Faculty of Natural Sciences and Mathematics

Quantitative analysis of the vascular network anatomy is critical for the understanding of the vasculature structure and function. In this study, we have combined microcomputed tomography (microCT) and computational analysis to provide quantitative three-dimensional geometrical and topological characterization of the normal kidney vasculature, and to investigate how 2 core genes of the Wnt/planar cell polarity, Frizzled4 and Frizzled6, affect vascular network morphogenesis. Experiments were performed on frizzled4 (Fzd4-/-) and frizzled6 (Fzd6-/-) deleted mice and littermate controls (WT) perfused with a contrast medium after euthanasia and exsanguination. The kidneys were scanned with a high-resolution (16 μm) microCT imaging system, followed by 3D reconstruction of the arterial vas-culature. Computational treatment includes decomposition of 3D networks based on Diameter-Defined Strahler Order (DDSO). We have calculated quantitative (i) Global scale parameters, such as the volume of the vasculature and its fractal dimension (ii) Structural parameters depending on the DDSO hierarchical levels such as hierarchical ordering, diameter, length and branching angles of the vessel segments, and (iii) Functional parameters such as estimated resistance to blood flow alongside the vascular tree and average density of terminal arterioles. In normal kidneys, fractal dimension was 2.07±0.11 (n = 7), and was significantly lower in Fzd4-/-(1.71±0.04; n = 4), and Fzd6-/-(1.54±0.09; n = 3) kidneys. The DDSO number was 5 in WT and Fzd4-/-, and only 4 in Fzd6-/-. Scaling characteristics such as diameter and length of vessel segments were altered in mutants, whereas bifurcation angles were not different from WT. Fzd4 and Fzd6 deletion increased vessel resistance, calculated using the Hagen-Poiseuille equation, for each DDSO, and decreased the density and the homogeneity of the distal vessel segments. Our results show that our methodology is suitable for 3D quantitative characterization of vascular Funding: Financial support for researchers' mobility: French-Slovenian Hubert-Curien partnership Proteus n˚33325NL Endothelial planar cell polarity and vascular network structure and functionality http://www.campusfrance.org/fr/PHC.

Collective beta cell activity in islets of Langerhans is critical for the supply of insulin within an organism. Even though individual beta cells are intrinsically heterogeneous, the presence of intercellular coupling mechanisms ensures coordinated activity and a well-regulated exocytosis of insulin. In order to get a detailed insight into the functional organization of the syncytium, we applied advanced analytical tools from the realm of complex network theory to uncover the functional connectivity pattern among cells composing the intact islet. The procedure is based on the determination of correlations between long temporal traces obtained from confocal functional multicellular calcium imaging of beta cells stimulated in a stepwise manner with a range of physiological glucose concentrations. Our results revealed that the extracted connectivity networks are sparse for low glucose concentrations, whereas for higher stimulatory levels they become more densely connected. Most importantly, for all ranges of glucose concentration beta cells within the islets form locally clustered functional sub-compartments, thereby indicating that their collective activity profiles exhibit a modular nature. Moreover, we show that the observed non-linear functional relationship between different network metrics and glucose concentration represents a well-balanced setup that parallels physiological insulin release. B eta cells secrete insulin in response to stimulation by energy rich molecules in a regulated manner and play a central role in whole-body energy homeostasis 1. In vivo, beta cells are organized into microorgans called islets of Langerhans. All beta cells of an islet of Langerhans are coupled into a single functional unit by means of the gap junction protein Connexin 36 (Cx36) that allows for electrical coupling and exchange of small signaling molecules between physically adjacent cells. One of these small signaling molecules being calcium ions 2. In this way, a coordinated activity in a large number of cells can be established, thereby leading to a regulated exocytosis of insulin 3,4. The mechanisms that govern insulin secretion at the single-cell level have been studied extensively. An increase in extracellular glucose concentration leads to an increased entry of glucose into the beta cell, an increased metabolic production of ATP and a decrease in the open probability of ATP-sensitive potassium ion channels. Consequently, the beta cell depolarizes and the voltage-sensitive calcium ion channels open to increase the intracellular calcium concentration ([Ca 21 ] i) that triggers the calcium-sensitive exocytosis of insulin granules. This calcium-induced exocytosis is believed to be augmented via a less well known amplifying pathway 5. The changes in membrane potential, [Ca 21 ] i as well as exocytosis occur in the form of synchronous oscillations 6–10. Insulin acting on different target cells in the body subsequently reduces glucose concentration to stop the stimulation of insulin release and prevent hypoglycemia by means of a negative feedback loop. At the tissue level however, the relationship between the collective activity of cell populations and hormone release is not completely understood 11. This is mainly due to the fact that until recently, our ability to study the physiology of many cells simultaneously had largely been limited by the existing experimental methods 12. The investigations of the intercellular communication between beta cells had mostly relied on imaging changes in

We study the functional connectivity patterns between beta cells in islets of Langerhans from mouse pancreas tissue slices. We build up the functional networks on the basis of correlations between calcium dynamics of individual cells, which were recorded by means of confocal laser-scanning calcium imaging. The extracted patterns of pairwise interactions between network cells, i.e. functional connections, are then scrutinized with conventional tools for network analysis. By calculating the network metrics of interest we can characterize the nature of functional connectivity patterns. Here we focus on the functional organization of the beta cell syncytium at different levels of stimulation with glucose. We show that under low glucose concentrations the networks are very sparse and segregated, whereas higher stimulation levels lead to denser and more efficient networks, which however are still quite modular. The proposed methods provide novel insights into the functional mechanisms and...

Nematic liquid crystalline structures within square wells are studied numerically using both Lebwohl-Lasher lattice semimicroscopic and the Landau-de Gennes mesoscopic approach. At lateral boundary wall strong planar anchoring is enforced. The cell thicknesshalong thezCartesian coordinate is assumed to be smaller than the characteristic square well sizeR. Using semimicroscopic modelling we restrict to effectively two-dimensional systems which we study in terms of the tensor nematic order parameter. We consider impact of appropriate nanoparticles (NPs) on nematic configuration for cases whereRbecomes comparable to the biaxial order parameter correlation length. In this case a star-like order reconstruction biaxial profile could be formed in absence of NPs. We demonstrate existence of a rich variety of different nematic structures, including topological defects, which are enabled by presence of appropriate NPs.

Research at the interface of statistical physics, evolutionary game theory, and network science has in the past two decades significantly improved our understanding of cooperation in structured populations. We know that networks with broad-scale degree distributions favor the emergence of robust cooperative clusters, and that temporal networks might preclude defectors to exploit cooperators, provided the later can sever their bad ties soon enough. In recent years, however, research has shifted from single and isolated networks to multilayer and interdependent networks. This has revealed new paths to cooperation, but also opened up new questions that remain to be answered. We here study how assortativity in connections between two different network layers affects public cooperation. The connections between the two layers determine to what extent payoffs in one network influence the payoffs in the other network. We show that assortative linking between the layers—connecting hubs of on...