Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

Complex brain networks: graph theoretical analysis of structural and functional systems

Molecular approaches to understanding the functional circuitry of the nervous system promise new insights into the relationship between genes, brain and behaviour. The cellular diversity of the brain necessitates a cellular resolution approach towards understanding the functional genomics of the nervous system. We describe here an anatomically comprehensive digital atlas containing the expression patterns of approximately 20,000 genes in the adult mouse brain. Data were generated using automated high-throughput procedures for in situ hybridization and data acquisition, and are publicly accessible online. Newly developed image-based informatics tools allow global genome-scale structural analysis and cross-correlation, as well as identification of regionally enriched genes. Unbiased fine-resolution analysis has identified highly specific cellular markers as well as extensive evidence of cellular heterogeneity not evident in classical neuroanatomical atlases. This highly standardized atlas provides an open, primary data resource for a wide variety of further studies concerning brain organization and function.

/pdf/genome-wide-atlas-of-gene-expression-in-the-adult-mouse-2j5ql1rdgm.pdf

Genome-wide atlas of gene expression in the adult mouse brain

Prelude. Cycle 1. Introduction. Cycle 2. Structure defines function. Cycle 3. Diversity of cortical functions is provided by inhibition. Cycle 4. Windows on the brain. Cycle 5. A system of rhythms: from simple to complex dynamics. Cycle 6. Synchronization by oscillation. Cycle 7. The brain's default state: self-organized oscillations in rest and sleep. Cycle 8. Perturbation of the default patterns by experience. Cycle 9. The gamma buzz: gluing by oscillations in the waking brain. Cycle 10. Perceptions and actions are brain state-dependent. Cycle 11. Oscillations in the "other cortex:" navigation in real and memory space. Cycle 12. Coupling of systems by oscillations. Cycle 13. The tough problem. References.

Rhythms of the brain

This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

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Dynamical Systems in Neuroscience

Functional magnetic resonance imaging (fMRI) is currently the mainstay of neuroimaging in cognitive neuroscience. Advances in scanner technology, image acquisition protocols, experimental design, and analysis methods promise to push forward fMRI from mere cartography to the true study of brain organization. However, fundamental questions concerning the interpretation of fMRI data abound, as the conclusions drawn often ignore the actual limitations of the methodology. Here I give an overview of the current state of fMRI, and draw on neuroimaging and physiological data to present the current understanding of the haemodynamic signals and the constraints they impose on neuroimaging data interpretation.

What we can do and what we cannot do with fMRI

The intrastriatal microcircuit is a predominantly inhibitory GABAergic network comprised of a majority of projection neurons [medium spiny neurons (MSNs)] and a minority of interneurons. The connectivity within this microcircuit is divided into two main categories: lateral connectivity between MSNs, and inhibition mediated by interneurons, in particular fast spiking (FS) cells. To understand the operation of striatum, it is essential to have a good description of the dynamic properties of these respective pathways and how they affect different types of striatal projection neurons. We recorded from neuronal pairs, triplets, and quadruplets in slices of rat and mouse striatum and analyzed the dynamics of synaptic transmission between MSNs and FS cells. Retrograde fluorescent labeling and transgenic EGFP (enhanced green fluorescent protein) mice were used to distinguish between MSNs of the direct (striatonigral) and indirect (striatopallidal) pathways. Presynaptic neurons were stimulated with trains of action potentials, and activity-dependent depression and facilitation of synaptic efficacy was recorded from postsynaptic neurons. We found that FS cells provide a strong and homogeneously depressing inhibition of both striatonigral and striatopallidal MSN types. Moreover, individual FS cells are connected to MSNs of both types. In contrast, both MSN types receive sparse and variable, depressing and facilitating synaptic transmission from nearby MSNs. The connection probability was higher for pairs with presynaptic striatopallidal MSNs; however, the variability in synaptic dynamics did not depend on the types of interconnected MSNs. The differences between the two inhibitory pathways were clear in both species and at different developmental stages. Our findings show that the two intrastriatal inhibitory pathways have fundamentally different dynamic properties that are, however, similarly applied to both direct and indirect striatal projections.

/pdf/dynamics-of-synaptic-transmission-between-fast-spiking-5f53373pn7.pdf

Dynamics of Synaptic Transmission between Fast-Spiking Interneurons and Striatal Projection Neurons of the Direct and Indirect Pathways

The neocortex has a high capacity for plasticity. To understand the full scope of this capacity, it is essential to know how neurons choose particular partners to form synaptic connections. By using multineuron whole-cell recordings and confocal microscopy we found that axons of layer V neocortical pyramidal neurons do not preferentially project toward the dendrites of particular neighboring pyramidal neurons; instead, axons promiscuously touch all neighboring dendrites without any bias. Functional synaptic coupling of a small fraction of these neurons is, however, correlated with the existence of synaptic boutons at existing touch sites. These data provide the first direct experimental evidence for a tabula rasa-like structural matrix between neocortical pyramidal neurons and suggests that pre- and postsynaptic interactions shape the conversion between touches and synapses to form specific functional microcircuits. These data also indicate that the local neocortical microcircuit has the potential to be differently rewired without the need for remodeling axonal or dendritic arbors.

https://www.pnas.org/content/pnas/102/3/880.full.pdf

The neocortical microcircuit as a tabula rasa

Multisensory Integration in the Mouse Striatum

Microcircuits in action--from CPGs to neocortex.

Exposure to valproic acid (VPA) during embryogenesis can cause several teratogenic effects, including developmental delays and in particular autism in humans if exposure occurs during the third week of gestation. We examined the postnatal effects of embryonic exposure to VPA on microcircuit properties of juvenile rat neocortex using in vitro electrophysiology. We found that a single prenatal injection of VPA on embryonic day 11.5 causes a significant enhancement of the local recurrent connectivity formed by neocortical pyramidal neurons. The study of the biophysical properties of these connections revealed weaker excitatory synaptic responses. A marked decrease of the intrinsic excitability of pyramidal neurons was also observed. Furthermore, we demonstrate a diminished number of putative synaptic contacts in connection between layer 5 pyramidal neurons. Local hyperconnectivity may render cortical modules more sensitive to stimulation and once activated, more autonomous, isolated, and more difficult to command. This could underlie some of the core symptoms observed in humans prenatally exposed to valproic acid.

/pdf/hyperconnectivity-of-local-neocortical-microcircuitry-54gd9yz6ie.pdf

Gilad Silberberg

Papers

Dynamics of Synaptic Transmission between Fast-Spiking Interneurons and Striatal Projection Neurons of the Direct and Indirect Pathways

The neocortical microcircuit as a tabula rasa

Multisensory Integration in the Mouse Striatum

Microcircuits in action--from CPGs to neocortex.

Hyperconnectivity of Local Neocortical Microcircuitry Induced by Prenatal Exposure to Valproic Acid