Mapping the detailed connectivity patterns of neural circuits is a central goal of neuroscience and has been the focus of extensive current research [4, 3]. The best quantitative approach to analyze the acquired data is still unclear but graph theory has been used with success [3, 1]. We present a graph theoretical model with vertices and edges representing neurons and synaptic connections, respectively. Our system is the zebrafish posterior lateral line sensorimotor pathway. The goal of our analysis is to elucidate mechanisms of information processing in this neural pathway by comparing the mathematical properties of its graph to those of other, previously described graphs. We create a zebrafish model based on currently known anatomical data. The degree distributions and small‐world measures of this model is compared to small‐world, random and 3‐compartment random graphs of the same size (with over 2500 nodes and 160,000 connections). We find that the zebrafish graph shows small‐worldness similar to other neural networks and does not have a scale‐free distribution of connections.
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30 November 2011
ADVANCES IN MATHEMATICAL AND COMPUTATIONAL METHODS: ADDRESSING MODERN CHALLENGES OF SCIENCE, TECHNOLOGY, AND SOCIETY
25–29 July 2011
Waterloo, (Canada)
Research Article|
November 30 2011
Computational Graph Theoretical Model of the Zebrafish Sensorimotor Pathway
Joshua M. Peterson;
Joshua M. Peterson
aDepartment of Mathematics, Humboldt State University, 1 Harpst St, Arcata, CA 95521
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Michael Stobb;
Michael Stobb
aDepartment of Mathematics, Humboldt State University, 1 Harpst St, Arcata, CA 95521
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Bori Mazzag;
Bori Mazzag
aDepartment of Mathematics, Humboldt State University, 1 Harpst St, Arcata, CA 95521
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Ethan Gahtan
Ethan Gahtan
bDepartment of Psychology, Humboldt State University, 1 Harpst St, Arcata, CA 95521
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AIP Conf. Proc. 1368, 139–142 (2011)
Citation
Joshua M. Peterson, Michael Stobb, Bori Mazzag, Ethan Gahtan; Computational Graph Theoretical Model of the Zebrafish Sensorimotor Pathway. AIP Conf. Proc. 30 November 2011; 1368 (1): 139–142. https://doi.org/10.1063/1.3663479
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