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.     

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     

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)     

The role of synaptic facilitation in spike coincidence detection

Using a realistic model of activity dependent dynamical synapse, which includes both depressing and facilitating mechanisms, we study the conditions in which a postsynaptic neuron efficiently detects temporal coincidences of spikes which arrive from N different presynaptic neurons at certain frequency f. A numerical and analytical treatment of that system shows that: (1) facilitation enhances the detection of correlated signals arriving from a subset of presynaptic excitatory neurons, and (2) the presence of facilitation yields to a better detection of firing rate changes in the presynaptic activity. We also observed that facilitation determines the existence of an optimal input frequency which allows the best performance for a wide (maximum) range of the neuron firing threshold. This optimal frequency can be controlled by means of facilitation parameters. Finally, we show that these results are robust even for very noisy signals and in the presence of synaptic fluctuations produced by the stochastic release of neurotransmitters.     

Neurochemical aspects of interneuronal communication

It is suggested that the term neurotransmission, which is used to designate neuronal communication at synaptic level, be associated to the less restrictive term neuromodulation. These two types of intercellular communication seem in fact to be two basically different mechanisms, both of which contribute to neuronal integration. The integration of neuronal information at cellular level appears to be more complex than the simple addition of excitatory plus inhibitory influences eliciting postsynaptic responses. Evidence has been obtained that non synaptic transmission can alter the capacity of a given synapse to transfer neuronal information from the presynaptic element to the postsynaptic neuron. For instance, presynaptic mechanisms provide evidence for the functional independence of the nerve terminals, since the release of neuromediators by the latter is sometimes independent of the axonal firing rate. Similarly, the somato-dendritic part of some neurons exhibits intrinsic functions, such as a dendritic release of neuromediator, suggesting that the control of the axonal firing rate takes place partly at this somato-dendritic level and does not depend for the totality on afferent axonic information. The intercellular operations which organize individual neurons into neuronal networks will also occur either at somato-dendritic level or at the level of specific nerve terminals selected as the result of presynaptic interactions. This integration of neuronal information also seems to take place at postsynaptic level, where cooperative interactions have been shown to occur between various receptors. These mechanisms will function at the level of a single nerve terminal containing more than one neuromediator. Neuromodulation can therefore be said to involve very efficient adaptive processes, which help to account for the fact that such large behavioral responses are expressed by such a small number of neuronal elements.     

Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns

Hebbian learning allows a network of spiking neurons to store and retrieve spatio-temporal patterns with a time resolution of 1 ms, despite the long postsynaptic and dendritic integration times. To show this, we introduce and analyze a model of spiking neurons, the spike response model, with a realistic distribution of axonal delays and with realistic postsynaptic potentials. Learning is performed by a local Hebbian rule which is based on the synchronism of presynaptic neurotransmitter release and some short-acting postsynaptic process. The time window of this synchronism determines the temporal resolution of pattern retrieval, which can be initiated by applying a short external stimulus pattern. Furthermore, a rate quantization is found in dependence upon the threshold value of the neurons, i.e., in a given time a pattern runsn times as often as learned, wheren is a positive integer (n 0). We show that all information about the spike pattern is lost if only mean firing rates (temporal average) or ensemble activities (spatial average) are considered. An average over several retrieval runs in order to generate a post-stimulus time histogram may also deteriorate the signal. The full information on a pattern is contained in the spike raster of a single run. Our results stress the importance, and advantage, of coding by spatio-temporal spike patterns instead of firing rates and average ensemble activity. The implications regarding modelling and experimental data analysis are discussed.     

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.     

A wide-acting peptidergic interneurone in the snail Helix pomatia : Graded recruitment and local firing of terminal processes

Simultaneous pre- and postsynaptic intracellular recordings were used to study the mechanism of presynaptic terminal recruitment in a multifunction interneurone in the snail Helix pomatia. The interneurone was presynaptic to at least 20 neurones. The synaptic efficiency was correlated with the presence of presynaptic depolarizing after-potentials (DAPs) electrotonically produced by the delayed firing of remote terminal processes. These processes have large swellings filled with neurosecretory vesicles. The terminals were recruited in a graded manner when the interneurone was fired with a prolonged current. The terminal recruitment was enhanced by stimulating various efferent nerves, which presumably activated presynaptic receptors for dopamine. A few animals (three out of 300) had two electrically coupled interneurones. Simultaneous recordings from both cells showed that the terminals could be fired independently of the soma-axon activity. The graded and local firing of the presynaptic terminals was attributed to the electrical load that the large boutons exert on electrotonically spreading presynaptic impulses.     

Calcium signaling in dendritic spines of hippocampal neurons

Intracellular Ca²⁺ dynamics have been measured using imaging techniques in dendrites and spines of CA3 hippocampal neurons in brain slice under both acute and tissue culture conditions. In response to presynatic stimulation, micromolar levels of Ca²⁺ are rapidly reached in spines of distal dendrites. If stimulus parameters are chosen judiciously so as to minimize postsynaptic firing, then the dendrite shaft increases are far less. Spine Ca²⁺ increases are largely dependent upon activation of NMDA receptors. At the large mossy fiber synapses, presynaptic stimuli also produce large Ca²⁺ increases but the differences in shaft-spine Ca²⁺ levels are much less; often they are insignificant. Also at these locations, postsynaptic firing, without presynaptic stimulation is sufficient to produce large increase in spine Ca²⁺ levels. 1994 John Wiley & Sons, Inc.     

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.     

The spike-timing dependence of plasticity

In spike-timing-dependent plasticity (STDP), the order and precise temporal interval between presynaptic and postsynaptic spikes determine the sign and magnitude of long-term potentiation (LTP) or depression (LTD). STDP is widely utilized in models of circuit-level plasticity, development, and learning. However, spike timing is just one of several factors (including firing rate, synaptic cooperativity, and depolarization) that govern plasticity induction, and its relative importance varies across synapses and activity regimes. This review summarizes this broader view of plasticity, including the forms and cellular mechanisms for the spike-timing dependence of plasticity, and, the evidence that spike timing is an important determinant of plasticity in?vivo.     

Statistical Analysis of Membrane Potential Fluctuations: Relation with Presynaptic Spike Train

In a study of integration at the single neuron level, the relationships between the postsynaptic membrane potential and the presynaptic spike train were analyzed. Fluctuations in membrane potential of neurons in the visceral ganglion of Aplysia were measured and described by histograms. The histogram estimates the probability density function of the membrane potential. Comparisons were made among histograms when there was no synaptic input, and when there was a single input in which variations were made in the PSP (postsynaptic potential) sign, i.e. excitatory or inhibitory, and arrival statistics, e.g. slow or fast, regular, Poisson-like, or patterned. This was examined in cells where the membrane potential was constant and in cells in which there was spontaneous pacemaker activity. The form of the histogram depended on whether the neuron was spontaneously quiescent or a pacemaker, or whether it received presynaptic input and, if it did, on the sign and temporal characteristics of such input. From such histograms the mean firing rate of output spike trains can be predicted; additional information of a temporal nature is required, however, to predict features of the interval structure of the output train. Suggestions are made concerning the way the nervous system might utilize the information summarized in the membrane potential histogram.     

Postsynaptic regulation of the development and long-term plasticity of Aplysia sensorimotor synapses in cell culture

The monosynaptic component of the neuronal circuit that mediates the withdrawal reflex of Aplysia californica can be reconstituted in dissociated cell culture. Study of these in vitro monosynaptic connections has yielded insights into the basic cellular mechanisms of synaptogenesis and long-term synaptic plasticity. One such insight has been that the development of the presynaptic sensory neurons is strongly regulated by the postsynaptic motor neuron. Sensory neurons which have been cocultured with a target motor neuron have more elaborate structures—characterized by neurites with more branches and varicosities—than do sensory neurons grown alone in culture or sensory neurons that have been cocultured with an inappropriate target cell. Another way in which the motor neuron regulates the development of sensory neurons is apparent when sensorimotor cocultures with two presynaptic cells are examined. In such cocultures the outgrowth from the different presynaptic cells is obviously segregated on the processes of the postsynaptic cell. By contrast, when two sensory neurons are placed into cell culture without a motor neuron, thier processes readily grow together. In addition to regulating the in vitro development of sensory neurons, the motor neuron also regulates learning-related changes in the structure of sensory neurons. Application of the endogenous facilitatory trasmitter serotonin (5-HT) causes long-term facilitation of in vitro sensorimotor synapses due in part to growth of new presynatpic varicosities. But 5-HT applied to sensory neurons alone in cultuer does not produce structural changes in these cells. More recently it has been found that sensorimotor synapses in cell culture can exhibit long-term potentiation (LTP). Like LTP of some hippocampal synapses, LTP of in vitro Aplysia syanpses is regulated by the voltage of the postsynaptic cell. Pairing high-frequency stimulation of sensory neurons with strong hyperpolarization of the motor neuron blocks the induction of LTP. Moreover, LTP of sensorimotor synapses can be induced in Hebbian fashion by pairing weak presynaptic stimulation with strong postsynaptic depolarization. These findings implicate a Habbian mechanism in classical conditioning in Aplysia. They also indicate that Hebbian LTP is a phylogenetically ancient form of synaptic plasticity. 1994 John Wiley & Sons, Inc.     

Transient Responses to Rapid Changes in Mean and Variance in Spiking Models

The mean input and variance of the total synaptic input to a neuron can vary independently, suggesting two distinct information channels. Here we examine the impact of rapidly varying signals, delivered via these two information conduits, on the temporal dynamics of neuronal firing rate responses. We examine the responses of model neurons to step functions in either the mean or the variance of the input current. Our results show that the temporal dynamics governing response onset depends on the choice of model. Specifically, the existence of a hard threshold introduces an instantaneous component into the response onset of a leaky-integrate-and-fire model that is not present in other models studied here. Other response features, for example a decaying oscillatory approach to a new steady-state firing rate, appear to be more universal among neuronal models. The decay time constant of this approach is a power-law function of noise magnitude over a wide range of input parameters. Understanding how specific model properties underlie these response features is important for understanding how neurons will respond to rapidly varying signals, as the temporal dynamics of the response onset and response decay to new steady-state determine what range of signal frequencies a population of neurons can respond to and faithfully encode.     

Pre- and postsynaptically expressed spike-timing-dependent plasticity contribute differentially to neuronal learning

A plethora of experimental studies have shown that long-term synaptic plasticity can be expressed pre- or postsynaptically depending on a range of factors such as developmental stage, synapse type, and activity patterns. The functional consequences of this diversity are not clear, although it is understood that whereas postsynaptic expression of plasticity predominantly affects synaptic response amplitude, presynaptic expression alters both synaptic response amplitude and short-term dynamics. In most models of neuronal learning, long-term synaptic plasticity is implemented as changes in connective weights. The consideration of long-term plasticity as a fixed change in amplitude corresponds more closely to post- than to presynaptic expression, which means theoretical outcomes based on this choice of implementation may have a postsynaptic bias. To explore the functional implications of the diversity of expression of long-term synaptic plasticity, we adapted a model of long-term plasticity, more specifically spike-timing-dependent plasticity (STDP), such that it was expressed either independently pre- or postsynaptically, or in a mixture of both ways. We compared pair-based standard STDP models and a biologically tuned triplet STDP model, and investigated the outcomes in a minimal setting, using two different learning schemes: in the first, inputs were triggered at different latencies, and in the second a subset of inputs were temporally correlated. We found that presynaptic changes adjusted the speed of learning, while postsynaptic expression was more efficient at regulating spike timing and frequency. When combining both expression loci, postsynaptic changes amplified the response range, while presynaptic plasticity allowed control over postsynaptic firing rates, potentially providing a form of activity homeostasis. Our findings highlight how the seemingly innocuous choice of implementing synaptic plasticity by single weight modification may unwittingly introduce a postsynaptic bias in modelling outcomes. We conclude that pre- and postsynaptically expressed plasticity are not interchangeable, but enable complimentary functions.     

Assembly of new individual excitatory synapses: time course and temporal order of synaptic molecule recruitment

Time-lapse microscopy, retrospective immunohistochemistry, and cultured hippocampal neurons were used to determine the time frame of individual glutamatergic synapse assembly and the temporal order in which specific molecules accumulate at new synaptic junctions. New presynaptic boutons capable of activity-evoked vesicle recycling were observed to form within 30 min of initial axodendritic contact. Clusters of the presynaptic active zone protein Bassoon were present in all new boutons. Conversely, clusters of the postsynaptic molecule SAP90/PSD-95 and glutamate receptors were found on average only approximately 45 min after such boutons were first detected. AMPA- and NMDA-type glutamate receptors displayed similar clustering kinetics. These findings suggest that glutamatergic synapse assembly can occur within 1-2 hr after initial contact and that presynaptic differentiation may precede postsynaptic differentiation.     

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。     

Inhibition of interneuron firing extends the spread of endocannabinoid signaling in the cerebellum

Endocannabinoids serve as retrograde messengers in many brain regions. These diffusible lipophilic molecules are released by postsynaptic cells and regulate presynaptic neurotransmitter release. Here we describe an additional mechanism that mediates the spread of endocannabinoid signaling to distant inhibitory synapses. Depolarization of cerebellar Purkinje cells reduced the firing rate of nearby interneurons, and this reduction in firing was blocked by the cannabinoid receptor antagonist AM251. The cannabinoid receptor agonist WIN55,212-2 also reduced firing rates in interneurons, and this inhibition arose from the activation of a small potassium conductance. Thus, endocannabinoids released from the dendrites of depolarized neurons can lead to inhibition of firing in nearby cells. Because interneurons can project over several hundred micrometers, this inhibition of firing allows cells to regulate synaptic inputs at distances well beyond the limits of endocannabinoid diffusion.     

Maturation of GABAergic Inhibition Promotes Strengthening of Temporally Coherent Inputs among Convergent Pathways

Spike-timing-dependent plasticity (STDP), a form of Hebbian plasticity, is inherently stabilizing. Whether and how GABAergic inhibition influences STDP is not well understood. Using a model neuron driven by converging inputs modifiable by STDP, we determined that a sufficient level of inhibition was critical to ensure that temporal coherence (correlation among presynaptic spike times) of synaptic inputs, rather than initial strength or number of inputs within a pathway, controlled postsynaptic spike timing. Inhibition exerted this effect by preferentially reducing synaptic efficacy, the ability of inputs to evoke postsynaptic action potentials, of the less coherent inputs. In visual cortical slices, inhibition potently reduced synaptic efficacy at ages during but not before the critical period of ocular dominance (OD) plasticity. Whole-cell recordings revealed that the amplitude of unitary IPSCs from parvalbumin positive (Pv+) interneurons to pyramidal neurons increased during the critical period, while the synaptic decay time-constant decreased. In addition, intrinsic properties of Pv+ interneurons matured, resulting in an increase in instantaneous firing rate. Our results suggest that maturation of inhibition in visual cortex ensures that the temporally coherent inputs (e.g. those from the open eye during monocular deprivation) control postsynaptic spike times of binocular neurons, a prerequisite for Hebbian mechanisms to induce OD plasticity.