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.     

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.     

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)     

A Nonlinear Cable Framework for Bidirectional Synaptic Plasticity

Finding the rules underlying how axons of cortical neurons form neural circuits and modify their corresponding synaptic strength is the still subject of intense research. Experiments have shown that internal calcium concentration, and both the precise timing and temporal order of pre and postsynaptic action potentials, are important constituents governing whether the strength of a synapse located on the dendrite is increased or decreased. In particular, previous investigations focusing on spike timing-dependent plasticity (STDP) have typically observed an asymmetric temporal window governing changes in synaptic efficacy. Such a temporal window emphasizes that if a presynaptic spike, arriving at the synaptic terminal, precedes the generation of a postsynaptic action potential, then the synapse is potentiated; however if the temporal order is reversed, then depression occurs. Furthermore, recent experimental studies have now demonstrated that the temporal window also depends on the dendritic location of the synapse. Specifically, it was shown that in distal regions of the apical dendrite, the magnitude of potentiation was smaller and the window for depression was broader, when compared to observations from the proximal region of the dendrite. To date, the underlying mechanism(s) for such a distance-dependent effect is (are) currently unknown. Here, using the ionic cable theory framework in conjunction with the standard calcium based plasticity model, we show for the first time that such distance-dependent inhomogeneities in the temporal learning window for STDP can be largely explained by both the spatial and active properties of the dendrite.     

Bursts shape the NMDA-R mediated spike timing dependent plasticity curve: role of burst interspike interval and GABAergic inhibition

Spike timing dependent plasticity (STDP) is a synaptic learning rule where the relative timing between the presynaptic and postsynaptic action potentials determines the sign and strength of synaptic plasticity. In its basic form STDP has an asymmetric form which incorporates both persistent increases and persistent decreases in synaptic strength. The basic form of STDP, however, is not a fixed property and depends on the dendritic location. An asymmetric curve is observed in the distal dendrites, whereas a symmetrical one is observed in the proximal ones. A recent computational study has shown that the transition from the asymmetry to symmetry is due to inhibition under certain conditions. Synapses have also been observed to be unreliable at generating plasticity when excitatory postsynaptic potentials and single spikes are paired at low frequencies. Bursts of spikes, however, are reliably signaled because transmitter release is facilitated. This article presents a two-compartment model of the CA1 pyramidal cell. The model is neurophysiologically plausible with its dynamics resulting from the interplay of many ionic and synaptic currents. Plasticity is measured by a deterministic Ca²⁺ dynamics model which measures the instantaneous calcium level and its time course in the dendrite and change the strength of the synapse accordingly. The model is validated to match the asymmetrical form of STDP from the pairing of a presynaptic (dendritic) and postsynaptic (somatic) spikes as observed experimentally. With the parameter set unchanged the model investigates how pairing of bursts with single spikes and bursts in the presence or absence of inhibition shapes the STDP curve. The model predicts that inhibition strength and frequency are not the only factors of the asymmetry-to-symmetry switch of the STDP curve. Burst interspike interval is another factor. This study is an important first step towards understanding how STDP is affected under natural firing patterns in vivo.     

Intrinsic stability of temporally shifted spike-timing dependent plasticity

Spike-timing dependent plasticity (STDP), a widespread synaptic modification mechanism, is sensitive to correlations between presynaptic spike trains and it generates competition among synapses. However, STDP has an inherent instability because strong synapses are more likely to be strengthened than weak ones, causing them to grow in strength until some biophysical limit is reached. Through simulations and analytic calculations, we show that a small temporal shift in the STDP window that causes synchronous, or nearly synchronous, pre- and postsynaptic action potentials to induce long-term depression can stabilize synaptic strengths. Shifted STDP also stabilizes the postsynaptic firing rate and can implement both Hebbian and anti-Hebbian forms of competitive synaptic plasticity. Interestingly, the overall level of inhibition determines whether plasticity is Hebbian or anti-Hebbian. Even a random symmetric jitter of a few milliseconds in the STDP window can stabilize synaptic strengths while retaining these features. The same results hold for a shifted version of the more recent "triplet" model of STDP. Our results indicate that the detailed shape of the STDP window function near the transition from depression to potentiation is of the utmost importance in determining the consequences of STDP, suggesting that this region warrants further experimental study.     

A learning theory for reward-modulated spike-timing-dependent plasticity with application to biofeedback

Reward-modulated spike-timing-dependent plasticity (STDP) has recently emerged as a candidate for a learning rule that could explain how behaviorally relevant adaptive changes in complex networks of spiking neurons could be achieved in a self-organizing manner through local synaptic plasticity. However, the capabilities and limitations of this learning rule could so far only be tested through computer simulations. This article provides tools for an analytic treatment of reward-modulated STDP, which allows us to predict under which conditions reward-modulated STDP will achieve a desired learning effect. These analytical results imply that neurons can learn through reward-modulated STDP to classify not only spatial but also temporal firing patterns of presynaptic neurons. They also can learn to respond to specific presynaptic firing patterns with particular spike patterns. Finally, the resulting learning theory predicts that even difficult credit-assignment problems, where it is very hard to tell which synaptic weights should be modified in order to increase the global reward for the system, can be solved in a self-organizing manner through reward-modulated STDP. This yields an explanation for a fundamental experimental result on biofeedback in monkeys by Fetz and Baker. In this experiment monkeys were rewarded for increasing the firing rate of a particular neuron in the cortex and were able to solve this extremely difficult credit assignment problem. Our model for this experiment relies on a combination of reward-modulated STDP with variable spontaneous firing activity. Hence it also provides a possible functional explanation for trial-to-trial variability, which is characteristic for cortical networks of neurons but has no analogue in currently existing artificial computing systems. In addition our model demonstrates that reward-modulated STDP can be applied to all synapses in a large recurrent neural network without endangering the stability of the network dynamics.     

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.     

Distributed network actions by nicotine increase the threshold for spike-timing-dependent plasticity in prefrontal cortex

Nicotine enhances attention and working memory by activating nicotinic acetylcholine receptors (nAChRs). The prefrontal cortex (PFC) is critical for these cognitive functions and is also rich in nAChR expression. Specific cellular and synaptic mechanisms underlying nicotine's effects on cognition remain elusive. Here we show that nicotine exposure increases the threshold for synaptic spike-timing-dependent potentiation (STDP) in layer V pyramidal neurons of the mouse PFC. During coincident presynaptic and postsynaptic activity, nicotine reduces dendritic calcium signals associated with action potential propagation by enhancing GABAergic transmission. This results from a series of presynaptic actions involving different PFC interneurons and multiple nAChR subtypes. Pharmacological block of nAChRs or GABA(A) receptors prevented nicotine's actions and restored STDP, as did increasing dendritic calcium signals with stronger postsynaptic activity. Thus, by activating nAChRs distributed throughout the PFC neuronal network, nicotine affects PFC information processing and storage by increasing the amount of postsynaptic activity necessary to induce STDP.     

Coding with spike shapes and graded potentials in cortical networks

In cortical neurones, analogue dendritic potentials are thought to be encoded into patterns of digital spikes. According to this view, neuronal codes and computations are based on the temporal patterns of spikes: spike times, bursts or spike rates. Recently, we proposed an 'action potential waveform code' for cortical pyramidal neurones in which the spike shape carries information. Broader somatic action potentials are reliably produced in response to higher conductance input, allowing for four times more information transfer than spike times alone. This information is preserved during synaptic integration in a single neurone, as back-propagating action potentials of diverse shapes differentially shunt incoming postsynaptic potentials and so participate in the next round of spike generation. An open question has been whether the information in action potential waveforms can also survive axonal conduction and directly influence synaptic transmission to neighbouring neurones. Several new findings have now brought new light to this subject, showing cortical information processing that transcends the classical models.     

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.     

LTD windows of the STDP learning rule and synaptic connections having a large transmission delay enable robust sequence learning amid background noise

Spike-timing-dependent synaptic plasticity (STDP) is a simple and effective learning rule for sequence learning. However, synapses being subject to STDP rules are readily influenced in noisy circumstances because synaptic conductances are modified by pre- and postsynaptic spikes elicited within a few tens of milliseconds, regardless of whether those spikes convey information or not. Noisy firing existing everywhere in the brain may induce irrelevant enhancement of synaptic connections through STDP rules and would result in uncertain memory encoding and obscure memory patterns. We will here show that the LTD windows of the STDP rules enable robust sequence learning amid background noise in cooperation with a large signal transmission delay between neurons and a theta rhythm, using a network model of the entorhinal cortex layer II with entorhinal-hippocampal loop connections. The important element of the present model for robust sequence learning amid background noise is the symmetric STDP rule having LTD windows on both sides of the LTP window, in addition to the loop connections having a large signal transmission delay and the theta rhythm pacing activities of stellate cells. Above all, the LTD window in the range of positive spike-timing is important to prevent influences of noise with the progress of sequence learning.     

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     

Unsupervised learning of visual features through spike timing dependent plasticity

Spike timing dependent plasticity (STDP) is a learning rule that modifies synaptic strength as a function of the relative timing of pre- and postsynaptic spikes. When a neuron is repeatedly presented with similar inputs, STDP is known to have the effect of concentrating high synaptic weights on afferents that systematically fire early, while postsynaptic spike latencies decrease. Here we use this learning rule in an asynchronous feedforward spiking neural network that mimics the ventral visual pathway and shows that when the network is presented with natural images, selectivity to intermediate-complexity visual features emerges. Those features, which correspond to prototypical patterns that are both salient and consistently present in the images, are highly informative and enable robust object recognition, as demonstrated on various classification tasks. Taken together, these results show that temporal codes may be a key to understanding the phenomenal processing speed achieved by the visual system and that STDP can lead to fast and selective responses.     

Axons Amplify Somatic Incomplete Spikes into Uniform Amplitudes in Mouse Cortical Pyramidal Neurons

Background

Action potentials are the essential unit of neuronal encoding. Somatic sequential spikes in the central nervous system appear various in amplitudes. To be effective neuronal codes, these spikes should be propagated to axonal terminals where they activate the synapses and drive postsynaptic neurons. It remains unclear whether these effective neuronal codes are based on spike timing orders and/or amplitudes.

Methodology/Principal Findings

We investigated this fundamental issue by simultaneously recording the axon versus soma of identical neurons and presynaptic vs. postsynaptic neurons in the cortical slices. The axons enable somatic spikes in low amplitude be enlarged, which activate synaptic transmission in consistent patterns. This facilitation in the propagation of sequential spikes through the axons is mechanistically founded by the short refractory periods, large currents and high opening probability of axonal voltage-gated sodium channels.

Conclusion/Significance

An amplification of somatic incomplete spikes into axonal complete ones makes sequential spikes to activate consistent synaptic transmission. Therefore, neuronal encoding is likely based on spike timing order, instead of graded analogues.     

Stimulus timing-dependent plasticity in cortical processing of orientation.

The relative timing of presynaptic and postsynaptic spikes plays a critical role in activity-induced synaptic modification. Here we examined whether plasticity of orientation selectivity in the visual cortex depends on stimulus timing. Repetitive pairing of visual stimuli at two orientations induced a shift in orientation tuning of cat cortical neurons, with the direction of the shift depending on the temporal order of the pair. Induction of a significant shift required that the interval between the pair fall within +/-40 ms, reminiscent of the temporal window for spike timing-dependent synaptic plasticity. Mirroring the plasticity found in cat visual cortex, similar conditioning also induced a shift in perceived orientation by human subjects, further suggesting functional relevance of this phenomenon. Thus, relative timing of visual stimuli can play a critical role in dynamic modulation of adult cortical function, perhaps through spike timing-dependent synaptic plasticity.     

Bayesian Computation Emerges in Generic Cortical Microcircuits through Spike-Timing-Dependent Plasticity

The principles by which networks of neurons compute, and how spike-timing dependent plasticity (STDP) of synaptic weights generates and maintains their computational function, are unknown. Preceding work has shown that soft winner-take-all (WTA) circuits, where pyramidal neurons inhibit each other via interneurons, are a common motif of cortical microcircuits. We show through theoretical analysis and computer simulations that Bayesian computation is induced in these network motifs through STDP in combination with activity-dependent changes in the excitability of neurons. The fundamental components of this emergent Bayesian computation are priors that result from adaptation of neuronal excitability and implicit generative models for hidden causes that are created in the synaptic weights through STDP. In fact, a surprising result is that STDP is able to approximate a powerful principle for fitting such implicit generative models to high-dimensional spike inputs: Expectation Maximization. Our results suggest that the experimentally observed spontaneous activity and trial-to-trial variability of cortical neurons are essential features of their information processing capability, since their functional role is to represent probability distributions rather than static neural codes. Furthermore it suggests networks of Bayesian computation modules as a new model for distributed information processing in the cortex.     

A Biophysical Basis for the Inter-spike Interaction of Spike-timing-dependent Plasticity

Although spike-timing-dependent plasticity (STDP) is well characterized when pre- and postsynaptic spikes are paired with a given time lag, how this generalizes for more complex spike-trains is unclear. Recent experiments demonstrate that contributions to synaptic plasticity from different spike pairs within a spike train do not add linearly. In the visual cortex conditioning with spike triplets shows that the effect of the first spike pair dominates over the second. Using a previously proposed calcium-dependent plasticity model, we show that short-term synaptic dynamics and interaction between successive back-propagating action potentials (BPAP) may jointly account for the nonlinearities observed. Paired-pulse depression and attenuation of BPAPs are incorporated into the model through the use-dependent depletion of pre- and postsynaptic resources, respectively. Simulations suggest that these processes may play critical roles in determining how STDP operates in the context of natural spike-trains.     

Quantal glutamate release is essential for reliable neuronal encodings in cerebral networks

Background

The neurons and synapses work coordinately to program the brain codes of controlling cognition and behaviors. Spike patterns at the presynaptic neurons regulate synaptic transmission. The quantitative regulations of synapse dynamics in spike encoding at the postsynaptic neurons remain unclear.

Methodology/Principal Findings

With dual whole-cell recordings at synapse-paired cells in mouse cortical slices, we have investigated the regulation of synapse dynamics to neuronal spike encoding at cerebral circuits assembled by pyramidal neurons and GABAergic ones. Our studies at unitary synapses show that postsynaptic responses are constant over time, such as glutamate receptor-channel currents at GABAergic neurons and glutamate transport currents at astrocytes, indicating quantal glutamate release. In terms of its physiological impact, our results demonstrate that the signals integrated from quantal glutamatergic synapses drive spike encoding at GABAergic neurons reliably, which in turn precisely set spike encoding at pyramidal neurons through feedback inhibition.

Conclusion/Significance

Our studies provide the evidences for the quantal glutamate release to drive the spike encodings precisely in cortical circuits, which may be essential for programming the reliable codes in the brain to manage well-organized behaviors.     

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.