Effect of the Topology and Delayed Interactions in Neuronal Networks Synchronization

Abstract

As important as the intrinsic properties of an individual nervous cell stands the network of neurons in which it is embedded and by virtue of which it acquires great part of its responsiveness and functionality. In this study we have explored how the topological properties and conduction delays of several classes of neural networks affect the capacity of their constituent cells to establish well-defined temporal relations among firing of their action potentials. This ability of a population of neurons to produce and maintain a millisecond-precise coordinated firing (either evoked by external stimuli or internally generated) is central to neural codes exploiting precise spike timing for the representation and communication of information. Our results, based on extensive simulations of conductance-based type of neurons in an oscillatory regime, indicate that only certain topologies of networks allow for a coordinated firing at a local and long-range scale simultaneously. Besides network architecture, axonal conduction delays are also observed to be another important factor in the generation of coherent spiking. We report that such communication latencies not only set the phase difference between the oscillatory activity of remote neural populations but determine whether the interconnected cells can set in any coherent firing at all. In this context, we have also investigated how the balance between the network synchronizing effects and the dispersive drift caused by inhomogeneities in natural firing frequencies across neurons is resolved. Finally, we show that the observed roles of conduction delays and frequency dispersion are not particular to canonical networks but experimentally measured anatomical networks such as the macaque cortical network can display the same type of behavior.

Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses

“…This difference is mainly result from phase slips induced by the time delay. Indeed, the delay-induced multiple synchronization states of neuronal activity are due to an intricate interplay between the inherent dynamics of constituting neurons and the locking between the delay time and the oscillatory period of neuronal spiking (Pérez et al 2011;Wang et al 2008Wang et al , 2009Wang et al , 2010. On the other hand, for both coupling types the local synchronization transition is more profound than the global synchronization transition, as the value of S glob is no larger than 0.5.…”

“…To measure the phase synchronization between neuron i and the set of its neighbors v(i), we calculate the quantity (Pérez et al 2011):…”

“…where t is the period of numerical integration.To measure the global phase synchronization, we first calculate the synchronization degree of neuron i with the rest of the network as (Pérez et al 2011)…”

“…Particularly, the effects of time delay on the synchronization among neurons have been extensively studied, and many interesting phenomena have been reported. It is shown that, as the delay increases, regions of irregular and regular propagating excitatory fronts related to the synchronization transitions appear intermittently in excitable small-world and scale-free neuronal networks (Pérez et al 2011;Wang et al 2008Wang et al , 2009Wang et al , 2010. However, most work has focus on the effect of time delay on the collective dynamics of the whole network; less attention has been given to its impact on the synchronization properties of locally connected neurons, i.e., local synchronization.…”

Neuronal Assembly Dynamics in Supervised and Unsupervised Learning Scenarios

“…Indeed, phase relationships contain a great deal of information on the temporal structure of neural signals, modulate neuron interactions, are associated with cognition and relate to memory formation and retrieval (Izhikevich, 1999;Womelsdorf et al, 2007;Masquelier et al, 2009;Kayser et al, 2009). Moreover, recent works have shown that specific topological properties of local and distant cortical areas support synchronisation despite the inherent axonal conduction delays, thereby providing a substrate upon which neuronal codes relying on precise interspike time can unfold (Vicente et al, 2008;Pérez et al, 2011).…”