Review
Dissecting functional connectivity of neuronal microcircuits: experimental and theoretical insights

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Structure–function studies of neuronal networks have recently benefited from considerable progress in different areas of investigation. Advances in molecular genetics and imaging have allowed for the dissection of neuronal connectivity with unprecedented detail whereas in vivo recordings are providing much needed clues as to how sensory, motor and cognitive function is encoded in neuronal firing. However, bridging the gap between the cellular and behavioral levels will ultimately require an understanding of the functional organization of the underlying neuronal circuits. One way to unravel the complexity of neuronal networks is to understand how their connectivity emerges during brain maturation. In this review, we will describe how graph theory provides experimentalists with novel concepts that can be used to describe and interpret these developing connectivity schemes.

Introduction

More than 20 years ago, Miles and Wong first made a puzzling and seminal observation: stimulating a single neuron could trigger network synchronization in disinhibited hippocampal slices [1]. A number of recent studies have similarly reported that stimulation of single neurons can affect population activity in vitro as well as in vivo 2, 3, 4, 5, 6, 7, 8, 9 (Figure 1). However, there are only a handful of such reports, probably because neurons with the ability to influence network dynamics are rare and/or conditions under which one can observe such phenomenon are specific. Regardless, the direct impact of single neurons on network and behavioral outputs demonstrates the importance of the specific structural and functional organization of the underlying circuitry 2, 7, 8. At this point, the next important step is therefore to understand how specific network structures can empower single neurons to govern network dynamics.

This is a timely issue because the neuroanatomical description of network structure is currently experiencing a new era, fed by recent advances in molecular genetics and light microscopy 10, 11. Novel methods such as optogenetics, heterologous receptor expression and retrogradely transported viral vectors allow both trans-synaptic circuit analysis in addition to targeted and precise control of single-cell firing 12, 13, 14, 15, 16. Parallel to the considerable advances in the description of neuronal network structure, the past decade has seen the emergence of powerful in vivo experimental strategies 17, 18, 19, 20, 21, 22, 23 to study how brain function is encoded in the firing of neuronal assemblies. Although in vivo analysis clearly demonstrates that brain functions might be encoded by specific neuronal activity patterns with characteristic temporal dynamics, information is often still lacking on the detailed neuroanatomical structure of the microcircuits activated during a particular behavioral task [24].

How can the gap between the in vivo exploration of function and fine neuroanatomical description of structure be filled? Complex network theory, a new field of theoretical studies that combines graph theory (structure) and complex systems (dynamics), provides neurobiologists with a framework to interpret structure–function relationships in neuronal networks. Therefore, in this review, we first introduce basic notions of network topology and connectivity to provide shared common definitions to the different areas of expertise. Next, we review applications of complex network theory to neurobiological questions, in particular, by analyzing structure–function relationships in the field of cortical development. We propose that network development provides an interesting and unique environment to dissect how microcircuits are organized to produce function. Because different functional microcircuits tend to develop sequentially, network development offers experimentalists successive temporal windows to observe the impact of individual microcircuits as they develop and give rise to different network dynamics. The application of graph theoretical concepts to these sequential periods allows one to link the structure and function of each microcircuit throughout development. Because, in many aspects, immature networks prefigure the end wiring map of adult circuits, such analyses should also ultimately reveal information about the final organization of mature neuronal networks.

Section snippets

Complex network theory: definitions

Network theory has recently gained much attention through its ability to describe and quantify social, technological and biological systems. In general, much work in network science focuses on the structure of the network and how this can give rise to various functions/dynamics. For example, the structure of social networks has been used to predict the spread of disease through society 25, 26. Furthermore, food webs have been created to understand predator–prey interactions 27, 28, the World

Developing neuronal networks help reveal the organization of adult neuronal connectivity

For several reasons, the study of developing neuronal networks provides conceptual and experimental tools to understand structure from a functional perspective, even in adult systems. First, in many ways, immature networks prefigure the fully developed wiring map of adult circuits because several lines of evidence indicate a strong genetic predetermination at early embryonic stages [73]. For example, it was recently shown that synapses develop specifically among sister excitatory neurons in the

Conclusion

Structure–function studies of neuronal networks are currently experiencing a very stimulating period because new technologies for probing cells and circuits are providing experimentalists with unprecedented access to neuronal physiology and anatomy at different scales and in the most physiological conditions possible. As larger datasets are obtained, the value of theoretical and computational neuroscience will continue to grow. Hence, theoretical and experimental neuroscientists should

Acknowledgments

We are indebted to Dr Jérôme Epsztejn for his major contribution to the initial stages of preparation of this review and for his critical comments. We thank Dr Y. Ben-Ari for critical reading of the review and Dror Kenett for useful suggestions of network analysis software. Research in the Cossart group is supported by grants from the European Research Council (ERC FP7 Young Investigators #242852), the Fondation pour la Recherche Medicale (Equipe FRM 2008), the Fondation Bettencourt Schueller,

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