Neural Coding with Graded Membrane Potential Changes and Spikes

The neural encoding of sensory stimuli is usually investigated for spike responses, although many neurons are known to convey information by graded membrane potential changes. We compare by model simulations how well different dynamical stimuli can be discriminated on the basis of spiking or graded responses. Although a continuously varying membrane potential contains more information than binary spike trains, we find situations where different stimuli can be better discriminated on the basis of spike responses than on the basis of graded responses. Spikes can be superior to graded membrane potential fluctuations if spikes sharpen the temporal structure of neuronal responses by amplifying fast transients of the membrane potential. Such fast membrane potential changes can be induced deterministically by the stimulus or can be due to membrane potential noise that is influenced in its statistical properties by the stimulus. The graded response mode is superior for discrimination between stimuli on a fine time scale.     

Fluorescence induction in Avena sativa investigated by modulated light

The structurated slow fluorescence induction of six days old seedlings of Avena sativa L., cv. Seger I (Svalöf, Sweden) has been investigated in its responses to systematic changes in the exciting conditions. The intensity of the exciting light was periodically altered between a high and a low value, and after the third period the resulting fluorescence induction curves became stationary. These stationary responses may all be resolved into four characteristic fluorescence transients, whose forms were rather independent of the exciting conditions. The heights of these transients were examined as a function of the exciting wavelength and the high level intensity. From these data it is concluded that the third transient originates from cyclic electron transport and that the fourth transient monitors the degree of energy transfer from the light harvesting complex to photosystem II. These two last transients of the induction curve are equivalent to the structurated slow fluorescence changes in ordinary induction curves.     

Firing-rate models capture essential response dynamics of LGN relay cells

Firing-rate models provide a practical tool for studying signal processing in the early visual system, permitting more thorough mathematical analysis than spike-based models. We show here that essential response properties of relay cells in the lateral geniculate nucleus (LGN) can be captured by surprisingly simple firing-rate models consisting of a low-pass filter and a nonlinear activation function. The starting point for our analysis are two spiking neuron models based on experimental data: a spike-response model fitted to data from macaque (Carandini et al. J. Vis., 20(14), 1–2011, 2007), and a model with conductance-based synapses and afterhyperpolarizing currents fitted to data from cat (Casti et al. J. Comput. Neurosci., 24(2), 235–252, 2008). We obtained the nonlinear activation function by stimulating the model neurons with stationary stochastic spike trains, while we characterized the linear filter by fitting a low-pass filter to responses to sinusoidally modulated stochastic spike trains. To account for the non-Poisson nature of retinal spike trains, we performed all analyses with spike trains with higher-order gamma statistics in addition to Poissonian spike trains. Interestingly, the properties of the low-pass filter depend only on the average input rate, but not on the modulation depth of sinusoidally modulated input. Thus, the response properties of our model are fully specified by just three parameters (low-frequency gain, cutoff frequency, and delay) for a given mean input rate and input regularity. This simple firing-rate model reproduces the response of spiking neurons to a step in input rate very well for Poissonian as well as for non-Poissonian input. We also found that the cutoff frequencies, and thus the filter time constants, of the rate-based model are unrelated to the membrane time constants of the underlying spiking models, in agreement with similar observations for simpler models.     

Spike-triggered dendritic calcium transients depend on synaptic activity in the cricket giant interneurons.

The relationship between electrical activity and spike-induced Ca2+ increases in dendrites was investigated in the identified wind-sensitive giant interneurons in the cricket. We applied a high-speed Ca2+ imaging technique to the giant interneurons, and succeeded in recording the transient Ca2+ increases (Ca2+ transients) induced by a single action potential, which was evoked by presynaptic stimulus to the sensory neurons. The dendritic Ca2+ transients evoked by a pair of action potentials accumulated when spike intervals were shorter than 100 ms. The amplitude of the Ca2+ transients induced by a train of spikes depended on the number of action potentials. When stimulation pulses evoking the same numbers of action potentials were separately applied to the ipsi- or contra-lateral cercal sensory nerves, the dendritic Ca2+ transients induced by these presynaptic stimuli were different in their amplitude. Furthermore, the side of presynaptic stimulation that evoked larger Ca2+ transients depended on the location of the recorded dendritic regions. This result means that the spike-triggered Ca2+ transients in dendrites depend on postsynaptic activity. It is proposed that Ca2+ entry through voltage-dependent Ca2+ channels activated by the action potentials will be enhanced by excitatory synaptic inputs at the dendrites in the cricket giant interneurons.     

Biophysical model of synaptic plasticity dynamics

We discuss a biophysical model of synaptic plasticity that provides a unified view of the outcomes of synaptic modification protocols, including: (1) prescribed time courses of postsynaptic intracellular Ca²⁺ release, (2) postsynaptic voltage clamping with presentation of presynaptic spike trains at various frequencies, (3) direct postsynaptic response to presynaptic spike trains at various frequencies, and (4) LTP/LTD as a response to precisely timed presynaptic and postsynaptic spikes.     

Spike‐triggered dendritic calcium transients depend on synaptic activity in the cricket giant interneurons

The relationship between electrical activity and spike‐induced Ca²⁺ increases in dendrites was investigated in the identified wind‐sensitive giant interneurons in the cricket. We applied a high‐speed Ca²⁺ imaging technique to the giant interneurons, and succeeded in recording the transient Ca²⁺ increases (Ca²⁺ transients) induced by a single action potential, which was evoked by presynaptic stimulus to the sensory neurons. The dendritic Ca²⁺ transients evoked by a pair of action potentials accumulated when spike intervals were shorter than 100 ms. The amplitude of the Ca²⁺ transients induced by a train of spikes depended on the number of action potentials. When stimulation pulses evoking the same numbers of action potentials were separately applied to the ipsi‐ or contra‐lateral cercal sensory nerves, the dendritic Ca²⁺ transients induced by these presynaptic stimuli were different in their amplitude. Furthermore, the side of presynaptic stimulation that evoked larger Ca²⁺ transients depended on the location of the recorded dendritic regions. This result means that the spike‐triggered Ca²⁺ transients in dendrites depend on postsynaptic activity. It is proposed that Ca²⁺ entry through voltage‐dependent Ca²⁺ channels activated by the action potentials will be enhanced by excitatory synaptic inputs at the dendrites in the cricket giant interneurons. © 2002 Wiley Periodicals, Inc. J Neurobiol 50: 234–244, 2002; DOI 10.1002/neu.10032     

Neuronal spike trains and stochastic point processes. I. The single spike train

In a growing class of neurophysiological experiments, the train of impulses (“spikes”) produced by a nerve cell is subjected to statistical treatment involving the time intervals between spikes. The statistical techniques available for the analysis of single spike trains are described and related to the underlying mathematical theory, that of stochastic point processes, i.e., of stochastic processes whose realizations may be described as series of point events occurring in time, separated by random intervals. For single stationary spike trains, several orders of complexity of statistical treatment are described; the major distinction is that between statistical measures that depend in an essential way on the serial order of interspike intervals and those that are order-independent. The interrelations among the several types of calculations are shown, and an attempt is made to ameliorate the current nomenclatural confusion in this field. Applications, interpretations, and potential difficulties of the statistical techniques are discussed, with special reference to types of spike trains encountered experimentally. Next, the related types of analysis are described for experiments which involve repeated presentations of a brief, isolated stimulus. Finally, the effects of nonstationarity, e.g. long-term changes in firing rate, on the various statistical measures are discussed. Several commonly observed patterns of spike activity are shown to be differentially sensitive to such changes. A companion paper covers the analysis of simultaneously observed spike trains.     

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.     

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

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Studying spike trains using a van Rossum metric with a synapse-like filter

Spike trains are unreliable. For example, in the primary sensory areas, spike patterns and precise spike times will vary between responses to the same stimulus. Nonetheless, information about sensory inputs is communicated in the form of spike trains. A challenge in understanding spike trains is to assess the significance of individual spikes in encoding information. One approach is to define a spike train metric, allowing a distance to be calculated between pairs of spike trains. In a good metric, this distance will depend on the information the spike trains encode. This method has been used previously to calculate the timescale over which the precision of spike times is significant. Here, a new metric is constructed based on a simple model of synaptic conductances which includes binding site depletion. Including binding site depletion in the metric means that a given individual spike has a smaller effect on the distance if it occurs soon after other spikes. The metric proves effective at classifying neuronal responses by stimuli in the sample data set of electro-physiological recordings from the primary auditory area of the zebra finch fore-brain. This shows that this is an effective metric for these spike trains suggesting that in these spike trains the significance of a spike is modulated by its proximity to previous spikes. This modulation is a putative information-coding property of spike trains.     

大鼠初级传入纤维与脊髓背角神经元间的动作电序列的突触传递

外周感觉神经元通过动作电位序列对信号进行编码,这些动作电位序列经过突触传递最终到达脑部。但是各种脉冲序列如何通过神经元之间的化学突触进行传递依然是一个悬而未决的问题。研究了初级传入A6纤维与背角神经元之间各种动作电位序列的突触传递过程。用于刺激的规则,周期、随机脉冲序列由短簇脉冲或单个脉冲构成。定义“事件”(event)为峰峰问期(intefspike interval)小于或等于规定阈值的最长动作电位串,然后从脉冲序列中提取事件间间期(interevent interval,IEI)。用时间,IEI图与回归映射的方法分析IEI序列,结果表明在突触后输出脉冲序列中可以检测到突触前脉冲序列的主要时间结构特征,特别是在短簇脉冲作为刺激单位时。通过计算输入与输出脉冲序列的互信息,发现短簇脉冲可以更可靠地跨突触传递由输入序列携带的神经信息。这些结果表明外周输入脉冲序列的主要时间结构特征可以跨突触传递,在突触传递神经信息的过程中短簇脉冲更为有效。这一研究在从突触传递角度探索神经信息编码方面迈出了一步。     

Weakly nonlinear analysis of a hyperbolic model for animal group formation

We consider an one-dimensional nonlocal hyperbolic model for group formation with application to self-organizing collectives of animals in homogeneous environments. Previous studies have shown that this model displays at least four complex spatial and spatiotemporal group patterns. Here, we use weakly nonlinear analysis to better understand the mechanisms involved in the formation of two of these patterns, namely stationary pulses and traveling trains. We show that both patterns arise through subcritical bifurcations from spatially homogeneous steady states. We then use these results to investigate the effect of two social interactions (attraction and alignment) on the structure of stationary and moving animal groups. While attraction makes the groups more compact, alignment has a dual effect, depending on whether the groups are stationary or moving. More precisely, increasing alignment makes the stationary groups compact, and the moving groups more elongated. Also, the results show the existence of a threshold for the total group density, above which, coordinated behaviors described by stationary and moving groups persist for a long time.      

Ca2+ signal summation and NFATc1 nuclear translocation in sympathetic ganglion neurons during repetitive action potentials

NFATc-mediated gene expression constitutes a critical step during neuronal development and synaptic plasticity. Although considerable information is available regarding the activation and functionality of specific NFATc isoforms, in neurons little is known about how sensitive NFAT nuclear translocation is to specific patterns of electrical activity. Here we used high-speed fluo-4 confocal imaging to monitor action potential (AP)-induced cytosolic Ca2+ transients in rat sympathetic neurons. We have recorded phasic and repetitive AP patterns, and corresponding Ca2+ transients initiated by either long (100-800 ms) current-clamp pulses, or single brief (2 ms) electrical field stimulation. We address the functional consequences of these AP and Ca2+ transient patterns, by using an adenoviral construct to express NFATc1-CFP and evaluate NFATc1-CFP nuclear translocation in response to specific patterns of electrical activity. Ten Hertz trains stimulation induced nuclear translocation of NFATc1, whereas 1 Hz trains did not. However, 1 Hz train stimulation did result in NFATc1 translocation in the presence of 2 mM Ba2+, which inhibits M-currents and promotes repetitive firing and the accompanying small (approximately 0.6 DeltaF/F0) repetitive and summating Ca2+ transients. Our results demonstrate that M-current inhibition-mediated spike frequency facilitation enhances cytosolic Ca2+ signals and NFATc1 nuclear translocation during trains of low frequency electrical stimulation.     

Further Study of the Relationship between Pre- and Postsynaptic Potentials in the Squid Giant Synapse

The minimal presynaptic depolarization (MPD) for producing a detectable postsynaptic potential (PSP) was lower than 25 mv in normal or tetrodotoxin (TTX)-containing seawater. The MPD was about 10 mv when a small amount of tetraethylammonium ions (TEA) was injected into the presynaptic terminal. Application of linearly increasing depolarizing current to the normal presynaptic terminal at times produced a PSP before a presynaptic spike was evoked; the rate of rise of the resulting PSP was much slower than that of a PSP triggered by the normal presynaptic spike. A brief depolarizing pulse that preceded the presynaptic spike in normal seawater or the initial transient presynaptic depolarization in TTX decreased the PSP. It increased the PSP when it was applied during the spike or initial transient depolarization. Hyperpolarizing pulses had the reverse effect. The Off-PSP was also modified by inserting pulses at an initial part of the recovery phase of the strong presynaptic depolarization. These results indicate further that increases in Na⁺ and K⁺ conductance during presynaptic spike activity are not a requirement for transmitter release; the rate of release of transmitter can be controlled by electrical manipulation of the presynaptic terminal; there is a superficial correspondence between the time courses of presynaptic depolarization and the resulting PSP. Thus presynaptic depolarization appears to be only the first step in the series of events constituting excitation-transmitter release coupling. It may not be a necessary step for the release mechanism.     

Reverse spikeology: predicting single spikes.

Neural models that simulate single spike trains can help us understand the basic principles of neural coding in vision. Keat et al. (2001) develop a hybrid model that combines spatiotemporal filtering with nonlinear spike generation. The model does a good job of predicting the responses of single retinal ganglion cells and thalamic relay neurons.     

Responses of Ca2+-binding proteins to localized,transient changes in intracellular [Ca2+

In smooth muscle cells, various transient, localized [Ca(2+)] changes have been observed that are thought to regulate cell function without necessarily inducing contraction. Although a great deal of effort has been put into detecting these transients and elucidating the mechanisms involved in their generation, the extent to which these transient Ca(2+) signals interact with intracellular Ca(2+)-binding molecules remains relatively unknown. To understand how the spatial and temporal characteristics of an intracellular Ca(2+) signal influence its interaction with Ca(2+)-binding proteins, mathematical models of Ca(2+) diffusion and regulation in smooth muscle cells were used to study Ca(2+) binding to prototypical proteins with one or two Ca(2+)-binding sites. Simulations with the models: (1) demonstrate the extent to which the rate constants for Ca(2+)-binding to proteins and the spatial and temporal characteristics of different Ca(2+) transients influence the magnitude and time course of the responses of these proteins to the transients; (2) predict significant differences in the responses of proteins with one or two Ca(2+)-binding sites to individual Ca(2+) transients and to trains of transients; (3) demonstrate how the kinetic characteristics determine the fidelity with which the responses of Ca(2+)-sensitive molecules reflect the magnitude and time course of transient Ca(2+) signals. Overall, this work demonstrates the clear need for complete information about the kinetics of Ca(2+) binding for determining how well Ca(2+)-binding molecules respond to different types of Ca(2+) signals. These results have important implications when considering the possible modulation of Ca(2+)- and Ca(2+)/calmodulin-dependent proteins by localized intracellular Ca(2+) transients in smooth muscle cells and, more generally, in other cell types.     

Robust odor coding via inhalation-coupled transient activity in the mammalian olfactory bulb

It has been proposed that a single sniff generates a "snapshot" of the olfactory world. However, odor coding on this timescale is poorly understood, and it is not known whether coding is invariant to changes in respiration frequency. We investigated this by recording spike trains from the olfactory bulb in awake, behaving rats. During rapid sniffing, odor inhalation triggered rapid and reliable cell- and odor-specific temporal spike patterns. These fine temporal responses conveyed substantial odor information within the first ～100 ms, and correlated with behavioral discrimination time on a trial-by-trial basis. Surprisingly, the initial transient portions of responses were highly conserved between rapid sniffing and slow breathing. Firing rates over the entire respiration cycle carried less odor information, did not correlate with behavior, and were poorly conserved across respiration frequency. These results suggest that inhalation-coupled transient activity forms a robust neural code that is invariant to changes in respiration behavior.     

Calcium transients in cerebellar granule cell presynaptic terminals.

Calcium ions act presynaptically to modulate synaptic strength and to trigger neurotransmitter release. Here we detect stimulus-evoked changes in residual free calcium ([Ca2+]i) in rat cerebellar granule cell presynaptic terminals. Granule cell axons, known as parallel fibers, and their associated boutons, were labeled with several calcium indicators. When parallel fibers were extracellularly activated with stimulus trains, calcium accumulated in the terminals, producing changes in the fluorescence of the indicators. During the stimulus train, the fluorescence change per pulse became progressively smaller with the high affinity indicators Fura-2 and calcium green-2 but remained constant with the low affinity dyes BTC and furaptra. In addition, fluorescence transients of high affinity dyes were slower than those of low affinity indicators, which appear to accurately report the time course of calcium transients. Simulations show that differences in the observed transients can be explained by the different affinities and off rates of the fluorophores. The return of [Ca2+]i to resting levels can be approximated by an exponential decay with a time constant of 150 ms. On the basis of the degree of saturation in the response of high affinity dyes observed during trains, we estimate that each action potential increases [Ca2+]i in the terminal by several hundred nanomolar. These findings indicate that in these terminals [Ca2+]i transients are much larger and faster than those observed in larger boutons, such as those at the neuromuscular junction. Such rapid [Ca2+]i dynamics may be found in many of the terminals in the mammalian brain that are similar in size to parallel fiber boutons.     

Analysis of the retina via suprafusion electroretinography.

Electroretinographic (ERG) transient responses elicited in monkeys by abrupt changes in the periodicity of a rapidly intermittent (suprafusion) luminance stimulus were studied experimentally, and analyzed and interpreted through a theory of dynamic retinal responses. The suprafusion ERG transients are confirmed to behave in accord with theoretical expectation, as elemental responses (retinal Green's functions). By aid of the theory the ERG wave-forms can be reduced to two significant elements. One element, accounting for approximately two-thirds of the total ERG variance, is strictly linear, and correlates well with simultaneously evoked cortical (VEP) transients which were previously related to suprafusion perception in humans. The other element, comprising approximately one-third the ERG transient, is a rectification, with properties indicating that it may arise from a specific layer of retinal neurons (amacrine cells); on this assumption the theory demonstrates that high-frequency nonlinear ERG flicker can isolate activities proximal and distal to the rectifying (amacrine) layer. Thus, the hypothesis of an amacrine origin for the rectifying element entails the possibility that suprafusion ERG studies could accomplish in vivo "dissection" of the human retina.     

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.