Sarah Feldt, Paolo Bonifazi and Rosa Cossart
Structure–function studies of neuronal networks have recently benefited from considerable progress in different areas of investigation.
However, bridging the gap between the cellular and behavioral levels will require an understanding ofthe 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.
Slide 4 - Objectives
The objective of this paper is to describe how graph theory provides experimentalists with novel concepts that can be used to describe developing connectivity schemesSlide 5 – Main points
Miles and Wong observed that stimulating a single neuron could trigger network synchronization in disinhibited hippocampal slices. A number of recent studies have reported that stimulation of single neurons can affect population activity in vitro as well as in vivo.
So, the next important step is to understand how specific network can empower single neurons togovern network dynamics.
Slide 7 – Figure 1
Figure 1. Figure to illustrate the network effects derived from stimulation of single-cell and which specific circuits it activates, effecting network dynamics. A) Hippocampal pyramidal cell from guinea pig; b)rodent hippocampal GABAergic interneurons; c) Layer V pyramidal cells from the rat motor cortex; d) neuronal level effect (causing burstmeasured with intracellular and extracellular electrophysiological recordings); e) microcircuit level (it triggered neuronal synchronization); f)behavioral level using in vitro electrophysiology, in vitro imaging and in vivo monitoring of whisker deflections
Slide 8 – Box 1
In general, much work in network science focuses on the structure of the network and how this can give rise to variousfunctions/dynamics.
In this framework, a network is defined by nodes, and links connect the nodes and define structure. Once the network structure of a system has been obtained, many metrics are used to quantify its properties.
Node degree(k): correspond to the total number of its links.
Shortest path length(l): minimal number of links between a pair of nodes. It doesn’t have spatial meaning!Clustering coefficient(C): estimate the density of connections locally between groups of neurons that share common nearest neighbors.
Slide 9 – Box 2
The most commonly investigated network topologies. Here some “kinds” of network topologies are presented.
Scale-free and small-world networks are the two main ones found in biological systems.
Scale-free networks: lack a characteristic scale, includehubs, i.e. rare super-connected nodes that can have a strong impact on the global dynamics.
Regular networks: all of the nodes have the same number of nearest neighbors, and the network has an ordered arrangement, have high density of connections between neighbors and therefore are characterized by high clustering coefficients. The characteristic path length increases as a power of the number ofnodes N.
Random networks: are obtained by distributing a total of m links to N nodes. In contrast to regular
networks, the characteristic path length increases logarithmically (i.e. slowly) with the total number of nodes N. Random networks lack an abundance of local connections, therefore they have a small clustering coefficient.
Small-world networks: share features with regular and randomnetworks. They have dense local connections like regular networks and short characteristic path lengths like random networks. Small-world networks can be obtained by introducing a few random connections within a regular network. These random connections do not interfere with the clustering coefficient but shorten the distance between previously distant nodes.
Slide 10 - Complex network theory...