On the spectrum of hypergraphs

Here we study the spectral properties of an underlying weighted graph of a non-uniform hypergraph by introducing different connectivity matrices, such as adjacency, Laplacian and normalized Laplacian matrices. We show that different structural properties of a hypergrpah, can be well studied using spectral properties of these matrices. Connectivity of a hypergraph is also investigated by the eigenvalues of these operators. Spectral radii of the same are bounded by the degrees of a hypergraph. The diameter of a hypergraph is also bounded by the eigenvalues of its connectivity matrices. We characterize different properties of a regular hypergraph characterized by the spectrum. Strong (vertex) chromatic number of a hypergraph is bounded by the eigenvalues. Cheeger constant on a hypergraph is defined and we show that it can be bounded by the smallest nontrivial eigenvalues of Laplacian matrix and normalized Laplacian matrix, respectively, of a connected hypergraph. We also show an approach to study random walk on a (non-uniform) hypergraph that can be performed by analyzing the spectrum of transition probability operator which is defined on that hypergraph. Ricci curvature on hypergraphs is introduced in two different ways. We show that if the Laplace operator, $\Delta$, on a hypergraph satisfies a curvature-dimension type inequality $CD (\mathbf{m}, \mathbf{K})$ with $\mathbf{m}>1$ and $\mathbf{K}>0$ then any non-zero eigenvalue of $- \Delta$ can be bounded below by $\frac{ \mathbf{m} \mathbf{K}}{ \mathbf{m} -1 }$. Eigenvalues of a normalized Laplacian operator defined on a connected hypergraph can be bounded by the Ollivier's Ricci curvature of the hypergraph

Experimentally increased group diversity improves disease resistance in an ant species.

A leading hypothesis linking parasites to social evolution is that more genetically diverse social groups better resist parasites. Moreover, group diversity can encompass factors other than genetic variation that may also influence disease resistance. Here, we tested whether group diversity improved disease resistance in an ant species with natural variation in colony queen number. We formed experimental groups of workers and challenged them with the fungal parasite Metarhizium anisopliae. Workers originating from monogynous colonies (headed by a single queen and with low genetic diversity) had higher survival than workers originating from polygynous ones, both in uninfected groups and in groups challenged with M. anisopliae. However, an experimental increase of group diversity by mixing workers originating from monogynous colonies strongly increased the survival of workers challenged with M. anisopliae, whereas it tended to decrease their survival in absence of infection. This experiment suggests that group diversity, be it genetic or environmental, improves the mean resistance of group members to the fungal infection, probably through the sharing of physiological or behavioural defences

Affinity purification of label-free tubulins from xenopus egg extracts

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Reusch, S., Biswas, A., Hirst, W. G., & Reber, S. Affinity purification of label-free tubulins from xenopus egg extracts. STAR Protocols, 1(3), (2020): 100151, doi:10.1016/j.xpro.2020.100151.Cytoplasmic extracts from unfertilized Xenopus eggs have made important contributions to our understanding of microtubule dynamics, spindle assembly, and scaling. Until recently, these in vitro studies relied on the use of heterologous tubulin. This protocol allows for the purification of physiologically relevant Xenopus tubulins in milligram yield, which are a complex mixture of isoforms with various post-translational modifications. The protocol is applicable to any cell or tissue of interest. For complete details on the use and execution of this protocol, please refer to Hirst et al. (2020).This article was prompted by our stay at the Marine Biological Laboratory (MBL), Woods Hole, MA, in the summer of 2016 funded by the Princeton-Humboldt Strategic Partnership Grant together with the lab of Sabine Petry (Princeton University). We are grateful to the National Xenopus Resource (NXR) for supplying frogs. For mass spectrometry, we would like to acknowledge the assistance of Benno Kuropka and Chris Weise from the Core Facility BioSupraMol supported by the Deutsche Forschungsgemeinschaft (DFG). We thank the Protein Expression Purification and Characterization (PEPC) facility at the MPI-CBG; in particular, we thank Aliona Bogdanova and Barbara Borgonovo. We thank all former and current members of the Reber lab for discussions and helpful advice, in particular Christoph Hentschel and Soma Zsoter for technical assistance. S.R. acknowledges funding from the IRI Life Sciences (Humboldt-Universität zu Berlin, Excellence Initiative/DFG). W.H. was supported by the Alliance Berlin Canberra co-funded by a grant from the Deutsche Forschungsgemeinschaft (DFG) for the International Research Training Group (IRTG) 2290 and the Australian National University

Acute influence of cigarette smoke in platelets, catecholamines and neurophysins in the normal conditions of daily life

Cigarette smoking is firmly linked to the occurrence of acute coronary events. In twenty-two healthy volunteers in normal conditions of daily life we studied the acute influence of smoking on the following parameters: beta-thromboglobulin, thromboxane B2, epinephrine, norepinephrine, estrogen-stimulated neurophysin, and nicotine-stimulated-neurophysin. Our results show that in our population and following our protocol, smoking did not induce platelet activation, thromboxane formation, catecholamine release or estrogen-stimulated-neurophysin secretion. However, smoking did provoke a significant increase of nicotine-stimulated-neurophysin (p<0.05) which reflects vasopressin increase and which might explain the high incidence of ischaemic accidents in cigarette smoking via the vasoactive properties of vasopressi

Differences in intrinsic tubulin dynamic properties contribute to spindle length control in Xenopus species

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Hirst, W. G., Biswas, A., Mahalingan, K. K., & Reber, S. Differences in intrinsic tubulin dynamic properties contribute to spindle length control in Xenopus species. Current Biology, 30(11), (2020): 2184-2190.e5, doi: 10.1016/j.cub.2020.03.067.The function of cellular organelles relates not only to their molecular composition but also to their size. However, how the size of dynamic mesoscale structures is established and maintained remains poorly understood [1, 2, 3]. Mitotic spindle length, for example, varies several-fold among cell types and among different organisms [4]. Although most studies on spindle size control focus on changes in proteins that regulate microtubule dynamics [5, 6, 7, 8], the contribution of the spindle’s main building block, the αβ-tubulin heterodimer, has yet to be studied. Apart from microtubule-associated proteins and motors, two factors have been shown to contribute to the heterogeneity of microtubule dynamics: tubulin isoform composition [9, 10] and post-translational modifications [11]. In the past, studying the contribution of tubulin and microtubules to spindle assembly has been limited by the fact that physiologically relevant tubulins were not available. Here, we show that tubulins purified from two closely related frogs, Xenopus laevis and Xenopus tropicalis, have surprisingly different microtubule dynamics in vitro. X. laevis microtubules combine very fast growth and infrequent catastrophes. In contrast, X. tropicalis microtubules grow slower and catastrophe more frequently. We show that spindle length and microtubule mass can be controlled by titrating the ratios of the tubulins from the two frog species. Furthermore, we combine our in vitro reconstitution assay and egg extract experiments with computational modeling to show that differences in intrinsic properties of different tubulins contribute to the control of microtubule mass and therefore set steady-state spindle length.This article was prompted by our stay at the Marine Biological Laboratory (MBL), Woods Hole, MA in the summer of 2016 funded by the Princeton-Humboldt Strategic Partnership Grant together with the lab of Sabine Petry (Princeton University). We thank Jeff Woodruff (UT Southwestern), David Drechsel (IMP), and Marcus J. Taylor (MPI IB) for constructive criticism and comments on the manuscript and Helena Jambor for constructive comments on figure design. We thank the AMBIO imaging facility (Charité, Berlin) and Nikon at MBL for imaging support, Aliona Bogdanova and Barbara Borgonovo (MPI CBG) for their help with protein purification, and Francois Nedelec (University of Cambridge) for help with Cytosim. We are grateful to the Görlich lab (MPI BPC), in particular Bastian Hülsmann and Jens Krull, and the NXR for supply with X. tropicalis frogs. We thank Antonina Roll-Mecak (National Institute of Neurological Disorders and Stroke) for help with mass spectrometry analysis and discussions and Duck-Yeon Lee in the Biochemistry Core (National Heart, Lung and Blood Institute) for access to mass spectrometers. For mass spectrometry, we would like to acknowledge the assistance of Benno Kuropka and Chris Weise from the Core Facility BioSupraMol supported by the Deutsche Forschungsgemeinschaft (DFG). We thank all former and current members of the Reber lab for discussion and helpful advice, in particular, Christoph Hentschel and Soma Zsoter for technical assistance and Sebastian Reusch for help with tubulin purification. S.R. acknowledges funding from the IRI Life Sciences (Humboldt-Universität zu Berlin, Excellence Initiative/DFG). W.G.H. was supported by the Alliance Berlin Canberra co-funded by a grant from the Deutsche Forschungsgemeinschaft (DFG) for the International Research Training Group (IRTG) 2290 and the Australian National University. K.K.M. was supported by funds in the Roll-Mecak lab, intramural program of the National Institute of Neurological Disorders and Stroke

Using Regular Languages to Explore the Representational Capacity of Recurrent Neural Architectures

The presence of Long Distance Dependencies (LDDs) in sequential data poses significant challenges for computational models. Various recurrent neural architectures have been designed to mitigate this issue. In order to test these state-of-the-art architectures, there is growing need for rich benchmarking datasets. However, one of the drawbacks of existing datasets is the lack of experimental control with regards to the presence and/or degree of LDDs. This lack of control limits the analysis of model performance in relation to the specific challenge posed by LDDs. One way to address this is to use synthetic data having the properties of subregular languages. The degree of LDDs within the generated data can be controlled through the k parameter, length of the generated strings, and by choosing appropriate forbidden strings. In this paper, we explore the capacity of different RNN extensions to model LDDs, by evaluating these models on a sequence of SPk synthesized datasets, where each subsequent dataset exhibits a longer degree of LDD. Even though SPk are simple languages, the presence of LDDs does have significant impact on the performance of recurrent neural architectures, thus making them prime candidate in benchmarking tasks.Comment: International Conference of Artificial Neural Networks (ICANN) 201

In Vitro reconstitution and imaging of microtubule dynamics by fluorescence and label-free microscopy

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Hirst, W. G., Kiefer, C., Abdosamadi, M. K., Schäffer, E., & Reber, S. In Vitro reconstitution and imaging of microtubule dynamics by fluorescence and label-free microscopy. STAR Protocols, 1(3), (2020): 100177, doi:10.1016/j.xpro.2020.100177.Dynamic microtubules are essential for many processes in the lives of eukaryotic cells. To study and understand the mechanisms of microtubule dynamics and regulation, in vitro reconstitution with purified components has proven a vital approach. Imaging microtubule dynamics can be instructive for a given species, isoform composition, or biochemical modification. Here, we describe two methods that visualize microtubule dynamics at high speed and high contrast: (1) total internal reflection fluorescence microscopy and (2) label-free interference reflection microscopy.We thank the AMBIO imaging facility (Charité, Berlin) and Nikon at MBL for imaging support. We thank all former and current members of the Reber lab for discussion and helpful advice, in particular Christoph Hentschel and Soma Zsoter for technical assistance. S.R. acknowledges funding by the IRI Life Sciences (Humboldt-Universität zu Berlin, Excellence Initiative/DFG). W.H. was supported by the Alliance Berlin Canberra co-funded by a grant from the Deutsche Forschungsgemeinschaft (DFG) for the International Research Training Group (IRTG) 2290 and the Australian National University. C.K. thanks the Deutsche Forschungsgesellschaft (DFG, JA 2589/1-1). C.K. and M.A. thank Steve Simmert and Tobias Jachowski former and current members of the Schäffer lab