Network Of Hodgkin-Huxley Neurons Research Articles

Chaotic resonance in hybrid scale-free neural networks

It has been recently shown that weak signal response of a neuron can be amplified with the help of chaotic fluctuations at an optimal intensity. This phenomenon is referred to as chaotic resonance (CR). Here, we numerically investigate the signal detection ability of nervous system via CR using hybrid coupled scale-free networks of Hodgkin-Huxley (H-H) neurons. Firstly, we find that chaotic internal fluctuations are prone to enhance signal response of neuron population, even with a weak connectivity, more than that of single isolated cell's. We show that gap junctions can satisfy the stability against such variability and the quality of perception due to synchronizability. We also show that intense hybrid network interaction with strong chemical coupling can induce the similar degree of stability and decent quality of CR performance. Our results imply that a balanced connectivity may respond to weak signals efficiently in the presence of optimal chaotic fluctuations and exhibit frequency selectivity.

A dynamic learning method for phase synchronization control in Hodgkin–Huxley neuronal networks

A dynamic learning method for phase synchronization control in Hodgkin–Huxley neuronal networks

Weak Signal Detection in the Hodgkin–Huxley Neural Network with Channel Blocks under Electromagnetic Stimulus

Neurons can detect weak signals in noisy cellular environments and complex backgrounds. Channel blocks have a great impact on the initiation and propagation of action potentials for neurons. The effects of channel blocks and electromagnetic stimulus on weak signal detection are studied in Hodgkin–Huxley neuronal network. The results suggest that the weak signal detection and the neural discharge behaviors of the neural network can be suppressed by the sodium channel blockage, whereas the block of potassium channels will have a positive impact on the signal detection and neuronal firing. For moderate membrane patch size, there is an optimal ratio of non-blocked potassium channels that maximize improvement in the detection of weak signals and the regularity of the neuronal activities. The combined influence of the two channel blocks on weak signal detection can be modulated by the ratio between the number of the sodium channels and potassium channels that function properly. The electromagnetic stimulus can significantly ameliorate the damage caused by the poisoning of sodium ion channels. In addition, synchronization of the neural network can promote weak signal detection.

Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance.

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter P, which controls STDP, on the characteristic rewiring frequency parameter F, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing P (which enhances the weakening effect of STDP on synaptic weights) and decreasing F (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter τ_{c} has some appropriate values. (ii) Increasing the synaptic time delay τ_{c} induces multiple CR (MCR)-the occurrence of multiple peaks in the degree of coherence as τ_{c} changes-in small-world and random networks, with MCR becoming more pronounced at smaller values of P and F. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

Local inhibitory networks support up to (N−1)!/lnN2 limit cycles in the presence of electronic noise and heterogeneity

A paradox in neuroscience is the large number of oscillations of small neural networks compared with the few oscillations observed in the conscious brain. It remains unclear what is the maximum number of synchronized oscillations a network can support and whether all or some of these oscillations would survive in noisy heterogenous circuits. Here, we attempt to answer these questions through a comprehensive study of local inhibitory networks of Hodgkin-Huxley neurons. We use a neuromorphic platform combining electronic noise and device-specific heterogeneity with tuneable extrinsic noise, tuneable network connectivity, and controlled initial conditions. As in the brain, stimuli are instantaneously integrated by analog circuits. This gives us the computing power needed to map the network dynamics over the entire phase space and demonstrate the full complement of limit cycles, basins of attraction, and dependence on network parameters. Our main finding is that the maximum number of limit cycles is equal to the combinatorial number of activation pathways through the network, allowing for coincident action potentials, and that all limit cycles are equally robust to noise and mild heterogeneity but highly dependent on inhibition delay and the timing of stimuli. We established the robustness of individual limit cycles by computing the detailed balance of bifurcations between attractors. This accounts for all transitions in a system where Lyapunov exponents are both positive and negative depending on phase space coordinates and noise intensity. Another interesting finding is the unexpected resilience of limit cycles to mild network heterogeneity. This occurs as stochastic processes recruit quiescent neurons whose subthreshold periodic oscillations help maintain the synchronization of limit cycles against heterogeneity.

Effects of magnetic fields on stochastic resonance in Hodgkin-Huxley neuronal network driven by Gaussian noise and non-Gaussian noise.

Stochastic resonance is a remarkable phenomenon that can enhance signal processing by the addition of random noise. However, the effect of magnetic fields on stochastic resonance under channel noises has been inadequately studied. In this paper, the stochastic resonance in Hodgkin-Huxley neuronal network under Gaussian channel noises and non-Gaussian channel noise were studied, and the effects of electromagnetic field stimulation on stochastic resonance were considered. The results indicate that stochastic resonance in neuronal networks can be induced by Gaussian channel noise and non-Gaussian Levy channel noise, and stochastic resonance may occur more easily under Levy channel noise. The resonance amplitude was significantly improved by selecting appropriate parameters of the magnetic field, while, a too strong magnetic field can be detrimental to the resonance amplitude. Magnetic fields may induce the enhancement of the resonance amplitude by increasing the firing frequency and spiking regularity.

Synchronization of interacted spiking neuronal networks with inhibitory coupling

• The synchronization index (SI) in two large interacted via inhibitory coupling networks oscillates periodically in time; the time intervals of high SI alternates with the time intervals of low SI. • The synchronization indexes in these networks exhibit either inphase or antiphase synchronization depending on the inhibitory coupling strength between them. We suppose that the underlying mechanism behind the antiphase dynamics lies in the cognitive resource redistribution between neuronal ensembles in the brain. • Excitatory coupling between the neurons inside the network affects the synchronization index. To maintain the neural network in the regimes of inphase or antiphase SI oscillations, we should keep a balance between excitatory and inhibitory connections. It suggests that the excitatory and the inhibitory currents should compensate each other. In other words, when one of them increases, the other must be increased too, and vice versa. • The coupling inside the input small network affects antiphase synchronization between two large networks. However, the scenario from positive and negative correlation and back between the large networks are only determined by inhibitory coupling between them. The development of mathematical models to describe neuronal interaction processes in the brain is a challenging task of nonlinear dynamics. Recent advances in biochemistry and neuroscience allow better understanding of biological mechanisms underlying the neuron functioning and synaptic connections between neurons. Moreover, significant progress in brain imaging sheds light on the structure of the brain network and certain aspects of neuronal dynamics. However, dynamical mechanisms leading to synchronization between different brain areas still remain unknown and require further investigation. To shed light on this issue, we consider two small-world networks of Hodgkin-Huxley neurons interacting via inhibitory coupling. We found that synchronization indices (SI) in both networks oscillate periodically in time, so that time intervals of high SI alternate with time intervals of low SI. Depending on the coupling strength, the two coupled networks can be in the regime of either in-phase or anti-phase synchronization. We suppose that the inherent mechanism behind such a behavior lies in the cognitive resource redistribution between neuronal ensembles of the brain.

Analysis of parameter changes of a neuronal network model using transfer entropy

Understanding the dynamics of coupled neurons is one of the fundamental problems in the analysis of neuronal model dynamics. The transfer entropy (TE) method is one of the primary analyses to explore the information flow between the neuronal populations. We perform the TE analysis on the two-neuron conductance-based Hodgkin-Huxley (HH) neuronal network to analyze how their connectivity changes due to conductances. We find that the information flow due to underlying synaptic connectivity changes direction by changing conductances individually and/or simultaneously as a result of TE analysis through numerical simulations.

Inhibitory autapses enhance coherence resonance of a neuronal network

The counterintuitive phenomenon that inhibitory autapses enhance coherence resonance (CR) is investigated in a Hodgkin–Huxley neuronal network, which can be well interpreted by post-inhibitory rebound (PIR) spikes. Noise can induce CR in the network with excitatory coupling. After introducing inhibitory autapses, multiple CRs induced by noise appear at multiple time delays of inhibitory autapses. The degree of CRs can be enhanced by inhibitory autapses with time delays approximating to 10 ms or the sum of 10 ms and multiples of the firing period. For these time delays, each delayed inhibitory current pulse can induce a PIR spike, which is a signature of the stable focus near the Hopf bifurcation. The degree of CRs can be reduced by inhibitory autapses for time delays nearly equaling multiples of the firing period, because the inhibitory autaptic current pulses take effect near the spikes, resulting in the reduced irregularity of the spikes. More detailed dynamics of CR is investigated in planes composed of every two parameters out of the noise intensity, the autaptic strength, and the time delay. The counterintuitive phenomenon that inhibitory autapses can enhance the CR degree is in contrast to the conventional notion that inhibitory effects suppress the neuronal activities, which not only enriches the content of nonlinear dynamics, but also provides an approach to modulate CR or the firing regularity of neuronal networks.

The extended Granger causality analysis for Hodgkin-Huxley neuronal models.

How to extract directions of information flow in dynamical systems based on empirical data remains a key challenge. The Granger causality (GC) analysis has been identified as a powerful method to achieve this capability. However, the framework of the GC theory requires that the dynamics of the investigated system can be statistically linearized; i.e., the dynamics can be effectively modeled by linear regressive processes. Under such conditions, the causal connectivity can be directly mapped to the structural connectivity that mediates physical interactions within the system. However, for nonlinear dynamical systems such as the Hodgkin-Huxley (HH) neuronal circuit, the validity of the GC analysis has yet been addressed; namely, whether the constructed causal connectivity is still identical to the synaptic connectivity between neurons remains unknown. In this work, we apply the nonlinear extension of the GC analysis, i.e., the extended GC analysis, to the voltage time series obtained by evolving the HH neuronal network. In addition, we add a certain amount of measurement or observational noise to the time series to take into account the realistic situation in data acquisition in the experiment. Our numerical results indicate that the causal connectivity obtained through the extended GC analysis is consistent with the underlying synaptic connectivity of the system. This consistency is also insensitive to dynamical regimes, e.g., a chaotic or non-chaotic regime. Since the extended GC analysis could in principle be applied to any nonlinear dynamical system as long as its attractor is low dimensional, our results may potentially be extended to the GC analysis in other settings.

Differential Covariance: A New Method to Estimate Functional Connectivity in fMRI.

Measuring functional connectivity from fMRI recordings is important in understanding processing in cortical networks. However, because the brain's connection pattern is complex, currently used methods are prone to producing false functional connections. We introduce differential covariance analysis, a new method that uses derivatives of the signal for estimating functional connectivity. We generated neural activities from dynamical causal modeling and a neural network of Hodgkin-Huxley neurons and then converted them to hemodynamic signals using the forward balloon model. The simulated fMRI signals, together with the ground-truth connectivity pattern, were used to benchmark our method with other commonly used methods. Differential covariance achieved better results in complex network simulations. This new method opens an alternative way to estimate functional connectivity.

Stimulus classification using chimera-like states in a spiking neural network

Abstract A complex network of bistable Hodgkin-Huxley (HH) neurons with excitatory coupling can exhibit a partially spiking chimera behavior. We propose to use this chimera-like state for classification of the entering stimulus amplitude in the neural network with coexisting resting and spiking states. Due to different additive noise applied to each neuron in the network, the neurons are nonidentical. Therefore, depending on the amplitude of the external current, a part of the neurons stays in the resting state, while another part oscillates. Keeping fixed the coupling strength between neurons inside the network, we train the neural network on external pulses with two different amplitudes to adjust the coupling strength between the network neurons and two output neurons. We consider two variants of the classifier, in the presence and in the absence of inhibitory coupling between output neurons, and study how the output neurons respond to the external pulses of different amplitudes. The accuracy of the proposed classifier reaches 100% when the output neurons are inhibitory coupled, so that only one of these neurons is activated.

Formation of spiral wave in Hodgkin-Huxley neuron networks with Gamma-distributed synaptic input

We adopt Gamma renewal process to describe the synaptic input of Hodgkin-Huxley neurons on a square lattice with no-flux boundary. Based on the eigenfunction expansion of Laplace operator, we show that the Hopf bifurcation point of the lattice is coincident with that of a single neuron model. By center manifold theorem and normal form theory, we prove that the Hopf bifurcation is subcritical. And then, we exhibit the effect of Gamma noise on the formation of spiral wave for the first time. It is revealed that the occurrence and elimination of the spiral wave can be controlled by adjusting the inhibitory-excitatory ratio and noise parameters. Since spiral waves may contribute to both normal cortical and pathological activities, the present investigation should be helpful for understanding the functional role of general neural noise.

Frequency cluster formation and slow oscillations in neural populations with plasticity.

We report the phenomenon of frequency clustering in a network of Hodgkin-Huxley neurons with spike timing-dependent plasticity. The clustering leads to a splitting of a neural population into a few groups synchronized at different frequencies. In this regime, the amplitude of the mean field undergoes low-frequency modulations, which may contribute to the mechanism of the emergence of slow oscillations of neural activity observed in spectral power of local field potentials or electroencephalographic signals at high frequencies. In addition to numerical simulations of such multi-clusters, we investigate the mechanisms of the observed phenomena using the simplest case of two clusters. In particular, we propose a phenomenological model which describes the dynamics of two clusters taking into account the adaptation of coupling weights. We also determine the set of plasticity functions (update rules), which lead to multi-clustering.

Channel noise effects on neural synchronization

Synchronization in neural networks is believed to be linked to cognitive processes, while abnormal synchronization has been associated with disorders such as epilepsy and schizophrenia. We examine the synchronization of small Hodgkin–Huxley neuronal networks. The principal features of Hodgkin–Huxley neurons are protein channels in the neural membrane that transition between open and closed states with voltage dependent rate constants. The standard assumption of infinitely many channels neglects the fact that real neurons have finitely many channels, which leads to fluctuations in the membrane voltage and modifies neuronal spike times. These fluctuations are referred to as channel noise. We demonstrate that regardless of channel noise magnitude, neurons in the network reach a steady state synchronization level dependent only on the number of neurons in the network, equivalent to the steady state level of uncoupled Poisson neurons. The channel noise only affects the time to reach the steady state synchronization level.

Chimera state in complex networks of bistable Hodgkin-Huxley neurons.

In this paper we study a chimera state in complex networks of bistable Hodgkin-Huxley neurons with excitatory coupling, which manifests as a termination of spiking activity of a part of interacting neurons. We provide a detailed investigation of this phenomenon in scale-free, small-world, and random networks and show that the chimera state is robust to the network topology. Nevertheless, network topological properties determine the stability of spatiotemporal states and therefore affect the excitability of the chimera state in the whole network. In particular, the scale-free network whose higher degree nodes are more stable to small perturbations is least exposed to chimera formation and exhibits an abrupt transition from a spiking to a silent regime. On the other hand, small-world and random networks are more likely to provide transitions to the chimera state.

Maximum entropy principle analysis in network systems with short-time recordings.

In many realistic systems, maximum entropy principle (MEP) analysis provides an effective characterization of the probability distribution of network states. However, to implement the MEP analysis, a sufficiently long-time data recording in general is often required, e.g., hours of spiking recordings of neurons in neuronal networks. The issue of whether the MEP analysis can be successfully applied to network systems with data from short-time recordings has yet to be fully addressed. In this work, we investigate relationships underlying the probability distributions, moments, and effective interactions in the MEP analysis and then show that, with short-time recordings of network dynamics, the MEP analysis can be applied to reconstructing probability distributions of network states that is much more accurate than the one directly measured from the short-time recording. Using spike trains obtained from both Hodgkin-Huxley neuronal networks and electrophysiological experiments, we verify our results and demonstrate that MEP analysis provides a tool to investigate the neuronal population coding properties for short-time recordings.

Synchronization of stochastic mean field networks of Hodgkin-Huxley neurons with noisy channels.

In this work we are interested in a mathematical model of the collective behavior of a fully connected network of finitely many neurons, when their number and when time go to infinity. We assume that every neuron follows a stochastic version of the Hodgkin-Huxley model, and that pairs of neurons interact through both electrical and chemical synapses, the global connectivity being of mean field type. When the leak conductance is strictly positive, we prove that if the initial voltages are uniformly bounded and the electrical interaction between neurons is strong enough, then, uniformly in the number of neurons, the whole system synchronizes exponentially fast as time goes to infinity, up to some error controlled by (and vanishing with) the channels noise level. Moreover, we prove that if the random initial condition is exchangeable, on every bounded time interval the propagation of chaos property for this system holds (regardless of the interaction intensities). Combining these results, we deduce that the nonlinear McKean-Vlasov equation describing an infinite network of such neurons concentrates, as time goes to infinity, around the dynamics of a single Hodgkin-Huxley neuron with chemical neurotransmitter channels. Our results are illustrated and complemented with numerical simulations.

A Scalable FPGA Architecture for Randomly Connected Networks of Hodgkin-Huxley Neurons.

Human intelligence relies on the vast number of neurons and their interconnections that form a parallel computing engine. If we tend to design a brain-like machine, we will have no choice but to employ many spiking neurons, each one has a large number of synapses. Such a neuronal network is not only compute-intensive but also memory-intensive. The performance and the configurability of the modern FPGAs make them suitable hardware solutions to deal with these challenges. This paper presents a scalable architecture to simulate a randomly connected network of Hodgkin-Huxley neurons. To demonstrate that our architecture eliminates the need to use a high-end device, we employ the XC7A200T, a member of the mid-range Xilinx Artix®-7 family, as our target device. A set of techniques are proposed to reduce the memory usage and computational requirements. Here we introduce a multi-core architecture in which each core can update the states of a group of neurons stored in its corresponding memory bank. The proposed system uses a novel method to generate the connectivity vectors on the fly instead of storing them in a huge memory. This technique is based on a cyclic permutation of a single prestored connectivity vector per core. Moreover, to reduce both the resource usage and the computational latency even more, a novel approximate two-level counter is introduced to count the number of the spikes at the synapse for the sparse network. The first level is a low cost saturated counter implemented on FPGA lookup tables that reduces the number of inputs to the second level exact adder tree. It, therefore, results in much lower hardware cost for the counter circuit. These techniques along with pipelining make it possible to have a high-performance, scalable architecture, which could be configured for either a real-time simulation of up to 5120 neurons or a large-scale simulation of up to 65536 neurons in an appropriate execution time on a cost-optimized FPGA.

Effect of Channel Block on Multiple Coherence Resonance Induced by Time Delay in Adaptive Neuronal Networks with Spike-Timing-Dependent Plasticity

In this paper, we study effect of channel block (CB) on multiple coherence resonance (MCR) in adaptive scale-free Hodgkin–Huxley neuronal networks with spike-timing-dependent plasticity (STDP). It is found that potassium CB suppresses MCR, but sodium CB can enhance MCR, and there is optimal sodium CB level by which MCR becomes most pronounced. In addition, STDP has a significant influence on the effect of CB on MCR. As adjusting rate [Formula: see text] of STDP increases, for potassium CB there is proper [Formula: see text] by which MCR is most pronounced; however, for sodium CB MCR is reduced. These findings could provide a new insight into effect of CB on information processing in neural systems.