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。     

A model of the mechanisms of formation of unit activity

Dependence of the temporal structure of the spike discharge of a neuron in a weakly interacting network on the characteristics of excitatory and inhibitory input flows and on cell parameters was analyzed by a mathematical model. The intensity of communication between individual neurons corresponded to the intensity of synaptic communication between real spinal neurons. The temporal course of trace and accommodation processes in the model was similar to that of these processes in real spinal neurons. Connection of inhibitory inputs and an increase in the intensity of their influences were shown to be equivalent to a decrease in the intensity of excitatory input flows. Changes in cell parameters had a significant effect on the spike discharge only in the case of weak input influences (the ratio of the amplitude of the combined ESP evoked by the input spike train to the threshold value of membrane potential at rest was about 1.2:1.0 to 1.4:1.0). An increase in the input flow intensity led to considerable reorganization of the firing pattern: Mean values of interspike intervals and their fluctuations were reduced, histograms of interspike intervals became more symmetrical, and periodic waves appeared on the autocorrelation histograms. It is concluded on the basis of these results and of data in the literature that the main factor determining reorganization of the temporal structure of unit activity in a network of weakly interacting cells is the intensity of the input flow.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 12, No. 2, pp. 199–207, March–April, 1980.     

Stochastic automaton models for interaction of excitatory and inhibitory impulse sequences in neurons

The mechanisms by which excitatory and inhibitory input impulse sequences interact in changing the spike probability in neurons are examined in the two mathematical neuron models; one is a real-time neuron model which is close to physiological reality, and the other a stochastic automaton model for the temporal pattern discrimination proposed in the previous paper (Tsukada et al., 1976), which is developed in this paper as neuron models for interaction of excitatory and inhibitory input impulse sequences. The interval distributions of the output spike train from these models tend to be multimodal and are compared with those used for experimental data, reported by Bishop et al. (1964) for geniculate neuron activity and Poisson process deleting model analyzed by Ten Hoopen et al. (1966). Special attention, moreover, should be paid to how different forms of inhibitory input are transformed into the output interval distributions through these neuron models. These results exhibit a clear correlation between inhibitory input form and output interval distribution. More detailed information on this mechanism is obtained from the computations of recurrence-time under the stationary condition to go from active state to itself for the first time, each of which is influenced by the inhibitory input forms. In addition to these facts, some resultant characteristics on interval histogram and serial correlation are discussed in relation to physiological data from the literature.     

Sharpening of directional selectivity from neural output of rabbit retina

The estimation of motion direction from time varying retinal images is a fundamental task of visual systems. Neurons that selectively respond to directional visual motion are found in almost all species. In many of them already in the retina direction selective neurons signal their preferred direction of movement. Scientific evidences suggest that direction selectivity is carried from the retina to higher brain areas. Here we adopt a simple integrate-and-fire neuron model, inspired by recent work of Casti et al. (2008), to investigate how directional selectivity changes in cells postsynaptic to directional selective retinal ganglion cells (DSRGC). Our model analysis shows that directional selectivity in the postsynaptic cells increases over a wide parameter range. The degree of directional selectivity positively correlates with the probability of burst-like firing of presynaptic DSRGCs. Postsynaptic potentials summation and spike threshold act together as a temporal filter upon the input spike train. Prior to the intricacy of neural circuitry between retina and higher brain areas, we suggest that sharpening is a straightforward result of the intrinsic spiking pattern of the DSRGCs combined with the summation of excitatory postsynaptic potentials and the spike threshold in postsynaptic neurons.     

Impact of fast sodium channel inactivation on spike threshold dynamics and synaptic integration

Neurons spike when their membrane potential exceeds a threshold value. In central neurons, the spike threshold is not constant but depends on the stimulation. Thus, input-output properties of neurons depend both on the effect of presynaptic spikes on the membrane potential and on the dynamics of the spike threshold. Among the possible mechanisms that may modulate the threshold, one strong candidate is Na channel inactivation, because it specifically impacts spike initiation without affecting the membrane potential. We collected voltage-clamp data from the literature and we found, based on a theoretical criterion, that the properties of Na inactivation could indeed cause substantial threshold variability by itself. By analyzing simple neuron models with fast Na inactivation (one channel subtype), we found that the spike threshold is correlated with the mean membrane potential and negatively correlated with the preceding depolarization slope, consistent with experiments. We then analyzed the impact of threshold dynamics on synaptic integration. The difference between the postsynaptic potential (PSP) and the dynamic threshold in response to a presynaptic spike defines an effective PSP. When the neuron is sufficiently depolarized, this effective PSP is briefer than the PSP. This mechanism regulates the temporal window of synaptic integration in an adaptive way. Finally, we discuss the role of other potential mechanisms. Distal spike initiation, channel noise and Na activation dynamics cannot account for the observed negative slope-threshold relationship, while adaptive conductances (e.g. K+) and Na inactivation can. We conclude that Na inactivation is a metabolically efficient mechanism to control the temporal resolution of synaptic integration.     

Spike timing dependent plasticity finds the start of repeating patterns in continuous spike trains

Experimental studies have observed Long Term synaptic Potentiation (LTP) when a presynaptic neuron fires shortly before a postsynaptic neuron, and Long Term Depression (LTD) when the presynaptic neuron fires shortly after, a phenomenon known as Spike Timing Dependent Plasticity (STDP). When a neuron is presented successively with discrete volleys of input spikes STDP has been shown to learn 'early spike patterns', that is to concentrate synaptic weights on afferents that consistently fire early, with the result that the postsynaptic spike latency decreases, until it reaches a minimal and stable value. Here, we show that these results still stand in a continuous regime where afferents fire continuously with a constant population rate. As such, STDP is able to solve a very difficult computational problem: to localize a repeating spatio-temporal spike pattern embedded in equally dense 'distractor' spike trains. STDP thus enables some form of temporal coding, even in the absence of an explicit time reference. Given that the mechanism exposed here is simple and cheap it is hard to believe that the brain did not evolve to use it.     

Neural spike generator entrainment by regularly spaced synaptic input

 It has been known for 30 years that the output of a repetitively firing neuron or pacemaker can be synchronized (locked) to regularly spaced inhibitory or excitatory postsynaptic input potentials. Conditions for stable locking have been determined mathematically, demonstrated in computer simulation, and locking has been observed in vivo. We have developed a neural spike generator circuit model which exhibits stable locking to externally derived simulated inhibitory or excitatory post-synaptic inputs. Conditions for stable 1 : 1 lock, in which pacemaker output frequency matches that of the periodic input, are derived. These take the form of expressions for stable delay and convergence factor which incorporate known or measurable parameters of the circuit model. The expressions have been evaluated and shown to compare satisfactorily with experimental observations of locking by our circuit model. Received: 28 March 1996 / Accepted in revised form: 18 February 1997     

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.     

Mathematical formulations of Hebbian learning

 Several formulations of correlation-based Hebbian learning are reviewed. On the presynaptic side, activity is described either by a firing rate or by presynaptic spike arrival. The state of the postsynaptic neuron can be described by its membrane potential, its firing rate, or the timing of backpropagating action potentials (BPAPs). It is shown that all of the above formulations can be derived from the point of view of an expansion. In the absence of BPAPs, it is natural to correlate presynaptic spikes with the postsynaptic membrane potential. Time windows of spike-time-dependent plasticity arise naturally if the timing of postsynaptic spikes is available at the site of the synapse, as is the case in the presence of BPAPs. With an appropriate choice of parameters, Hebbian synaptic plasticity has intrinsic normalization properties that stabilizes postsynaptic firing rates and leads to subtractive weight normalization. Received: 1 February 2002 / Accepted: 28 March 2002 Correspondence to: W. Gerstner (e-mail: wulfram.gerstner@epfl.ch, Tel.: +41-21-6936713, Fax: +41-21-6935263)     

Properties of synaptic noise in tonically active human motoneurons

The objective of these experiments was to determine the amount of synaptic noise on the cell membrane at various intervals after an action potential in a motoneuron firing at a specified frequency. Sources of noise such as variations in the level of voluntary drive were minimized by selecting only segments of the spike train in which the unit was running within prescribed frequency limits. The level of the membrane potential of the motoneuron during these intervals was determined using two test “pulses” (compound Ia excitatory postsynaptic potentials) of known amplitude. This enabled the probability of the membrane potential falling within a voltage “window” of known size at known times after the preceding spike to be determined. The probability density histograms showed that the fluctuations of membrane potential about a target interspike trajectory (i.e., the membrane noise) increased with time after the preceding spike. These fluctuations in the membrane potential can be accounted for by a one-dimensional “random walk” model of membrane noise. This model explains the salient features of the interval histograms, such as positive skewness at low target frequencies. A quantitative test of the model demonstrated its applicability to the motor pools of tibialis and masseter.     

Computational Consequences of Temporally Asymmetric Learning Rules: I. Differential Hebbian Learning

Temporally asymetric learning rules governing plastic changes in synaptic efficacy have recently been identified in physiological studies. In these rules, the exact timing of pre- and postsynaptic spikes is critical to the induced change of synaptic efficacy. The temporal learning rules treated in this article are approximately antisymmetric; the synaptic efficacy is enhanced if the postsynaptic spike follows the presynaptic spike by a few milliseconds, but the efficacy is depressed if the postsynaptic spike precedes the presynaptic spike. The learning dynamics of this rule are studied using a stochastic model neuron receiving a set of serially delayed inputs. The average change of synaptic efficacy due to the temporally antisymmetric learning rule is shown to yield differential Hebbian learning. These results are demonstrated with both mathematical analyses and computer simulations, and connections with theories of classical conditioning are discussed.     

Predicting the synaptic information efficacy in cortical layer 5 pyramidal neurons using a minimal integrate-and-fire model

Synaptic information efficacy (SIE) is a statistical measure to quantify the efficacy of a synapse. It measures how much information is gained, on the average, about the output spike train of a postsynaptic neuron if the input spike train is known. It is a particularly appropriate measure for assessing the input–output relationship of neurons receiving dynamic stimuli. Here, we compare the SIE of simulated synaptic inputs measured experimentally in layer 5 cortical pyramidal neurons in vitro with the SIE computed from a minimal model constructed to fit the recorded data. We show that even with a simple model that is far from perfect in predicting the precise timing of the output spikes of the real neuron, the SIE can still be accurately predicted. This arises from the ability of the model to predict output spikes influenced by the input more accurately than those driven by the background current. This indicates that in this context, some spikes may be more important than others. Lastly we demonstrate another aspect where using mutual information could be beneficial in evaluating the quality of a model, by measuring the mutual information between the model’s output and the neuron’s output. The SIE, thus, could be a useful tool for assessing the quality of models of single neurons in preserving input–output relationship, a property that becomes crucial when we start connecting these reduced models to construct complex realistic neuronal networks.     

Intracellular recording from the giant synapse of the squid

1. Recording with glass micropipette electrodes inserted close to the synaptic region, in the presynaptic and in the postsynaptic fibers of the giant synapse in the stellate ganglion of the squid, has been accomplished. 2. The forms of the spike and of the synaptic potential are very much like those reported earlier (Bullock, 1948) from macroelectrodes. The crest time and the rate of fall are labile and depend on the state of fatigue, though the time of initiation of the postsynaptic potential does not. 3. It is concluded after examination of both intra- and extracellular recordings that there is a real synaptic delay of the order of 1 or 2 milliseconds at 15–20°C. 4. There is sometimes a very small and sometimes no visible deflection in the intracellular postsynaptic record attributable to the presynaptic spike. It is concluded that transmission cannot be electrical. 5. The amplitude of the postsynaptic potential can be controlled over some range by the amplitude of the presynaptic potential. 6. Hyperpolarization of the postsynaptic membrane results in increase in amplitude of spikes up to 200 millivolts, in increase in the membrane potential level at which the spike flares up, but in no considerable change in the amplitude in postsynaptic potential. 7. The postsynaptic potential can add to the late falling phase and the undershoot of an antidromic spike in the postfiber but cannot add to the crest or early part of the falling phase. The earliest part of the antidromic spike during which the postsynaptic potential can add is probably a period of refractoriness to electrical shock by analogy with the properties of the axon.     

Quantification and statistical verification of neuronal stimulus responses from noisy spike train data

Usually neuronal responses to short-lasting stimuli are displayed as peri-stimulus time histogram. The function estimated by such a histogram allows to obtain informations about stimulus-induced postsynaptic events as long as the interpretation is restricted to the first response component after the stimulus. The interpretation of secondary response components is much more difficult, as they may be either due to stimulus effects or represent an echo of the primary response. In the present paper two output functions are developed that do not show such an echoing of responses. The first one, the interspike interval change function, represents an ideal way to quantify a neuronal stimulus response as its amplitude was found to be almost independent of the stimulation strategy used during acquisition of the spike train data. The other function, the displaced impulses function, allows to verify the statistical significance of an observed response component. Both functions may be estimated from stimulus-correlated spike train data, even if the neuron under investigation shows considerable interspike-interval variability in the absence of stimulation. The concepts underlying these neuronal output functions are developed on simulated responses of a Hodgkin-Huxley-type model for a mammalian neuron at body temperature that is exposed to a transient excitatory conductance increase. Additionally, estimation of these output functions is also demonstrated on responses of human soleus motoneurons that were exposed to electrical stimuli of the tibial nerve in the popliteal fossa.     

Membrane Potential Fluctuations Determine the Precision of Spike Timing and Synchronous Activity: A Model Study

It is much debated on what time scale information is encoded by neuronal spike activity. With a phenomenological model that transforms time-dependent membrane potential fluctuations into spike trains, we investigate constraints for the timing of spikes and for synchronous activity of neurons with common input. The model of spike generation has a variable threshold that depends on the time elapsed since the previous action potential and on the preceding membrane potential changes. To ensure that the model operates in a biologically meaningful range, the model was adjusted to fit the responses of a fly visual interneuron to motion stimuli. The dependence of spike timing on the membrane potential dynamics was analyzed. Fast membrane potential fluctuations are needed to trigger spikes with a high temporal precision. Slow fluctuations lead to spike activity with a rate about proportional to the membrane potential. Thus, for a given level of stochastic input, the frequency range of membrane potential fluctuations induced by a stimulus determines whether a neuron can use a rate code or a temporal code. The relationship between the steepness of membrane potential fluctuations and the timing of spikes has also implications for synchronous activity in neurons with common input. Fast membrane potential changes must be shared by the neurons to produce synchronous activity.     

Dual synaptic plasticity in the hippocampus: Hebbian and spatiotemporal learning dynamics

We assume that Hebbian learning dynamics (HLD) and spatiotemporal learning dynamics (SLD) are involved in the mechanism of synaptic plasticity in the hippocampal neurons. While HLD is driven by pre- and postsynaptic spike timings through the backpropagating action potential, SLD is evoked by presynaptic spike timings alone. Since the backpropagation attenuates as it nears the distal dendrites, we assume an extreme case as a neuron model where HLD exists only at proximal dendrites and SLD exists only at the distal dendrites. We examined how the synaptic weights change in response to three types of synaptic inputs in computer simulations. First, in response to a Poisson train having a constant mean frequency, the synaptic weights in HLD and SLD are qualitatively similar. Second, SLD responds more rapidly than HLD to synchronous input patterns, while each responds to them. Third, HLD responds more rapidly to more frequent inputs, while SLD shows fluctuating synaptic weights. These results suggest an encoding hypothesis in that a transient synchronous structure in spatiotemporal input patterns will be encoded into distal dendrites through SLD and that persistent synchrony or firing rate information will be encoded into proximal dendrites through HLD.     

Basic principles of synaptic physiology illustrated by a computer model

A computer model is described that simulates many basic aspects of chemical synapse physiology. The model consists of two displays, the first being a pictorial diagram of the anatomical connections between two presynaptic neurons and one postsynaptic neuron. Either or both of the presynaptic cells can be stimulated from a control panel with variable control of the number of pulses and firing rate; the resulting presynaptic action potentials are animated. The second display plots the membrane potential of the postsynaptic cell versus time following presynaptic stimulation. The model accurately simulates temporal and spatial summation when the presynaptic cells are arranged and stimulated in parallel and simulates presynaptic inhibition when they are arranged and stimulated in series. Excitatory and inhibitory postsynaptic potentials can be demonstrated by altering the nature of the ionic conductance change occurring on the postsynaptic cell. The effects on summation of changing length constant or time constant of the postsynaptic cell can also be illustrated. The model is useful for teaching these concepts to medical, graduate, or undergraduate students and can also be used as a self-directed computer laboratory exercise. It is available for free download from the internet.     

Mechanism of inhibition following reflex discharge in spinal cord interneurons

Using the method of microelectrode (intracellular and extracellular) recording, the mechanism of inhibition following reflex discharge in interneurons of the lumbosacral section of the spinal cord of cats on activation of cutaneous and high-threshold muscle afferents was studied. It was shown that the postdischarge depression of the reflex responses 10–20 msec after the moment of activation of the neuron is due to afterprocesses in the same neuron and presynaptic pathways. The depression of spike potentials from the 20th to the 100th msec is produced by inhibitory postsynaptic potentials (IPSP). During the development of IPSP the inhibition of spike potentials can be due to both a decrease of the depolarization of the postsynaptic membrane below the critical threshold and a decrease of sensitivity of the cell membrane to the depolarizing action of the excitatory postsynaptic potential (EPSP). At intervals between the stimuli of 30–100 msec the duration of EPSP after the first stimulus does not differ from that after the second stimulus. Hence, it is suggested that the presynaptic mechanisms do not play an essential part in this type of inhibition of interneurons. The inhibition following the excitation favors the formation of a discrete message to the neurons of higher orders.I. P. Pavlov Institute of Physiology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 2, No. 1, pp. 3–9, January–February, 1970.