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.
Highlights
A self-organized coordination between individual agents is often the hallmark of many natural and man-made complex systems
Numerical studies have incorporated the features of nonhomogeneities and complex network structures into the analysis of neuronal populations
We study the effect that the rewiring probability and the number of connected neighbors have on the synchronization of the system
Summary
A self-organized coordination between individual agents is often the hallmark of many natural and man-made complex systems. There is experimental evidence for rhythmic and correlated firing of neurons, the functional role of such collective dynamics is still at debate [4]. To elucidate this question it is necessary to describe the parameter space and the mechanisms underlying the variety of neuronal oscillations and synchrony that has been reported [5]. The exact conditions under which large populations of neurons spontaneously synchronize are in general not fully understood, even in the non-delayed coupling case In the latter case, Mirollo and Strogatz analytically demonstrated that synchrony can be a stable state for a population of globally pulse-coupled oscillators [6]. The detailed role of the nodes degree distribution, long range connections, average path length, and clustering on the level of synchronization and oscillatory behavior of the network have been addressed [7,8,9]
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