Fast Response and Temporal Coherent Oscillations in Small-World Networks

Abstract

We have investigated the role that different connectivity regimes play in the dynamics of a network of Hodgkin-Huxley neurons by computer simulations. The different connectivity topologies exhibit the following features: random topologies give rise to fast system response yet are unable to produce coherent oscillations in the average activity of the network; on the other hand, regular topologies give rise to coherent oscillations, but in a temporal scale that is not in accordance with fast signal processing. Finally, small-world topologies, which fall between random and regular ones, take advantage of the best features of both, giving rise to fast system response with coherent oscillations. PACS numbers: 87.18.Sn, 84.35. + i, 87.18.Bb In a recent Letter by Watts and Strogatz [1] it was shown that small-world (SW) networks enhance signalpropagation speed, computational power, and synchronizability. SW stands for a network whose connectivity topology is placed somewhere between a regular and a completely random connectivity. The main properties of these specific networks are that they can be highly clustered like regular networks and, at the same time, have small path lengths like random ones. Therefore, SW networks may have properties given neither in regular nor in random networks [2]. In this Letter we have extended Watts and Strogatz's general framework by introducing dynamical elements in the network nodes. Our source of inspiration is based on a phenomenon observed in the olfactory antennal lobe (AL) of the locust [3]. The AL is a group of around 800 neurons whose functional role is to relay information from the olfactory receptors to higher areas of the brain for further processing. Two main features have been observed in the dynamics of the AL. First, there is a fast response of the AL when the stimulus is presented. Second, when an odor is presented to the insect, coherent oscillations of 20 Hz in the local field potential (LFP) are measured [3]. Summarizing, fast coherent oscillations are observed. There are also other systems in the brain that present coherent LFP oscillations, hence, hinting to the generality of these phenomena (see [4,5]).The cooperative behavior of large assemblies of dynamical elements has been the subject of many investigations [6][7][8][9][10]. In all of them the connectivity between the elements of the network was either regular (local or global all-to-all) or random. However, none of these studies incorporates a comparative analysis of network dynamics for all the different connectivity topologies.In the present work we want to show that in order to provide fast response and coherent oscillations a SW topology is required. Without the coherent oscillations the AL seems to lose its ability to process the information incoming from the sensors [3]. The model we propose for this study is made of an array of nonidentical Hodgkin-Huxley elements coupled by excitatory synapses. The unit dynamics is described by the following set of coupled ordinary differential equations:ᠨ n a n ͑V ...

Robust emergence of small-world structure in networks of spiking neurons

“…Patterns of coherence were studied in HodgkinHuxley neurons (Lago-Fernandez et al 2000;Kwon and Moon 2002) and in networks of Hindmarsh-Rose neurons (Bucolo et al 2002). Synchrony (Masuda and Aihara 2004) and self-sustained dynamic activity (Roxin et al 2004) have been described in small-world network of leaky integrate-and-fire neurons.…”

Natural world physical, brain operational, and mind phenomenal space–time

“…Apparently, the loss of both small-world and scale-free characteristics has been linked to various brain disorders [283][284][285], suggesting that these properties of functional connectivity are important for brain operation. For example, it was shown that networks with smallworld characteristics are able to process information efficiently at both local and global levels [286], give rise to a fast system response with coherent oscillations [287], promote synchronized oscillations [288], allow both functional specialization and global integration, and maintain low wiring costs [281]. It is speculated that exactly these advantages might be the reasons for why these small-world and scale-free characteristics have evolved in the brain during the course of evolution [278].…”

Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling

“…In recent years, neuronal dynamics on complex networks, e.g., small-world (SW) ones [12], has actually become a focal research topic in theoretical neuroscience [14][15][16][17][18][19], and network topology could play vital role in neuronal synchronization or coding dynamics. In this work, we also address such issues by performing similar studies on SW networks.…”

“…For instance, Gaussian white noise can induce coherence resonance in FitzHughNagumo (FHN) and Hodgkin-Huxley (HH) neuronal models [4][5][6], Perc et al [7,8] showed that channel noise in coupled HH neurons can control the spontaneous spike regularity, and the effects of correlated noise on spike coherence and spike firing rate of coupled neurons have also been investigated thoroughly in various neuronal systems [9][10][11] by Kurths. On the other hand, due to the complex topological connections, real neuronal networks often exhibit small-world and scale-free features [12,13], so spatiotemporal dynamics on complex neuronal networks has attracted increasing attention [14][15][16][17]. In previous works, we found that spatial synchronization and temporal coherence, which are practically absent in regular networks, can be greatly enhanced by random shortcuts between the neurons [18][19][20].…”