Numerical analysis of the relation between interactions and structure in a molecular fluid

Coarse graining is a popular technique used in physics to speed up the computer simulation of molecular fluids. An essential part of this technique is a method that solves the inverse problem of determining the interaction potential or its parameters from the given structural data. Due to discrepancies between model and reality, the potential is not unique, such that stability of such method and its convergence to a meaningful solution are issues.rnrnIn this work, we investigate empirically whether coarse graining can be improved by applying the theory of inverse problems from applied mathematics. In particular, we use the singular value analysis to reveal the weak interaction parameters, that have a negligible influence on the structure of the fluid and which cause non-uniqueness of the solution. Further, we apply a regularizing Levenberg-Marquardt method, which is stable against the mentioned discrepancies. Then, we compare it to the existing physical methods - the Iterative Boltzmann Inversion and the Inverse Monte Carlo method, which are fast and well adapted to the problem, but sometimes have convergence problems.rnrnFrom analysis of the Iterative Boltzmann Inversion, we elaborate a meaningful approximation of the structure and use it to derive a modification of the Levenberg-Marquardt method. We engage the latter for reconstruction of the interaction parameters from experimental data for liquid argon and nitrogen. We show that the modified method is stable, convergent and fast. Further, the singular value analysis of the structure and its approximation allows to determine the crucial interaction parameters, that is, to simplify the modeling of interactions. Therefore, our results build a rigorous bridge between the inverse problem from physics and the powerful solution tools from mathematics. rn

Gene expression analysis in ‘Candidatus Phytoplasma mali’-resistant and -susceptible Malus genotypes

Apple proliferation (AP) disease is the most important graft-transmissible and vector-borne disease of apple in Europe. ‘Candidatus Phytoplasma mali’ (Ca. P. mali) is the causal agent of AP. Apple (Malus x domestica) and other Malus species are the only known woody hosts. In European apple orchards, the cultivars are mainly grafted on one rootstock, M. x domestica cv. M9. M9 like all other M. x domestica cultivars is susceptible to ‘Ca. P. mali’. Resistance to AP was found in the wild genotype Malus sieboldii (MS) and in MS-derived hybrids but they were characterised by poor agronomic value. The breeding of a new rootstock carrying the resistant and the agronomic traits was the major aim of a project of which this work is a part. The objective was to shed light into the unknown resistance mechanism. The plant-phytoplasma interaction was studied by analysing differences between the ‘Ca. P. mali’-resistant and -susceptible genotypes related to constitutively expressed genes or to induced genes during infection. The cDNA-Amplified Fragment Length Polymorphism (cDNA-AFLP) technique was employed in both approaches. Differences related to constitutively expressed genes were identified between two ‘Ca. P. mali’-resistant hybrid genotypes (4551 and H0909) and the ‘Ca. P. mali’-susceptible M9. 232 cDNA-AFLP bands present in the two resistant genotypes but absent in the susceptible one were isolated but several different products associated to each band were found. Therefore, two different macroarray hybridisation experiments were performed with the cDNA-AFLP fragments yielding 40 sequences encoding for genes of unknown function or a wide array of functions including plant defence. In the second approach, individuation and analysis of the induced genes was carried out exploiting an in vitro system in which healthy and ‘Ca. P. mali’-infected micropropagated plants were maintained under controlled conditions. Infection trials using in vitro grafting of ‘Ca. P. mali’ showed that the resistance phenotype could be reproduced in this system. In addition, ex vitro plants were generated as an independent control of the genes differentially expressed in the in vitro plants. The cDNA-AFLP analysis in in vitro plants yielded 63 bands characterised by over-expression in the infected state of both the H0909 and MS genotypes. The major part (37 %) of the associated sequences showed homology with products of unknown function. The other genes were involved in plant defence, energy transport/oxidative stress response, protein metabolism and cellular growth. Real-time qPCR analysis was employed to validate the differential expression of the genes individuated in the cDNA-AFLP analysis. Since no internal controls were available for the study of the gene expression in Malus, an analysis on housekeeping genes was performed. The most stably expressed genes were the elongation factor-1 α (EF1) and the eukaryotic translation initiation factor 4-A (eIF4A). Twelve out of 20 genes investigated through qPCR were significantly differentially expressed in at least one genotype either in in vitro plants or in ex vitro plants. Overall, about 20% of the genes confirmed their cDNA-AFLP expression pattern in M. sieboldii or H0909. On the contrary, 30 % of the genes showed down-regulation or were not differentially expressed. For the remaining 50 % of the genes a contrasting behaviour was observed. The qPCR data could be interpreted as follows: the phytoplasma infection unbalance photosynthetic activity and photorespiration down-regulating genes involved in photosynthesis and in the electron transfer chain. As result, and in contrast to M. x domestica genotypes, an up-regulation of genes of the general response against pathogens was found in MS. These genes involved the pathway of H2O2 and the production of secondary metabolites leading to the hypothesis that a response based on the accumulation of H2O2 in MS would be at the base of its resistance. This resembles a phenomenon known as “recovery” where the spontaneous remission of the symptoms is observed in old susceptible plants but occurring in a stochastic way while the resistance in MS is an inducible but stable feature. As additional product of this work three cDNA-AFLP-derived markers were developed which showed independent distribution among the seedlings of two breeding progenies and were associated to a genomic region characteristic of MS. These markers will contribute to the development of molecular markers for the resistance as well as to map the resistance on the Malus genome.

Structural analysis of the major lightharvesting complex II by electron paramagnetic resonance (EPR) : comparison between monomers and trimers

Der Haupt-Lichtsammenkomplex II (LHCII) höherer Pflanzen ist das häufigsternMembranprotein der Welt und in die chloroplastidäre Thylakoidmembran integriert. DerrnLHCII kann als Modellsystem genutzt werden, um die Funktionsweise vonrnMembranproteinen besser zu verstehen, da 96 % seiner Struktur kristallografisch aufgelöstrnist und er in rekombinanter Form in vitro rückgefaltet werden kann. Hierbei entsteht einrnvoll funktionaler Protein-Pigment.Komplex, der nahezu identisch mit der in vivo Varianternist.rnElektronenparamagnetischen Resonanz (EPR) Spektroskopie ist eine hoch sensitive undrnideal geeignete Methode, um die Strukturdynamik von Proteinen zu untersuchen. Hierzurnist eine ortsspezifische Markierung mit Spinsonden notwendig, die kovalent an Cysteinernbinden. Möglich wird dies, indem sorgfältig ausgewählte Aminosäuren gegen Cysteinerngetauscht werden, ohne dass die Funktionsweise des LHCII beeinträchtigt wird.rnIm Rahmen dieser Arbeit wurden die Stabilität des verwendeten Spinmarkers und diernProbenqualität verbessert, indem alle Schritte der Probenpräparation untersucht wurden.rnMithilfe dieser Erkenntnisse konnte sowohl die Gefahr einer Proteinaggregation als auchrnein Verlust des EPR Signals deutlich vermindert werden. In Kombination mit derrngleichzeitigen Etablierung des Q-Band EPR können nun deutlich geringer konzentrierternProben zuverlässig vermessen werden. Darüber hinaus wurde eine reproduzierbarernMethode entwickelt, um heterogene Trimere herzustellen. Diese bestehen aus einemrndoppelt markierten Monomer und zwei unmarkierten Monomeren und erlauben es, diernkristallografisch unvollständig aufgelöste N-terminale Domäne im monomeren undrntrimeren Assemblierungsgrad zu untersuchen. Die Ergebnisse konnten einerseits diernVermutung bestätigen, dass diese Domäne im Vergleich zum starren Proteinkern sehrrnflexibel ist und andererseits, dass sie in Monomeren noch mobiler ist als in Trimeren.rnZudem wurde die lumenale Schleifenregion bei unterschiedlichen pH Werten undrnvariierender Pigmentzusammensetzung untersucht, da dieser Bereich sehr kontroversrndiskutiert wird. Die Messergebnisse offenbarten, dass diese Region starre und flexiblerernSektionen aufweist. Während der pH Wert keinen Einfluss auf die Konformation hatte,rnzeigte sich, dass die Abwesenheit von Neoxanthin zu einer Änderung der Konformationrnführt. Weiterführende Analysen der strukturellen Dynamik des LHCII in einerrnLipidmembran konnten hingegen nicht durchgeführt werden, da dies eine gerichteternInsertion des rückgefalteten Proteins in Liposomen erfordert, was trotz intensiverrnVersuche nicht zum Erfolg führte.