Sensitive dependence of the coefficient of variation of interspike intervals on the lower boundary of membrane potential for the leaky integrate-and-fire neuron model

After the report of Softky and Koch [Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334-350], leaky integrate-and-fire models have been investigated to explain high coefficient of variation (CV) of interspike intervals (ISIs) at high firing rates observed in the cortex. The purpose of this paper is to study the effect of the position of a lower boundary of membrane potential on the possible value of CV of ISIs based on the diffusional leaky integrate-and-fire models with and without reversal potentials. Our result shows that the irregularity of ISIs for the diffusional leaky integrate-and-fire neuron significantly changes by imposing a lower boundary of membrane potential, which suggests the importance of the position of the lower boundary as well as that of the firing threshold when we study the statistical properties of leaky integrate-and-fire neuron models. It is worth pointing out that the mean-CV plot of ISIs for the diffusional leaky integrate-and-fire neuron with reversal potentials shows a close similarity to the experimental result obtained in Softky and Koch [Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334-350].     

Computer simulation of introductory neurophysiology

A computer-assisted learning (CAL) package, NeuroLab, developed for use by first-year university students undertaking professional programs in the health area, is described and evaluated. NeuroLab is a simulation of a laboratory, in which students are able to impale neurons to measure resting membrane potentials and subsequently undertake experiments including measuring resting membrane potentials, determining threshold potentials, measuring refractory periods, and examining effects on membrane potential through altering the membrane permeability to sodium and potassium ions. Students find the package to be a worthwhile learning experience, with 81 +/- 2.2% reporting the package increased their understanding of neuron function, and 78 +/- 2.5% expressing a desire for more CAL packages. Exposure to the package resulted in significantly higher mean scores in a multiple-choice question test on measuring neuron membrane potentials compared with those who were not exposed (mean scores out of 4 of 2.42 and 2.02, respectively, P < 0.001).     

The morphological basis of intracellular measurements in the cockroach tactile spine neuron

Summary The femoral tactile spine of the cockroach (Periplaneta americana) contains a single sensory neuron, which adapts rapidly and completely to step deformations of the spine. Techniques for stable intracellular recording from the tactile spine neuron have recently been established, allowing electrophysiological investigation of mechanotransduction and adaptation in this sensory neuron. However, intracellular recordings from the neuron produce a wide range of action potential heights and thresholds, raising the possibility that some penetrations are in adjacent, but closely coupled supporting glial cells. This problem is exacerbated because the cell cannot be visualized during penetration.Systematic measurements of action potential heights and thresholds were made in tactile spine cells, together with identification of some penetrated cells by intracellular injection of Lucifer Yellow. All stained cells were clearly sensory neurons, although their action potentials amplitudes varied from 9 mV to 80 mV. Smaller action potentials were broader than larger action potentials, and the changes in height and shape could be explained by a simple cable conduction model using measured morphological and electrical parameters. The model could also account for the observed relationship between action potential height and threshold.These results indicate that reliable recording from the tactile spine neuron is possible, but that variability in the positions of the penetration or the spike initiating zone cause an apparently wide range of electrophysiological measurements.     

Diffusion models for firing of a neuron with varying threshold

A stochastic model for the firing of a neuron with refractory properties is treated analytically. Refractory behavior is modeled by a threshold function θ(t) which is infinite immediately after the neuron fires, as well as during the absolute refractory period, and then decreases monotonically to the quiescent threshold level, θ_∞, during the relative refractory period. Using Wald's identity, input-output relations are derived analytically for the exponential threshold which has a time constant equal to the membrane time constant. A method for computing these relations for a general threshold is presented and is explicitly used for the general exponential threshold and the Hagiwara threshold, θ(t) = θ_∞e^α/t, where a is a constant.     

A study of the connection between the interneuron initiating pacemaker activity in a bursting neuron and the bursting neuron of the snailHelix pomatia

The connection between an interneuron initiating pacemaker activity in the bursting RPa1 neuron and the bursting neuron itself (Pin and Gola, 1983) has been analyzed in the snail Helix pomatia. Prolonged depolarization of the interneuronal membrane produced in it a series of action potentials as well as a parallel initiation or enhancement of bursting activity in the RPa1 neuron. If the discharge in the interneuron was evoked by short current pulses of threshold amplitude, no bursting activity was seen in the RPa1 neuron. However, short stimuli delivered on the background of subthreshold depolarization of the interneuronal membrane produced bursting activity in the RPa1 neuron. Under voltage-clamp conditions a slow inward current could be recorded in the RPa1 neuronal membrane after stimulation of the interneuron with a latency of about 2 sec. Short shifts of the holding potential in the hyperpolarizing direction at the maximum of this current produced a transient outward current. Replacement of extracellular Ca2+ by Mg2+ ions, as well as addition of 1 mM CdCl2 to the external solution, prevented the response to the interneuronal stimulation in the RPa1 neuron. Electron microscopic investigation of the interneuron has shown the abundance of Golgi complexes in its cytoplasm with electron-dense granules in their vicinity. It is concluded that the connection between the interneuron and the bursting neuron is of chemical origin, based on secretion by the former of some substances which activate at least two types of ionic channels in the membrane of the RPa1 neuron.     

The evolution of plant action potentials

Because certain primitive behavioral responses in the large sea snail Aplysia have recently been linked to neurophysiological events at a synaptic level, special interest attaches to the role played by calcium ions at such synapses. Using an extended version of the model applied earlier to trace the flow of energy and information through a ganglion of the medicinal leech (Triffet &; Green, 1980), the authors investigate the electropotential effects of small transient localized changes in the calcium concentration near the inner membrane surface of a neuron in the resting state.When this state is well below the firing threshold, changes in Ca²⁺ concentration less than 10^?8 M are shown to result only in low-level harmonic background oscillations. When the potential of the neurons is closer to threshold, however, and/or the Ca²⁺ concentration is of the order of 10^?8 M, easily recognizable graded potentials appear, and these grow into firing peaks when the calcium concentration is increased still further.Though no attempt is made to deal with the amplification effects dependent on calcium-vesicle interactions and the related release of transmitter molecules, a unified mechanism for the underlying calcium ion dynamics is proposed. Graded potentials of increasing size are associated with a progressive localized thickening of the inner and outer Debye layers. Moreover, the transverse and longitudinal calcium currents set up in such regions prove adequate to account for both the depletion of Ca²⁺ ions necessary to achieve habituation, and the increase in their concentration required for sensitization.     

Nonlinear neuronal mode analysis of action potential encoding in the cockroach tactile spine neuron

 Neuronal mode analysis is a recently developed technique for modelling the behavior of nonlinear systems whose outputs consist of action potentials. The system is modelled as a set of parallel linear filters, or modes, which feed into a multi-input threshold. The characteristics of the principal modes and the multi-input threshold device can be derived from Laguerre function expansions of the computed first- and second-order Volterra kernels when the system is stimulated with a randomly varying input. Neuronal mode analysis was used to model the encoder properties of the cockroach tactile spine neuron, a nonlinear, rapidly adapting, sensory neuron with reliable behavior. The analysis found two principal modes, one rapid and excitatory, the other slower and inhibitory. The two modes have analogies to two of the pathways in a block-structured model of the encoder that was developed from previous physiological investigations of the neuron. These results support the block-structured model and offer a new approach to identifying the components responsible for the nonlinear dynamic properties of this neuronal encoder. Received: 30 December 1994/Accepted in revised form: 25 April 1995     

Interactions between dissociated rat sympathetic neurons and skeletal muscle cells developing in cell culture: II. Synaptic mechanisms

Dissociated rat sympathetic neurons and skeletal myotubes were grown in mass cultures and microcultures as described in the accompanying paper (C. A. Nurse, 1981, Develop. Biol.88, 55–70). Excitatory synaptic interactions developed between neuron and neuron and between neuron and myotube. Electrical coupling occurred rarely. More often, the interaction was chemical and as shown in the accompanying paper, cholinergic. At the chemical neuronmyotube junctions, spontaneous miniature potentials (mejp's), sensitive to d-tubocurarine, occurred infrequently (1–20/min) and their discharge appeared random; their amplitude distribution was skew at all ages (up to ca. 4 weeks) even when the myotube was innervated by a single neuron in microculture. The evoked postsynaptic potentials (ejp's) in the myotubes were sensitive in conventional ways to the extracellular calcium (Ca_o) and magnesium (Mg_o) concentrations, and several tests suggested that transmission was quantal. In a few cases where a single neuron innervated a myotube in microculture, the estimated mean quantal unit size (assuming “Poisson” release) was similar to the mode of the spontaneous mejp amplitude histogram, suggesting that many of the spontaneous units were similar to the evoked units. At several junctions the quantal content m_o, estimated by the “failure” method, varied nonlinearly with Ca_o over the range 0.2–1.2 mM; data could be fitted by a power relation where the power ranged from 2.6 to 5.2.     

Ion channel noise can explain firing correlation in auditory nerves

Sensory neurons code information about stimuli in their sequence of action potentials (spikes). Intuitively, the spikes should represent stimuli with high fidelity. However, generating and propagating spikes is a metabolically expensive process. It is therefore likely that neural codes have been selected to balance energy expenditure against encoding error. Our recently proposed optimal, energy-constrained neural coder (Jones et al. Frontiers in Computational Neuroscience, 9, 61 2015) postulates that neurons time spikes to minimize the trade-off between stimulus reconstruction error and expended energy by adjusting the spike threshold using a simple dynamic threshold. Here, we show that this proposed coding scheme is related to existing coding schemes, such as rate and temporal codes. We derive an instantaneous rate coder and show that the spike-rate depends on the signal and its derivative. In the limit of high spike rates the spike train maximizes fidelity given an energy constraint (average spike-rate), and the predicted interspike intervals are identical to those generated by our existing optimal coding neuron. The instantaneous rate coder is shown to closely match the spike-rates recorded from P-type primary afferents in weakly electric fish. In particular, the coder is a predictor of the peristimulus time histogram (PSTH). When tested against in vitro cortical pyramidal neuron recordings, the instantaneous spike-rate approximates DC step inputs, matching both the average spike-rate and the time-to-first-spike (a simple temporal code). Overall, the instantaneous rate coder relates optimal, energy-constrained encoding to the concepts of rate-coding and temporal-coding, suggesting a possible unifying principle of neural encoding of sensory signals.     

A nonlinear model of step responses in the cockroach tactile spine neuron

Rapid sensory adaptation in the cockroach tactile spine neuron has previously been associated with a labile threshold for action potentials, which changes with the membrane potential by a process involving two time constants. A feed-forward, variable-threshold model has previously been used to account for the frequency response function of the neuron when stimulated with small-signal, white-noise currents. Here, we used a range of accurately controlled steps of extracellular current to stimulate the neuron. The same model was able to predict the individual step responses and could also fit the entire set of step responses from a single neuron if an initial, saturating, static nonlinearity was included. These results indicate that the two-time-constant, variable-threshold model can account for most of the rapidly adapting behavior of the tactile spine neuron.     

Evaluation of synaptic potential dynamics from evoked impulse activity of neurons]

To evaluate intracellular potentials in the region of spike initiation of function lambda (t) is suggested which describes the dependence on time of the density of conditional probability of generation by the neuron of the first impulse in response to the stimulus. Qualitative correspondence of the dynamics of membrane potentials and function lambda (t) is demonstrated on the analog model. The application of the function lambda (t) to the classification of the neurons of auditory system is shown to be promising. The difference between the function lambda (t) and normalized poststimulus histogram allows to evaluate the refracteriness of the neuron.     

锥体神经元的连接模式对突触后局部电位的依赖

脑皮层的功能连接模式与突触可塑性密切相关,受突触空间分布和刺激模式等多种因素的影响。尽管越来越多的证据表明突触可塑性不仅受突触后动作电位而且还受突触后局部树突电位的影响,但是目前尚不清楚神经元的功能连接模式是否和怎样依赖于突触后局部电位的。为此,本文建立了一个无需硬边界设置的、突触后局部膜电位依赖的可塑性模型。该模型具有突触强度的自平衡能力并且能够再现多种突触可塑性实验结果。基于该模型对两个锥体神经元的功能连接模式进行仿真的结果表明,当突触后局部电位都处于亚阈值时两个神经元无功能连接,如果一个神经元的突触后膜电位高于阈值电位则产生向该神经元的单向连接,当两个神经元的突触后膜电位都超过阈值电位时则产生双向连接,说明突触后局部膜电位分布是神经元功能连接模式形成的关键。研究结果加深了神经网络连接模式形成机制的理解,对学习和记忆的研究具有重要意义。     

Excitability of the soma in central nervous system neurons

The ability of the soma of a spinal dorsal horn neuron, a spinal ventral horn neuron (presumably a motoneuron), and a hippocampal pyramidal neuron to generate action potentials was studied using patch-clamp recordings from rat spinal cord slices, the "entire soma isolation" method, and computer simulations. By comparing original recordings from an isolated soma of a dorsal horn neuron with simulated responses, it was shown that computer models can be adequate for the study of somatic excitability. The modeled somata of both spinal neurons were unable to generate action potentials, showing only passive and local responses to current injections. A four- to eightfold increase in the original density of Na(+) channels was necessary to make the modeled somata of both spinal neurons excitable. In contrast to spinal neurons, the modeled soma of the hippocampal pyramidal neuron generated spikes with an overshoot of +9 mV. It is concluded that the somata of spinal neurons cannot generate action potentials and seem to resist their propagation from the axon to dendrites. In contrast, the soma of the hippocampal pyramidal neuron is able to generate spikes. It cannot initiate action potentials in the intact neurons, but it can support their back-propagation from the axon initial segment to dendrites.     

Why are insect olfactory receptor neurons grouped into sensilla? The teachings of a model investigating the effects of the electrical interaction between neurons on the transepithelial potential and the neuronal transmembrane potential

Insect olfactory receptor neurons are compartmentalized in sensilla. In a sensillum, typically two receptor neurons are in close contact and can influence each other through electrical interaction during stimulation. This interaction is passive, non-synaptic and a consequence of the electrical structure of the sensillum. It is analysed in a sensillum model and its effects on the neuron receptor potentials are investigated. The neurons in a sensillum can be both sensitive to a given odorant compound with the same sensory threshold or with different thresholds, or only one neuron be sensitive to the odorant. These three types of sensilla are compared with respect to maximum amplitude, threshold and dynamic range of the potentials. It is found that gathering neurons in the same sensillum is disadvantageous if they are identical, but can be advantageous if their thresholds differ. Application of these results to actual recordings from pheromone and food-odour olfactory sensilla is discussed.     

Pickpocket1 Is an Ionotropic Molecular Sensory Transducer

The molecular transformation of an external stimulus into changes in sensory neuron activity is incompletely described. Although a number of molecules have been identified that can respond to stimuli, evidence that these molecules can transduce stimulation into useful neural activity is lacking. Here we demonstrate that pickpocket1 (ppk1), a Drosophila homolog of mammalian Degenerin/epithelial sodium channels, encodes an acid-sensing sodium channel that conducts a transient depolarizing current in multidendritic sensory neurons of Drosophila melanogaster. Stimulation of Ppk1 is sufficient to bring these sensory neurons to threshold, eliciting a burst of action potentials. The transient nature of the neural activity produced by Ppk1 activation is the result of Ppk1 channel gating properties. This model is supported by the observation of enhanced bursting activity in neurons expressing a gain of function ppk1 mutant harboring the degenerin mutation. These findings demonstrate that Ppk1 can function as an ionotropic molecular sensory transducer capable of transforming the perception of a stimulus into phasic neuronal activity in sensory neurons.     

利用膜片钳技术标记脑片神经元的方法

目的:介绍一种利用膜片钳技术标记脑片神经元形态的方法.方法:利用振动切片机切好实验目标部位的脑片,用含有NeurobiotinTM Tracer的电极内液灌注玻璃微电极,并进行全细胞膜片钳记录;实验结束后将脑片先用4％多聚甲醛固定、漂洗,再用含有Streptavidin-Texas Red和Triton X-100的P...     

Some Effects of Calcium Ions on the Action Potential of Single Nodes of Ranvier

Action potentials of single frog nerve fibers were recorded with the air-gap method in "low Ca" (0.26 mM) and "high Ca" (4.2 mM) solutions and compared to spikes in normal Ringer''s (1.05 mM Ca). On increasing (Ca)_o the action potentials became shorter, the "knee" during the falling phase as well as the threshold for abolition moved to internal potentials more positive, and the spike recovery during the relative refractory period was faster. Outward current pulses applied during an action potential affected its configuration more in low Ca than in high Ca. The onset of the delayed rectification (in the absence of Na) was found faster in high Ga. After-potentials during anelectrotonus declined more rapidly in high Ca than in low Ca. The results are compared primarily with the voltage-clamp analysis of Ca effects on squid axons and satisfactory qualitative agreement is reached.     

Removal of rapid sensory adaptation from an insect mechanoreceptor neuron by oxidizing agents which affect sodium channel inactivation

1. The femoral tactile spine of the cockroach is a mechanoreceptor with a single sensory neuron. The response to a step movement is a burst of action potentials which decays to zero in about 1 s. This rapid adaptation is a property of the action potential initiating region of the neuron. 2. The oxidizing agents chloramine-T and N-chlorosuccinimide selectively and irreversibly remove sodium channel inactivation from neurons in several preparations and are believed to act by oxidation of methionine or cysteine residues in the proteins of the sodium channel. 3. Chloramine-T and N-chlorosuccinimide, applied for a controlled time period, eliminated the rapid adaptation of the tactile spine neuron to an electrical depolarization. After treatment it fired tonically in response to a steady current stimulus. Longer applications of the agents eventually raised the threshold for action potential initiation. 4. Threshold behavior in the tactile spine neuron was characterized by measuring strength-duration relationships for stimulation with extracellular current pulses at the action potential initiating region. The two oxidizing agents caused a voltage-dependent modification of the dynamic threshold properties which led to the change from rapidly adapting to tonic behavior. 5. Two stronger oxidizing agents, N-bromoacetamide and N-bromosuccinimide, raised the threshold of the neuron without removing rapid adaptation. These two agents act similarly to chloramine-T and N-chlorosuccinimide on sodium inactivation in other neurons but are believed to oxidize the tryptophan, tyrosine and histidine residues of proteins in addition to cysteine and methionine.(ABSTRACT TRUNCATED AT 250 WORDS)