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      Functional Connectivity in Islets of Langerhans from Mouse Pancreas Tissue Slices

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          Abstract

          We propose a network representation of electrically coupled beta cells in islets of Langerhans. Beta cells are functionally connected on the basis of correlations between calcium dynamics of individual cells, obtained by means of confocal laser-scanning calcium imaging in islets from acute mouse pancreas tissue slices. Obtained functional networks are analyzed in the light of known structural and physiological properties of islets. Focusing on the temporal evolution of the network under stimulation with glucose, we show that the dynamics are more correlated under stimulation than under non-stimulated conditions and that the highest overall correlation, largely independent of Euclidean distances between cells, is observed in the activation and deactivation phases when cells are driven by the external stimulus. Moreover, we find that the range of interactions in networks during activity shows a clear dependence on the Euclidean distance, lending support to previous observations that beta cells are synchronized via calcium waves spreading throughout islets. Most interestingly, the functional connectivity patterns between beta cells exhibit small-world properties, suggesting that beta cells do not form a homogeneous geometric network but are connected in a functionally more efficient way. Presented results provide support for the existing knowledge of beta cell physiology from a network perspective and shed important new light on the functional organization of beta cell syncitia whose structural topology is probably not as trivial as believed so far.

          Author Summary

          Complex network theory has provided new tools for studying the structure and function of complex systems. A particularly attractive avenue in this context is the analysis of biological systems, since structural principles of complex networks have been identified at all scales of functioning of living organisms. In the present paper, we propose a construction of a complex network representation of pancreatic islets of Langerhans. In this microorgan, interconnected beta cells produce and secrete insulin, an anabolic hormone that controls the level of nutrients in the blood. We determine the functional connectivity on the basis of patterns of correlations between experimentally measured calcium dynamics in individual beta cells. The extracted pattern of pairwise interactions between network elements, i.e. beta cells, is then scrutinized with conventional tools for network analysis. Our findings are largely reconcilable with known structural and functional properties but also point to the presence of unexpected small-world attributes that appear to represent a general organizational principle of the functional connectivity between beta cells. We argue that complex network analysis applied to islets of Langerhans is a valuable new tool in the physiologist's analytical repertoire, and in the future it could help deepen our understanding of their physiology.

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          Emergence of scaling in random networks

          Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites. A model based on these two ingredients reproduces the observed stationary scale-free distributions, indicating that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
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            Lethality and centrality in protein networks

            In this paper we present the first mathematical analysis of the protein interaction network found in the yeast, S. cerevisiae. We show that, (a) the identified protein network display a characteristic scale-free topology that demonstrate striking similarity to the inherent organization of metabolic networks in particular, and to that of robust and error-tolerant networks in general. (b) the likelihood that deletion of an individual gene product will prove lethal for the yeast cell clearly correlates with the number of interactions the protein has, meaning that highly-connected proteins are more likely to prove essential than proteins with low number of links to other proteins. These results suggest that a scale-free architecture is a generic property of cellular networks attributable to universal self-organizing principles of robust and error-tolerant networks and that will likely to represent a generic topology for protein-protein interactions.
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              Emergence of scaling in random networks

              Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                February 2013
                February 2013
                28 February 2013
                : 9
                : 2
                : e1002923
                Affiliations
                [1 ]Institute of Physiology, Faculty of Medicine, University of Maribor, Maribor, Slovenia
                [2 ]Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia
                [3 ]Faculty of Civil Engineering, University of Maribor, Maribor, Slovenia
                [4 ]Faculty of Education, University of Maribor, Maribor, Slovenia
                [5 ]CIPKeBiP-Centre of Excellence for Integrated Approaches in Chemistry and Biology of Proteins, Ljubljana, Slovenia
                [6 ]CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Maribor, Slovenia
                Princeton University, United States of America
                Author notes

                The authors have declared that no competing interests exist.

                Conceived and designed the experiments: AS MG JD MSR DK. Performed the experiments: AS JD. Analyzed the data: AS MG JD. Contributed reagents/materials/analysis tools: AS MG MP MSR. Wrote the paper: AS MG JD MP MM MSR DK.

                Article
                PCOMPBIOL-D-12-01156
                10.1371/journal.pcbi.1002923
                3585390
                23468610
                e12fa0f0-ff84-471b-bec7-3f74f8265346
                Copyright @ 2013

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 17 July 2012
                : 28 December 2012
                Page count
                Pages: 12
                Funding
                This work was supported by the Slovenian Research Agency Program P3-0310-2334, grant J1―4055, and Grant J3-2290-2334, MPG Partner Group Program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Mathematics
                Applied Mathematics
                Complex Systems
                Topology
                Medicine
                Anatomy and Physiology
                Endocrine System
                Endocrine Physiology
                Physiological Processes
                Homeostasis
                Endocrinology

                Quantitative & Systems biology
                Quantitative & Systems biology

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