Epigenetic regulation of Epichloë festucae secondary metabolite biosynthesis and symbiotic interaction with Lolium perenne : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Genetics at Massey University, Palmerston North, New Zealand

Histone methylation is one of several epigenetic layers for transcriptional regulation. Most studies on the importance of this histone modification in regulating fungal secondary metabolite gene expression and pathogenicity have focussed on the role of histone methyltransferases, while few studies have focussed on the role of histone demethylases that catalyse the reversal of the modification. Epichloë festucae (Ascomycota) is an endophyte that forms a mutualistic interaction with perennial ryegrass. The fungus contributes to the symbiosis by the production of several classes of secondary metabolites, these have anti-insect and/or anti-mammalian activity. The EAS and LTM clusters in E. festucae are located subtelomerically and contain the biosynthetic genes for two of these important metabolites which are only synthesised in planta. Thus, in the host plant these genes are highly expressed, but they are tightly silenced in culture conditions. Previous study has shown that histone H3K9 and H3K27 methylation and their corresponding histone methyltransferases are important for this process. In this study, the role of histone lysine demethylases (KDMs) in regulating these genes and the symbiotic interaction is described. Eight candidate histone demethylases (Jmj1-Jmj8) were identified in E. festucae, among these proteins are homologues of mammalian KDM4, KDM5, KDM8, JMDJ7, and N. crassa Dmm-1. The genes for the proteins were overexpressed in E. festucae and histone methylation levels were determined in the strains. Overexpression of the genes was not observed to cause any change to the culture and symbiotic phenotypes of the fungus. Western blot analysis subsequently identified one of the proteins, KdmB, as the histone H3K4me3 demethylase. Further analysis by ChIP- and RT-qPCR showed that demethylation of H3K4me3 by KdmB at the eas/ltm genes is crucial for the activation of these genes in planta. The full expression of several other telomeric genes was similarly found to require KdmB. On the other hand, the COMPASS H3K4 methyltransferase complex subunit CclA that is required for H3K4 trimethylation in E. festucae represses the eas/ltm genes in culture conditions by maintaining H3K4me3 levels at the loci. Thus, these findings suggest a repressive role for H3K4me3 at these subtelomeric secondary metabolite loci and are consistent with the role of H3K4me3 in yeast telomeric silencing. Disruption of kdmB did not affect the symbiotic interaction of E. festucae with the host grass but severely reduced the levels of lolitrem B, an animal neurotoxin. At the same time, the levels of ergovaline, another animal toxin, and peramine, an insect feeding deterrent, were not affected. Therefore, disruption or inhibition of KdmB may also serve as a promising approach for future endophyte improvement programmes. The E. festucae homologue of KDM8 (an H3K36me2 demethylase), Jmj4, was further investigated in this study but no H3K6 demethylase activity was found for the protein. Both disruption and overexpression of the gene encoding Jmj4 similarly had no effect on the culture and symbiotic phenotypes of E. festucae. However, deletion of setB, encoding the homologue of yeast Set2 (H3K36 methyltransferase) specifically reduced histone H3K36me3 levels in E. festucae. This contrasts with deletion of Set2 in other fungi which affected H3K36 mono-, di- and trimethylation. The ΔsetB mutant was severely impeded in development, and was unable to establish infection of the host plant. Introduction of the wild-type setB gene reversed these phenotypes. This study shows that H3K4 trimethylation controlled by CclA and KdmB is an important regulator of subtelomeric secondary metabolite genes in E. festucae but not for the symbiotic interaction of the fungus with perennial ryegrass. On the other hand, the histone H3K36 methyltransferase SetB specifically controls H3K36 trimethylation in E. festucae and is required for normal vegetative growth and ability of the fungus to infect the host plant

Lattice Magnetic Walks

Sums of walks for charged particles (e.g. Hofstadter electrons) on a square lattice in the presence of a magnetic field are evaluated. Returning loops are systematically added to directed paths to obtain the unrestricted propagators. Expressions are obtained for special values of the magnetic flux-per-plaquette commensurate with the flux quantum. For commensurate and incommensurate values of the flux, the addition of small returning loops does not affect the general features found earlier for directed paths. Lattice Green's functions are also obtained for staggered flux configurations encountered in models of high-Tc superconductors.Comment: 31 pages, Plain TeX, 2 figures (available upon request), UR-CM-93-10-1

An empirical study of the tails of mutual fund size

The mutual fund industry manages about a quarter of the assets in the U.S. stock market and thus plays an important role in the U.S. economy. The question of how much control is concentrated in the hands of the largest players is best quantitatively discussed in terms of the tail behavior of the mutual fund size distribution. We study the distribution empirically and show that the tail is much better described by a log-normal than a power law, indicating less concentration than, for example, personal income. The results are highly statistically significant and are consistent across fifteen years. This contradicts a recent theory concerning the origin of the power law tails of the trading volume distribution. Based on the analysis in a companion paper, the log-normality is to be expected, and indicates that the distribution of mutual funds remains perpetually out of equilibrium.Comment: 6 pages, 3 figure

Graph matching: relax or not?

We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly-stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving 2n equality and n^2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic

Source-Channel Coding for the Multiple-Access Relay Channel

This work considers reliable transmission of general correlated sources over the multiple-access relay channel (MARC) and the multiple-access broadcast relay channel (MABRC). In MARCs only the destination is interested in a reconstruction of the sources, while in MABRCs both the relay and the destination want to reconstruct the sources. We assume that both the relay and the destination have correlated side information. We find sufficient conditions for reliable communication based on operational separation, as well as necessary conditions on the achievable source-channel rate. For correlated sources transmitted over fading Gaussian MARCs and MABRCs we find conditions under which informational separation is optimal.Comment: Presented in ISWCS 2011, Aachen, German

On Joint Source-Channel Coding for Correlated Sources Over Multiple-Access Relay Channels

We study the transmission of correlated sources over discrete memoryless (DM) multiple-access-relay channels (MARCs), in which both the relay and the destination have access to side information arbitrarily correlated with the sources. As the optimal transmission scheme is an open problem, in this work we propose a new joint source-channel coding scheme based on a novel combination of the correlation preserving mapping (CPM) technique with Slepian-Wolf (SW) source coding, and obtain the corresponding sufficient conditions. The proposed coding scheme is based on the decode-and-forward strategy, and utilizes CPM for encoding information simultaneously to the relay and the destination, whereas the cooperation information from the relay is encoded via SW source coding. It is shown that there are cases in which the new scheme strictly outperforms the schemes available in the literature. This is the first instance of a source-channel code that uses CPM for encoding information to two different nodes (relay and destination). In addition to sufficient conditions, we present three different sets of single-letter necessary conditions for reliable transmission of correlated sources over DM MARCs. The newly derived conditions are shown to be at least as tight as the previously known necessary conditions.Comment: Accepted to TI

Source-Channel Coding Theorems for the Multiple-Access Relay Channel

We study reliable transmission of arbitrarily correlated sources over multiple-access relay channels (MARCs) and multiple-access broadcast relay channels (MABRCs). In MARCs only the destination is interested in reconstructing the sources, while in MABRCs both the relay and the destination want to reconstruct them. In addition to arbitrary correlation among the source signals at the users, both the relay and the destination have side information correlated with the source signals. Our objective is to determine whether a given pair of sources can be losslessly transmitted to the destination for a given number of channel symbols per source sample, defined as the source-channel rate. Sufficient conditions for reliable communication based on operational separation, as well as necessary conditions on the achievable source-channel rates are characterized. Since operational separation is generally not optimal for MARCs and MABRCs, sufficient conditions for reliable communication using joint source-channel coding schemes based on a combination of the correlation preserving mapping technique with Slepian-Wolf source coding are also derived. For correlated sources transmitted over fading Gaussian MARCs and MABRCs, we present conditions under which separation (i.e., separate and stand-alone source and channel codes) is optimal. This is the first time optimality of separation is proved for MARCs and MABRCs.Comment: Accepted to IEEE Transaction on Information Theor