10 research outputs found

    In-phase and anti-phase synchronization in noisy Hodgkin-Huxley neurons

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    We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation time of an action potential along the neuronal axon. We quantify this delay-coupling of the Pyragas-type in terms of the difference between corresponding presynaptic and postsynaptic membrane potentials. For an elementary neuronal network consisting of two coupled neurons we detect characteristic stochastic synchronization patterns which exhibit multiple phase-flip bifurcations: The phase-flip bifurcations occur in form of alternate transitions from an in-phase spiking activity towards an anti-phase spiking activity. Interestingly, these phase-flips remain robust in strong channel noise and in turn cause a striking stabilization of the spiking frequency

    Effect of the electromagnetic induction on a modified memristive neural map model

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    The significance of discrete neural models lies in their mathematical simplicity and computational ease. This research focuses on enhancing a neural map model by incorporating a hyperbolic tangent-based memristor. The study extensively explores the impact of magnetic induction strength on the model's dynamics, analyzing bifurcation diagrams and the presence of multistability. Moreover, the investigation extends to the collective behavior of coupled memristive neural maps with electrical, chemical, and magnetic connections. The synchronization of these coupled memristive maps is examined, revealing that chemical coupling exhibits a broader synchronization area. Additionally, diverse chimera states and cluster synchronized states are identified and discussed

    Temporal integration and 1/f power scaling in a circuit model of cerebellar interneurons

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    This document is the Accepted Manuscript version of a published work that appeared in final form in Journal of Neurophysiology after peer review and technical editing by the publisher. Under embargo until 1 July 2018. To access the final edited and published work see: https://doi.org/10.1152/jn.00789.2016.Inhibitory interneurons interconnected via electrical and chemical (GABAA receptor) synapses form extensive circuits in several brain regions. They are thought to be involved in timing and synchronization through fast feedforward control of principal neurons. Theoretical studies have shown, however, that whereas self-inhibition does indeed reduce response duration, lateral inhibition, in contrast, may generate slow response components through a process of gradual disinhibition. Here we simulated a circuit of interneurons (stellate and basket cells) of the molecular layer of the cerebellar cortex and observed circuit time constants that could rise, depending on parameter values, to >1 s. The integration time scaled both with the strength of inhibition, vanishing completely when inhibition was blocked, and with the average connection distance, which determined the balance between lateral and self-inhibition. Electrical synapses could further enhance the integration time by limiting heterogeneity among the interneurons and by introducing a slow capacitive current. The model can explain several observations, such as the slow time course of OFF-beam inhibition, the phase lag of interneurons during vestibular rotation, or the phase lead of Purkinje cells. Interestingly, the interneuron spike trains displayed power that scaled approximately as 1/f at low frequencies. In conclusion, stellate and basket cells in cerebellar cortex, and interneuron circuits in general, may not only provide fast inhibition to principal cells but also act as temporal integrators that build a very short-term memory.NEW & NOTEWORTHY The most common function attributed to inhibitory interneurons is feedforward control of principal neurons. In many brain regions, however, the interneurons are densely interconnected via both chemical and electrical synapses but the function of this coupling is largely unknown. Based on large-scale simulations of an interneuron circuit of cerebellar cortex, we propose that this coupling enhances the integration time constant, and hence the memory trace, of the circuit.Peer reviewe

    29th Annual Computational Neuroscience Meeting: CNS*2020

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    Meeting abstracts This publication was funded by OCNS. The Supplement Editors declare that they have no competing interests. Virtual | 18-22 July 202

    A study of bursting in the preBotzinger Complex

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    The preBotzinger complex (PBC) of the mammalian brainstem is a heterogeneous neuronal network underlying the inspiration phase of the respiratory rhythm. Through excitatory synapses and a nontrivial network architecture, a synchronous, network-wide bursting rhythm emerges. On the other hand, during synaptic isolation, PBC neurons display three types of intrinsic dynamics: quiescence, bursting, or tonic activity. This work seeks to shed light on how the network rhythm emerges from the challenging architecture and heterogeneous population. Recent debate surrounding the role of intrinsically bursting neurons in the rhythmogenesis of the PBC inspires us to evaluate its role in a three-cell network. We found no advantage for intrinsically bursting neurons in forming synchronous network bursting; instead, intrinsically quiescent neurons were identified as a key mechanism. This analysis involved only studying the persistent sodium (NaP) current. Another important current for the PBC is the calcium-activated nonspecific cationic (CAN) current, which, when combined with a Na/K pump, was previously shown to be capable of producing bursts in coupled tonically active cells. In the second part of this study, we explore the interactions of the NaP and CAN currents, both currents are ubiquitous in the PBC. Using geometric singular perturbation theory and bifurcation analysis, we established the mechanisms through which reciprocally coupled pairs of neurons can generate various activity patterns. In particular, we highlighted how the NaP current could enhance the range of the strength of the CAN current for which bursts occur. We also were able to detail a novel bursting pattern seen in data, but not seen in previous models. With a foundation of understanding heterogeneity in the NaP and CAN currents, we again turned out attention to networks. For the third portion of the dissertation, we examine the effects that heterogeneity in the neuronal dynamics and coupling architecture can impose upon synchronous bursting of the entire network. We again found no significant advantage to including intrinsically bursting neurons in the network, and the best networks were characterized by an increased presence of quiescent neurons. We also described the way the NaP and CAN currents interact on the network scale to promote synchronous bursting

    Studying spontaneous brain activity with neuroimaging methods and mathematical modelling

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    The study of spontaneous brain activity using functional Magnetic Resonance Imaging (fMRI) is a relatively young and rapidly developing field born in the mid-nineties. So far, sufficiently solid foundations have been established, mainly in validating the neuronal origin of a significant component of observed low-frequency fluctuations in the 'resting state' fMRI signal. Nevertheless, the field is still facing several major challenges. This thesis first reviews the current state of knowledge and subsequently proceeds to present original research results that are directed towards overcoming these challenges. The first challenge stems from the indirect nature of the fMRI recordings, obscuring the interpretation in terms of the underlying neuronal activity. Two investigations related to this are presented. First, I show that increased head-movement, epiphenomenal to altered states of consciousness, can lead to spurious increases in low-frequency fluctuations in fMRI signal. This may adversely affect inferences on the underlying neurophysiological processes. Second, I demonstrate a direct electrophysiological correlate of increased synchronisation of fMRI activity in areas of the much studied default-mode network. By directly studying electrophysiological correlates of fMRI-based functional connectivity, this study took a pioneering approach to confirming the biological validity of the fMRI functional connectivity concept. Another widely debated question within the field is the optimal method for extracting relevant information from the extreme volumes of neuroimaging data. I present an investigation providing insights and practical recommendations for this question, based on assessing the interdependence information neglected by the commonly used linear correlation for fMRI functional connectivity studies. The results suggest that in typical resting state data, the nonlinear contributions to instantaneous connectivity are negligible. The third major challenge of the field is the integration of the experimental evidence into theoretical models of spontaneous brain activity. In the last part of this thesis, such models are discussed in detail, focusing on the two crucial features of observed spontaneous brain activity: functional connectivity and low-frequency fluctuations. Two specific mechanisms for emergence of the latter are proposed, depending either on the local synchronisation dynamics or the regulatory action of particular neuromodulators. The thesis concludes with discussion of the questions arising from the presented results in the context of the most recent development in the wider field

    The Evolution, Analysis, and Design of Minimal Spiking Neural Networks for Temporal Pattern Recognition

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    All sensory stimuli are temporal in structure. How a pattern of action potentials encodes the information received from the sensory stimuli is an important research question in neurosciencce. Although it is clear that information is carried by the number or the timing of spikes, the information processing in the nervous system is poorly understood. The desire to understand information processing in the animal brain led to the development of spiking neural networks (SNNs). Understanding information processing in spiking neural networks may give us an insight into the information processing in the animal brain. One way to understand the mechanisms which enable SNNs to perform a computational task is to associate the structural connectivity of the network with the corresponding functional behaviour. This work demonstrates the structure-function mapping of spiking networks evolved (or handcrafted) for recognising temporal patterns. The SNNs are composed of simple yet biologically meaningful adaptive exponential integrate-and-fire (AdEx) neurons. The computational task can be described as identifying a subsequence of three signals (say ABC) in a random input stream of signals ("ABBBCCBABABCBBCAC"). The topology and connection weights of the networks are optimised using a genetic algorithm such that the network output spikes only for the correct input pattern and remains silent for all others. The fitness function rewards the network output for spiking after receiving the correct pattern and penalises spikes elsewhere. To analyse the effect of noise, two types of noise are introduced during evolution: (i) random fluctuations of the membrane potential of neurons in the network at every network step, (ii) random variations of the duration of the silent interval between input signals. It has been observed that evolution in the presence of noise produced networks that were robust to perturbation of neuronal parameters. Moreover, the networks also developed a form of memory, enabling them to maintain network states in the absence of input activity. It has been demonstrated that the network states of an evolved network have a one-to-one correspondence with the states of a finite-state transducer (FST) { a model of computation for time-structured data. The analysis of networks indicated that the task of recognition is accomplished by transitions between network states. Evolution may overproduce synaptic connections, pruning these superfluous connections pronounced structural similarities among individuals obtained from different independent runs. Moreover, the analysis of the pruned networks highlighted that memory is a property of self-excitation in the network. Neurons with self-excitatory loops (also called autapses) could sustain spiking activity indefinitely in the absence of input activity. To recognise a pattern of length n, a network requires n+1 network states, where n states are maintained actively with autapses and the penultimate state is maintained passively by no activity in the network. Simultaneously, the role of other connections in the network is identified. Of particular interest, three interneurons in the network are found to have a specialized role: (i) the lock neuron is always active, preventing the output from spiking unless it is released by the penultimate signal in the correct pattern, exposing the output neuron to spike for the correct last signal, (ii) the switch neuron is responsible for switching the network between the inter-signal states and the start state, and (iii) the accept neuron produces spikes in the output neuron when the network receives the last correct input. It also sends a signal to the switch neuron, transforming the network back into the start state Understanding how information is processed in the evolved networks led to handcrafting network topologies for recognising more extended patterns. The proposed rules can extend network topologies to recognize temporal patterns up to length six. To validate the handcrafted topology, a genetic algorithm is used to optimise its connection weights. It has been observed that the maximum number of active neurons representing a state in the network increases with the pattern length. Therefore, the suggested rules can handcraft network topologies only up to length 6. Handcrafting network topologies, representing a network state with a fixed number of active neurons requires further investigation

    Studying spontaneous brain activity with neuroimaging methods and mathematical modelling

    Get PDF
    The study of spontaneous brain activity using functional Magnetic Resonance Imaging (fMRI) is a relatively young and rapidly developing field born in the mid-nineties. So far, sufficiently solid foundations have been established, mainly in validating the neuronal origin of a significant component of observed low-frequency fluctuations in the 'resting state' fMRI signal. Nevertheless, the field is still facing several major challenges. This thesis first reviews the current state of knowledge and subsequently proceeds to present original research results that are directed towards overcoming these challenges. The first challenge stems from the indirect nature of the fMRI recordings, obscuring the interpretation in terms of the underlying neuronal activity. Two investigations related to this are presented. First, I show that increased head-movement, epiphenomenal to altered states of consciousness, can lead to spurious increases in low-frequency fluctuations in fMRI signal. This may adversely affect inferences on the underlying neurophysiological processes. Second, I demonstrate a direct electrophysiological correlate of increased synchronisation of fMRI activity in areas of the much studied default-mode network. By directly studying electrophysiological correlates of fMRI-based functional connectivity, this study took a pioneering approach to confirming the biological validity of the fMRI functional connectivity concept. Another widely debated question within the field is the optimal method for extracting relevant information from the extreme volumes of neuroimaging data. I present an investigation providing insights and practical recommendations for this question, based on assessing the interdependence information neglected by the commonly used linear correlation for fMRI functional connectivity studies. The results suggest that in typical resting state data, the nonlinear contributions to instantaneous connectivity are negligible. The third major challenge of the field is the integration of the experimental evidence into theoretical models of spontaneous brain activity. In the last part of this thesis, such models are discussed in detail, focusing on the two crucial features of observed spontaneous brain activity: functional connectivity and low-frequency fluctuations. Two specific mechanisms for emergence of the latter are proposed, depending either on the local synchronisation dynamics or the regulatory action of particular neuromodulators. The thesis concludes with discussion of the questions arising from the presented results in the context of the most recent development in the wider field
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