Noise-tolerant stimulus discrimination by synchronization with depressing synapses

 Some synapses between cortical pyramidal neurons exhibit a rapid depression of excitatory postsynaptic potentials for successive presynaptic spikes. Since depressing synapses do not transmit information on sustained presynaptic firing rates, it has been speculated that they are favorable for temporal coding. In this paper, we study the dynamical effects of depressing synapses on stimulus-induced transient synchronization in a simple network of inhibitory interneurons and excitatory neurons, assuming that the recurrent excitation is mediated by depressing synapses. This synchronization occurs in a temporal pattern which depends on a given stimulus. Since the presence of noise is always a potential hazard in temporal coding, we investigate the extent to which noise in stimuli influences the synchronization phenomena. It is demonstrated that depressing synapses greatly contribute to suppressing the influences of noise on the stimulus-specific temporal patterns of synchronous firing. The timing-based Hebbian learning revealed by physiological experiments is shown to stabilize the temporal patterns in cooperation with synaptic depression. Thus, the times at which synchronous firing occurs provides a reliable information representation in the presence of synaptic depression. Received: 5 July 2000 / Accepted in revised form: 12 January 2001     

Statistical characteristics of climbing fiber spikes necessary for efficient cerebellar learning

 Mean firing rates (MFRs), with analogue values, have thus far been used as information carriers of neurons in most brain theories of learning. However, the neurons transmit the signal by spikes, which are discrete events. The climbing fibers (CFs), which are known to be essential for cerebellar motor learning, fire at the ultra-low firing rates (around 1 Hz), and it is not yet understood theoretically how high-frequency information can be conveyed and how learning of smooth and fast movements can be achieved. Here we address whether cerebellar learning can be achieved by CF spikes instead of conventional MFR in an eye movement task, such as the ocular following response (OFR), and an arm movement task. There are two major afferents into cerebellar Purkinje cells: parallel fiber (PF) and CF, and the synaptic weights between PFs and Purkinje cells have been shown to be modulated by the stimulation of both types of fiber. The modulation of the synaptic weights is regulated by the cerebellar synaptic plasticity. In this study we simulated cerebellar learning using CF signals as spikes instead of conventional MFR. To generate the spikes we used the following four spike generation models: (1) a Poisson model in which the spike interval probability follows a Poisson distribution, (2) a gamma model in which the spike interval probability follows the gamma distribution, (3) a max model in which a spike is generated when a synaptic input reaches maximum, and (4) a threshold model in which a spike is generated when the input crosses a certain small threshold. We found that, in an OFR task with a constant visual velocity, learning was successful with stochastic models, such as Poisson and gamma models, but not in the deterministic models, such as max and threshold models. In an OFR with a stepwise velocity change and an arm movement task, learning could be achieved only in the Poisson model. In addition, for efficient cerebellar learning, the distribution of CF spike-occurrence time after stimulus onset must capture at least the first, second and third moments of the temporal distribution of error signals. Received: 28 January 2000 / Accepted in revised form: 2 August 2000     

Spike-timing dependent synaptic plasticity: a phenomenological framework

 In this paper a phenomenological model of spike-timing dependent synaptic plasticity (STDP) is developed that is based on a Volterra series-like expansion. Synaptic weight changes as a function of the relative timing of pre- and postsynaptic spikes are described by integral kernels that can easily be inferred from experimental data. The resulting weight dynamics can be stated in terms of statistical properties of pre- and postsynaptic spike trains. Generalizations to neurons that fire two different types of action potentials, such as cerebellar Purkinje cells where synaptic plasticity depends on correlations in two distinct presynaptic fibers, are discussed. We show that synaptic plasticity, together with strictly local bounds for the weights, can result in synaptic competition that is required for any form of pattern formation. This is illustrated by a concrete example where a single neuron equipped with STDP can selectively strengthen those synapses with presynaptic neurons that reliably deliver precisely timed spikes at the expense of other synapses which transmit spikes with a broad temporal distribution. Such a mechanism may be of vital importance for any neuronal system where information is coded in the timing of individual action potentials. Received: 23 January 2002 / Accepted: 28 March 2002 Correspondence to: W.M. Kistler (e-mail: kistler@anat.fgg.eur.nl Fax: +31 10 408 5459)     

Encoding of luminance and contrast by linear and nonlinear synapses in the retina

Understanding how neural circuits transmit information is technically challenging because the neural code is contained in the activity of large numbers of neurons and synapses. Here, we use genetically encoded reporters to image synaptic transmission across a population of sensory neurons-bipolar cells in the retina of live zebrafish. We demonstrate that the luminance sensitivities of these synapses varies over 10(4) with a log-normal distribution. About half the synapses made by ON and OFF cells alter their polarity of transmission as a function of luminance to generate a triphasic tuning curve with distinct maxima and minima. These nonlinear synapses signal temporal contrast with greater sensitivity than linear ones. Triphasic tuning curves increase the dynamic range over which bipolar cells signal light and improve the efficiency with which luminance information is transmitted. The most efficient synapses signaled luminance using just 1 synaptic vesicle per second per distinguishable gray level.     

A Synaptic Mechanism for Temporal Filtering of Visual Signals

The visual system transmits information about fast and slow changes in light intensity through separate neural pathways. We used in vivo imaging to investigate how bipolar cells transmit these signals to the inner retina. We found that the volume of the synaptic terminal is an intrinsic property that contributes to different temporal filters. Individual cells transmit through multiple terminals varying in size, but smaller terminals generate faster and larger calcium transients to trigger vesicle release with higher initial gain, followed by more profound adaptation. Smaller terminals transmitted higher stimulus frequencies more effectively. Modeling global calcium dynamics triggering vesicle release indicated that variations in the volume of presynaptic compartments contribute directly to all these differences in response dynamics. These results indicate how one neuron can transmit different temporal components in the visual signal through synaptic terminals of varying geometries with different adaptational properties.     

Axon initial segment Kv1 channels control axonal action potential waveform and synaptic efficacy

Action potentials are binary signals that transmit information via their rate and temporal pattern. In this context, the axon is thought of as a transmission line, devoid of a role in neuronal computation. Here, we show a highly localized role of axonal Kv1 potassium channels in shaping the action potential waveform in the axon initial segment (AIS) of layer 5 pyramidal neurons independent of the soma. Cell-attached recordings revealed a 10-fold increase in Kv1 channel density over the first 50 microm of the AIS. Inactivation of AIS and proximal axonal Kv1 channels, as occurs during slow subthreshold somatodendritic depolarizations, led to a distance-dependent broadening of axonal action potentials, as well as an increase in synaptic strength at proximal axonal terminals. Thus, Kv1 channels are strategically positioned to integrate slow subthreshold signals, providing control of the presynaptic action potential waveform and synaptic coupling in local cortical circuits.     

Spatial and temporal correlations of spike trains in frog retinal ganglion cells

For a neuron, firing activity can be in synchrony with that of others, which results in spatial correlation; on the other hand, spike events within each individual spike train may also correlate with each other, which results in temporal correlation. In order to investigate the relationship between these two phenomena, population neurons’ activities of frog retinal ganglion cells in response to binary pseudo-random checker-board flickering were recorded via a multi-electrode recording system. The spatial correlation index (SCI) and temporal correlation index (TCI) were calculated for the investigated neurons. Statistical results showed that, for a single neuron, the SCI and TCI values were highly related—a neuron with a high SCI value generally had a high TCI value, and these two indices were both associated with burst activities in spike train of the investigated neuron. These results may suggest that spatial and temporal correlations of single neuron’s spiking activities could be mutually modulated; and that burst activities could play a role in the modulation. We also applied models to test the contribution of spatial and temporal correlations for visual information processing. We show that a model considering spatial and temporal correlations could predict spikes more accurately than a model does not include any correlation.     

Temporal pattern discrimination of impulse sequences in the computer-simulated nerve cells

This paper deals with some properties of temporal pattern discrimination performed by single digital-computer simulated synaptic cells. To clarify these properties, the Shannon's entropy method which is a basic notion in the information theory and a fundamental approach for the design of pattern classification system was applied to input-output relations of the digital computer simulated synaptic cells. We used the average mutual information per symbol as a measure for the temporal pattern sensitivity of the nerve cells, and the average response entropy per symbol as a measure for the frequency transfer characteristics. To use these measures, the probability of a post-synaptic spike as a function of the recent history of pre-synaptic intervals was examined in detail. As the results of such application, it was found that the EPSP size is closely related to the pattern of impulse sequences of the input, and the average mutual information per symbol for EPSP size is given by a bimodal curve with two maximum values. One is a small EPSP size and the other is a large EPSP size. In two maximum points, the structure of the temporal pattern discrimination reverses each other. In addition, the relation between the mean frequency, or the form of impulse sequences of the input, and the average mutual information per symbol has been examined. The EPSP size at one maximum point of average mutual information is in inverse proportion to the magnitude of input mean frequency which relates to the convergence number of input terminal, while that at the other maximum point is proportional to that of the mean frequency. Moreover, the temporal pattern discrimination is affected remarkably by whether successive interspike intervals of the input are independent or not in the statistical sense. Computer experiments were performed by the semi-Markov processes with three typical types of transition matrixes and these shuffling processes. The average mutual informations in the cases of these semi-Markov processes are in contrast to those of the shuffling processes which provide a control case. The temporal structure of successive interspike intervals of the input is thus a significant factor in pattern discrimination at synaptic level.     

Astrocytes optimize the synaptic transmission of information

Chemical synapses transmit information via the release of neurotransmitter-filled vesicles from the presynaptic terminal. Using computational modeling, we predict that the limited availability of neurotransmitter resources in combination with the spontaneous release of vesicles limits the maximum degree of enhancement of synaptic transmission. This gives rise to an optimal tuning that depends on the number of active zones. There is strong experimental evidence that astrocytes that enwrap synapses can modulate the probabilities of vesicle release through bidirectional signaling and hence regulate synaptic transmission. For low-fidelity hippocampal synapses, which typically have only one or two active zones, the predicted optimal values lie close to those determined by experimentally measured astrocytic feedback, suggesting that astrocytes optimize synaptic transmission of information.     

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.     

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。     

Stability analysis of a mathematical neuron model

The “second method” of Liapunov is used to perform a stability analysis of a mathematical model of the neuron. This analysis is based on the hypothesis that the firing of the neuron coincides with a temporary state of instability of the system, and that the initiation of all-or-none process depends on the magnitude of membrane depolarization and its first time derivative. It is found that the stability (and hence the possibility of a second firing) is restored approximately when the rate of membrane repolarization is at a maximum. This result predicts that the duration of the period of absolute refractoriness in neurons would be about 75 per cent of the spike duration, and thus shorter than the value usually obtained from experimental measurements.     

Regulation of gap junction coupling in the developing neocortex

In the developing mammalian, neocortex gap junctions represent a transient, metabolic, and electrical communication system. These gap junctions may play a crucial role during the formation and refinement of neocortical synaptic circuitries. This article focuses on two major points. First, the influence of gap junctions on electrotonic cell properties will be considered. Both the time-course and the amplitude of synaptic potentials depend,inter alia, on the integration capabilities of the postsynaptic neurons. These capabilities are, to a considerable extent, determined by the electrotonic characteristics of the postsynaptic cell. As a consequence, the efficacy of chemical synaptic inputs may be crucially affected by the presence of gap junctions. The second major topic is the regulation of gap junctional communication by neurotransmitters via second messenger pathways. The monoaminergic neuromodulators dopamine, nordrenaline, and serotonin reduce gap junction coupling via activation of two different intracellular signaling cascades—the cAMP/protein kinase A pathway and the IP₃/Ca²⁺/protein kinase C pathway, 013 respectively. In addition, gap junctional communication seems to be modulated by the nitric oxide (NO)/cGMP system. Since NO production can be stimulated by glutamate-induced calcium influx, the NO/cGMP-dependent modulation of gap junctions might represent a functional link between developing glutamatergic synaptic transmission and the gap junctional network. Thus, it might be of particular importance in view of a role of gap junctions during the process of circuit formation.     

Using trophic hierarchy to understand food web structure

Link arrangement in food webs is determined by the species' feeding habits. This work investigates whether food web topology is organized in a gradient of trophic positions from producers to consumers. To this end, we analyzed 26 food webs for which the consumption rate of each species was specified. We computed the trophic positions and the link densities of all species in the food webs. Link density measures how much each species contributes to the distribution of energy in the system. It is expressed as the number of links species establish with other nodes, weighted by their magnitude. We computed these two metrics using various formulations developed in the ecological network analysis framework. Results show a positive correlation between trophic position and link density across all the systems, regardless the specific formulas used to measure the two quantities. We performed the same analysis on the corresponding binary matrices (i.e. removing information about rates). In addition, we investigated the relation between trophic position and link density in: a) simulated binary webs with same connectance as the original ones; b) weighted webs with constant topology but randomized link strengths and c) weighted webs with constant connectance where both topology and link strengths are randomized. The correlation between the two indices attenuates, vanishes or becomes negative in the case of binary food webs and simulated data (weighted and unweighted).
According to our analysis, link density in food webs decreases with trophic position so that it is greatly reduced toward the top of the trophic hierarchy. This outcome, that seems to challenge previous conclusions based on null models, strongly depends on link quantification. Including interaction strengths may improve substantially our understanding of food web organization, and possibly contradict results based on the analysis of binary webs.     

Some implications of the short-term synaptic plasticity for neuronal computation: a model study

Spikes arriving at the synaptic connection produce short-term plastic changes of the synaptic efficacy. Model experiments have shown that paired-pulse facilitation attaining its maximum after a specific interval between a pair of arriving spikes might turn a “weak” plastic synapse attached to an integrate-and-fire neuron to a frequency-tuned device. Resulting computational capabilities create biologically plausible mechanisms of information processing relating to: (i) real-time identification of temporal patterns in a stream of random spiking activity (a recognition problem); and (ii) codetermination of the specific activity routing among neurons (an addressing problem) resulting in definite spatio-temporal patterns of the output activity (an input-output pattern problem).     

Efficiency of neural transmission as a function of synaptic noise, threshold, and source characteristics

There has been a growing interest in the estimation of information carried by a single neuron and multiple single units or population of neurons to specific stimuli. In this paper we analyze, inspired by article of Levy and Baxter (2002), the efficiency of a neuronal communication by considering dendrosomatic summation as a Shannon-type channel (1948) and by considering such uncertain synaptic transmission as part of the dendrosomatic computation. Specifically, we study Mutual Information between input and output signals for different types of neuronal network architectures by applying efficient entropy estimators. We analyze the influence of the following quantities affecting transmission abilities of neurons: synaptic failure, activation threshold, firing rate and type of the input source. We observed a number of surprising non-intuitive effects. It turns out that, especially for lower activation thresholds, significant synaptic noise can lead even to twofold increase of the transmission efficiency. Moreover, the efficiency turns out to be a non-monotonic function of the activation threshold. We find a universal value of threshold for which a local maximum of Mutual Information is achieved for most of the neuronal architectures, regardless of the type of the source (correlated and non-correlated). Additionally, to reach the global maximum the optimal firing rates must increase with the threshold. This effect is particularly visible for lower firing rates. For higher firing rates the influence of synaptic noise on the transmission efficiency is more advantageous. Noise is an inherent component of communication in biological systems, hence, based on our analysis, we conjecture that the neuronal architecture was adjusted to make more effective use of this attribute.     

Computer simulation of a cerebellar cortex compartment

Computer simulation experiments are described regarding information storage and retrieval at a network consisting of one Purkinje cell and 20,000 granule cells. The information content depends on a scheme type and the properties of Purkinje cells. It is shown that a practically attainable information record efficiency is of the order 0.6 bit per binary memorising synapse. Associative information recall is demonstrated for the Marr's memory unit and expressions are derived for an information-content estimation based on parameter values obtained by simulation. The consequences of this computer simulation for physiological experiments are extensively discussed.     

Extracellular ATP Hydrolysis Inhibits Synaptic Transmission by Increasing pH Buffering in the Synaptic Cleft

Neuronal computations strongly depend on inhibitory interactions. One such example occurs at the first retinal synapse, where horizontal cells inhibit photoreceptors. This interaction generates the center/surround organization of bipolar cell receptive fields and is crucial for contrast enhancement. Despite its essential role in vision, the underlying synaptic mechanism has puzzled the neuroscience community for decades. Two competing hypotheses are currently considered: an ephaptic and a proton-mediated mechanism. Here we show that horizontal cells feed back to photoreceptors via an unexpected synthesis of the two. The first one is a very fast ephaptic mechanism that has no synaptic delay, making it one of the fastest inhibitory synapses known. The second one is a relatively slow (τ≈200 ms), highly intriguing mechanism. It depends on ATP release via Pannexin 1 channels located on horizontal cell dendrites invaginating the cone synaptic terminal. The ecto-ATPase NTPDase1 hydrolyses extracellular ATP to AMP, phosphate groups, and protons. The phosphate groups and protons form a pH buffer with a pKa of 7.2, which keeps the pH in the synaptic cleft relatively acidic. This inhibits the cone Ca²⁺ channels and consequently reduces the glutamate release by the cones. When horizontal cells hyperpolarize, the pannexin 1 channels decrease their conductance, the ATP release decreases, and the formation of the pH buffer reduces. The resulting alkalization in the synaptic cleft consequently increases cone glutamate release. Surprisingly, the hydrolysis of ATP instead of ATP itself mediates the synaptic modulation. Our results not only solve longstanding issues regarding horizontal cell to photoreceptor feedback, they also demonstrate a new form of synaptic modulation. Because pannexin 1 channels and ecto-ATPases are strongly expressed in the nervous system and pannexin 1 function is implicated in synaptic plasticity, we anticipate that this novel form of synaptic modulation may be a widespread phenomenon.     

Control of targeted flexor movements of the human arm at different levels of the possibility for their preprograming

Contribution of the processes of central preprograming of an equilibrium target position of the limb link was studied by testing two variants of motor task in humans. In the first variant, the tested person could obtain visual information about the target position before the movement initiation. In the second variant, such information initially was absent and was presented only in the course of the movement performance. It has been shown that in both variants the pattern of EMG activity of flexor muscles, which realize the movement (and, respectively, the pattern of motor commands, i.e., efferent activity of spinal motoneurons) demonstrated no fundamental differences. Therefore, it can be supposed that the attainment of a target level in both cases was preprogramed only to a limited extent; more probably, it was provided by successive current control of the limb link position. This control is based, first of all, on dynamic changes of the control signals. In general, data of the experiments are in agreement with the impulse—temporal hypothesis of control of targeted movements.     

Control of neural information transmission by synaptic dynamics.

The computational processing of a neural system is strongly influenced by the dynamical characteristics of the information transmission between neurons. In this work, the control of neural information transmission by synaptic dynamics is investigated by means of a master-equation-based stochastic model of pre-synaptic release of neurotransmitter-containing vesicles. The model incorporates facilitation of vesicle fusion with the pre-synaptic membrane due to intracellular calcium ions and depletion of readily releasable vesicles. The message to be transmitted is coded by the pre-synaptic firing sequence, and the received signal corresponds to the post-synaptic membrane potential response. At the sending end, the stochastic character of the vesicle release contributes to the entropy of the probability distribution of the number of vesicles released and represents noise with respect to information transmission. At the receiving end, the generation of post-synaptic membrane potentials is influenced by the temporal behaviour of ionic currents and membrane charging and is determined by means of a low-dimensional model. The rate and temporal types of neural coding are compatible with limiting cases of the synaptic information transmission as a function of initial vesicle release probability and pre-synaptic firing rate. The effects of the nonlinear dependencies of the vesicle release probability on intracellular calcium concentration and number of available vesicles are analysed. The model is compared with phenomenological and reduced models, a principal advantage being the capability of also determining fluctuations of dynamic variables Copyright 2002 Academic Press.