956 resultados para Pathogen-host interaction


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Small propagules like pollen or fungal spores may be dispersed by the wind over distances of hundreds or thousands of kilometres,even though the median dispersal may be only a few metres. Such long-distance dispersal is a stochastic event which may be exceptionally important in shaping a population. It has been found repeatedly in field studies that subpopulations of wind-dispersed fungal pathogens virulent on cultivars with newly introduced, effective resistance genes are dominated by one or very few genotypes. The role of propagule dispersal distributions with distinct behaviour at long distances in generating this characteristic population structure was studied by computer simulation of dispersal of clonal organisms in a heterogeneous environment with fields of unselective and selective hosts. Power-law distributions generated founder events in which new, virulent genotypes rapidly colonized fields of resistant crop varieties and subsequently dominated the pathogen population on both selective and unselective varieties, in agreement with data on rust and powdery mildew fungi. An exponential dispersal function, with extremely rare dispersal over long distances, resulted in slower colonization of resistant varieties by virulent pathogens or even no colonization if the distance between susceptible source and resistant target fields was sufficiently large. The founder events resulting from long-distance dispersal were highly stochastic and exact quantitative prediction of genotype frequencies will therefore always be difficult.

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The influence of geographical origin, host animal and presence of the stx gene on the virulence of Escherichia coli O26 strains from ruminants was determined in this study. A clear association was found between the virulence profile and geographical origin of Shiga-toxigenic E. coli (STEC) O26 strains, with UK STEC O26 strains harbouring virtually identical profiles, whilst central European strains showed considerable heterogeneity in plasmid-encoded genes. The former group were also more likely to be non-motile and katP gene positive. Comparison of UK STEC and atypical enteropathogenic E. coli (aEPEC O26 strains showed that the presence of the stx1 gene was positively correlated with the presence of espP and katP genes and negatively associated with the presence of the yagP-yagT region and with rhamnose fermentation. In contrast to the uniform profiles of STEC O26 strains from ruminants in the UK, aEPEC O26 strains of bovine and ovine origin showed diverse profiles both within and between groups, and could not be separated into discrete groups. These results indicate that the characteristics of UK O26 strains from ruminants are distinct from those of O26 strains from ruminants and humans in other regions in central Europe. Such differences are expected to influence the zoonotic potential of this pathogen and the subsequent incidence of O26-associated human disease.

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Each human body plays host to a microbial population which is both numerically vast (at around 1014 microbial cells) and phenomenally diverse (over 1,000 species). The majority of the microbial species in the gut have not been cultured but the application of culture-independent approaches for high throughput diversity and functionality analysis has allowed characterisation of the diverse microbial phylotypes present in health and disease. Studies in monozygotic twins, showing that these retain highly similar microbiota decades after birth and initial colonisation, are strongly indicative that diversity of the microbiome is host-specific and affected by the genotype. Microbial diversity in the human body is reflected in both richness and evenness. Diversity increases steeply from birth reaching its highest point in early adulthood, before declining in older age. However, in healthy subjects there appears to be a core of microbial phylotypes which remains relatively stable over time. Studies of individuals from diverse geopraphies suggest that clusters of intestinal bacterial groups tend to occur together, constituting ‘enterotypes’. So variation in intestinal microbiota is stratified rather than continuous and there may be a limited number of host/microbial states which respond differently to environmental influences. Exploration of enterotypes and functional groups may provide biomarkers for disease and insights into the potential for new treatments based on manipulation of the microbiome. In health, the microbiota interact with host defences and exist in harmonious homeostasis which can then be disturbed by invading organisms or when ‘carpet bombing’ by antibiotics occurs. In a portion of individuals with infections, the disease will resolve itself without the need for antibiotics and microbial homeostasis with the host’s defences is restored. The administration of probiotics (live microorganisms which when administered in adequate amounts confer a health benefit on the host) represents an artificial way to enhance or stimulate these natural processes. The study of innate mechanisms of antimicrobial defence on the skin, including the production of numerous antimicrobial peptides (AMPs), has shown an important role for skin commensal organisms. These organisms may produce AMPs, and also amplify the innate immune responses to pathogens by activating signalling pathways and processing host produced AMPs. Research continues into how to enhance and manipulate the role of commensal organisms on the skin. The challenges of skin infection (including diseases caused by multiply resistant organisms) and infestations remain considerable. The potential to re-colonise the skin to replace or reduce pathogens, and exploring the relationship between microbiota elsewhere and skin diseases are among a growing list of research targets. Lactobacillus species are among the best known ‘beneficial’ bacterial members of the human microbiota. Of the approximately 120 species known, about 15 are known to occur in the human vagina. These organisms have multiple properties, including the production of lactic acid, hydrogen peroxide and bacteriocins, which render the vagina inhospitable to potential pathogens. Depletion of the of the normal Lactobacillus population and overgrowth of vaginal anaerobes, accompanied by the loss of normal vaginal acidity can lead to bacterial vaginosis – the commonest cause of abnormal vaginal discharge in women. Some vaginal anaerobes are associated with the formation of vaginal biofilms which serve to act as a reservoir of organisms which persists after standard antibiotic therapy of bacterial vaginosis and may help to account for the characteristically high relapse rate in the condition. Administration of Lactobacillus species both vaginally and orally have shown beneficial effects in the treatment of bacterial vaginosis and such treatments have an excellent overall safety record. Candida albicans is a frequent coloniser of human skin and mucosal membranes, and is a normal part of the microbiota in the mouth, gut and vagina. Nevertheless Candida albicans is the most common fungal pathogen worldwide and is a leading cause of serious and often fatal nosocomial infections. What turns this organism from a commensal to a pathogen is a combination of increasing virulence in the organism and predisposing host factors that compromise immunity. There has been considerable research into the use of probiotic Lactobacillus spp. in vaginal candidiasis. Studies in reconstituted human epithelium and monolayer cell cultures have shown that L. rhamnosus GG can protect mucosa from damage caused by Candida albicans, and enhance the immune responses of mucosal surfaces. Such findings offer the promise that the use of such probiotic bacteria could provide new options for antifungal therapy. Studies of changes of the human intestinal microbiota in health and disease are complicated by its size and diversity. The Alimentary Pharmabiotic Centre in Cork (Republic of Ireland) has the mission to ‘mine microbes for mankind’ and its work illustrates the potential benefits of understanding the gut microbiota. Work undertaken at the centre includes: mapping changes in the microbiota with age; studies of the interaction between the microbiota and the gut; potential interactions between the gut microbiota and the central nervous system; the potential for probiotics to act as anti-infectives including through the production of bacteriocins; and the characterisation of interactions between gut microbiota and bile acids which have important roles as signalling molecules and in immunity. The important disease entity where the role of the gut microbiota appears to be central is the Irritable Bowel Syndrome (IBS). IBS patients show evidence of immune activation, impaired gut barrier function and abnormal gut microbiota. Studies with probiotics have shown that these organisms can exert anti-inflammatory effects in inflammatory bowel disease and may strengthen the gut barrier in IBS of the diarrhoea-predominant type. Formal randomised trials of probiotics in IBS show mixed results with limited benefit for some but not all. Studies confirm that administered probiotics can survive and temporarily colonise the gut. They can also stimulate the numbers of other lactic acid bacilli in the gut, and reduce the numbers of pathogens. However consuming live organisms is not the only way to influence gut microbiota. Dietary prebiotics are selectively fermented ingredients that can change the composition and/or activity of the gastrointestinal microbiota in beneficial ways. Dietary components that reach the colon, and are available to influence the microbiota include poorly digestible carbohydrates, such as non-starch polysaccharides, resistant starch, non-digestible oligosaccharides (NDOs) and polyphenols. Mixtures of probiotic and prebiotic ingredients that can selectively stimulate growth or activity of health promoting bacteria have been termed ‘synbiotics’. All of these approaches can influence gut microbial ecology, mainly to increase bifidobacteria and lactobacilli, but metagenomic approaches may reveal wider effects. Characterising how these changes produce physiological benefits may enable broader use of these tactics in health and disease in the future. The current status of probiotic products commercially available worldwide is less than ideal. Prevalent problems include misidentification of ingredient organisms and poor viability of probiotic microorganisms leading to inadequate shelf life. On occasions these problems mean that some commercially available products cannot be considered to meet the definition of a probiotic product. Given the potential benefits of manipulating the human microbiota for beneficial effects, there is a clear need for improved regulation of probiotics. The potential importance of the human microbiota cannot be overstated. ‘We feed our microbes, they talk to us and we benefit. We just have to understand and then exploit this.’ (Willem de Vos).

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Background Staphylococcus aureus is a major cause of healthcare associated mortality, but like many important bacterial pathogens, it is a common constituent of the normal human body flora. Around a third of healthy adults are carriers. Recent evidence suggests that evolution of S. aureus during nasal carriage may be associated with progression to invasive disease. However, a more detailed understanding of within-host evolution under natural conditions is required to appreciate the evolutionary and mechanistic reasons why commensal bacteria such as S. aureus cause disease. Therefore we examined in detail the evolutionary dynamics of normal, asymptomatic carriage. Sequencing a total of 131 genomes across 13 singly colonized hosts using the Illumina platform, we investigated diversity, selection, population dynamics and transmission during the short-term evolution of S. aureus. Principal Findings We characterized the processes by which the raw material for evolution is generated: micro-mutation (point mutation and small insertions/deletions), macro-mutation (large insertions/deletions) and the loss or acquisition of mobile elements (plasmids and bacteriophages). Through an analysis of synonymous, non-synonymous and intergenic mutations we discovered a fitness landscape dominated by purifying selection, with rare examples of adaptive change in genes encoding surface-anchored proteins and an enterotoxin. We found evidence for dramatic, hundred-fold fluctuations in the size of the within-host population over time, which we related to the cycle of colonization and clearance. Using a newly-developed population genetics approach to detect recent transmission among hosts, we revealed evidence for recent transmission between some of our subjects, including a husband and wife both carrying populations of methicillin-resistant S. aureus (MRSA). Significance This investigation begins to paint a picture of the within-host evolution of an important bacterial pathogen during its prevailing natural state, asymptomatic carriage. These results also have wider significance as a benchmark for future systematic studies of evolution during invasive S. aureus disease.

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The incidence and severity of light leaf spot epidemics caused by the ascomycete fungus Pyrenopeziza brassicae on UK oilseed rape crops is increasing. The disease is currently controlled by a combination of host resistance, cultural practices and fungicide applications. We report decreases in sensitivities of modern UK P. brassicae isolates to the azole (imidazole and triazole) class of fungicides. By cloning and sequencing the P. brassicae CYP51 (PbCYP51) gene, encoding the azole target sterol 14α-demethylase, we identified two non-synonymous mutations encoding substitutions G460S and S508T associated with reduced azole sensitivity. We confirmed the impact of the encoded PbCYP51 changes on azole sensitivity and protein activity by heterologous expression in a Saccharomyces cerevisiae mutant YUG37::erg11 carrying a controllable promoter of native CYP51 expression. In addition, we identified insertions in the predicted regulatory regions of PbCYP51 in isolates with reduced azole sensitivity. The presence of these insertions was associated with enhanced transcription of PbCYP51 in response to sub-inhibitory concentrations of the azole fungicide tebuconazole. Genetic analysis of in vitro crosses of sensitive and resistant isolates confirmed the impact of PbCYP51 alterations in coding and regulatory sequences on a reduced sensitivity phenotype, as well as identifying a second major gene at another locus contributing to resistance in some isolates. The least sensitive field isolates carry combinations of upstream insertions and non-synonymous mutations, suggesting PbCYP51 evolution is on-going and the progressive decline in azole sensitivity of UK P. brassicae populations will continue. The implications for the future control of light leaf spot are discussed.

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Buildings affect people in various ways. They can help us to work more effectively; they also present a wide range of stimuli for our senses to react to. Intelligent buildings are designed to be aesthetic in sensory terms not just visually appealing but ones in which occupants experience delight, freshness, airiness, daylight, views out and social ambience. All these factors contribute to a general aesthetic which gives pleasure and affects one’s mood. If there is to be a common vision, it is essential for architects, engineers and clients to work closely together throughout the planning, design, construction and operational stages which represent the conception, birth and life of the building. There has to be an understanding of how patterns of work are best suited to a particular building form served by appropriate environmental systems. A host of technologies are emerging that help these processes, but in the end it is how we think about achieving responsive buildings that matters. Intelligent buildings should cope with social and technological changes and also be adaptable to short-term and long-term human needs. We live through our senses. They rely on stimulation from the tasks we are focused on; people around us but also the physical environment. We breathe air and its quality affects the olfactory system; temperature is felt by thermoreceptors in the skin; sound enters our ears; the visual scene is beheld by our eyes. All these stimuli are transmitted along the sensory nervous system to the brain for processing from which physiological and psychological reactions and judgments are formed depending on perception, expectancies and past experiences. It is clear that the environmental setting plays a role in this sensory process. This is the essence of sensory design. Space plays its part as well. The flow of communication is partly electronic but also largely by people meeting face to face. Our sense of space wants different things at different times. Sometimes privacy but other times social needs have to be satisfied besides the organizational requirement to have effective human communications throughout the building. In general if the senses are satisfied people feel better and work better.

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Over the past 50 years, many millions of European honey bee (Apis mellifera) colonies have died as the ectoparasitic mite, Varroa destructor, has spread around the world. Subsequent studies have indicated that the mite's association with a group of RNA viral pathogens (Deformed Wing Virus, DWV) correlates with colony death. Here, we propose a phenomenon known as superinfection exclusion that provides an explanation of how certain A. mellifera populations have survived, despite Varroa infestation and high DWV loads. Next-generation sequencing has shown that a non-lethal DWV variant 'type B' has become established in these colonies and that the lethal 'type A' DWV variant fails to persist in the bee population. We propose that this novel stable host-pathogen relationship prevents the accumulation of lethal variants, suggesting that this interaction could be exploited for the development of an effective treatment that minimises colony losses in the future.The ISME Journal advance online publication, 27 October 2015; doi:10.1038/ismej.2015.186.

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There are over 500 candidate secreted effector proteins (CSEPs) or Blumeria effector candidates (BECs) specific to the barley powdery mildew pathogen Blumeria graminis f.sp. hordei. The CSEP/BEC proteins are expressed and predicted to be secreted by biotrophic feeding structures called haustoria. Eight BECs are required for the formation of functional haustoria. These include the RNase-like effector BEC1054 (synonym CSEP0064). In order to identify host proteins targeted by BEC1054, recombinant BEC1054 was expressed in E. coli, solubilized, and used in pull-down assays from barley protein extracts. Many putative interactors were identified by LC-MS/MS after subtraction of unspecific binders in negative controls. Therefore, a directed yeast-2-hybrid assay, developed to measure the effectiveness of the interactions in yeast, was used to validate putative interactors. We conclude that BEC1054 may target several host proteins, including a glutathione-S-transferase, a malate dehydrogenase, and a pathogen-related-5 protein isoform, indicating a possible role for BEC1054 in compromising well-known key players of defense and response to pathogens. In addition, BEC1054 interacts with an elongation factor 1 gamma. This study already suggests that BEC1054 plays a central role in barley powdery mildew virulence by acting at several levels.

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Acute kidney injury (AKI) is an important clinical syndrome characterized by abnormalities in the hydroelectrolytic balance. Because of high rates of morbidity and mortality (from 15% to 60%) associated with AKI, the study of its pathophysiology is critical in searching for clinical targets and therapeutic strategies. Severe sepsis is the major cause of AKI. The host response to sepsis involves an inflammatory response, whereby the pathogen is initially sensed by innate immune receptors (pattern recognition receptors [PRRs]). When it persists, this immune response leads to secretion of proinflammatory products that induce organ dysfunction such as renal failure and consequently increased mortality. Moreover, the injured tissue releases molecules resulting from extracellular matrix degradation or dying cells that function as alarmines, which are recognized by PRR in the absence of pathogens in a second wave of injury. Toll-like receptors (TLRs) and NOD-like receptors (NLRs) are the best characterized PRRs. They are expressed in many cell types and throughout the nephron. Their activation leads to translocation of nuclear factors and synthesis of proinflammatory cytokines and chemokines. TLRs` signaling primes the cells for a robust inflammatory response dependent on NLRs; the interaction of TLRs and NLRs gives rise to the multiprotein complex known as the inflammasome, which in turn activates secretion of mature interleukin 1 beta and interleukin 18. Experimental data show that innate immune receptors, the inflammasome components, and proinflammatory cytokines play crucial roles not only in sepsis, but also in organ-induced dysfunction, especially in the kidneys. In this review, we discuss the significance of the innate immune receptors in the development of acute renal injury secondary to sepsis.

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Toll-like receptors (TLRs) present in innate immune cells recognize pathogen molecular patterns and influence immunity to control the host-parasite interaction. The objective of this study was to characterize the involvement of TLR4 in the innate and adaptive immunity to Paracoccidioides brasiliensis, the most important primary fungal pathogen of Latin America. We compared the responses of C3H/HeJ mice, which are naturally defective in TLR4 signaling, with those of C3H/HePas mice, which express functional receptors, after in vitro and in vivo infection with P. brasiliensis. Unexpectedly, we verified that TLR4-defective macrophages infected in vitro with P. brasiliensis presented decreased fungal loads associated with impaired synthesis of nitric oxide, interleukin-12 (IL-12), and macrophage chemotactic protein 1 (MCP-1). After intratracheal infection with 1 million yeasts, TLR4-defective mice developed reduced fungal burdens and decreased levels of pulmonary nitric oxide, proinflammatory cytokines, and antibodies. TLR4-competent mice produced elevated levels of IL-12 and tumor necrosis factor alpha (TNF-alpha), besides cytokines of the Th17 pattern, indicating a proinflammatory role for TLR4 signaling. The more severe infection of TLR4-normal mice resulted in increased influx of activated macrophages and T cells to the lungs and progressive control of fungal burdens but impaired expansion of regulatory T cells (Treg cells). In contrast, TLR4-defective mice were not able to clear their diminished fungal burdens totally, a defect associated with deficient activation of T-cell immunity and enhanced development of Treg cells. These divergent patterns of immunity, however, resulted in equivalent mortality rates, indicating that control of elevated fungal growth mediated by vigorous inflammatory reactions is as deleterious to the hosts as low fungal loads inefficiently controlled by limited inflammatory reactions.

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The mechanisms that govern the initial interaction between Paracoccidioides brasiliensis, a primary dimorphic fungal pathogen, and cells of the innate immunity need to be clarified. Our previous studies showed that Toll-like receptor 2 (TLR2) and TLR4 regulate the initial interaction of fungal cells with macrophages and the pattern of adaptive immunity that further develops. The aim of the present investigation was to assess the role of MyD88, an adaptor molecule used by TLRs to activate genes of the inflammatory response in pulmonary paracoccidioidomycosis. Studies were performed with normal and MyD88(-/-) C57BL/6 mice intratracheally infected with P. brasiliensis yeast cells. MyD88(-/-) macrophages displayed impaired interaction with fungal yeast cells and produced low levels of IL-12, MCP-1, and nitric oxide, thus allowing increased fungal growth. Compared with wild-type (WT) mice, MyD88(-/-) mice developed a more severe infection of the lungs and had marked dissemination of fungal cells to the liver and spleen. MyD88(-/-) mice presented low levels of Th1, Th2, and Th17 cytokines, suppressed lymphoproliferation, and impaired influx of inflammatory cells to the lungs, and this group of cells comprised lower numbers of neutrophils, activated macrophages, and T cells. Nonorganized, coalescent granulomas, which contained high numbers of fungal cells, characterized the severe lesions of MyD88(-/-) mice; the lesions replaced extensive areas of several organs. Therefore, MyD88(-/-) mice were unable to control fungal growth and showed a significantly decreased survival time. In conclusion, our findings demonstrate that MyD88 signaling is important in the activation of fungicidal mechanisms and the induction of protective innate and adaptive immune responses against P. brasiliensis.

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Aims Periodontal disease (PD) and airway allergic inflammation (AL) present opposing inflammatory immunological features and clinically present an inverse correlation. However, the putative mechanisms underlying such opposite association are unknown. Material and Methods Balb/C mice were submitted to the co-induction of experimental PD (induced by Actinobacillus actinomycetemcomitans oral inoculation) and AL [induced by sensitization with ovalbumin (OVA) and the subsequent OVA challenges], and evaluated regarding PD and AL severity, immune response [cytokine production at periodontal tissues, and T-helper transcription factors in submandibular lymph nodes (LNs)] and infection parameters. Results PD/AL co-induction decreased PD alveolar bone loss and periodontal inflammation while experimental AL parameters were unaltered. An active functional interference was verified, because independent OVA sensitization and challenge not modulate PD outcome. PD+AL group presented decreased tumour necrosis factor-alpha (TNF-alpha), interleukin (IL)-1 beta, -gamma, IL-17A, receptor activator of nuclear factor kappa-light-chain-enhancer of activated B cells ligand and matrix metalloproteinase (MMP)-13 levels in periodontal tissues, while IL-4 and IL-10 levels were unaltered by AL co-induction. AL co-induction also resulted in upregulated T-bet and related orphan receptor gamma and downregulated GATA3 levels expression in submandibular LNs when compared with PD group. Conclusion Our results demonstrate that the interaction between experimental periodontitis and allergy involves functional immunological interferences, which restrains experimental periodontitis development by means of a skewed immune response.

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Ticks are blood feeding parasites transmitting a wide variety of pathogens to their vertebrate hosts. The vector competence of ticks is tightly linked with their immune system. Despite its importance, our knowledge of tick innate immunity is still inadequate and the limited number of sufficiently characterized immune molecules and cellular reactions are dispersed across numerous tick species. The phagocytosis of microbes by tick hemocytes seems to be coupled with a primitive complement-like system, which possibly involves self/nonself recognition by fibrinogen-related lectins and the action of thioester-containing proteins. Ticks do not seem to possess a pro-phenoloxidase system leading to melanization and also coagulation of tick hemolymph has not been experimentally proven. They are capable of defending themselves against microbial infection with a variety of antimicrobial peptides comprising lysozymes, defensins and molecules not found in other invertebrates. Virtually nothing is known about the signaling cascades involved in the regulation of tick antimicrobial immune responses. Midgut immunity is apparently the decisive factor of tick vector competence. The gut content is a hostile environment for ingested microbes, which is mainly due to the antimicrobial activity of hemoglobin fragments generated by the digestion of the host blood as well as other antimicrobial peptides. Reactive oxygen species possibly also play an important role in the tick-pathogen interaction. The recent release of the Ixodes scapularis genome and the feasibility of RNA interference in ticks promise imminent and substantial progress in tick innate immunity research.

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P>Scedosporium apiospermum is an emerging agent of opportunistic mycoses in humans. Previously, we showed that mycelia of S. apiospermum secreted metallopeptidases which were directly linked to the destruction of key host proteins. In this study, we analysed the effect of metallopeptidase inhibitors on S. apiospermum development. As germination of inhaled conidia is a crucial event in the infectious process of S. apiospermum, we studied the morphological transformation induced by the incubation of conidia in Sabouraud-dextrose medium at 37 degrees C. After 6 h, some conidia presented a small projection resembling a germ-tube. A significant increase, around sixfold, in the germ-tube length was found after 12 h, and hyphae were exclusively observed after 24 h. Three distinct metallopeptidase inhibitors were able to arrest the transformation of conidia into hyphae in different ways; for instance, 1,10-phenanthroline (PHEN) completely blocked this process at 10 mu mol l-1, while ethylenediamine tetraacetic acid (EDTA) and ethylene glycol-bis (beta-aminoethyl ether; EGTA) only partially inhibited the differentiation at up to 10 mmol l-1. EGTA did not promote any significant reduction in the conidial growth, while PHEN and EDTA, both at 10 mmol l-1, inhibited the proliferation around 100% and 65%, respectively. The secretion of polypeptides into the extracellular environment and the metallopeptidase activity secreted by mycelia were completely inhibited by PHEN. These findings suggest that metallo-type enzymes could be potential targets for future therapeutic interventions against S. apiospermum.

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One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible-infected-recovered) epidemiological model. We show that disorder expressed in the host morphology and anisotropy reduces the probability of epidemic outbreak and thus makes the system more resistant to epidemic outbreaks. We obtain general analytical estimates for minimally safe bounds for an invasion threshold and then illustrate their validity by considering an example of host data for branching hosts (salamander retinal ganglion cells). Several spatial arrangements of hosts with different degrees of heterogeneity have been considered in order to separately analyse the role of shape complexity and anisotropy in the host population. The estimates for invasion threshold are linked to morphological characteristics of the hosts that can be used for determining the threshold for invasion in practical applications.