Mean-field analysis of selective persistent activity in presence of short-term synaptic depression

Mean-Field theory is extended to recurrent networks of spiking neurons endowed with short-term depression (STD) of synaptic transmission. The extension involves the use of the distribution of interspike intervals of an integrate-and-fire neuron receiving a Gaussian current, with a given mean and variance, in input. This, in turn, is used to obtain an accurate estimate of the resulting postsynaptic current in presence of STD. The stationary states of the network are obtained requiring self-consistency for the currents—those driving the emission processes and those generated by the emitted spikes. The model network stores in the distribution of two-state efficacies of excitatory-to-excitatory synapses, a randomly composed set of external stimuli. The resulting synaptic structure allows the network to exhibit selective persistent activity for each stimulus in the set. Theory predicts the onset of selective persistent, or working memory (WM) activity upon varying the constitutive parameters (e.g. potentiated/depressed long-term efficacy ratio, parameters associated with STD), and provides the average emission rates in the various steady states. Theoretical estimates are in remarkably good agreement with data “recorded” in computer simulations of the microscopic model. Action Editor: Karen Sigvardt     

Hebbian spike-driven synaptic plasticity for learning patterns of mean firing rates

Synaptic plasticity is believed to underlie the formation of appropriate patterns of connectivity that stabilize stimulus-selective reverberations in the cortex. Here we present a general quantitative framework for studying the process of learning and memorizing of patterns of mean spike rates. General considerations based on the limitations of material (biological or electronic) synaptic devices show that most learning networks share the palimpsest property: old stimuli are forgotten to make room for the new ones. In order to prevent too-fast forgetting, one can introduce a stochastic mechanism for selecting only a small fraction of synapses to be changed upon the presentation of a stimulus. Such a mechanism can be easily implemented by exploiting the noisy fluctuations in the pre- and postsynaptic activities to be encoded. The spike-driven synaptic dynamics described here can implement such a selection mechanism to achieve slow learning, which is shown to maximize the performance of the network as an associative memory.     

Kinetic models of spike-timing dependent plasticity and their functional consequences in detecting correlations

Spike-timing dependent plasticity (STDP) is a type of synaptic modification found relatively recently, but the underlying biophysical mechanisms are still unclear. Several models of STDP have been proposed, and differ by their implementation, and in particular how synaptic weights saturate to their minimal and maximal values. We analyze here kinetic models of transmitter-receptor interaction and derive a series of STDP models. In general, such kinetic models predict progressive saturation of the weights. Various forms can be obtained depending on the hypotheses made in the kinetic model, and these include a simple linear dependence on the value of the weight (“soft bounds”), mixed soft and abrupt saturation (“hard bound”), or more complex forms. We analyze in more detail simple soft-bound models of Hebbian and anti-Hebbian STDPs, in which nonlinear spike interactions (triplets) are taken into account. We show that Hebbian STDPs can be used to selectively potentiate synapses that are correlated in time, while anti-Hebbian STDPs depress correlated synapses, despite the presence of nonlinear spike interactions. This correlation detection enables neurons to develop a selectivity to correlated inputs. We also examine different versions of kinetics-based STDP models and compare their sensitivity to correlations. We conclude that kinetic models generally predict soft-bound dynamics, and that such models seem ideal for detecting correlations among large numbers of inputs.     

A computational study of synaptic mechanisms of partial memory transfer in cerebellar vestibulo-ocular-reflex learning

There is a debate regarding whether motor memory is stored in the cerebellar cortex, or the cerebellar nuclei, or both. Memory may be acquired in the cortex and then be transferred to the cerebellar nuclei. Based on a dynamical system modeling with a minimal set of variables, we theoretically investigated possible mechanisms of memory transfer and consolidation in the context of vestibulo-ocular reflex learning. We tested different plasticity rules for synapses in the cerebellar nuclei and took robustness of behavior against parameter variation as the criterion of plausibility of a model variant. In the most plausible scenarios, mossy-fiber nucleus-neuron synapses or Purkinje-cell nucleus-neuron synapses are plastic on a slow time scale and store permanent memory, whose content is passed from the cerebellar cortex storing transient memory. In these scenarios, synaptic strengths are potentiated when the mossy-fiber afferents to the nuclei are active during a pause in Purkinje-cell activities. Furthermore, assuming that mossy fibers create a limited variety of signals compared to parallel fibers, our model shows partial memory transfer from the cortex to the nuclei.     

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.     

Effect of synaptic plasticity on sensory coding and steady-state filtering properties in the electric sense

Our modeling study examines short-term plasticity at the synapse between afferents from electroreceptors and pyramidal cells in the electrosensory lateral lobe (ELL) of the weakly electric fish Apteronotus leptorhynchus. It focusses on steady-state filtering and coherence-based coding properties. While developed for electroreception, our study exposes general functional features for different mixtures of depression and facilitation. Our computational model, constrained by the available in vivo and in vitro data, consists of a synapse onto a deterministic leaky integrate-and-fire (LIF) neuron. The synapse is either depressing (D), facilitating (F) or both (FD), and is driven by a sinusoidally or randomly modulated Poisson process. Due to nonlinearity, numerically computed input-output transfer functions are used to determine the filtering properties. The gain of the response at each sinusoidally modulated frequency is computed by dividing the fitted amplitudes of the input and output cycle histograms of the LIF models. While filtering is always low-pass for F alone, D alone exhibits a gain resonance (non-monotonicity) at a frequency that decreases with increasing recovery time constant of synaptic depression (tau(d)). This resonance is mitigated by the presence of F. For D, F and FD, coherence improves as the synaptic conductance time constant (tau(g)) increases, yet the mutual information per spike decreases. The information per spike for D and F follows opposite trends as their respective time constants increase. The broadband but non-monotonic gain and coherence functions seen in vivo suggest that D and perhaps FD dynamics are involved at this synapse. Our results further predict that the likely synaptic configuration is a slower tau(g), e.g. via a mixture of AMPA and NMDA synapses, and a relatively smaller synaptic facilitation time constant (tau(f)) and larger tau(d) (with tau(f) smaller than tau(d) and tau(g)). These results are compatible with known physiology.     

Are binary synapses superior to graded weight representations in stochastic attractor networks?

Synaptic plasticity is an underlying mechanism of learning and memory in neural systems, but it is controversial whether synaptic efficacy is modulated in a graded or binary manner. It has been argued that binary synaptic weights would be less susceptible to noise than graded weights, which has impelled some theoretical neuroscientists to shift from the use of graded to binary weights in their models. We compare retrieval performance of models using both binary and graded weight representations through numerical simulations of stochastic attractor networks. We also investigate stochastic attractor models using multiple discrete levels of weight states, and then investigate the optimal threshold for dilution of binary weight representations. Our results show that a binary weight representation is not less susceptible to noise than a graded weight representation in stochastic attractor models, and we find that the load capacities with an increasing number of weight states rapidly reach the load capacity with graded weights. The optimal threshold for dilution of binary weight representations under stochastic conditions occurs when approximately 50% of the smallest weights are set to zero.     

Synaptic consolidation: an approach to long-term learning

Synaptic plasticity is thought to be the basis of learning and memory, but it is mostly studied on the timescale of mere minutes. This review discusses synaptic consolidation, a process that enables synapses to retain their strength for a much longer time (days to years), instead of returning to their original value. The process involves specific plasticity-related proteins, and depends on the dopamine D1/D5 receptors. Here, we review the research on synaptic consolidation, describing electrophysiology experiments, recent modeling work, as well as behavioral correlates.     

Homeostatic plasticity in the CNS: synaptic and intrinsic forms

The study of experience-dependent plasticity has been dominated by questions of how Hebbian plasticity mechanisms act during learning and development. This is unsurprising as Hebbian plasticity constitutes the most fully developed and influential model of how information is stored in neural circuits and how neural circuitry can develop without extensive genetic instructions. Yet Hebbian plasticity may not be sufficient for understanding either learning or development: the dramatic changes in synapse number and strength that can be produced by this kind of plasticity tend to threaten the stability of neural circuits. Recent work has suggested that, in addition to Hebbian plasticity, homeostatic regulatory mechanisms are active in a variety of preparations. These mechanisms alter both the synaptic connections between neurons and the intrinsic electrical properties of individual neurons, in such a way as to maintain some constancy in neuronal properties despite the changes wrought by Hebbian mechanisms. Here we review the evidence for homeostatic plasticity in the central nervous system, with special emphasis on results from cortical preparations.     

Involvement of afadin in the formation and remodeling of synapses in the hippocampus

In the hippocampus, synapses are formed between mossy fiber terminals and CA3 pyramidal cell dendrites and comprise highly developed synaptic junctions (SJs) and puncta adherentia junctions (PAJs). Dynamic remodeling of synapses in the hippocampus is implicated in learning and memory. Components of both the nectin-afadin and cadherin-catenin cell adhesion systems exclusively accumulate at PAJs. We investigated the role of afadin at synapses in mice in which the afadin gene was conditionally inactivated in hippocampal neurons. In these mutant mice, the signals for not only nectins, but also N-cadherin and β-catenin, were hardly detected in the CA3 area, in addition to loss of the signal for afadin, resulting in disruption of PAJs. Ultrastructural analysis revealed an increase in the number of perforated synapses, suggesting the instability of SJs. These results indicate that afadin is involved not only in the assembly of nectins and cadherins at synapses, but also in synaptic remodeling.     

Interplay between Short- and Long-Term Plasticity in Cell-Assembly Formation

Various hippocampal and neocortical synapses of mammalian brain show both short-term plasticity and long-term plasticity, which are considered to underlie learning and memory by the brain. According to Hebb’s postulate, synaptic plasticity encodes memory traces of past experiences into cell assemblies in cortical circuits. However, it remains unclear how the various forms of long-term and short-term synaptic plasticity cooperatively create and reorganize such cell assemblies. Here, we investigate the mechanism in which the three forms of synaptic plasticity known in cortical circuits, i.e., spike-timing-dependent plasticity (STDP), short-term depression (STD) and homeostatic plasticity, cooperatively generate, retain and reorganize cell assemblies in a recurrent neuronal network model. We show that multiple cell assemblies generated by external stimuli can survive noisy spontaneous network activity for an adequate range of the strength of STD. Furthermore, our model predicts that a symmetric temporal window of STDP, such as observed in dopaminergic modulations on hippocampal neurons, is crucial for the retention and integration of multiple cell assemblies. These results may have implications for the understanding of cortical memory processes.     

Learning in spiking neural networks by reinforcement of stochastic synaptic transmission

It is well-known that chemical synaptic transmission is an unreliable process, but the function of such unreliability remains unclear. Here I consider the hypothesis that the randomness of synaptic transmission is harnessed by the brain for learning, in analogy to the way that genetic mutation is utilized by Darwinian evolution. This is possible if synapses are "hedonistic," responding to a global reward signal by increasing their probabilities of vesicle release or failure, depending on which action immediately preceded reward. Hedonistic synapses learn by computing a stochastic approximation to the gradient of the average reward. They are compatible with synaptic dynamics such as short-term facilitation and depression and with the intricacies of dendritic integration and action potential generation. A network of hedonistic synapses can be trained to perform a desired computation by administering reward appropriately, as illustrated here through numerical simulations of integrate-and-fire model neurons.     

Depressing synapse as a detector of frequency change

In this article we discuss the short-term synaptic depression using a mathematical model. We derive the model of synaptic depression caused by the depletion of synaptic vesicles for the case of infinitely short stimulation time and show that the analytical formulas for the postsynaptic potential (PSP) and kinetic functions take simple closed form. A solution in this form allows an analysis of the characteristics of depression as a function of the models parameters and the derivation of analytic formulas for measures of short time synaptic depression commonly used in experimental studies. Those formulas are used to validate the model by fitting it to two types of synapses described in the literature. Given the fitted parameters we discuss the behavior of the synapse in situations involving frequency change. We also indicate a possible role of depressing synapses in information processing as not only a filter of high frequency input but as a detector of the return from high frequency stimulation to the stimulation within frequency band specific for a given synapse.     

Synapse elimination from the mouse neuromuscular junction in vitro: A non-hebbian activity-dependent process

The effect of action potentials on elimination of mouse neuromuscular junctions (NMJ) was studied in a three compartment cell culture preparation. Axons from superior cervical ganglion or ventral spinal cord neurons in two lateral compartments formed multiple neuromuscular junctions with muscle cells in a central compartment. The loss of synapses over a 2–7-day period was determined by serial electrophysiological recording and a functional assay. Electrical stimulation of axons from one side compartment during this period, using 30-Hz bursts of 2-s duration, repeated at 10-s intervals, caused a significant increase in synapse elimination compared to unstimulated cultures (p< 0.001). The extent of homosynaptic and heterosynaptic elimination was comparable, i. e., of the 226 functional synapses of each type studied, 111 (49%) of the synapses that had been stimulated were eliminated, and 87 (39%) of unstimulated synapses on the same muscle cells were eliminated. Also, simultaneous bilateral stimulation caused significantly greater elimination of synapses than unilateral stimulation (p< 0.005). These observations are contrary to the Hebbian hypothesis of synaptic plasticity. A spatial effect of stimulus-induced synapse elimination was also evident following simultaneous bilateral stimulation. Prior to stimulation, most muscle cells were innervated by axons from both side compartments, but after bilateral stimulation, muscle cells were predominantly unilaterally innervated by axons from the closer compartment. These experiments suggest that synapse elimination at the NMJ is an activity-dependent process, but it does not follow Hebbian or anti-Hebbian rules of synaptic plasticity. Rather, elimination is a consequence of postsynaptic activation and a function of location of the muscle cell relative to the neuron. An interaction between spatial and activity-dependent effects on synapse elimination could help produce optimal refinement of synaptic connections during postnatal development. © 1993 John Wiley & Sons, Inc.     

Hebbian errors in learning: An analysis using the Oja model

Background: Recent work on long term potentiation in brain slices shows that Hebb's rule is not completely synapse-specific, probably due to intersynapse diffusion of calcium or other factors. We previously suggested that such errors in Hebbian learning might be analogous to mutations in evolution.Methods and findings: We examine this proposal quantitatively, extending the classical Oja unsupervised model of learning by a single linear neuron to include Hebbian inspecificity. We introduce an error matrix E, which expresses possible crosstalk between updating at different connections. When there is no inspecificity, this gives the classical result of convergence to the first principal component of the input distribution (PC1). We show the modified algorithm converges to the leading eigenvector of the matrix EC, where C is the input covariance matrix. In the most biologically plausible case when there are no intrinsically privileged connections, E has diagonal elements Q and off-diagonal elements (1-Q)/(n-1), where Q, the quality, is expected to decrease with the number of inputs n and with a synaptic parameter b that reflects synapse density, calcium diffusion, etc. We study the dependence of the learning accuracy on b, n and the amount of input activity or correlation (analytically and computationally). We find that accuracy increases (learning becomes gradually less useful) with increases in b, particularly for intermediate (i.e., biologically realistic) correlation strength, although some useful learning always occurs up to the trivial limit Q=1/n.Conclusions and significance: We discuss the relation of our results to Hebbian unsupervised learning in the brain. When the mechanism lacks specificity, the network fails to learn the expected, and typically most useful, result, especially when the input correlation is weak. Hebbian crosstalk would reflect the very high density of synapses along dendrites, and inevitably degrades learning.     

Irregular dynamics in up and down cortical states

Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a biologically motivated stochastic model of up and down transitions. The model is constituted by a simple bistable rate dynamics, where the synaptic current is modulated by short-term synaptic processes which introduce stochasticity and temporal correlations. A complete analysis of our model, both with mean-field approaches and numerical simulations, shows the appearance of complex transitions between high (up) and low (down) neural activity states, driven by the synaptic noise, with permanence times in the up state distributed according to a power-law. We show that the experimentally observed large fluctuation in up and down permanence times can be explained as the result of sufficiently noisy dynamical synapses with sufficiently large recovery times. Static synapses cannot account for this behavior, nor can dynamical synapses in the absence of noise.     

Synaptic imbalances in endogenous psychoses

Based on the formalism of logical balance, imbalances of information processing in tripartite synapses are described as a possible explanation for the pathophysiology of endogenous psychoses like depression, mania and schizophrenia. A tripartite synapse consists of the presynapse, the synaptic cleft, the postsynapse (neuronal components) and the glia (glial components). According to the logic of balance in a living system, the number of values and the number of variables must be equal. In a tripartite synapse the neuronal components are interpreted as values, the glial components as variables. In line with this novel synaptic model, three elementary synaptic imbalances can be deduced. First, tripartite synapses are underbalanced if the variables outnumber the values. Such a system state may cause depression. Second, if the values outnumber the variables, the tripartite synapses are overbalanced which may be responsible for mania. Third, if no functional variables are available at all, tripartite synapses process information unbalanced which may cause schizophrenia. The basic symptoms of these psychobiological disorders can be deduced from this novel synaptic model.