Delay-induced destabilization of entrainment of nerve impulses on ephaptically coupled nerve fibers

We study the effect of delay on the synchronization of two nerve impulses traveling along two ephaptically coupled, unmyelinated nerve fibers. The system is modeled as a pair of delay-coupled Fitzhugh-Nagumo equations. A multiple-scale perturbation approach is used for the analysis of these equations in the limit of weak coupling. In the absence of delay, two pulses with identical speeds are shown to be entrained precisely. However, as the delay is increased beyond a critical value, we show that this precise entrainment becomes unstable. We make quantitative estimates for the actual values of delay at which this can occur in the case of squid giant axons and compare them with the relevant time-scales involved

Hippocampal sharp-Wave ripples influence selective activation of the default mode network

The default mode network (DMN) is a commonly observed resting-state network (RSN) that includes medial temporal, parietal, and prefrontal regions involved in episodic memory [1-3]. The behavioral relevance of endogenous DMN activity remains elusive, despite an emerging literature correlating resting fMRI fluctuations with memory performance [4, 5]-particularly in DMN regions [6-8]. Mechanistic support for the DMN's role in memory consolidation might come from investigation of large deflections (sharp-waves) in the hippocampal local field potential that co-occur with high-frequency (>80 Hz) oscillations called ripples-both during sleep [9, 10] and awake deliberative periods [11-13]. Ripples are ideally suited for memory consolidation [14, 15], since the reactivation of hippocampal place cell ensembles occurs during ripples [16-19]. Moreover, the number of ripples after learning predicts subsequent memory performance in rodents [20-22] and humans [23], whereas electrical stimulation of the hippocampus after learning interferes with memory consolidation [24-26]. A recent study in macaques showed diffuse fMRI neocortical activation and subcortical deactivation specifically after ripples [27]. Yet it is unclear whether ripples and other hippocampal neural events influence endogenous fluctuations in specific RSNs-like the DMN-unitarily. Here, we examine fMRI datasets from anesthetized monkeys with simultaneous hippocampal electrophysiology recordings, where we observe a dramatic increase in the DMN fMRI signal following ripples, but not following other hippocampal electrophysiological events. Crucially, we find increases in ongoing DMN activity after ripples, but not in other RSNs. Our results relate endogenous DMN fluctuations to hippocampal ripples, thereby linking network-level resting fMRI fluctuations with behaviorally relevant circuit-level neural dynamics

Linking entropy at rest with the underlying structural connectivity in the healthy and lesioned brain

The brain is a network that mediates information processing through a wide range of states. The extent of state diversity is a reflection of the entropy of the network. Here we measured the entropy of brain regions (nodes) in empirical and modeled functional networks reconstructed from resting state fMRI to address the connection of entropy at rest with the underlying structure measured through diffusion spectrum imaging. Using 18 empirical and 18 modeled stroke networks, we also investigated the effect that focal lesions have on node entropy and information diffusion. Overall, positive correlations between node entropy and structure were observed, especially between node entropy and node strength in both empirical and modeled data. Although lesions were restricted to one hemisphere in all stroke patients, entropy reduction was not only present in nodes from the damaged hemisphere, but also in nodes from the contralesioned hemisphere, an effect replicated in modeled stroke networks. Globally, information diffusion was also affected in empirical and modeled strokes compared with healthy controls. This is the first study showing that artificial lesions affect local and global network aspects in very similar ways compared with empirical strokes, shedding new light into the functional nature of stroke.In this work, G.D. was supported by the ERC Advanced Grant DYSTRUCTURE (n. 295129), by the Spanish Research Project PSI2016-75688-P (AEI/FEDER) and by the European Union’s Horizon 2020 research and innovation program under grant agreement n. 720270 (HBP SGA1). M.A. was supported by the ERC Advanced Grant DYSTRUCTURE (n. 295129). A.P.-A. was supported by a Juan de la Cierva fellowship (IJCI-2014–066) from the Spanish Ministry of Economy and Competitiveness. V.M.S. was supported by the Research Personnel Training program (PSI2013-42091-P) funded by the Spanish Ministry of Economy and Competitiveness