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

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

On the basis of data from brain network science, Bullmore and Sporns propose that brain organization is shaped by an economical trade-off between minimizing wiring cost and maximizing the efficiency of information transfer between neuronal populations and discuss this idea in the context of psychiatric and neurological disorders. The brain is expensive, incurring high material and metabolic costs for its size — relative to the size of the body — and many aspects of brain network organization can be mostly explained by a parsimonious drive to minimize these costs. However, brain networks or connectomes also have high topological efficiency, robustness, modularity and a 'rich club' of connector hubs. Many of these and other advantageous topological properties will probably entail a wiring-cost premium. We propose that brain organization is shaped by an economic trade-off between minimizing costs and allowing the emergence of adaptively valuable topological patterns of anatomical or functional connectivity between multiple neuronal populations. This process of negotiating, and re-negotiating, trade-offs between wiring cost and topological value continues over long (decades) and short (millisecond) timescales as brain networks evolve, grow and adapt to changing cognitive demands. An economical analysis of neuropsychiatric disorders highlights the vulnerability of the more costly elements of brain networks to pathological attack or abnormal development.

The economy of brain network organization

In electrically nonexcitable cells, Ca2+ influx is essential for regulating a host of kinetically distinct processes involving exocytosis, enzyme control, gene regulation, cell growth and prolifera...

Store-operated calcium channels.

The journal of neuroscience : the official journal of the Society for Neuroscience.

https://www.cell.com/neuron/pdf/S0896-6273(02)00677-3.pdf

The sigma receptor as a ligand-regulated auxiliary potassium channel subunit

https://www.cell.com/trends/neurosciences/pdf/S0166-2236(02)02254-3.pdf

cGMP and S-nitrosylation: two routes for modulation of neuronal excitability by NO.

https://www.cell.com/neuron/pdf/S0896-6273(15)00560-7.pdf

Altered neuronal and circuit excitability in Fragile X Syndrome

FMRP Regulates Neurotransmitter Release and Synaptic Information Transmission by Modulating Action Potential Duration via BK channels

The vesicles that package neurotransmitters fall into two distinct classes, large dense-core vesicles (LDCVs) and small synaptic vesicles, the coexistence of which is widespread in nerve terminals1. High resolution capacitance recording reveals unitary steps proportional to vesicle size. Measurements of capacitance steps during LDCV and secretory granule fusion in endocrine and immune cells have provided important insights into exocytosis2,3,4; however, extending these measurements to small synaptic vesicles has proven difficult. Here we report single vesicle capacitance steps in posterior pituitary nerve terminals. These nerve terminals contain neuropeptide-laden LDCVs, as well as microvesicles. Microvesicles are similar to synaptic vesicles in size, morphology5 and molecular composition6,7,8, but their contents are unknown. Capacitance steps of two characteristic sizes, corresponding with microvesicles and LDCVs, were detected in patches of nerve terminal membrane. Both types of vesicles fuse in response to depolarization-induced Ca2+ entry. Both undergo a reversible fusion process commonly referred to as ‘kiss-and-run’, but only rarely. Fusion pores seen during microvesicle kiss-and-run have a conductance of 19 pS, 11 times smaller than LDCV fusion pores. Thus, LDCVs and microvesicles use structurally different intermediates during exocytosis.

Vitaly A. Klyachko

Papers

The sigma receptor as a ligand-regulated auxiliary potassium channel subunit

cGMP and S-nitrosylation: two routes for modulation of neuronal excitability by NO.

Altered neuronal and circuit excitability in Fragile X Syndrome

FMRP Regulates Neurotransmitter Release and Synaptic Information Transmission by Modulating Action Potential Duration via BK channels

Capacitance steps and fusion pores of small and large-dense-core vesicles in nerve terminals