The Basso-Dixon Formula and Calabi-Yau Geometry

We analyse the family of Calabi-Yau varieties attached to four-point fishnet integrals in two dimensions. We find that the Picard-Fuchs operators for fishnet integrals are exterior powers of the Picard-Fuchs operators for ladder integrals. This implies that the periods of the Calabi-Yau varieties for fishnet integrals can be written as determinants of periods for ladder integrals. The representation theory of the geometric monodromy group plays an important role in this context. We then show how the determinant form of the periods immediately leads to the well-known Basso-Dixon formula for four-point fishnet integrals in two dimensions. Notably, the relation to Calabi-Yau geometry implies that the volume is also expressible via a determinant formula of Basso-Dixon type. Finally, we show how the fishnet integrals can be written in terms of iterated integrals naturally attached to the Calabi-Yau varieties.Comment: 42 page

Critical Kauffman networks under deterministic asynchronous update

We investigate the influence of a deterministic but non-synchronous update on Random Boolean Networks, with a focus on critical networks. Knowing that ``relevant components'' determine the number and length of attractors, we focus on such relevant components and calculate how the length and number of attractors on these components are modified by delays at one or more nodes. The main findings are that attractors decrease in number when there are more delays, and that periods may become very long when delays are not integer multiples of the basic update step.Comment: 8 pages, 3 figures, submitted to a journa

Comparative study on gene set and pathway topology-based enrichment methods

Background Enrichment analysis is a popular approach to identify pathways or sets of genes which are significantly enriched in the context of differentially expressed genes. The traditional gene set enrichment approach considers a pathway as a simple gene list disregarding any knowledge of gene or protein interactions. In contrast, the new group of so called pathway topology-based methods integrates the topological structure of a pathway into the analysis. Methods We comparatively investigated gene set and pathway topology-based enrichment approaches, considering three gene set and four topological methods. These methods were compared in two extensive simulation studies and on a benchmark of 36 real datasets, providing the same pathway input data for all methods. Results In the benchmark data analysis both types of methods showed a comparable ability to detect enriched pathways. The first simulation study was conducted with KEGG pathways, which showed considerable gene overlaps between each other. In this study with original KEGG pathways, none of the topology-based methods outperformed the gene set approach. Therefore, a second simulation study was performed on non-overlapping pathways created by unique gene IDs. Here, methods accounting for pathway topology reached higher accuracy than the gene set methods, however their sensitivity was lower. Conclusions We conducted one of the first comprehensive comparative works on evaluating gene set against pathway topology-based enrichment methods. The topological methods showed better performance in the simulation scenarios with non-overlapping pathways, however, they were not conclusively better in the other scenarios. This suggests that simple gene set approach might be sufficient to detect an enriched pathway under realistic circumstances. Nevertheless, more extensive studies and further benchmark data are needed to systematically evaluate these methods and to assess what gain and cost pathway topology information introduces into enrichment analysis. Both types of methods for enrichment analysis require further improvements in order to deal with the problem of pathway overlaps

Prediction of lethal and synthetically lethal knock-outs in regulatory networks

The complex interactions involved in regulation of a cell's function are captured by its interaction graph. More often than not, detailed knowledge about enhancing or suppressive regulatory influences and cooperative effects is lacking and merely the presence or absence of directed interactions is known. Here we investigate to which extent such reduced information allows to forecast the effect of a knock-out or a combination of knock-outs. Specifically we ask in how far the lethality of eliminating nodes may be predicted by their network centrality, such as degree and betweenness, without knowing the function of the system. The function is taken as the ability to reproduce a fixed point under a discrete Boolean dynamics. We investigate two types of stochastically generated networks: fully random networks and structures grown with a mechanism of node duplication and subsequent divergence of interactions. On all networks we find that the out-degree is a good predictor of the lethality of a single node knock-out. For knock-outs of node pairs, the fraction of successors shared between the two knocked-out nodes (out-overlap) is a good predictor of synthetic lethality. Out-degree and out-overlap are locally defined and computationally simple centrality measures that provide a predictive power close to the optimal predictor.Comment: published version, 10 pages, 6 figures, 2 tables; supplement at http://www.bioinf.uni-leipzig.de/publications/supplements/11-01

The formalin test does not probe inflammatory pain but excitotoxicity in rodent skin

Abstract The most widely used formalin test to screen antinociceptive drug candidates is still apostrophized as targeting inflammatory pain, in spite of strong opposing evidence published. In our rat skin‐nerve preparation ex vivo, recording from all classes of sensory single‐fibers (n = 32), 30 units were transiently excited by formaldehyde concentrations 1–100 mM applied to receptive fields (RFs) for 3 min, C and Aδ‐fibers being more sensitive (1–30 mM) than Aβ−fibers. From 30 mM on, ~1% of the concentration usually injected in vivo, all RFs were defunctionalized and conduction in an isolated sciatic nerve preparation was irreversibly blocked. Thus, formaldehyde, generated a state of ‘anesthesia dolorosa’ in the RFs in so far as after a quiescent interphase all fibers with unmyelinated terminals developed a second phase of vigorous discharge activity which correlated well in time course and magnitude with published pain‐related behaviors. Sural nerve filament recordings in vivo confirmed that higher formalin concentrations (> 42 mM) have to be injected to the skin to induce this second phase of discharge. Patch‐clamp and calcium‐imaging confirmed TRPA1 as the primary transducer of formaldehyde (10 mM) effects on mouse sensory neurons. However, stimulated CGRP release from isolated skin of TRPA1+/+ and TRPA1–/– mice showed a convergence of the saturating concentration‐response curves at 100 mM formaldehyde, which did not occur with nerve and trachea preparations. Finally, skin‐nerve recordings from C and Aδ‐fibers of TRPA1–/– mice revealed a massive reduction in formaldehyde (30 mM)‐evoked discharge. However, the remaining activity was still biphasic, thus confirming additional unspecific excitotoxic actions of the fixative that diffuses along still excitable axons as previously published. The multiplicity of formaldehyde's actions requires extensive discussion and literature review, leading to a fundamental reevaluation of the formalin test

Crystallization dynamics and interface stability of strontium titanate thin films on silicon

Different physical vapor deposition methods have been used to fabricate strontium titanate thin films. Within the binary phase diagram of SrO and TiO2 the stoichiometry ranges from Ti rich to Sr rich, respectively. The crystallization of these amorphous SrTiO3 layers is investigated by in situ grazing-incidence X-ray diffraction using synchrotron radiation. The crystallization dynamics and evolution of the lattice constants as well as crystallite sizes of the SrTiO3 layers were determined for temperatures up to 1223 K under atmospheric conditions applying different heating rates. At approximately 473 K, crystallization of perovskite-type SrTiO3 is initiated for Sr-rich electron beam evaporated layers, whereas Sr-depleted sputter-deposited thin films crystallize at 739 K. During annealing, a significant diffusion of Si from the substrate into the SrTiO3 layers occurs in the case of Sr-rich composition. This leads to the formation of secondary silicate phases which are observed by X-ray diffraction, transmission electron microscopy and X-ray photoelectron spectroscopy

Carcinoma cells misuse the host tissue damage response to invade the brain

The metastatic colonization of the brain by carcinoma cells is still barely understood, in particular when considering interactions with the host tissue. The colonization comes with a substantial destruction of the surrounding host tissue. This leads to activation of damage responses by resident innate immune cells to protect, repair, and organize the wound healing, but may distract from tumoricidal actions. We recently demonstrated that microglia, innate immune cells of the CNS, assist carcinoma cell invasion. Here we report that this is a fatal side effect of a physiological damage response of the brain tissue. In a brain slice coculture model, contact with both benign and malignant epithelial cells induced a response by microglia and astrocytes comparable to that seen at the interface of human cerebral metastases. While the glial damage response intended to protect the brain from intrusion of benign epithelial cells by inducing apoptosis, it proved ineffective against various malignant cell types. They did not undergo apoptosis and actually exploited the local tissue reaction to invade instead. Gene expression and functional analyses revealed that the C-X-C chemokine receptor type 4 (CXCR4) and WNT signaling were involved in this process. Furthermore, CXCR4-regulated microglia were recruited to sites of brain injury in a zebrafish model and CXCR4 was expressed in human stroke patients, suggesting a conserved role in damage responses to various types of brain injuries. Together, our findings point to a detrimental misuse of the glial damage response program by carcinoma cells resistant to glia-induced apoptosis

BDNF: mRNA expression in urine cells of patients with chronic kidney disease and its role in kidney function

Podocyte loss and changes to the complex morphology are major causes of chronic kidney disease (CKD). As the incidence is continuously increasing over the last decades without sufficient treatment, it is important to find predicting biomarkers. Therefore, we measured urinary mRNA levels of podocyte genes NPHS1, NPHS2, PODXL and BDNF, KIM-1, CTSL by qRT-PCR of 120 CKD patients. We showed a strong correlation between BDNF and the kidney injury marker KIM-1, which were also correlated with NPHS1, suggesting podocytes as a contributing source. In human biopsies, BDNF was localized in the cell body and major processes of podocytes. In glomeruli of diabetic nephropathy patients, we found a strong BDNF signal in the remaining podocytes. An inhibition of the BDNF receptor TrkB resulted in enhanced podocyte dedifferentiation. The knockdown of the orthologue resulted in pericardial oedema formation and lowered viability of zebrafish larvae. We found an enlarged Bowman's space, dilated glomerular capillaries, podocyte loss and an impaired glomerular filtration. We demonstrated that BDNF is essential for glomerular development, morphology and function and the expression of BDNF and KIM-1 is highly correlated in urine cells of CKD patients. Therefore, BDNF mRNA in urine cells could serve as a potential CKD biomarker