Analysis of Chaotic Resonance in Izhikevich Neuron Model

In stochastic resonance (SR), the presence of noise helps a nonlinear system amplify a weak (sub-threshold) signal. Chaotic resonance (CR) is a phenomenon similar to SR but without stochastic noise, which has been observed in neural systems. However, no study to date has investigated and compared the characteristics and performance of the signal responses of a spiking neural system in some chaotic states in CR. In this paper, we focus on the Izhikevich neuron model, which can reproduce major spike patterns that have been experimentally observed. We examine and classify the chaotic characteristics of this model by using Lyapunov exponents with a saltation matrix and Poincaré section methods in order to address the measurement challenge posed by the state-dependent jump in the resetting process. We found the existence of two distinctive states, a chaotic state involving primarily turbulent movement and an intermittent chaotic state. In order to assess the signal responses of CR in these classified states, we introduced an extended Izhikevich neuron model by considering weak periodic signals, and defined the cycle histogram of neuron spikes as well as the corresponding mutual correlation and information. Through computer simulations, we confirmed that both chaotic states in CR can sensitively respond to weak signals. Moreover, we found that the intermittent chaotic state exhibited a prompter response than the chaotic state with primarily turbulent movement.     

STOCHASTIC RESONANCE MEASURED BY THEMUTUAL INFORMATION IN THE NEURONSTHAT TRANSMIT CHAOTIC SPIKE TRAINS

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STOCHASTIC RESONANCE MEASURED BY THEMUTUAL INFORMATION IN THE NEURONSTHAT TRANSMIT CHAOTIC SPIKE TRAINS

The spike trains generated by a neuron model are studied by the methods of nonlinear time series analysis. The results show that the spike trains are chaotic. To investigate effect of noise on transmission of chaotic spike trains, this chaotic spike trains are used as a discrete subthreshold input signal to the integrate-and-fire neuronal model and the FitzHugh-Nagumo(FHN) neuronal model working in noisy environment. The mutual information between the input spike trains and the output spike trains is calculated, the result shows that the transformation of information encoded by the chaotic spike trains is optimized by some level of noise, and stochastic resonance(SR) measured by mutual information is a property available for neurons to transmit chaotic spike trains.     

Dendritic I h Selectively Blocks Temporal Summation of Unsynchronized Distal Inputs in CA1 Pyramidal Neurons

The active dendritic conductances shape the input-output properties of many principal neurons in different brain regions, and the various ways in which they regulate neuronal excitability need to be investigated to better understand their functional consequences. Using a realistic model of a hippocampal CA1 pyramidal neuron, we show a major role for the hyperpolarization-activated current, Ih, in regulating the spike probability of a neuron when independent synaptic inputs are activated with different degrees of synchronization and at different distances from the soma. The results allowed us to make the experimentally testable prediction that the Ih in these neurons is needed to reduce neuronal excitability selectively for distal unsynchronized, but not for synchronized, inputs.     

Distance-dependent differences in synapse number and AMPA receptor expression in hippocampal CA1 pyramidal neurons

The ability of synapses throughout the dendritic tree to influence neuronal output is crucial for information processing in the brain. Synaptic potentials attenuate dramatically, however, as they propagate along dendrites toward the soma. To examine whether excitatory axospinous synapses on CA1 pyramidal neurons compensate for their distance from the soma to counteract such dendritic filtering, we evaluated axospinous synapse number and receptor expression in three progressively distal regions: proximal and distal stratum radiatum (SR), and stratum lacunosum-moleculare (SLM). We found that the proportion of perforated synapses increases as a function of distance from the soma and that their AMPAR, but not NMDAR, expression is highest in distal SR and lowest in SLM. Computational models of pyramidal neurons derived from these results suggest that they arise from the compartment-specific use of conductance scaling in SR and dendritic spikes in SLM to minimize the influence of distance on synaptic efficacy.     

Mutual information and redundancy in spontaneous communication between cortical neurons

An important question in neural information processing is how neurons cooperate to transmit information. To study this question, we resort to the concept of redundancy in the information transmitted by a group of neurons and, at the same time, we introduce a novel concept for measuring cooperation between pairs of neurons called relative mutual information (RMI). Specifically, we studied these two parameters for spike trains generated by neighboring neurons from the primary visual cortex in the awake, freely moving rat. The spike trains studied here were spontaneously generated in the cortical network, in the absence of visual stimulation. Under these conditions, our analysis revealed that while the value of RMI oscillated slightly around an average value, the redundancy exhibited a behavior characterized by a higher variability. We conjecture that this combination of approximately constant RMI and greater variable redundancy makes information transmission more resistant to noise disturbances. Furthermore, the redundancy values suggest that neurons can cooperate in a flexible way during information transmission. This mostly occurs via a leading neuron with higher transmission rate or, less frequently, through the information rate of the whole group being higher than the sum of the individual information rates—in other words in a synergetic manner. The proposed method applies not only to the stationary, but also to locally stationary neural signals.     

Emergence of resonances in neural systems: the interplay between adaptive threshold and short-term synaptic plasticity

In this work we study the detection of weak stimuli by spiking (integrate-and-fire) neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing mean-field techniques as well as numerical simulations, we found that there are two possible noise levels which optimize signal transmission. This new finding is in contrast with the classical theory of stochastic resonance which is able to predict only one optimal level of noise. We found that the complex interplay between adaptive neuron threshold and activity-dependent synaptic mechanisms is responsible for this new phenomenology. Our main results are confirmed by employing a more realistic FitzHugh-Nagumo neuron model, which displays threshold variability, as well as by considering more realistic stochastic synaptic models and realistic signals such as poissonian spike trains.     

Spike tranfer in statistical neuron assemblies. II. Neuron--nonlinear spike source]

The mathematical model of the neuron function is known to rely on space summing of excitement. The spikes contribute to the inner state of the neuron the farther from cell soma the synapses are located. The difference between excitatory and inhibitory effect results in spike firing if only neural firing threshold is achieved. The values of spike flux have been estimated on the basis of the model of CA3 sector of the Hippocampus and were found to be 15 divided by 35 imp/s.     

Auditory information coding by modeled cochlear nucleus neurons

In this paper we use information theory to quantify the information in the output spike trains of modeled cochlear nucleus globular bushy cells (GBCs). GBCs are part of the sound localization pathway. They are known for their precise temporal processing, and they code amplitude modulations with high fidelity. Here we investigated the information transmission for a natural sound, a recorded vowel. We conclude that the maximum information transmission rate for a single neuron was close to 1,050 bits/s, which corresponds to a value of approximately 5.8 bits per spike. For quasi-periodic signals like voiced speech, the transmitted information saturated as word duration increased. In general, approximately 80% of the available information from the spike trains was transmitted within about 20 ms. Transmitted information for speech signals concentrated around formant frequency regions. The efficiency of neural coding was above 60% up to the highest temporal resolution we investigated (20 μs). The increase in transmitted information to that precision indicates that these neurons are able to code information with extremely high fidelity, which is required for sound localization. On the other hand, only 20% of the information was captured when the temporal resolution was reduced to 4 ms. As the temporal resolution of most speech recognition systems is limited to less than 10 ms, this massive information loss might be one of the reasons which are responsible for the lack of noise robustness of these systems.     

Stochastic resonance induced by fluctuation in liquid membrane oscillator without input signals

We investigated numerically the dynamic behavior of the oil/water liquid membrane, which is a promising model for excitable bio-membrane. When we use noise to modulate the parameters in simulation, noise-induced coherent oscillation is observed. With the increment of the noise intensity, the coherence of noise-induced oscillation can go through a maximum, which indicating the occurrence of stochastic resonance (SR) without input signals. We compared the SR effects under the condition that noise is added to different control parameters. When noise was added to both of the parameters, a complicated SR-like phenomemon was observed. The interaction of coherent SRs induced by two independent noises is discussed. The possibly constructive role of noise in some sensory cells is discussed also.     

Encoding of spatio-temporal input characteristics by a CA1 pyramidal neuron model

The in vivo activity of CA1 pyramidal neurons alternates between regular spiking and bursting, but how these changes affect information processing remains unclear. Using a detailed CA1 pyramidal neuron model, we investigate how timing and spatial arrangement variations in synaptic inputs to the distal and proximal dendritic layers influence the information content of model responses. We find that the temporal delay between activation of the two layers acts as a switch between excitability modes: short delays induce bursting while long delays decrease firing. For long delays, the average firing frequency of the model response discriminates spatially clustered from diffused inputs to the distal dendritic tree. For short delays, the onset latency and inter-spike-interval succession of model responses can accurately classify input signals as temporally close or distant and spatially clustered or diffused across different stimulation protocols. These findings suggest that a CA1 pyramidal neuron may be capable of encoding and transmitting presynaptic spatiotemporal information about the activity of the entorhinal cortex-hippocampal network to higher brain regions via the selective use of either a temporal or a rate code.     

A role for synaptic inputs at distal dendrites: instructive signals for hippocampal long-term plasticity

Synaptic potentials originating at distal dendritic locations are severely attenuated when they reach the soma and, thus, are poor at driving somatic spikes. Nonetheless, distal inputs convey essential information, suggesting that such inputs may be important for compartmentalized dendritic signaling. Here we report a new plasticity rule in which stimulation of distal perforant path inputs to hippocampal CA1 pyramidal neurons induces long-term potentiation at the CA1 proximal Schaffer collateral synapses when the two inputs are paired at a precise interval. This subthreshold form of heterosynaptic plasticity occurs in the absence of somatic spiking but requires activation of both NMDA receptors and IP(3) receptor-dependent release of Ca(2+) from internal stores. Our results suggest that direct sensory information arriving at distal CA1 synapses through the perforant path provide compartmentalized, instructive signals that assess the saliency of mnemonic information propagated through the hippocampal circuit to proximal synapses.     

Identification of Active Membrane Areas in the Giant Neuron of Aplysia

Intracellular and extracellular potentials were simultaneously recorded from the soma and different parts of the axon of the giant cell of Aplysia. Evidence was obtained that for all modes of stimulation the spike originates in the axon at some distance from the cell body. The conduction of the spike is blocked at a distance of 200 to 300 µ from the soma for the antidromic spike, closer to the soma for an orthodromic spike. This event is recorded in the soma as a small or A spike. After some delay, a spike is initiated in the resting part of the axon and in the axon hillock; the soma is invaded only afterwards. The response of these three parts of the neuron is recorded in the soma as the big or S spike.     

SP-SR interneurones: a novel class of neurones of the CA2 region of the hippocampus

The CA2 region of the hippocampus has distinctive properties and inputs and may be linked with the pathology of specific psychiatric and neurological disorders. It is, therefore, important to understand CA2 circuitry and its involvement in the circuitry of the hippocampus. Properties of CA2 basket cells have been reported. However, other classes of CA2 interneurones with cell bodies located in stratum pyramidale remained to be described. In this study, the unusual axonal arbors of a novel subclass of dendrite-preferring CA2 interneurones whose somata are located in the pyramidal cell layer was revealed following intracellular recordings and biocytin labeling. One to four apical dendrites emerged from the soma, branched in stratum radiatum (SR) forming a tuft, but rarely penetrated stratum lacunosum-moleculare (SLM). One or two basal dendrites branched close to the soma, the branches extended through stratum oriens (SO) and often reached the alveus. Unlike CA2 bistratified cells, the axons of these cells arborized almost exclusively in SR with few, if any, branches extending to stratum pyramidale (SP), SO, or SLM. These interneurones again, unlike bistratified cells, were immunonegative for parvalbumin and cholecystokinin. Electrophysiologically, they were similar to some CA2 basket and bistratified cells in that they presented a "sag" in response to hyperpolarizing current injections and displayed spike frequency adaptation. They targeted the apical dendrites of neighboring CA2 pyramidal cells and received inputs from them.     

双层Hodgkin-Huxley神经元网络中的随机共振

随机共振是一种非零噪声优化系统响应的现象。运用信噪比的评价方式,研究单个Hodgkin-Huxley神经元及其所构建的双层神经元网络中的随机共振,来模拟生物感觉系统中检测微弱信号的随机共振现象。结果表明,单个神经元在阈值下存在噪声优化系统检测性能的随机共振现象,但是最优的噪声强度却随外部信号性质的改变而变化;双层神经元网络不但可以在固定的噪声强度上对一定幅度范围内的阈下信号进行优化检测,而且噪声的存在并没有降低网络对阈上信号的检测能力。     

Effects of Lithium on Different Membrane Components of Crayfish Stretch Receptor Neurons

Unlike several other varieties of input membrane, that of the crayfish stretch receptor develops a generator potential in response to stretch when all the Na of the medium is replaced with Li. However, Li depolarizes the receptor neuron, the soma membrane becoming more depolarized than that of the axon. During exposure to Li the cell usually fires spontaneously for a period, and when it becomes quiescent spike electrogenesis fails in the soma but persists in the axon. These effects are seen in the rapidly adapting as well as the slowly adapting cells. The block of spike electrogenesis of the soma membrane is only partly due to the Li-induced depolarization and a significant role must be ascribed to a specific effect of Li.     

Neuronal Spike Initiation Modulated by Extracellular Electric Fields

Based on a reduced two-compartment model, the dynamical and biophysical mechanism underlying the spike initiation of the neuron to extracellular electric fields is investigated in this paper. With stability and phase plane analysis, we first investigate in detail the dynamical properties of neuronal spike initiation induced by geometric parameter and internal coupling conductance. The geometric parameter is the ratio between soma area and total membrane area, which describes the proportion of area occupied by somatic chamber. It is found that varying it could qualitatively alter the bifurcation structures of equilibrium as well as neuronal phase portraits, which remain unchanged when varying internal coupling conductance. By analyzing the activating properties of somatic membrane currents at subthreshold potentials, we explore the relevant biophysical basis of spike initiation dynamics induced by these two parameters. It is observed that increasing geometric parameter could greatly decrease the intensity of the internal current flowing from soma to dendrite, which switches spike initiation dynamics from Hopf bifurcation to SNIC bifurcation; increasing internal coupling conductance could lead to the increase of this outward internal current, whereas the increasing range is so small that it could not qualitatively alter the spike initiation dynamics. These results highlight that neuronal geometric parameter is a crucial factor in determining the spike initiation dynamics to electric fields. The finding is useful to interpret the functional significance of neuronal biophysical properties in their encoding dynamics, which could contribute to uncovering how neuron encodes electric field signals.     

The Spread of Excitation among Neurons in the Heart Ganglion of the Stomatopod, Squilla oratoria

Neurons in the heart ganglion of the mantis shrimp (a stomatopod crustacean) are functionally tightly linked together. The extracellular action potential from the whole trunk very often shows a complex form, but the response is all-or-none to the applied stimulus, indicating that the excitation in one neuron spreads very rapidly to all others. Application of isotonic MgCl₂ solution or repetitive stimulation sometimes separates the spike into its components. The resting potential of the soma membrane is 50 to 60 mv. External stimulation elicits a spike of 60 to 80 mv amplitude with a step on its rising phase. Hyperpolarization reveals one more inflection on the rising phase. These inflections divide the soma action potential into three parts, A₁, A₂, and B spikes in that order from the foot. The B spike disappears on increasing the hyperpolarization, but A₁ and A₂ remain, indicating that B originates from the soma membrane, whereas A₁ and A₂ originate from the two axons of the bipolar cell. Thus the impulse invades the soma from two directions, one from the stimulated side, the other from the other side via the "parallel axons" and the "side-connections;" the latter are presumed to interconnect the axons. When the parallel axons are cut, conduction takes place across the soma with a greatly reduced safety factor and a prolonged conduction time. Neuron-to-neuron transmission takes place in either direction.     

Effects of active versus passive dendritic membranes on the transfer properties of a simulated neuron

In a simulated neuron with a dendritic tree, the relative effects of active and passive dendritic membranes on transfer properties were studied. The simulations were performed by means of a digital computer. The computations calculated the changes in transmembrane voltages of many compartments over time as a function of other biophysical variables. These variables were synaptic input intensity, critical firing threshold, rate of leakage of current across the membrane, and rate of longitudinal current spread between compartments. For both passive and active dendrites, the transfer properties of the soma studied for different rates of longitudinal current spread. With low rates of current spread, graded changes in firing threshold produced correspondingly graded changes in output discharge. With high rates of current spread, the neuron became a bistable operator where spiking was enhanced if the threshold was below a certain level and suppressed if the threshold was above that level. Since alterations in firing threshold were shown to have the same effect on firing rate as alterations in synaptic input intensity, the neuron can be said to change from graded to contrast-enhancing in its response to stimuli of different intensities. The presence or absence of dendritic spiking was found to have a significant effect on the integrative properties of the simulated neuron. In particular, contrast enhancement was considerably more pronounced in neurons with passive than with active dendrites in that somatic spike rates reached a higher maximum when dendrites were passive. With active dendrites, a less intense input was needed to initiate somatic spiking than with passive dendrites because a distal dendritic spike could easily propagate by means of longitudinal current spread to the soma. Once somatic spiking was initiated, though, spike rates tended to be lower with active than with passive dendrites because the soma recovered more slowly from its post-spike refractory period if it was also influenced by refractory periods in the dendrites. The experiment of comparing neurons with active and passive dendrites was repeated at a different, higher value of synaptic input. The same differences in transfer properties between the active and passive cases emerged as before. Spiking patterns in neurons with active dendrites were also affected by the time distribution of synaptic inputs. In a previous study, inputs had been random over both space and time, varying about a predetermined mean, whereas in the present study, inputs were random over space but uniform over time. When inputs were made uniform over time, spiking became more difficult to initiate and the transition from graded to bistable response became less sharp.