On primes in arithmetic progressions and bounded gaps between many primes

We prove that the primes below $x$ are, on average, equidistributed in arithmetic progressions to smooth moduli of size up to $x^{1/2+1/40-\epsilon}$. The exponent of distribution $\tfrac{1}{2} + \tfrac{1}{40}$ improves on a result of Polymath, who had previously obtained the exponent $\tfrac{1}{2} + \tfrac{7}{300}$. As a consequence, we improve results on intervals of bounded length which contain many primes, showing that $\liminf_{n \rightarrow \infty} (p_{n+m}-p_n) = O(\exp(3.8075 m))$. The main new ingredient of our proof is a modification of the q-van der Corput process. It allows us to exploit additional averaging for the exponential sums which appear in the Type I estimates of Polymath.Comment: 40 page

Limiting stochastic processes of shift-periodic dynamical systems

A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display rich dynamical behaviour. The integer parts $\lfloor x_n \rfloor$ give a discrete-time random walk for a suitable initial distribution of $x_0$ and converge in certain limits to Brownian motion or more general L\'evy processes. Furthermore, for certain shift-periodic maps with small holes on $[0,1]$, convergence of trajectories to a continuous-time random walk is shown in a limit.Comment: Submitted to Proceedings of the Royal Society A: Mathematical, Physical & Engineering Science

Der Einfluss des ökologischen Landbaus auf das Raumnutzungsverhalten von Feldhasen (Lepus europaeus)

Agricultural intensification (AI) negatively affects biodiversity due to e.g. high-input farming. Organic farming can counteract this negative trend. Here, we studied movement behavior of the European brown hare (Lepus europaeus), which frequently occurs in agricultural landscapes but also suffers from AI with declining population densities. We measured home range sizes in relation to local field management (organic vs. conventional farming) in Upper Bavarian, Germany. Results showed that home ranges sizes decreased with increasing amount of organically managed area, while there was no relationship between conventional farmed area and hares’ movement behavior. Higher resource availability in organic fields decrease home range sizes and may therefore positively influences individual fitness and possibly boosts hare densities

A synthetic peptide library for benchmarking crosslinking-mass spectrometry search engines for proteins and protein complexes

Crosslinking-mass spectrometry (XL-MS) serves to identify interaction sites between proteins. Numerous search engines for crosslink identification exist, but lack of ground truth samples containing known crosslinks has precluded their systematic validation. Here we report on XL-MS data arising from measuring synthetic peptide libraries that provide the unique benefit of knowing which identified crosslinks are true and which are false. The data are analysed with the most frequently used search engines and the results filtered to an estimated false discovery rate of 5%. We find that the actual false crosslink identification rates range from 2.4 to 32%, depending on the analysis strategy employed. Furthermore, the use of MS-cleavable crosslinkers does not reduce the false discovery rate compared to non-cleavable crosslinkers. We anticipate that the datasets acquired during this research will further drive optimisation and development of XL-MS search engines, thereby advancing our understanding of vital biological interactions

Genome, secretome and glucose transport highlight unique features of the protein production host Pichia pastoris

<p>Abstract</p> <p>Background</p> <p><it>Pichia pastoris </it>is widely used as a production platform for heterologous proteins and model organism for organelle proliferation. Without a published genome sequence available, strain and process development relied mainly on analogies to other, well studied yeasts like <it>Saccharomyces cerevisiae</it>.</p> <p>Results</p> <p>To investigate specific features of growth and protein secretion, we have sequenced the 9.4 Mb genome of the type strain DSMZ 70382 and analyzed the secretome and the sugar transporters. The computationally predicted secretome consists of 88 ORFs. When grown on glucose, only 20 proteins were actually secreted at detectable levels. These data highlight one major feature of <it>P. pastoris</it>, namely the low contamination of heterologous proteins with host cell protein, when applying glucose based expression systems. Putative sugar transporters were identified and compared to those of related yeast species. The genome comprises 2 homologs to <it>S. cerevisiae </it>low affinity transporters and 2 to high affinity transporters of other Crabtree negative yeasts. Contrary to other yeasts, <it>P. pastoris </it>possesses 4 H⁺/glycerol transporters.</p> <p>Conclusion</p> <p>This work highlights significant advantages of using the <it>P. pastoris </it>system with glucose based expression and fermentation strategies. As only few proteins and no proteases are actually secreted on glucose, it becomes evident that cell lysis is the relevant cause of proteolytic degradation of secreted proteins. The endowment with hexose transporters, dominantly of the high affinity type, limits glucose uptake rates and thus overflow metabolism as observed in <it>S. cerevisiae</it>. The presence of 4 genes for glycerol transporters explains the high specific growth rates on this substrate and underlines the suitability of a glycerol/glucose based fermentation strategy. Furthermore, we present an open access web based genome browser <url>http://www.pichiagenome.org</url>.</p

The response to unfolded protein is involved in osmotolerance of Pichia pastoris

Background The effect of osmolarity on cellular physiology has been subject of investigation in many different species. High osmolarity is of importance for biotechnological production processes, where high cell densities and product titers are aspired. Several studies indicated that increased osmolarity of the growth medium can have a beneficial effect on recombinant protein production in different host organisms. Thus, the effect of osmolarity on the cellular physiology of Pichia pastoris, a prominent host for recombinant protein production, was studied in carbon limited chemostat cultures at different osmolarities. Transcriptome and proteome analyses were applied to assess differences upon growth at different osmolarities in both, a wild type strain and an antibody fragment expressing strain. While our main intention was to analyze the effect of different osmolarities on P. pastoris in general, this was complemented by studying it in context with recombinant protein production. Results In contrast to the model yeast Saccharomyces cerevisiae, the main osmolyte in P. pastoris was arabitol rather than glycerol, demonstrating differences in osmotic stress response as well as energy metabolism. 2D Fluorescence Difference Gel electrophoresis and microarray analysis were applied and demonstrated that processes such as protein folding, ribosome biogenesis and cell wall organization were affected by increased osmolarity. These data indicated that upon increased osmolarity less adaptations on both the transcript and protein level occurred in a P. pastoris strain, secreting the Fab fragment, compared with the wild type strain. No transcriptional activation of the high osmolarity glycerol (HOG) pathway was observed at steady state conditions. Furthermore, no change of the specific productivity of recombinant Fab was observed at increased osmolarity. Conclusion These data point out that the physiological response to increased osmolarity is different to S. cerevisiae. Increased osmolarity resulted in an unfolded protein response (UPR) like response in P. pastoris and lead to pre-conditioning of the recombinant Fab producing strain of P. pastoris to growth at high osmolarity. The current data demonstrate a strong similarity of environmental stress response mechanisms and recombinant protein related stresses. Therefore, these results might be used in future strain and bioprocess engineering of this biotechnologically relevant yeast

Expression of MAGE-C1/CT7 and selected cancer/testis antigens in ovarian borderline tumours and primary and recurrent ovarian carcinomas

MAGE-C1/CT7, NY-ESO-1, GAGE and MAGE-A4 are members of the cancer/testis (CT) antigen family, which have been proposed as potential targets for cancer immunotherapy. To determine the prevalence and biologic relevance of the novel CT antigen MAGE-C1/CT7 and other antigens, 36 ovarian borderline tumours (BTs), 230 primary ovarian carcinomas (OCs) and 80 recurrent OCs were immunohistochemically analysed using the monoclonal antibodies CT7-33 (MAGE-C1/CT7), E978 (NY-ESO-1), clone 26 (GAGE) and 57B (MAGE-A4). Positivity of at least one CT antigen was present in 39.5% (81/205) of primary OC and in 50% (26/52) of all recurrences. Expression of the novel CT antigen MAGE-C1/CT7 was most commonly seen with positivity in 24.5% of primary and 35.1% of recurrent OC. MAGE-A4, GAGE and NY-ESO-1 expressions were seen in 22.7, 13.9 and 7.1% of primary and 22.6, 17.5 and 8.9% of recurrent OC, respectively. Analysis of histological subtypes (serous, endometrioid, clear cell, mucinous and transitional) exhibited variable expression with negativity in all mucinous OC. High-grade serous OC revealed CT antigen expression in 5.6 to 28% with MAGE-C1/CT7 being the most frequent, but without correlation with stage or overall survival. MAGE-C1/CT7 expression and coexpression of CT antigens were significantly correlated with grade of endometrioid OC. None of the BT showed CT antigen expression. No significant correlation was seen with stage, overall survival or response to chemotherapy. In summary, CT antigens are expressed in a certain subset of OC with no expression in BT or OC of mucinous histology. These findings may have implications for the design of polyvalent vaccination strategies for ovarian carcinoma