Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays

Abstract

Multielectrode recordings have revealed zero time lag synchronization among remote cerebral cortical areas. However, the axonal conduction delays among such distant regions can amount to several tens of milliseconds. It is still unclear which mechanism is giving rise to isochronous discharge of widely distributed neurons, despite such latencies. Here, we investigate the synchronization properties of a simple network motif and found that, even in the presence of large axonal conduction delays, distant neuronal populations self-organize into lag-free oscillations. According to our results, cortico-cortical association fibers and certain corticothalamo-cortical loops represent ideal circuits to circumvent the phase shifts and time lags associated with conduction delays.thalamocortical system ͉ isochronous oscillations ͉ phase locking ͉ long-range synchronization ͉ axonal latency C ells in the visual cortex of mammals tend to fire simultaneously when activated by related features of a visual stimulus (1-4). This observation provided some of the early evidence that the nervous system may use an internal temporal code to process information. Since then, multicell electrophysiological studies have revealed the synchronous discharge of neurons distributed in different structures of the cerebral cortex, hippocampal formation, and thalamus (5, 6). Its biological significance derives from the observation that such precise and coordinated spike timing correlates with perception and behavioral performance (7-10). Remarkably, synchrony of neuronal activity is not limited to short-range interactions within a cortical patch. Interareal synchronization across cortical regions including interhemispheric areas has been observed in several tasks (7,9,(11)(12)(13)(14). The topological specificity and temporal unfolding of the synchrony reported in such studies are in agreement with its assumed role of subserving the effective ''coupling'' of the neuronal dynamics of the respective regions (9, 15).Beyond its functional relevance, the zero time lag synchrony among such distant neuronal ensembles must be established by mechanisms that are able to compensate for the delays involved in the neuronal communication. Latencies in conducting nerve impulses down axonal processes can amount to delays of several tens of milliseconds between the generation of a spike in a presynaptic cell and the elicitation of a postsynaptic potential (16). The question is how, despite such temporal delays, the reciprocal interactions between two brain regions can lead to the associated neural populations to fire in unison.Direct cortico-cortical fibers are major pathways of transareal communication and thus one principal substrate for the establishment of long-range synchrony. For instance, severing the corpus callosum was observed to disrupt the interhemispheric synchrony among homotopic cortical areas 17 in the cat (17). However, it is not clear whether direct excitatory corticocortical connections alone can mediate the zero phase synchronization of reciproca...

Delayed-feedback control: arbitrary and distributed delay-time and noninvasive control of synchrony in networks with heterogeneous delays

“…This is common in a variety of systems where the delay times are given by a continuous distribution [48,[52][53][54]. The model can be written as follows:…”

“…Nevertheless, most studies have assumed that all the interactions occur with the same time delay and, up to now, little is known about stabilizing UPOs and controlling the synchrony patterns in networks coupled with heterogeneous delays. For instance, the dynamics of an array of chaotic logistic maps coupled with random delay times [47], the effects of heterogeneous delays in the coupling of two excitable neural systems [48,49] or a neural network [50], and amplitude death in the Stuart-Landau system coupled with distributed delays [51][52][53] or periodically modulated delay [54] were investigated.…”

Probing scale interaction in brain dynamics through synchronization

“…The interaction mechanism is bidirectional. This architecture was used by Vicente et al [27] and Gollo et al [28] to demonstrate the emergence of zero-lag synchronization mediated by dynamical relaying between NN populations. In our case, the output of each NM is converted into a firing rate (see equation (2.9)) impinging on a subpopulation of 2000 neurons within the NN.…”

“…In fact, if all three neuronal populations were described by NNs (or by NMs, for that matter) synchronization will also arise (see, for instance, the studies of Vicente et al [27] and Gollo et al [28] for the case of three coupled NNs leading to zero-lag synchronization). Neither do we claim that two brain oscillators can synchronize only through the mediation of a third (see, for instance, the study of David & Friston [12] for an example of synchronization between two coupled NMs).…”

Role of delay in the mechanism of cluster formation

“…Delay may enhance the coordination among the connected nodes leading to an enhancement of synchronization identifying underlying connection topology, which had been the main theme of a few recent studies, but observation of a D mechanism behind the cluster formation in delayed coupled networks is a new insight suggesting that delayinduced synchronization may lead to a completely different relation between functional clusters and topology, than relations observed for the undelayed evolution. Our study draws its significance in understanding synchronization in real world networks such as neural networks, where clusters are formed due to delayed interactions between neurons [23] and may be of D type [24]. An analysis presented for bipartite and periodic cases help in discerning a possible impact of τ on the coupled evolution in such systems.…”