The complex world of the small brain
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BioMed Central Page 1 of 1 (page number not for citation purposes) BMC Neuroscience Open Access Poster presentation The complex world of the small brain Michelle Rudolph* and Alain Destexhe Address: UNIC, CNRS, Avenue de la Terrasse 1, 91198 Gif-sur-Yvette, France Email: Michelle Rudolph* - [email protected] * Corresponding author Since Stanley Milgram's "six degrees of separation", the interest in the topological structure of network graphs and implications for their functional role experienced a dra- matic surge. 40 years later, small-world and scale-free properties, with the latter being generally viewed as a cru- cial prerequisite for complex dynamical behaviours, are identified as a unifying feature of many real-world net- works. However, the study and characterisation of com- plexity at the level of neuronal populations such as cortical microcircuits, large-scale functional networks or, ultimately, the whole brain still remains a technically and mathematically difficult and, therefore, widely unsolved task. Moreover, recent research shows that small-world and scale-free connectivity are just two out of a vast pleth- ora of applicable graph-theoretical measures to yield a more accurate characterisation of the networks structural or functional properties. In this contribution we provide a detailed comparative characterisation of publicly available brain networks. The latter include structural areal connectivity graphs from the cat cortex, macaque and macaque visual cortex, as well as cellular networks of C. elegans and corresponding subnet- works formed by chemical synapses and gap junctions only. Graph theoretical tools applied include node degree and correlation, edge distance, clustering and cycle, entropy, hierarchical, centrality, spectral and complexity measures, as well as the study of subgraphs and fractal properties. Moreover, extensions of these measures incor- porating weight and spatial information are proposed and applied to graphs where such data were available. Our analysis shows that, first, in agreement with numer- ous previous studies, all investigated systems exhibit small-world properties (i.e. small average geodesic dis- tance and high clustering coefficient) when relational graphs are considered. Second, for many other measures, marked differences (e.g. for efficiency and vulnerability) between the investigated networks were found, thus revealing a rich universe of structural qualities. We argue that the latter forces a re-evaluation of the question about structural prerequisites for functionally complex dynami- cal behaviours. Third, the incorporation of weight and spatial information qualitatively alters some conclusions drawn from the analysis of corresponding relational graphs, thus arguing for a careful re-evaluation of real- world networks in the context weighted and spatial graph theory. In summary, our study suggests that a deeper understand- ing of the functional dynamics and role, and possible dif- ferences in the latter, of neural and brain networks necessitate their detailed structural characterisation beyond small-world and scale-free qualities. Moreover, a detailed graph-theoretical characterisation of structural and functional brain networks will allow to constraint developmental mechanisms which lead to the preference of specific network topologies over others. Finally, study- ing structural and functional patterns on the global scale with the full weight of graph theory could provide an alternative way to argue for complexity as an emergent quality of brain networks which goes beyond a pure description of the wealth of structural and functional properties observed in isolated neural systems. from Sixteenth Annual Computational Neuroscience Meeting: CNS*2007 Toronto, Canada. 7–12 July 2007 Published: 6 July 2007 BMC Neuroscience 2007, 8(Suppl 2):P21 doi:10.1186/1471-2202-8-S2-P21 <supplement> <title> <p>Sixteenth Annual Computational Neuroscience Meeting: CNS*2007</p> </title> <editor>William R Holmes</editor> <note>Meeting abstracts – A single PDF containing all abstracts in this Supplement is available <a href="http:www.biomedcentral.com/content/pdf/1471-2202-8-S2-full.pdf">here</a></note> <url>http://www.biomedcentral.com/content/pdf/1471-2202-8-S2-info.pdf</url> </supplement> © 2007 Rudolph and Destexhe; licensee BioMed Central Ltd.
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Transcript of The complex world of the small brain
BioMed Central
Page 1 of 1(page number not for citation purposes)
BMC Neuroscience
Open AccessPoster presentationThe complex world of the small brainMichelle Rudolph* and Alain Destexhe
Address: UNIC, CNRS, Avenue de la Terrasse 1, 91198 Gif-sur-Yvette, France
Email: Michelle Rudolph* - [email protected]
* Corresponding author
Since Stanley Milgram's "six degrees of separation", theinterest in the topological structure of network graphs andimplications for their functional role experienced a dra-matic surge. 40 years later, small-world and scale-freeproperties, with the latter being generally viewed as a cru-cial prerequisite for complex dynamical behaviours, areidentified as a unifying feature of many real-world net-works. However, the study and characterisation of com-plexity at the level of neuronal populations such ascortical microcircuits, large-scale functional networks or,ultimately, the whole brain still remains a technically andmathematically difficult and, therefore, widely unsolvedtask. Moreover, recent research shows that small-worldand scale-free connectivity are just two out of a vast pleth-ora of applicable graph-theoretical measures to yield amore accurate characterisation of the networks structuralor functional properties.
In this contribution we provide a detailed comparativecharacterisation of publicly available brain networks. Thelatter include structural areal connectivity graphs from thecat cortex, macaque and macaque visual cortex, as well ascellular networks of C. elegans and corresponding subnet-works formed by chemical synapses and gap junctionsonly. Graph theoretical tools applied include node degreeand correlation, edge distance, clustering and cycle,entropy, hierarchical, centrality, spectral and complexitymeasures, as well as the study of subgraphs and fractalproperties. Moreover, extensions of these measures incor-porating weight and spatial information are proposed andapplied to graphs where such data were available.
Our analysis shows that, first, in agreement with numer-ous previous studies, all investigated systems exhibitsmall-world properties (i.e. small average geodesic dis-tance and high clustering coefficient) when relationalgraphs are considered. Second, for many other measures,marked differences (e.g. for efficiency and vulnerability)between the investigated networks were found, thusrevealing a rich universe of structural qualities. We arguethat the latter forces a re-evaluation of the question aboutstructural prerequisites for functionally complex dynami-cal behaviours. Third, the incorporation of weight andspatial information qualitatively alters some conclusionsdrawn from the analysis of corresponding relationalgraphs, thus arguing for a careful re-evaluation of real-world networks in the context weighted and spatial graphtheory.
In summary, our study suggests that a deeper understand-ing of the functional dynamics and role, and possible dif-ferences in the latter, of neural and brain networksnecessitate their detailed structural characterisationbeyond small-world and scale-free qualities. Moreover, adetailed graph-theoretical characterisation of structuraland functional brain networks will allow to constraintdevelopmental mechanisms which lead to the preferenceof specific network topologies over others. Finally, study-ing structural and functional patterns on the global scalewith the full weight of graph theory could provide analternative way to argue for complexity as an emergentquality of brain networks which goes beyond a puredescription of the wealth of structural and functionalproperties observed in isolated neural systems.
from Sixteenth Annual Computational Neuroscience Meeting: CNS*2007Toronto, Canada. 7–12 July 2007
Published: 6 July 2007
BMC Neuroscience 2007, 8(Suppl 2):P21 doi:10.1186/1471-2202-8-S2-P21
<supplement> <title> <p>Sixteenth Annual Computational Neuroscience Meeting: CNS*2007</p> </title> <editor>William R Holmes</editor> <note>Meeting abstracts – A single PDF containing all abstracts in this Supplement is available <a href="http:www.biomedcentral.com/content/pdf/1471-2202-8-S2-full.pdf">here</a></note> <url>http://www.biomedcentral.com/content/pdf/1471-2202-8-S2-info.pdf</url> </supplement>
© 2007 Rudolph and Destexhe; licensee BioMed Central Ltd.
