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Dancing Neurons

How the synaptic connections in a spiking neural network influence its dynamics

Dancing Neurons

See text for caption. Source: Staatliche Kunsthalle Karlsruhe

Understanding the dynamic processes that evolve in brain networks requires an exact knowledge of their network architecture. Regarding the circuit layout of their synaptic connections such networks could be organized in many different ways: There are “random” networks where neurons wire up with other neurons haphazardly, whereas in “assortative” networks there exist hub neurons with more connections than most others, and with a preference to hook up with other hubs. Comparing such network topologies, Stojan Jovanović and Prof. Dr. Stefan Rotter from the Bernstein Center Freiburg and the cluster of excellence BrainLinks-BrainTools showed in their recent computational study how specific forms of connectivity influence the strength of what is called “third-order correlations”. These correlations quantify the statistical relations in groups of three neurons that coordinate their action potentials, as dancers would do when they coordinate their steps. Applying a mathematical model known as the Hawkes process, they were able to successfully compute the level of such correlations in networks of known topology, comprising both excitatory and inhibitory neurons. This result helps to understand how network topology determines the activity dynamics of brain networks, which is the basis of all brain functions including sensory processing, movement control, and abstract problem solving.

"In groups of three neurons with synchronized action potentials, third-order correlations measure the abundance of coordinated spike triplets,” says Jovanović. “We specifically asked what level of synchrony would arise considering the way in which neurons are connected.” For this purpose, the researchers looked at two very distinct models of network topology: The first was a random “Erdős-Rényi” type network, in which each connection between a pair of cells is established independently of all the others, with a specific given probability. The other one was an assortative network with a rich-club topology as described above. Using recent results from the theory of Hawkes processes, they found that in random networks the level of third-order correlations can be mathematically determined on the basis of some global parameters, like the connection probability and the average strength of coupling. “In networks with cliques of hubs, on the other hand, making any kind of prediction about the level of third-order synchrony requires knowing more details about the connectivity,” Jovanović concludes. As many biological phenomena can be viewed as dynamical processes on a graph, understanding the coordinated activity of nodes (“dancing neurons”) in such a network is of great importance, as it helps to characterize and understand the behavior of a very complex system – our brain.
 
Original Publication:
 
Image Caption:
The painting Children Dancing in a Ring by Hans Thoma (1839–1924) provides a metaphorical illustration of higher-order correlations in neural networks: Neurons can – like in a dance – organize themselves dynamically as a group. 
 
 
Contact:
Prof. Dr. Stefan Rotter
Managing Director, Bernstein Center Freiburg
Faculty of Biology
University of Freiburg
Phone: +49 (0)761 203 9316
Fax: +49 (0)761 203 9559 
E-mail: stefan.rotter@biologie.uni-freiburg.de
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