Bursaphelenchus antoniae sp. n. (Nematoda: Parasitaphelenchidae) associated with Hylobius sp. from Pinus pinaster in Portugal

Bursaphelenchus antoniae sp. n. is described and illustrated. Dauer juveniles were isolated from the body of the large pine weevil, Hylobius sp., collected from maritime pine (Pinus pinaster) stumps, in Portugal. Bursaphelenchus antoniae sp. n. was reared and maintained in P. pinaster wood segments and on Petri dish cultures of the fungi Botrytis cinerea and Monilinia fructicola. The new species is characterised by a relatively small body length of ca 583 μm (females) and 578 μm (males), a lateral field with two incisures, presence of a small vulval flap and a conoid female tail with a rounded or pointed terminus. Males have stout spicules with a disc-like cucullus and seven caudal papillae arranged as a single midventral precloacal papilla, one precloacal pair and two postcloacal pairs. In the character of the lateral field, B. antoniae sp. n. comes close to B. abietinus, B. rainulfi and B. hylobianum, whilst spicule characters place it within the piniperdae-group sensu Ryss et al. Morphologically, B. antoniae sp. n. is closest to B. hylobianum; the spicules of these two species having flattened, wing-like, alae on the distal third of the lamina. Bursaphelenchus antoniae sp. n. is distinguished from B. hylobianum on the arrangement of the caudal papillae (two vs three pairs). ITS-RFLP profiles and the failure to hybridise support the separation of the two species. Phylogenetic analysis of the new species, based on the 18S rDNA sequence, supports the inclusion of this new species in the B. hylobianum-group sensu Braasch. Sequence analysis of the 28S rDNA D2/D3 domain did not place the new species in a definite group.

Satellite DNA as a target for TaqMan real-time PCR detection of the pinewood nematode, Bursaphelenchus xylophilus

The pinewood nematode (PWN), Bursaphelenchus xylophilus , is a major pathogen of conifers, which impacts on forest health, natural ecosystem stability and international trade. As a consequence, it has been listed as a quarantine organism in Europe. A real-time PCR approach based on TaqMan chemistry was developed to detect this organism. Specific probe and primers were designed based on the sequence of the Msp I satellite DNA family previously characterized in the genome of the nematode. The method proved to be specific in tests with target DNA from PWN isolates from worldwide origin. From a practical point of view, detection limit was 1 pg of target DNA or one individual nematode. In addition, PWN genomic DNA or single individuals were positively detected in mixed samples in which B. xylophilius was associated with the closely related non-pathogenic species B. mucronatus , up to the limit of 0.01% or 1% of the mixture, respectively. The real-time PCR assay was also used in conjunction with a simple DNA extraction method to detect PWN directly in artificially infested wood samples. These results demonstrate the potential of this assay to provide rapid, accurate and sensitive molecular identification of the PWN in relation to pest risk assessment in the field and quarantine regulation.

Bursaphelenchus xylophilus : opportunities in comparative genomics and molecular host–parasite interactions

Most Bursaphelenchus species are fungal feeding nematodes that colonize dead or dying trees. However, Bursaphelenchus xylophilus , the pine wood nematode, is also a pathogen of trees and is the causal agent of pine wilt disease. B. xylophilus is native to North America and here it causes little damage to trees. Where it is introduced to new regions it causes huge damage. The most severely affected areas are found in the Far East but more recently B. xylophilus has been introduced into Portugal and the potential for damage here is also high. As incidence and severity of pine wilt disease are linked to temperature we suggest that climate change is likely to exacerbate the problems caused by B. xylophilus and, in addition, will extend (northwards in Europe) the range in which pine wilt disease can occur. Here we review what is currently known about the interactions of B. xylophilus with its hosts, including recent developments in our understanding of the molecular biology of pathogenicity in the nematode. We also examine the potential developments that could be made by more widespread use of genomics tools to understand interactions between B. xylophilus , bacterial pathogens that have been implicated in disease and host trees.

The History of Expansion of the Genus Bursaphelenchus (Nematoda: Aphelenchida: Parasitaphelenchidae)

Because of globalization and removal of geographical barriers, frequent biological invasions of introduced species become an urgent environmental problem. According to the Convention on Biological Diversity (CBD), precise identification of dangerous aggressive species at the early stages of their invasion to new regions is the most important component of the environmental control and monitoring. To resist the potential environmental hazard, the precise data are required on the current distribution and history of expansion of pests that are of global economic importance.

On the vulval morphology of some species of Bursaphelenchus (Nematoda: Parasitaphelenchinae)

The vulval pattern of six species of the genus Bursaphelenchus (B. abruptus, B. conicaudatus, B. fraudulentus, B. luxuriosae, B. mucronatus and B. xylophilus) was studied using scanning electron microscopy. A terminology for the vulval region structures observed is proposed herein and illustrated by micrographs and line drawings. It was shown that, of the studied species, only B. mucronatus and B. xylophilus share an identical morphology of the vulval region, all other species differing significantly from each other and from both B. mucronatus and B. xylophilus. This study indicates the diagnostic potential for variation in vulval morphology within Bursaphelenchus and it is recommended that such features are recorded in all future descriptions.

A rapid staining-assisted wood sampling method for PCR-based detection of pine wood nematode Bursaphelenchus xylophilus in Pinus massoniana wood tissue

For reasons of unequal distribution of more than one nematode species in wood, and limited availability of wood samples required for the PCR-based method for detecting pinewood nematodes in wood tissue of Pinus massoniana, a rapid staining-assisted wood sampling method aiding PCR-based detection of the pine wood nematode Bursaphelenchus xylophilus (Bx) in small wood samples of P. massoniana was developed in this study. This comprised a series of new techniques: sampling, mass estimations of nematodes using staining techniques, and lowest limit Bx nematode mass determination for PCR detection. The procedure was undertaken on three adjoining 5-mg wood cross-sections, of 0.5 · 0.5 · 0.015 cm dimension, that were cut from a wood sample of 0.5 · 0.5 · 0.5 cm initially, then the larger wood sample was stained by acid fuchsin, from which two 5-mg wood cross-sections (that adjoined the three 5-mg wood cross-sections, mentioned above) were cut. Nematode-staining-spots (NSSs) in each of the two stained sections were counted under a microscope at 100· magnification. If there were eight or more NSSs present, the adjoining three sections were used for PCR assays. The B. xylophilus – specific amplicon of 403 bp (DQ855275) was generated by PCR assay from 100.00% of 5-mg wood cross-sections that contained more than eight Bx NSSs by the PCR assay. The entire sampling procedure took only 10 min indicating that it is suitable for the fast estimation of nematode numbers in the wood of P. massonina as the prelimary sample selections for other more expensive Bx-detection methods such as PCR assay.

Progress in the use of scanning electron microscopy (SEM) applied to the taxonomy of the genus Bursaphelenchus (Nematoda: Parasitaphelenchidae)

The scanning electron microscope (SEM) has been a major tool in detailed morphological observations of plant parasitic nematodes during the last 30 years, efficiently complementing light microscopical (LM) studies. Nematodes are extremely difficult to observe and characterize due to their small size (aprox. 1 mm long) and paucity of morphological characters, so detailed surface observations of several organs and nematode regions are of the highest value. Among plant parasitic nematodes, one of the most devastating species is the “pinewood nematode” (PWN), Bursaphelenchus xylophilus, which has been a major problem for forest species, and in particular pines, in Asia (Japan, China, Korea) and has been recently detected in the European Union (Portugal). B. xylophilus belongs to a closely related, morphologically similar group of species, within the genus Bursaphelenchus, and designated by the “xylophilus group”. SEM has become a crucial tool in observing several genital characters of males and females, such as male genital papillae, male copulatory spicules, female vulval flap and female genital papillae.s In this presentation, we will show how SEM has been utilized to observe and characterize the shape of the vulval flap, the presence/ absence of papillae near the flap, and confirm the presence and the arrangement of the male genital papillae. LM is also used in this work to show its value as a complementary tool to SEM, in both genital characteristics and other, general, characters of the genus Bursaphelenchus, such as the male bursa and cephalic region.

Taxonomic databases for Bursaphelenchus and other aphelenchoid nematodes

Nematodes are the most abundant metazoans, comprising more than 80% of all animals alive today. Since 1743, when Needham (Needham, 1743) described the first nematode, approximately 20,000 - 30,000 species have been named, with estimates of species remaining to be described ranging from 100,000 to 1 million (Blaxter, 2004; De Ley, 2000). Unfortunately, the taxonomic community is woefully inadequate for this task. The number of taxonomists currently describing new species of nematodes around the world is less than 100, and significant increases are not expected. If each of these taxonomists were able to describe 10 new species every year, it would take between 100 to 1,000 years to name these yet to be described species.

Bursaphelenchus pinophilus Brzeski & Baujard, 1997 (Nematoda: Parasitaphelenchinae) associated with nematangia on Pityogenes bidentatus (Herbst, 1783) (Coleoptera: Scolytinae), from the Czech Republic

The occurrence of Bursaphelenchus species in the Czech Republic is poorly known, the first report of the genus being made by Kubátová et al. (2000) who reported the association of B. eremus with the hyphomycetous microfungus, Esteya vermicola, and the bark beetle, Scolytus intricatus, collected from Quercus robur, in central Bohemia. To date, four other species have been reported from the country, namely B. fungivorus (Braasch et al., 2002), B. hofmanni (see Braasch, 2001), B. mucronatus (see Braasch, 2001) and B. vallesianus (Gaar et al., 2006). More recently, a survey for Bursaphelenchus species associated with bark- and wood-boring insects in the Czech Republic identified B. pinophilus Brzeski & Baujard, 1997 from the Moravia region. Although this represents a new country record, it was also associated with nematangia on the hind wings of a new insect vector. A total of 404 bark- and wood-boring insects were collected from declining or symptomatic trees and screened for the presence of Bursaphelenchus. Bark and longhorn beetles were captured manually after debarking parts of the trunk displaying symptoms of insect attacks. Longhorn beetle larvae were also collected together with logs cut from the trunk. Logs were kept at room temperature in the laboratory until insect emergence. Each adult insect was individually dissected in water and examined for nematodes. All nematodes resembling dauer juveniles of Bursaphelenchus were collected and identified by molecular characterisation using a region of ribosomal DNA (rDNA) containing the internal transcribed spacer regions ITS1 and ITS2. ITS-RFLP analyses using five restriction enzymes (AluI, HaeIII, HinfI, MspI, RsaI) were performed to generate the species-specific profile according to Burgermeister et al. (2009). Species identification was also confirmed by morphological data after culture of the dauers on Botrytis cinerea Pers. ex Ft., growing in 5% malt extract agar. During this survey, only species belonging to the Curculionidae, subfamily Scolytinae, revealed the presence of nematodes belonging to Bursaphelenchus. Dauers of this genus were found aggregated under the elytra in nematangia formed at the root of the hind wings (Fig. 1). The dauers were identified from 12 individuals of Pityogenes bidentatus (Herbst, 1783) (Coleoptera: Scolytinae) collected under the bark of Pinus sylvestris trunks. Each insect carried ca 10-100 dauers. The ITS-RFLP patterns of the dauers so obtained confirmed the identification of B. pinophilus associated with this insect species. Bursaphelenchus pinophilus has been found mainly in Europe and has been reported from various countries such as Poland (Brzeski & Baujard, 1997), Germany (Braasch, 2001), and Portugal (Penas et al., 2007). The recent detection of this species associated with dead P. koraiensis in Korea (Han et al., 2009) expands its geographical distribution and potential importance. It has been found associated only with Pinus species, but very little is known about the insect vector. The bark beetle, Hylurgus ligniperda, was initially suggested as the insect vector by Pe-nas et al. (2006), although the nematode associated with this insect was later reclassified as B. sexdentati by morphological and molecular analysis (Penas et al., 2007). According to the literature, P. bidentatus has been cited as a vector of Ektaphelenchus sp. (Kakuliya, 1966) in Georgia, and an unidentified nematode species in Spain (Roberston et al., 2008). Interestingly, B. pinophilus was found in the nematangia formed at the root of the hind wings of P. bidentatus. Although this phenomenon is not so common in other Bursaphelenchus species, B. rufipennis has been found recently in such a structure on the hind wings of the insect Dendroctonus rufipennis (Kanzaki et al., 2008). Although other nematode species (e.g., Ektaphelenchus spp.) are frequently found associated within the same nematangia (see Kanzaki et al., 2008), in this particular case, only dauers of B. pinophilus were identified. The association between B. pinophilus and P. bidentatus represents the first report of this biological association and the association with the Scolytinae strengthens the tight and specific links between this group of Bursaphelenchus species and members of the Scolytinae (Ryss et al., 2005).

Genetic diversity of entomopathogenic nematodes (Nematoda: Steinernematidae and Heterorhabditidae) and the nematode Bursaphelenchus xylophilus (Nematoda: Aphelenchoididae) from continental Portugal

“Diversidade genética dos nemátodes entomopatogénicos (Nematoda: Steinernematidae e Heterorhabditidae) e do nemátode Bursaphelenchus xylophilus (Nematoda: Aphelenchoididade) em Portugal continental” Os nematodes entomopatogénicos são utilizados como agentes de controlo biológico. Para compreender a sua diversidade, foi realizada uma prospecção em Portugal. Cinco espécies, nomeadamente Steinernema feltiae, S. intermedium, S. kraussei, Steinernema sp. e Heterorhabditis bacteriophora foram identificadas. As sequências de ITS, região D2D3 do 28S rRNA, COXI e cytb foram utilizadas para estudar a diversidade genética das duas espécies mais abundantes, S. feltiae and H. bacteriophora, não tendo sido encontradas diferenças significativas entre isolados. O nemátode da madeira do pinheiro, Bursaphelenchus xylophilus, provoca doença nos pinheiros tendo sido detectada pela primeira vez na Europa e em Portugal em 1999. Para avaliar a diversidade genética dos isolados Portugueses e identificar o padrão de propagação da doença, foram utilizadas a sequência da região IGS do 5.8S rRNA, e os genes cytb e cellulase, combinados com os padrões ISSR. Os padrões de ISSR mostraram elevada diversidade genética entre os recentes isolados Portugueses, sugerindo a possibilidade de uma nova introdução. As árvores filogenéticas dos genes da celulase e cytb sugeriram uma origem Asiática para os isolados Portugueses; ABSTRACT: Entomopathogenic nematodes are used as biocontrol agents. To understand their diversity, a survey was undertaken in Portugal. Five species, namely Steinernema feltiae, S. intermedium, S. kraussei, Steinernema sp. and Heterorhabditis bacteriophora were identified. The ITS, 28S rRNA D2D3 region, COXI and cytb sequences, used to study the genetic diversity of the two most abundant species, S. feltiae and H. bacteriophora, showed no significant differences among the isolates. Bursaphelenchus xylophilus causes severe disease in pine trees and was detected for the first time in Europe and in Portugal in 1999. To evaluate the genetic diversity of Portuguese isolates and identify disease spread pathways, the sequence of 5.8S rRNA IGS region, cytb and cellulase genes, combined with ISSR fingerprints were used. ISSR fingerprints show a high genetic variability among recent Portuguese isolates, suggesting the possibility of a new introduction. Phylogenetic trees based on cellulase and cytb genes suggests an Asian origin for Portuguese isolates.

Assessment of the genetic diversity of the pinewood nematode, Bursaphelenchus xylophilus, in Portugal

O nemátode da madeira do pinheiro (NMP), Bursaphelenchus xylophiius, tem uma extensa distribuição na América do Norte, e encontra-se atualmente distribuído ao longo da maioria dos territórios de Canadá e dos Estados Unidos. Durante o último século, esta espécie foi transportada pelo Homem para outras regiões do mundo (não-nativas), associadas com o comércio e o fluxo global de produtos de origem florestal. Atualmente, esta espécie invasiva está reportada para algumas regiões do SE asiático (China, Japão, Coreia e Taiwan) e mais recentemente para a Europa (Portugal). Devido ao impacto que este organismo agente da doença da murchidão dos pinheiros causa nas florestas nativas destas regiões esta espécie assume uma elevada importância económica a nível mundial Em Portugal, a distribuição do NMP encontra-se confinada a uma área restrita e limitada (500 000 ha), a sul de Lisboa (península de Setúbal); contudo, constitui uma das maiores ameaças às florestas de pinheiro do país e da UE. Ate recentemente, nenhum consenso existia quanto à origem do NMP em Portugal. Diversas hipóteses têm sido colocadas para explicar esta introdução, nomeadamente a partir de zonas onde o nematode ocorre naturalmente (América do Norte), ou de outras áreas (não-nativas) onde o nematode se comporta como uma espécie invasiva (Leste da Ásia). A fim de avaliar a variabilidade genética do NMP proveniente da área afetada em Portugal, foram utilizadas várias técnicas moleculares, designadamente o random amplified polymorphic DNA (RAPD-PCR) e o satellite DNA (satDNA). No caso do RAPD-PCR, foram utilizados 24 isolados do NMP provenientes de Portugal, 1 proveniente da América do Norte e 1 da Ásia, tendo sido utilizado como out-group um isolado de B. mucronatus. A partir dos 28 RAPD primers utilizados obtiveram-se 640 fragmentos. No caso do satDNA, foram utilizados 21 isolados do NMP provenientes de Portugal, obtendo-se no total 206 sequências da família MspI. Ambos os métodos revelaram uma elevada similaridade genética entre os vários isolados do NMP da área afetada em Portugal O nível reduzido de diversidade genética obtido entre os isolados portugueses do NMP, permite concluir que se trata de uma única introdução deste organismo em Portugal, e proveniente de uma região asiática. A inexistência de uma de correlação entre a variabilidade genética e a distribuição geográfica do NMP dentro da área afetada em Portugal, indica que o NMP se encontra distribuído de forma uniforme ao longo de toda a área afetada, provavelmente relacionado com a distribuição e a expansão natural do inseto vector. The pinewood nematode (PWN), Bursaphelenchus xylophilus, has a wide distribution in North America, and is present throughout most of the territories of Canada and the United Stata. During the last century, this species has been transported by man to several non-native regions of the world, associated with trade and the global flow of forest products. Up to date, this invasive species has been reported from Asia (PR China, Japan, Korea and Taiwan) and more recently in Europe (Portugal). Due to the impact on native pine forests of these regions, this nematode species, the causal agent of pine wilt disease, is of great economic importance worldwide. In Portugal, the distribution of the PWN has been constrained to a relatively small area (500 000 ha) in the south of Lisbon (Setúbal Peninsula); however, it has become the most serious threat to pine forests in the country. Until recently, no consensus had emerged on the possible pathway of the PWN introduction in Portugal. Several hypotheses have been put forward to explain this introduction, such as an origin from endemic areas where the nematode naturally occurs (North America), or non-endemic areas where the nematode behaves as an exotic pest (East Asia). Random amplified polymorphic DNA (RAPD-PCR) and satellite DNA (satDNA) techniques were used in order to assess the level of genetic variability and genetic relationships, among several isolates of the PWN, representative of the entire affected area in Portugal. In the case of RAPD-PCR, 24 Portuguese isolates, plus two additional isolates of B. xylophilus, representing North America and East Asia were included. B. mucronatus was used as an out-group. Twenty-eight random primers generated a total of 640 DNA fragments. With satDNA, 206 Mspl sequence repeats were obtained from 21 Portuguese isolates of B. xylophilus. Both molecular methods revealed a high genetic similarity among the Portuguese isolates, and the low level of genetic diversity strongly suggests that they were dispersed recently from a single introduction, and from East Asia. The lack of apparent relationship between the genetic variability and the geographic distribution of the PWN within the affected area, suggests that the recent introduction of this pest (and pathogen) in Portugal has been uniformly distributed since its establishment, probably following the natural distribution and expansion of the insect vector.

Regenerative potential of corneal endothelium from patients with fuchs endothelial corneal dystrophy

La dystrophie cornéenne endothéliale de Fuchs (FECD, pour l’abréviation du terme anglais « Fuchs endothelial corneal dystrophy ») est une maladie de l'endothélium cornéen. Sa pathogenèse est mal connue. Aucun traitement médical n’est efficace. Le seul traitement existant est chirurgical et consiste dans le remplacement de l’endothélium pathologique par un endothélium sain provenant de cornées de la Banque des yeux. Le traitement chirurgical, en revanche, comporte 10% de rejet immunologique. Des modèles expérimentaux sont donc nécessaires afin de mieux comprendre cette maladie ainsi que pour le développement de traitements alternatifs. Le but général de cette thèse est de développer un modèle expérimental de la FECD en utilisant le génie tissulaire. Ceci a été réalisé en trois étapes. 1) Tout d'abord, l'endothélium cornéen a été reconstruit par génie tissulaire en utilisant des cellules endothéliales en culture, provenant de patients atteints de FECD. Ce modèle a ensuite été caractérisé in vitro. Brièvement, les cellules endothéliales cornéennes FECD ont été isolées à partir de membranes de Descemet prélevées lors de greffes de cornée. Les cellules au deuxième ou troisième passages ont ensuite été ensemencées sur une cornée humaine préalablement décellularisée. Suivant 2 semaines de culture, les endothélia cornéens reconstruits FECD (n = 6) ont été évalués à l'aide d'histologie, de microscopie électronique à transmission et d’immunomarquages de différentes protéines. Les endothélia cornéens reconstruits FECD ont formé une monocouche de cellules polygonales bien adhérées à la membrane de Descemet. Les immunomarquages ont démontré la présence des protéines importantes pour la fonctionnalité de l’endothélium cornéen telles que Na+-K+/ATPase α1 et Na+/HCO3-, ainsi qu’une expression faible et uniforme de la protéine clusterine. 2) Deux techniques chirurgicales (DSAEK ; pour « Descemet stripping automated endothelial keratoplasty » et la kératoplastie pénétrante) ont été comparées pour la transplantation cornéenne dans le modèle animal félin. Les paramètres comparés incluaient les défis chirurgicaux et les résultats cliniques. La technique « DSAEK » a été difficile à effectuer dans le modèle félin. Une formation rapide de fibrine a été observée dans tous les cas DSAEK (n = 5). 3) Finalement, la fonctionnalité in vivo des endothélia cornéens reconstruits FECD a été évaluée (n = 7). Les évaluations in vivo comprenaient la transparence, la pachymétrie et la tomographie par cohérence optique. Les évaluations post-mortem incluaient la morphométrie des cellules endothéliales, la microscopie électronique à transmission et des immunomarquage de protéines liées à la fonctionnalité. Après la transplantation, la pachymétrie a progressivement diminué et la transparence a progressivement augmenté. Sept jours après la transplantation, 6 des 7 greffes étaient claires. La microscopie électronique à transmission a montré la présence de matériel fibrillaire sous-endothélial dans toutes les greffes d’endothelia reconstruits FECD. Les endothélia reconstruits exprimaient aussi des protéines Na+-K+/ATPase et Na+/HCO3-. En résumé, cette thèse démontre que les cellules endothéliales de la cornée à un stade avancé FECD peuvent être utilisées pour reconstruire un endothélium cornéen par génie tissulaire. La kératoplastie pénétrante a été démontrée comme étant la procédure la plus appropriée pour transplanter ces tissus reconstruits dans l’œil du modèle animal félin. La restauration de l'épaisseur cornéenne et de la transparence démontrent que les greffons reconstruits FECD sont fonctionnels in vivo. Ces nouveaux modèles FECD démontrent une réhabilitation des cellules FECD, permettant d’utiliser le génie tissulaire pour reconstruire des endothelia fonctionnels à partir de cellules dystrophiques. Les applications potentielles sont nombreuses, y compris des études physiopathologiques et pharmacologiques.

Picard-Fuchs equations of dimensionally regulated Feynman integrals

Zusammenfassung In der vorliegenden Arbeit besch¨aftige ich mich mit Differentialgleichungen von Feynman– Integralen. Ein Feynman–Integral h¨angt von einem Dimensionsparameter D ab und kann f¨ur ganzzahlige Dimension als projektives Integral dargestellt werden. Dies ist die sogenannte Feynman–Parameter Darstellung. In Abh¨angigkeit der Dimension kann ein solches Integral divergieren. Als Funktion in D erh¨alt man eine meromorphe Funktion auf ganz C. Ein divergentes Integral kann also durch eine Laurent–Reihe ersetzt werden und dessen Koeffizienten r¨ucken in das Zentrum des Interesses. Diese Vorgehensweise wird als dimensionale Regularisierung bezeichnet. Alle Terme einer solchen Laurent–Reihe eines Feynman–Integrals sind Perioden im Sinne von Kontsevich und Zagier. Ich beschreibe eine neue Methode zur Berechnung von Differentialgleichungen von Feynman– Integralen. ¨ Ublicherweise verwendet man hierzu die sogenannten ”integration by parts” (IBP)– Identit¨aten. Die neue Methode verwendet die Theorie der Picard–Fuchs–Differentialgleichungen. Im Falle projektiver oder quasi–projektiver Variet¨aten basiert die Berechnung einer solchen Differentialgleichung auf der sogenannten Griffiths–Dwork–Reduktion. Zun¨achst beschreibe ich die Methode f¨ur feste, ganzzahlige Dimension. Nach geeigneter Verschiebung der Dimension erh¨alt man direkt eine Periode und somit eine Picard–Fuchs–Differentialgleichung. Diese ist inhomogen, da das Integrationsgebiet einen Rand besitzt und daher nur einen relativen Zykel darstellt. Mit Hilfe von dimensionalen Rekurrenzrelationen, die auf Tarasov zur¨uckgehen, kann in einem zweiten Schritt die L¨osung in der urspr¨unglichen Dimension bestimmt werden. Ich beschreibe außerdem eine Methode, die auf der Griffiths–Dwork–Reduktion basiert, um die Differentialgleichung direkt f¨ur beliebige Dimension zu berechnen. Diese Methode ist allgemein g¨ultig und erspart Dimensionswechsel. Ein Erfolg der Methode h¨angt von der M¨oglichkeit ab, große Systeme von linearen Gleichungen zu l¨osen. Ich gebe Beispiele von Integralen von Graphen mit zwei und drei Schleifen. Tarasov gibt eine Basis von Integralen an, die Graphen mit zwei Schleifen und zwei externen Kanten bestimmen. Ich bestimme Differentialgleichungen der Integrale dieser Basis. Als wichtigstes Beispiel berechne ich die Differentialgleichung des sogenannten Sunrise–Graphen mit zwei Schleifen im allgemeinen Fall beliebiger Massen. Diese ist f¨ur spezielle Werte von D eine inhomogene Picard–Fuchs–Gleichung einer Familie elliptischer Kurven. Der Sunrise–Graph ist besonders interessant, weil eine analytische L¨osung erst mit dieser Methode gefunden werden konnte, und weil dies der einfachste Graph ist, dessen Master–Integrale nicht durch Polylogarithmen gegeben sind. Ich gebe außerdem ein Beispiel eines Graphen mit drei Schleifen. Hier taucht die Picard–Fuchs–Gleichung einer Familie von K3–Fl¨achen auf.