Prevalence of Xanthomonas euvesicatoria on Pepper in Brazil

Bacterial spot, caused by Xanthomonas spp., is one of the major diseases of pepper in Brazil, causing considerable losses to crop productivity. The efficient management of the disease is hampered by the high variability of the causal agents. In Brazil, there is no knowledge of which species of Xanthomonas occurs on pepper. In this study, 59 strains of Xanthomonas spp. isolated from different pepper‐producing regions of Brazil were characterized by biochemical and molecular techniques. Results showed the prevalence of X. euvesicatoria as the causal agent of bacterial spot on pepper in Brazil.     

Multilocus Sequence Analysis of Xanthomonads Causing Bacterial Spot of Tomato and Pepper Plants Reveals Strains Generated by Recombination among Species and Recent Global Spread of Xanthomonas gardneri

Four Xanthomonas species are known to cause bacterial spot of tomato and pepper, but the global distribution and genetic diversity of these species are not well understood. A collection of bacterial spot-causing strains from the Americas, Africa, Southeast Asia, and New Zealand were characterized for genetic diversity and phylogenetic relationships using multilocus sequence analysis of six housekeeping genes. By examining strains from different continents, we found unexpected phylogeographic patterns, including the global distribution of a single multilocus haplotype of X. gardneri, possible regional differentiation in X. vesicatoria, and high species diversity on tomato in Africa. In addition, we found evidence of multiple recombination events between X. euvesicatoria and X. perforans. Our results indicate that there have been shifts in the species composition of bacterial spot pathogen populations due to the global spread of dominant genotypes and that recombination between species has generated genetic diversity in these populations.     

Analysis of pathogenicity mutants of a bacteriocin producing Xanthomonas perforans

Since the initial discovery of Xanthomonas perforans on tomato in 1991, it has completely displaced Xanthomonas euvesicatoria as the bacterial spot of tomato pathogen in Florida. Previous research has shown that X. perforans produces at least three different bacteriocin-like compounds (BcnA, BcnB, BcnC) antagonistic toward X. euvesicatoria strains. In this study pathogenicity-attenuated, bacteriocin-producing mutants of X. perforans were created to determine their potential as biological control agents for control of X. euvesicatoria. Several candidate genes were chosen based on previous studies in which mutant phenotypes exhibited reduced virulence in either X. perforans (OpgH_Xcv) or the closely related X. euvesicatoria strain 85-10 (hpaB, hpaC, xopA, xopD, avrBs2 and gumD). Each candidate gene in X. perforans was amplified and PCR-assisted deletion mutagenesis was performed in the wild-type (wt) X. perforans strain to create potential attenuation mutants. Each mutant was tested for growth rate, disease severity and antagonism toward X. euvesicatoria strains. Three mutants, XopA, opgH, and gumD were significantly less pathogenic than the wild-type strain with the opgH mutant reaching significantly lower internal populations than all other mutants except hpaC. The opgH-strain was the most affected in its ability to grow internally in plant tissue while inhibiting X. euvesicatoria populations equal to or more than the other mutant strains. This mutant strain could potentially be used as part of an effective biological control strategy.     

<Emphasis Type="Italic">Xanthomonas gardneri</Emphasis> exoenzymatic activity towards plant tissue

Bacterial spot caused by Xanthomonas spp. is an important tomato and pepper disease worldwide. Recent outbreaks of bacterial spot disease in Central Brazil and Canada have been attributed to Xanthomonas gardneri, which is also recognized as group D of Xanthomonas campestris pv. vesicatoria. Carotenoid-like pigments called xanthomonadins, which are diagnostic for yellow Xanthomonas spp., were extracted from X. gardneri. It was shown that the model plant Arabidopsis thaliana, member of the Brassicaceae family, can develop disease symptoms in response to different isolates of X. gardneri. Secretion of enzymes has been shown to play an important role in pathogenicity for different pathogens, and to begin to understand the interaction of X. gardneri and A. thaliana, a biochemical analysis of secreted proteins in the presence of A. thaliana leaves was performed. Different enzymatic activities such as for cellulase, α-arabinofuranosidase, pectinase, invertase and xylanase were assayed. In the presence of leaves, cellulase activity was highest after 60 and 72 h of growth and α-arabinofuranosidase activity was detected between 12 and 72 h of growth. Pectinase, invertase and xylanase activities were not detected. Cellulase and α-arabinofuranosidase activities may be important for X. gardneri acquisition of plant nutrients through degradation of cellulose fibers and hemicellulose of the cell wall, respectively, to the invasion of the host tissue and/or may generate signal molecules that are recognized by the plant. This is the first study to address how X. gardneri responds to host plant tissue.     

Xanthomonas perforans Colonization Influences Salmonella enterica in the Tomato Phyllosphere

Salmonella enterica rarely grows on healthy, undamaged plants, but its persistence is influenced by bacterial plant pathogens. The interactions between S. enterica, Xanthomonas perforans (a tomato bacterial spot pathogen), and tomato were characterized. We observed that virulent X. perforans, which establishes disease by suppressing pathogen-associated molecular pattern (PAMP)-triggered immunity that leads to effector-triggered susceptibility, created a conducive environment for persistence of S. enterica in the tomato phyllosphere, while activation of effector-triggered immunity by avirulent X. perforans resulted in a dramatic reduction in S. enterica populations. S. enterica populations persisted at ∼10 times higher levels in leaves coinoculated with virulent X. perforans than in those where S. enterica was applied alone. In contrast, S. enterica populations were ∼5 times smaller in leaves coinoculated with avirulent X. perforans than in leaves inoculated with S. enterica alone. Coinoculation with virulent X. perforans increased S. enterica aggregate formation; however, S. enterica was not found in mixed aggregates with X. perforans. Increased aggregate formation by S. enterica may serve as the mechanism of persistence on leaves cocolonized by virulent X. perforans. S. enterica association with stomata was altered by X. perforans; however, it did not result in appreciable populations of S. enterica in the apoplast even in the presence of large virulent X. perforans populations. Gene-for-gene resistance against X. perforans successively restricted S. enterica populations. Given the effect of this interaction, breeding for disease-resistant cultivars may be an effective strategy to limit both plant disease and S. enterica populations and, consequently, human illness.     

Induction of resistance in tomato against Xanthomonas perforans by lipopolysaccharides of the pathogen

The goal of this study was to investigate the role of lipopolysaccharides (LPS) in induction of resistance in tomato against the causal agent of bacterial spot, Xanthomonas perforans. The results showed that pre-treatment with LPS leads to enhancing resistance of tomato against X. perforans. In addition, expression profiling of β-1,3-glucanase (BGL), Phenylalanine ammonia-lyase (PAL) and catalase (CAT) was examined during the induced resistance by LPS. The effect of LPS on induction of BGL, PAL and CAT was demonstrated in the present study. The data suggest that the effect of LPS on resistance of tomato against X. perforans could be through activation of some defence genes such as of BGL, PAL and CAT which afford defence responses against the pathogen. Our findings might help to better understanding the molecular bases of the induced resistance by LPS.     

Surface-motility induction,attraction and hitchhiking between bacterial species promote dispersal on solid surfaces

The ability to move on solid surfaces provides ecological advantages for bacteria, yet many bacterial species lack this trait. We found that Xanthomonas spp. overcome this limitation by making use of proficient motile bacteria in their vicinity. Using X. perforans and Paenibacillus vortex as models, we show that X. perforans induces surface motility, attracts proficient motile bacteria and ‘rides'' them for dispersal. In addition, X. perforans was able to restore surface motility of strains that lost this mode of motility under multiple growth cycles in the lab. The described interaction occurred both on agar plates and tomato leaves and was observed between several xanthomonads and motile bacterial species. Thus, suggesting that this motility induction and hitchhiking strategy might be widespread and ecologically important. This study provides an example as to how bacteria can rely on the abilities of their neighboring species for their own benefit, signifying the importance of a communal organization for fitness.     

Whole genome sequences reveal the Xanthomonas perforans population is shaped by the tomato production system

Modern agricultural practices increase the potential for plant pathogen spread, while the advent of affordable whole genome sequencing enables in-depth studies of pathogen movement. Population genomic studies may decipher pathogen movement and population structure as a result of complex agricultural production systems. We used whole genome sequences of 281 Xanthomonas perforans strains collected within one tomato production season across Florida and southern Georgia fields to test for population genetic structure associated with tomato production system variables. We identified six clusters of X. perforans from core gene SNPs that corresponded with phylogenetic lineages. Using whole genome SNPs, we found genetic structure among farms, transplant facilities, cultivars, seed producers, grower operations, regions, and counties. Overall, grower operations that produced their own transplants were associated with genetically distinct and less diverse populations of strains compared to grower operations that received transplants from multiple sources. The degree of genetic differentiation among components of Florida’s tomato production system varied between clusters, suggesting differential dispersal of the strains, such as through seed or contaminated transplants versus local movement within farms. Overall, we showed that the genetic variation of a bacterial plant pathogen is shaped by the structure of the plant production system.Subject terms: Applied microbiology, Population genetics, Microbial ecology, Microbial ecology     

Plant Pathogen-Induced Water-Soaking Promotes Salmonella enterica Growth on Tomato Leaves

Plant pathogen infection is a critical factor for the persistence of Salmonella enterica on plants. We investigated the mechanisms responsible for the persistence of S. enterica on diseased tomato plants by using four diverse bacterial spot Xanthomonas species that differ in disease severities. Xanthomonas euvesicatoria and X. gardneri infection fostered S. enterica growth, while X. perforans infection did not induce growth but supported the persistence of S. enterica. X. vesicatoria-infected leaves harbored S. enterica populations similar to those on healthy leaves. Growth of S. enterica was associated with extensive water-soaking and necrosis in X. euvesicatoria- and X. gardneri-infected plants. The contribution of water-soaking to the growth of S. enterica was corroborated by an increased growth of populations on water-saturated leaves in the absence of a plant pathogen. S. enterica aggregates were observed with bacterial spot lesions caused by either X. euvesicatoria or X. vesicatoria; however, more S. enterica aggregates formed on X. euvesicatoria-infected leaves as a result of larger lesion sizes per leaf area and extensive water-soaking. Sparsely distributed lesions caused by X. vesicatoria infection do not support the overall growth of S. enterica or aggregates in areas without lesions or water-soaking; S. enterica was observed as single cells and not aggregates. Thus, pathogen-induced water-soaking and necrosis allow S. enterica to replicate and proliferate on tomato leaves. The finding that the pathogen-induced virulence phenotype affects the fate of S. enterica populations in diseased plants suggests that targeting of plant pathogen disease is important in controlling S. enterica populations on plants.     

Integrated biological control of bacterial speck and spot of tomato under field conditions using foliar biological control agents and plant growth-promoting rhizobacteria

Integration of foliar bacterial biological control agents and plant growth promoting rhizobacteria (PGPR) was investigated to determine whether biological control of bacterial speck of tomato, caused by Pseudomonas syringae pv. tomato, and bacterial spot of tomato, caused by Xanthomonas campestris pv. vesicatoria and Xanthomonas vesicatoria, could be improved. Three foliar biological control agents and two selected PGPR strains were employed in pairwise combinations. The foliar biological control agents had previously demonstrated moderate control of bacterial speck or bacterial spot when applied as foliar sprays. The PGPR strains were selected in this study based on their capacity to induce resistance against bacterial speck when applied as seed and soil treatments in the greenhouse. Field trials were conducted in Alabama, Florida, and California for evaluation of the efficacy in control of bacterial speck and in Alabama and Florida for control of bacterial spot. The foliar biological control agent P. syringae strain Cit7 was the most effective of the three foliar biological control agents, providing significant suppression of bacterial speck in all field trials and bacterial spot in two out of three field trials. When applied as a seed treatment and soil drench, PGPR strain Pseudomonas fluorescens 89B-61 significantly reduced foliar severity of bacterial speck in the field trial in California and in three of six disease ratings in the field trials in Alabama. PGPR strains 89B-61 and Bacillus pumilus SE34 both provided significant suppression of bacterial spot in the two field trials conducted in Alabama. Combined use of foliar biological control agent Cit7 and PGPR strain 89B-61 provided significant control of bacterial speck and spot of tomato in each trial. In one field trial, control was enhanced significantly with combined biological control agents compared to single agent inoculations. These results suggest that some PGPR strains may induce plant resistance under field conditions, providing effective suppression of bacterial speck and spot of tomato, and that there may be some benefit to the integration of rhizosphere-applied PGPR and foliar-applied biological control agents.     

Occurrence and Characterization of the Bacterial Spot Pathogen Xanthomonas euvesicatoria on Pepper in Iran

We report in this study for the first time the occurrence of bacterial spot of pepper in Iran and both phenotypic and genetic characterization of its causal agent, Xanthomonas euvesicatoria. Pepper plants grown in 15 of 30 surveyed private gardens and commercial fields were infected by the pathogen in Marand County, East Azerbaijan Province, north‐western Iran. The obtained strains of X. euvesicatoria had different amylolytic and pectolytic activities compared with those reported for this species elsewhere. Pathogenicity tests showed that strains isolated from diseased pepper are able to infect tomato, in addition to pepper. Host range of the pathogen was assessed on eight annual plant species including crops and weeds by measuring the population dynamics. The host range assessment showed that in addition to pepper and tomato, known hosts of X. euvesicatoria, the Iranian strains were able to colonize a number of new hosts such as nightshade and common bean. In contrast, none of them were able to build up their population on cowpea, eggplant, bindweed and zucchini. All X. euvesicatoria strains obtained in this study were sensitive to copper sulphate and streptomycin at concentrations higher than 20 and 50 mg/l, respectively. Phylogenetic analyses of the strains using the sequences of gyrB and hrpB genes confirmed their species as X. euvesicatoria. Given a direct commercial trade of fresh solanaceous vegetables between Iran and Turkey, it is hypothesized that the pathogen entered north‐western Iran from eastern parts of Turkey through infected plant materials. Finally, the role of prevention – based on the use of healthy planting materials and resistant and/or tolerant plant varieties – to contain the potential disease epidemics is discussed.     

The noncanonical type III secretion system of Xanthomonas translucens pv. graminis is essential for forage grass infection

Xanthomonas translucens pv. graminis (Xtg) is a gammaproteobacterium that causes bacterial wilt on a wide range of forage grasses. To gain insight into the host–pathogen interaction and to identify the virulence factors of Xtg, we compared a draft genome sequence of one isolate (Xtg29) with other Xanthomonas spp. with sequenced genomes. The type III secretion system (T3SS) encoding a protein transport system for type III effector (T3E) proteins represents one of the most important virulence factors of Xanthomonas spp. In contrast with other Xanthomonas spp. assigned to clade 1 on the basis of phylogenetic analyses, we identified an hrp (hypersensitive response and pathogenicity) gene cluster encoding T3SS components and a representative set of 35 genes encoding putative T3Es in the genome of Xtg29. The T3SS was shown to be divergent from the hrp gene clusters of other sequenced Xanthomonas spp. Xtg mutants deficient in T3SS regulating and structural genes were constructed to clarify the role of the T3SS in forage grass colonization. Italian ryegrass infection with these mutants led to significantly reduced symptoms (P < 0.05) relative to plants infected with the wild‐type strain. This showed that the T3SS is required for symptom evocation. In planta multiplication of the T3SS mutants was not impaired significantly relative to the wild‐type, indicating that the T3SS is not required for survival until 14 days post‐infection. This study represents the first major step to understanding the bacterial colonization strategies deployed by Xtg and may assist in the identification of resistance (R) genes in forage grasses.     

一株拮抗黄单胞菌的贝莱斯芽孢杆菌的分离和鉴定

【目的】为了筛选防治水稻条斑病(bacterial leaf streak,BLS)的生防细菌。【方法】以水稻条斑病菌(Xanthomonas oryzae pv. oryzicola,Xoc)的模式菌株RS105为靶标菌,采用平板稀释和抑菌圈法,从空心菜根际土壤中筛选到一株对RS105具有拮抗作用的细菌菌株504。通过形态学、生理生化特征以及16SrDNA和gyrA序列分析对菌株504进行了鉴定。利用牛津杯法测定504对植物病原黄单胞菌的拮抗活性及其无菌发酵液拮抗活性的稳定性。通过PCR扩增预测504编码合成脂肽类和聚酮类化合物的合成相关基因。采用苗期水稻注射接菌法来评价水稻组织中504对Xoc的拮抗活性。【结果】菌株鉴定结果表明504为贝莱斯芽孢杆菌,命名为Bacillusvelezensis504。抑菌实验显示,B.velezensis504对黄单胞菌属的细菌具有较好的抑菌活性,对水稻白叶枯病菌(X. oryzae pv. oryzae,Xoo)的拮抗效果最显著。基因预测结果显示,B. velezensis 504含有fenA、dhbA、sfrA、bmyA、beaS、dfnA及bacA等编码脂肽类和聚酮糖类抑菌化合物的基因簇。其无菌发酵液的活性物质耐高温和蛋白酶降解,但不耐强酸、强碱,在pH值为5.5–8.9时仍具有稳定的拮抗活性。在高感水稻品种原丰早上,B. velezensis 504对Xoc在水稻叶片中引起的水渍症状具有显著的抑制作用。【结论】B. velezensis 504能够特异性拮抗黄单胞菌,在黄单胞菌引起的细菌性病害的生物防治中将具有较大的应用潜力。     

Arsenic pollution from human activities drives changes in soil microbial community characteristics

Soil arsenic (As) pollution not only decreases plant productivity but also soil quality, in turn hampering sustainable agricultural development. Despite the negative effects of As contamination on rice yield and quality being reported widely, the responses of microbial communities and co-occurrence networks in paddy soil to As pollution have not been explored. Here, based on high-throughput sequencing technologies, we investigated bacterial abundance and diversity in paddy soils with different levels of As contamination, and constructed associated microbial co-occurrence networks. As pollution reduced soil bacterial diversity significantly (p < 0.001). In addition, bioavailable As concentrations were negatively correlated with Actinobacteria and Acidobacteria relative abundance (p < 0.05). Conversely, As pollution had a positive relationship with Chloroflexi, Betaproteobacteria, and Bacteroidetes relative abundance (p < 0.05). Firmicutes relative abundance decreased with an increase in total As concentration. The ecological clusters and key groups in bacterial co-occurrence networks exhibited distinct trends with an increase in As pollution. Notably, Acidobacteria play an important role in maintaining microbial networks in As contaminated soils. Overall, we provide empirical evidence that As contamination influences soil microbial community structure, posing a threat to soil ecosystem health and sustainable agriculture.     

Excess copper in soil as a factor affecting bacterial spots caused by <Emphasis Type="Italic">Xanthomonas vesicatoria</Emphasis> in tomato plants; bio-interaction between two stress factors and their influence on plants

The investigations presented in this paper focus on studying the influence of excess soil copper levels in young tomato plants and their relationship to bacterial spot severity caused by Xanthomonas vesicatoria race T3. The plants were grown under greenhouse conditions in pots containing soil artificially contaminated with copper in concentrations of 250 and 400 mg kg⁻¹. Both stress factors were applied individually and in combination. Soil copper levels did influence bacterial spot severity. The copper doses applied restricted bacterial spot growth. Strongest responses were observed when the pathogen was infiltrated into seeds. Deformations of plant, as well as increased plastid synthesis inhibition occurred when the plants were exposed to copper and X. vesicatoria. The applicability of the investigation is related to the fight against bacterial spot caused by X. vesicatoria in tomatoes grown on copper-polluted soils. In this case, the remedial action should be carried out very carefully in order to avoid additional damage to plants.     

Isolation and characterization of antagonistic bacteria against bacterial leaf spot of Euphorbia pulcherrima

Aims: To investigate the inhibition potential of leaf‐associated bacteria against the pathogen of bacterial leaf spot of Euphorbia pulcherrima. Methods and Results: Seven out of 200 bacterial strains were effective antagonists by in vitro screening and the two strains PAB241 and PAB242 significantly reduced the disease incidence and severity as foliar treatments of E. pulcherrima. The two effective strains, PAB241 and PAB242, were both identified as Bacillus amyloliquefaciens by a polyphasic approach including phenotypic feature, carbon source utilization profile, fatty acid methyl esters and analysis of 16S rRNA gene sequence. In addition, the suspensions of B. amyloliquefaciens PAB241 and PAB242 showed antibacterial activities against the pathogen of bacterial leaf spot of E. pulcherrima under different treatments. Conclusions: The leaf‐associated bacteria, B. amyloliquefaciens PAB241 and PAB242, markedly inhibited the growth of X. axonopodis pv. poinsettiicola under different treatments and protected E. pulcherrima from pathogen infection in growth chamber conditions. Significance and Impact of the Study: This is the first study that showed B. amyloliquefaciens from plant leaves was a potential bactericide against bacterial leaf spot of E. pulcherrima.     

Isolation and characterization of Bacillus sp. strain BC01 from soil displaying potent antagonistic activity against plant and fish pathogenic fungi and bacteria

Fungal and bacterial pathogens infect a diverse range of hosts including various plant and animal species. Fungal and bacterial diseases, especially of plants and aquatic animals, such as fish, lead to significant damage to crops and aquaculture, respectively, worldwide. The present study was conducted to isolate and characterize potent Bacillus strains with significant antagonistic activity against the major plant and fish pathogenic fungi and bacteria. We randomly collected 22 isolates of Bacillus from the soil, rhizosphere, and sediment from different parts of Bangladesh. Initial characterization, based on in vitro antagonistic activity on the culture plate, resulted in the selection of four gram-positive Bacillus sp. isolates. Among these, the isolate BC01, obtained from soil demonstrated the highest broad-spectrum anti-bacterial and anti-fungal activities. We confirmed the genus of BC01 to be Bacillus by morphological and biochemical tests as well as using molecular data analysis tools, including the study of 16s rDNA, phylogenetic relationship, and evolutionary divergence scores. The isolate significantly inhibited the mycelial growth of the plant pathogen, Penicillium digitatum and fish pathogen, Aphanomyces invadans in vitro. The anti-bacterial effect of the isolate was also evaluated against Pseudomonas spp. and Xanthomonas spp., the two deadliest plant pathogens, and Aeromonas veronii, Pseudomonas fluorescens, and Streptococcus iniae, three major fish pathogens that are primarily responsible for global aquaculture loss. The results of the present study could pave the way for developing potent drugs to combat microbial infection of plants and fish.     

Strong associations between plant genotypes and bacterial communities in a natural salt marsh

Although microbial communities have been shown to vary among plant genotypes in a number of experiments in terrestrial ecosystems, relatively little is known about this relationship under natural conditions and outside of select model systems. We reasoned that a salt marsh ecosystem, which is characterized by twice‐daily flooding by tides, would serve as a particularly conservative test of the strength of plant–microbial associations, given the high degree of abiotic regulation of microbial community assembly resulting from alternating periods of inundation and exposure. Within a salt marsh in the northeastern United States, we characterized genotypes of the foundational plant Spartina alterniflora using microsatellite markers, and bacterial metagenomes within marsh soil based on pyrosequencing. We found significant differences in bacterial community composition and diversity between bulk and rhizosphere soil, and that the structure of rhizosphere communities varied depending on the growth form of, and genetic variation within, the foundational plant S. alterniflora. Our results indicate that there are strong plant–microbial associations within a natural salt marsh, thereby contributing to a growing body of evidence for a relationship between plant genotypes and microbial communities from terrestrial ecosystems and suggest that principles of community genetics apply to this wetland type.     

Inferring the contribution of sexual reproduction,migration and off‐season survival to the temporal maintenance of microbial populations: a case study on the wheat fungal pathogen Puccinia striiformis f.sp. tritici

Understanding the mode of temporal maintenance of plant pathogens is an important domain of microbial ecology research. Due to the inconspicuous nature of microbes, their temporal maintenance cannot be studied directly through tracking individuals and their progeny. Here, we suggest a series of population genetic analyses on molecular marker variation in temporally spaced samples to infer about the relative contribution of sexual reproduction, off‐season survival and migration to the temporal maintenance of pathogen populations. We used the proposed approach to investigate the temporal maintenance of wheat yellow rust pathogen, Puccinia striiformis f.sp. tritici (PST), in the Himalayan region of Pakistan. Multilocus microsatellite genotyping of PST isolates revealed high genotypic diversity and recombinant population structure across all locations, confirming the existence of sexual reproduction in this region. The genotypes were assigned to four genetic groups, revealing a clear differentiation between zones with and without Berberis spp., the alternate host of PST, with an additional subdivision within the Berberis zone. The lack of any differentiation between samples across two sampling years, and the very infrequent resampling of multilocus genotypes over years at a given location was consistent with limited over‐year clonal survival, and a limited genetic drift. The off‐season oversummering population in the Berberis zone, likely to be maintained locally, served as a source of migrants contributing to the temporal maintenance in the non‐Berberis zone. Our study hence demonstrated the contribution of both sexual recombination and off‐season oversummering survival to the temporal maintenance of the pathogen. These new insights into the population biology of PST highlight the general usefulness of the analytical approach proposed.