Proper holomorphic mappings between symmetrized ellipsoids

We characterize the existence of proper holomorphic mappings in the special class of bounded $(1,2,...,n)$-balanced domains in $\mathbb{C}^n$, called the symmetrized ellipsoids. Using this result we conclude that there are no non-trivial proper holomorphic self-mappings in the class of symmetrized ellipsoids. We also describe the automorphism groupof these domains.Comment: 10 pages, some modification

Obligate Biotroph Pathogens of the Genus Albugo Are Better Adapted to Active Host Defense Compared to Niche Competitors

Recent research suggested that plants behave differently under combined versus single abiotic and biotic stress conditions in controlled environments. While this work has provided a glimpse into how plants might behave under complex natural conditions, it also highlights the need for field experiments using established model systems. In nature, diverse microbes colonize the phyllosphere of Arabidopsis thaliana, including the obligate biotroph oomycete genus Albugo, causal agent of the common disease white rust. Biotrophic, as well as hemibiotrophic plant pathogens are characterized by efficient suppression of host defense responses. Lab experiments have even shown that Albugo sp. can suppress non-host resistance, thereby enabling otherwise avirulent pathogen growth. We asked how a pathogen that is vitally dependent on a living host can compete in nature for limited niche space while paradoxically enabling colonization of its host plant for competitors? To address this question, we used a proteomics approach to identify differences and similarities between lab and field samples of Albugo sp.-infected and -uninfected A. thaliana plants. We could identify highly similar apoplastic proteomic profiles in both infected and uninfected plants. In wild plants, however, a broad range of defense-related proteins were detected in the apoplast regardless of infection status, while no or low levels of defense-related proteins were detected in lab samples. These results indicate that Albugo sp. do not strongly affect immune responses and leave distinct branches of the immune signaling network intact. To validate our findings and to get mechanistic insights, we tested a panel of A. thaliana mutant plants with induced or compromised immunity for susceptibility to different biotrophic pathogens. Our findings suggest that the biotroph pathogen Albugo selectively interferes with host defense under different environmental and competitive pressures to maintain its ecological niche dominance. Adaptation to host immune responses while maintaining a partially active host immunity seems advantageous against competitors. We suggest a model for future research that considers not only host–microbe but in addition microbe–microbe and microbe–host environment factors

Custom Distinctions in the Interaction of G-protein β Subunits with N-type (CaV2.2) Versus P/Q-type (CaV2.1) Calcium Channels

Inhibition of N- (Cav2.2) and P/Q-type (Cav2.1) calcium channels by G-proteins contribute importantly to presynaptic inhibition as well as to the effects of opiates and cannabinoids. Accordingly, elucidating the molecular mechanisms underlying G-protein inhibition of voltage-gated calcium channels has been a major research focus. So far, inhibition is thought to result from the interaction of multiple proposed sites with the Gβγ complex (Gβγ). Far less is known about the important interaction sites on Gβγ itself. Here, we developed a novel electrophysiological paradigm, “compound-state willing-reluctant analysis,” to describe Gβγ interaction with N- and P/Q-type channels, and to provide a sensitive and efficient screen for changes in modulatory behavior over a broad range of potentials. The analysis confirmed that the apparent (un)binding kinetics of Gβγ with N-type are twofold slower than with P/Q-type at the voltage extremes, and emphasized that the kinetic discrepancy increases up to ten-fold in the mid-voltage range. To further investigate apparent differences in modulatory behavior, we screened both channels for the effects of single point alanine mutations within four regions of Gβ1, at residues known to interact with Gα. These residues might thereby be expected to interact with channel effectors. Of eight mutations studied, six affected G-protein modulation of both N- and P/Q-type channels to varying degrees, and one had no appreciable effect on either channel. The remaining mutation was remarkable for selective attenuation of effects on P/Q-, but not N-type channels. Surprisingly, this mutation decreased the (un)binding rates without affecting its overall affinity. The latter mutation suggests that the binding surface on Gβγ for N- and P/Q-type channels are different. Also, the manner in which this last mutation affected P/Q-type channels suggests that some residues may be important for “steering” or guiding the protein into the binding pocket, whereas others are important for simply binding to the channel

Exhausting domains of the symmetrized bidisc

We show that the symmetrized bidisc may be exhausted by strongly linearly convex domains. It shows in particular the existence of a strongly linearly convex domain that cannot be exhausted by domains biholomorphic to convex ones.Comment: 6 page

Applications of Hilbert Module Approach to Multivariable Operator Theory

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space \clh associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: $$\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,$$where $p \in \mathbb{C}[z_1, \ldots, z_n]$ and $h \in \mathcal{H}$. A companion survey provides an introduction to the theory of Hilbert modules and some (Hilbert) module point of view to multivariable operator theory. The purpose of this survey is to emphasize algebraic and geometric aspects of Hilbert module approach to operator theory and to survey several applications of the theory of Hilbert modules in multivariable operator theory. The topics which are studied include: generalized canonical models and Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert spaces, a class of simple submodules and quotient modules of the Hardy modules over polydisc, commutant lifting theorem, similarity and free Hilbert modules, left invertible multipliers, inner resolutions, essentially normal Hilbert modules, localizations of free resolutions and rigidity phenomenon. This article is a companion paper to "An Introduction to Hilbert Module Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in Handbook of Operator Theory, Springe

Obtaining deeper insights into microbiome diversity using a simple method to block host and nontargets in amplicon sequencing

Abstract Profiling diverse microbiomes is revolutionizing our understanding of biological mechanisms and ecologically relevant problems, including metaorganism (host + microbiome) assembly, functions and adaptation. Amplicon sequencing of multiple conserved, phylogenetically informative loci has therefore become an instrumental tool for many researchers. Investigations in many systems are hindered, however, since essential sequencing depth can be lost by amplification of nontarget DNA from hosts or overabundant microorganisms. Here, we introduce “blocking oligos”, a low‐cost and flexible method using standard oligonucleotides to block amplification of diverse nontargets and software to aid their design. We apply them primarily in leaves, where exceptional challenges with host amplification prevail. A . thaliana ‐specific blocking oligos applied in eight different target loci reduce undesirable host amplification by up to 90%. To expand applicability, we designed universal 16S and 18S rRNA gene plant blocking oligos for targets that are conserved in diverse plant species and demonstrate that they efficiently block five plant species from five orders spanning monocots and dicots ( Bromus erectus , Plantago lanceolata , Lotus corniculatus , Amaranth sp., Arabidopsis thaliana ). These can increase alpha diversity discovery without biasing beta diversity patterns and do not compromise microbial load information inherent to plant‐derived 16S rRNA gene amplicon sequencing data. Finally, we designed and tested blocking oligos to avoid amplification of 18S rRNA genes of a sporulating oomycete pathogen, demonstrating their effectiveness in applications well beyond plants. Using these tools, we generated a survey of the A . thaliana leaf microbiome based on eight loci targeting bacterial, fungal, oomycete and other eukaryotic microorganisms and discuss complementarity of commonly used amplicon sequencing regions for describing leaf microbiota. This approach has potential to make questions in a variety of study systems more tractable by making amplicon sequencing more targeted, leading to deeper, systems‐based insights into microbial discovery. For fast and easy design for blocking oligos for any nontarget DNA in other study systems, we developed a publicly available R package

Some comments on developments in exact solutions in statistical mechanics since 1944

Lars Onsager and Bruria Kaufman calculated the partition function of the Ising model exactly in 1944 and 1949. Since then there have been many developments in the exact solution of similar, but usually more complicated, models. Here I shall mention a few, and show how some of the latest work seems to be returning once again to the properties observed by Onsager and Kaufman.Comment: 28 pages, 5 figures, section on six-vertex model revise