in sheep and the new cytogenetic map is presented as part of this review. This review will also summarize the current cytogenomic status of the sheep genome, describe current activities in the sheep cytogenomics research sector, and will discuss the cytogenomics data in context with other major sheep genomics projects.

Genetic mapping of the belt pattern in Brown Swiss cattle to BTA3

The white belt pattern of Brown Swiss cattle is characterized by a lack of melanocytes in a stretch of skin around the midsection. This pattern is of variable width and sometimes the belt does not fully circle the body. To identify the gene responsible for this colour variation, we performed linkage mapping of the belted locus using six segregating half-sib families including 104 informative meioses for the belted character. The pedigree confirmed a monogenic autosomal dominant inheritance of the belted phenotype in Brown Swiss cattle. We performed a genome scan using 186 microsatellite markers in a subset of 88 animals of the six families. Linkage with the belt phenotype was detected at the telomeric region of BTA3. Fine-mapping and haplotype analysis using 19 additional markers in this region refined the critical region of the belted locus to a 922-kb interval on BTA3. As the corresponding human and mouse chromosome segments contain no obvious candidate gene for this coat colour trait, the mutation causing the belt pattern in the Brown Swiss cattle might help to identify an unknown gene influencing skin pigmentation.

Identification and phenotypic characterization of a second collagen adhesin, Scm, and genome-based identification and analysis of 13 other predicted MSCRAMMs, including four distinct pilus loci, in Enterococcus faecium.

Attention has recently been drawn to Enterococcus faecium because of an increasing number of nosocomial infections caused by this species and its resistance to multiple antibacterial agents. However, relatively little is known about the pathogenic determinants of this organism. We have previously identified a cell-wall-anchored collagen adhesin, Acm, produced by some isolates of E. faecium, and a secreted antigen, SagA, exhibiting broad-spectrum binding to extracellular matrix proteins. Here, we analysed the draft genome of strain TX0016 for potential microbial surface components recognizing adhesive matrix molecules (MSCRAMMs). Genome-based bioinformatics identified 22 predicted cell-wall-anchored E. faecium surface proteins (Fms), of which 15 (including Acm) had characteristics typical of MSCRAMMs, including predicted folding into a modular architecture with multiple immunoglobulin-like domains. Functional characterization of one [Fms10; redesignated second collagen adhesin of E. faecium (Scm)] revealed that recombinant Scm(65) (A- and B-domains) and Scm(36) (A-domain) bound to collagen type V efficiently in a concentration-dependent manner, bound considerably less to collagen type I and fibrinogen, and differed from Acm in their binding specificities to collagen types IV and V. Results from far-UV circular dichroism measurements of recombinant Scm(36) and of Acm(37) indicated that these proteins were rich in beta-sheets, supporting our folding predictions. Whole-cell ELISA and FACS analyses unambiguously demonstrated surface expression of Scm in most E. faecium isolates. Strikingly, 11 of the 15 predicted MSCRAMMs clustered in four loci, each with a class C sortase gene; nine of these showed similarity to Enterococcus faecalis Ebp pilus subunits and also contained motifs essential for pilus assembly. Antibodies against one of the predicted major pilus proteins, Fms9 (redesignated EbpC(fm)), detected a 'ladder' pattern of high-molecular-mass protein bands in a Western blot analysis of cell surface extracts from E. faecium, suggesting that EbpC(fm) is polymerized into a pilus structure. Further analysis of the transcripts of the corresponding gene cluster indicated that fms1 (ebpA(fm)), fms5 (ebpB(fm)) and ebpC(fm) are co-transcribed, a result consistent with those for pilus-encoding gene clusters of other Gram-positive bacteria. All 15 genes occurred frequently in 30 clinically derived diverse E. faecium isolates tested. The common occurrence of MSCRAMM- and pilus-encoding genes and the presence of a second collagen-binding protein may have important implications for our understanding of this emerging pathogen.

HLA-DPB1 and DPB2 are genetic loci for systemic sclerosis: a genome-wide association study in Koreans with replication in North Americans.

OBJECTIVE: To identify systemic sclerosis (SSc) susceptibility loci via a genome-wide association study. METHODS: A genome-wide association study was performed in 137 patients with SSc and 564 controls from Korea using the Affymetrix Human SNP Array 5.0. After fine-mapping studies, the results were replicated in 1,107 SSc patients and 2,747 controls from a US Caucasian population. RESULTS: The single-nucleotide polymorphisms (SNPs) (rs3128930, rs7763822, rs7764491, rs3117230, and rs3128965) of HLA-DPB1 and DPB2 on chromosome 6 formed a distinctive peak with log P values for association with SSc susceptibility (P=8.16x10(-13)). Subtyping analysis of HLA-DPB1 showed that DPB1*1301 (P=7.61x10(-8)) and DPB1*0901 (P=2.55x10(-5)) were the subtypes most susceptible to SSc in Korean subjects. In US Caucasians, 2 pairs of SNPs, rs7763822/rs7764491 and rs3117230/rs3128965, showed strong association with SSc patients who had either circulating anti-DNA topoisomerase I (P=7.58x10(-17)/4.84x10(-16)) or anticentromere autoantibodies (P=1.12x10(-3)/3.2x10(-5)), respectively. CONCLUSION: The results of our genome-wide association study in Korean subjects indicate that the region of HLA-DPB1 and DPB2 contains the loci most susceptible to SSc in a Korean population. The confirmatory studies in US Caucasians indicate that specific SNPs of HLA-DPB1 and/or DPB2 are strongly associated with US Caucasian patients with SSc who are positive for anti-DNA topoisomerase I or anticentromere autoantibodies.

Mouse models and quantitative trait loci of susceptibility to bleomycin- and radiation-induced pulmonary fibrosis

Radiotherapy involving the thoracic cavity and chemotherapy with the drug bleomycin are both dose limited by the development of pulmonary fibrosis. From evidence that there is variation in the population in susceptibility to pulmonary fibrosis, and animal data, it was hypothesized that individual variation in susceptibility to bleomycin-induced, or radiation-induced, pulmonary fibrosis is, in part, genetically controlled. In this thesis a three generation mouse genetic model of C57BL/6J (fibrosis prone) and C3Hf/Kam (fibrosis resistant) mouse strains and F1 and F2 (F1 intercross) progeny derived from the parental strains was developed to investigate the genetic basis of susceptibility to fibrosis. In the bleomycin studies the mice received 100 mg/kg (125 for females) of bleomycin, via mini osmotic pump. The animals were sacrificed at eight weeks following treatment or when their breathing rate indicated respiratory distress. In the radiation studies the mice were given a single dose of 14 or 16 Gy (Co$\sp{60})$ to the whole thorax and were sacrificed when moribund. The phenotype was defined as the percent of fibrosis area in the left lung as quantified with image analysis of histological sections. Quantitative trait loci (QTL) mapping was used to identify the chromosomal location of genes which contribute to susceptibility to bleomycin-induced pulmonary fibrosis in C57BL/6J mice compared to C3Hf/Kam mice and to determine if the QTL's which influence susceptibility to bleomycin-induced lung fibrosis in these progenitor strains could be implicated in susceptibility to radiation-induced lung fibrosis. For bleomycin, a genome wide scan revealed QTL's on chromosome 17, at the MHC, (LOD = 11.7 for males and 7.2 for females) accounting for approximately 21% of the phenotypic variance, and on chromosome 11 (LOD = 4.9), in male mice only, adding 8% of phenotypic variance. The bleomycin QTL on chromosome 17 was also implicated for susceptibility to radiation-induced fibrosis (LOD = 5.0) and contributes 7% of the phenotypic variance in the radiation study. In conclusion, susceptibility to both bleomycin-induced and radiation-induced pulmonary fibrosis are heritable traits, and are influenced by a genetic factor which maps to a genomic region containing the MHC. ^

Mapping epileptic activity: sources or networks for the clinicians?

Epileptic seizures of focal origin are classically considered to arise from a focal epileptogenic zone and then spread to other brain regions. This is a key concept for semiological electro-clinical correlations, localization of relevant structural lesions, and selection of patients for epilepsy surgery. Recent development in neuro-imaging and electro-physiology and combinations, thereof, have been validated as contributory tools for focus localization. In parallel, these techniques have revealed that widespread networks of brain regions, rather than a single epileptogenic region, are implicated in focal epileptic activity. Sophisticated multimodal imaging and analysis strategies of brain connectivity patterns have been developed to characterize the spatio-temporal relationships within these networks by combining the strength of both techniques to optimize spatial and temporal resolution with whole-brain coverage and directional connectivity. In this paper, we review the potential clinical contribution of these functional mapping techniques as well as invasive electrophysiology in human beings and animal models for characterizing network connectivity.

Replication and fine-mapping of a QTL for recurrent airway obstruction in European Warmblood horses.

Recurrent airway obstruction (RAO), or 'heaves', is a common performance-limiting allergic respiratory disease of mature horses. It is related to sensitization and exposure to mouldy hay and has a familial basis with a complex mode of inheritance. In a previous study, we detected a QTL for RAO on ECA 13 in a half-sib family of European Warmblood horses. In this study, we genotyped additional markers in the family and narrowed the QTL down to about 1.5 Mb (23.7-25.2 Mb). We detected the strongest association with SNP BIEC2-224511 (24,309,405 bp). We also obtained SNP genotypes in an independent cohort of 646 unrelated Warmblood horses. There was no genome-wide significant association with RAO in these unrelated horses. However, we performed a genotypic association study of the SNPs on ECA 13 in these unrelated horses, and the SNP BIEC2-224511 also showed the strongest association with RAO in the unrelated horses (p(raw) = 0.00037). The T allele at this SNP was associated with RAO both in the family and the unrelated horses. Thus, the association study in the unrelated animals provides independent support for the previously detected QTL. The association study allows further narrowing of the QTL interval to about 0.5 Mb (24.0-24.5 Mb). We sequenced the coding regions of the genes in the critical region but did not find any associated coding variants. Therefore, the causative variant underlying this QTL is likely to be a regulatory mutation.

Molecular cloning, expression analysis and assignment of the porcine tumor necrosis factor superfamily member 10 gene (TNFSF10) to SSC13q34-->q36 by fluorescence in situ hybridization and radiation hybrid mapping

We have cloned the complete coding region of the porcine TNFSF10 gene. The porcine TNFSF10 cDNA has an ORF of 870 nucleotides and shares 85% identity with human TNFSF10, and 75% and 72% identity with rat and mouse Tnfsf10 coding sequences, respectively. The deduced porcine TNFSF10 protein consists of 289 amino acids with the calculated molecular mass of 33.5 kDa and a predicted pI of 8.15. The amino acid sequence similarities correspond to 86, 72 and 70% when compared with human, rat and mouse sequences, respectively. Northern blot analysis detected TNFSF10-specific transcripts (approximately 1.7 kb) in various organs of a 10-week-old pig, suggesting ubiquitous expression. Real-time RT-PCR studies of various organs from fetal (days 73 and 98) and postnatal stages (two weeks, eight months) demonstrated developmental and tissue-specific regulation of TNFSF10 mRNA abundance. The chromosomal location of the porcine TNFSF10 gene was determined by FISH of a specific BAC clone to metaphase chromosomes. This TNFSF10 BAC clone has been assigned to SSC13q34-->q36. Additionally, the localization of the TNFSF10 gene was verified by RH mapping on the porcine IMpRH panel.

Spatial variability and potential impacts of climate change on flood and debris flow hazard zone mapping and implications for risk management

The main goals of this study were to identifythe alpine torrent catchments that are sensitive to climatic changes and to assess the robustness of the methods for the elaboration of flood and debris flow hazard zone maps to specific effects of climate changes. In this study, a procedure for the identification and localization of torrent catchments in which the climate scenarios will modify the hazard situation was developed. In two case studies, the impacts of a potential increase of precipitation intensities to the delimited hazard zones were studied. The identification and localization of the torrent and river catchments, where unfavourable changes in the hazard situation occur, could eliminate speculative and unnecessary measures against the impacts of climate changes like a general enlargement of hazard zones or a general over dimensioning of protection structures for the whole territory. The results showed a high spatial variability of the sensitivity of catchments to climate changes. In sensitive catchments, the sediment management in alpine torrents will meet future challenges due to a higher rate for sediment removal from retention basins. The case studies showed a remarkable increase of the areas affected by floods and debris flow when considering possible future precipitation intensities in hazard mapping. But, the calculated increase in extent of future hazard zones lay within the uncertainty of the methods used today for the delimitation of the hazard zones. Thus, the consideration of the uncertainties laying in the methods for the elaboration of hazard zone maps in the torrent and river catchments sensitive to climate changes would provide a useful instrument for the consideration of potential future climate conditions. The study demonstrated that weak points in protection structures in future will become more important in risk management activities.

Physical and functional mapping of a novel tumor suppressor locus for prostate cancer within chromosome 10p12.31-q11

Prostate cancer remains the second leading cause of male cancer deaths in the United States, yet the molecular mechanisms underlying this disease remain largely unknown. Cytogenetic and molecular analyses of prostate tumors suggest a consistent association with the loss of chromosome 10. Previously, we have defined a novel tumor suppressor locus PAC-1 within chromosome 10pter-q11. Introduction of the short arm of chromosome 10 into a prostatic adenocarcinoma cell line PC-3H resulted in dramatic tumor suppression and restoration of a programmed cell death pathway. Using a combined approach of comparative genomic hybridization and microsatellite analysis of PC-3H, I have identified a region of hemizygosity within 10p12-p15. This region has been shown to be involved in frequent loss of heterozygosity in gliomas and melanoma. To functionally dissect the region within chromosome 10p containing PAC-1, we developed a strategy of serial microcell fusion, a technique that allows the transfer of defined fragments of chromosome 10p into PC-3H. Serial microcell fusion was used to transfer defined 10p fragments into a mouse A9 fibrosarcoma cell line. Once characterized by FISH and microsatellite analyses, the 10p fragments were subsequently transferred into PC-3H to generate a panel of microcell hybrid clones containing overlapping deletions of chromosome 10p. In vivo and microsatellite analyses of these PC hybrids identified a small chromosome 10p fragment (an estimated 31 Mb in size inclusive of the centromere) that when transferred into the PC-3H background, resulted in significant tumor suppression and limited a region of functional tumor suppressor activity to chromosome 10p12.31-q11. This region coincides with a region of LOH demonstrated in prostate cancer. These studies demonstrate the utility of this approach as a powerful tool to limit regions of functional tumor suppressor activity. Furthermore, these data used in conjunction with data generated by the Human Genome Project lent a focused approach to identify candidate tumor suppressor genes involved in prostate cancer. ^

The genetic basis of thoracic aortic aneurysms and dissections: Genetic heterogeneity and mapping of TAAD1 and TAAD2 loci

Thoracic aortic aneurysms leading to aortic dissections (TAAD) are a major cause of morbidity and mortality in the United States. TAAD is a complication of some known genetic disorders, such as Marfan syndrome and Turner syndrome, but the majority of familial cases are not due to a known genetic syndrome. Previous studies by our group have established that nonsyndromic, familial TAAD is inherited in an autosomal dominant manner with decreased penetrance and variable expression. Using one large family with multiple members with TAAD for the genome wide scan, a major locus for familial TAAD was mapped to 5q13–14 (TAAD1). Nine out of 15 families studied were linked to this locus, establishing that TAAD1 was a major locus, and that there was genetic heterogeneity for the condition. Mapping of TAAD2 locus was accomplished using a single large family with multiple members with TAAD not linked to known loci of aneurysm formation. This established a second novel locus for familial TAAD on 3p24–25 (LOD score of 4.3), termed the TAAD2 locus. Two putative loci with suggestive LOD scores were mapped on 4q and 12q through a genome scan carried out using three families. TAAD phenotype in 12 families did not segregate with known loci, indicating further genetic heterogeneity. An STS-tagged BAC based contig was constructed for 7.8Mb and 25Mb critical interval of TAAD1 and TAAD2 respectively and characterized to identify the defective gene. The hypothesis that the defective genes responsible for the TAAD1 and TAAD2 encoded extracellular matrix (ECM) proteins, the major components of the elastic fiber system in the aortic media was tested. Four genes encoding ECM proteins, versican, thrombospondin-3, CRTL1, on TAAD1 and FBLN2 at TAAD2 were sequenced, but no disease-causing mutations were identified. Studies to identify the defective gene are initiated through the positional candidate gene approach using combination of bioinformatics and expression studies. The identification of the TAAD susceptibility genes will allow for presymptomatic diagnosis of individuals at risk for this life threatening disease. The identification of the molecular defects that contribute to TAAD will also further our understanding of the proteins that provide structural integrity to the aortic wall. ^