Neuromodulation of STDP through short-term changes in firing causality

Spike timing dependent plasticity (STDP) likely plays an important role in forming and changing connectivity patterns between neurons in our brain. In a unidirectional synaptic connection between two neurons, it uses the causal relation between spiking activity of a presynaptic input neuron and a postsynaptic output neuron to change the strength of this connection. While the nature of STDP benefits unsupervised learning of correlated inputs, any incorporation of value into the learning process needs some form of reinforcement. Chemical neuromodulators such as Dopamine or Acetylcholine are thought to signal changes between external reward and internal expectation to many brain regions, including the basal ganglia. This effect is often modelled through a direct inclusion of the level of Dopamine as a third factor into the STDP rule. While this gives the benefit of direct control over synaptic modification, it does not account for observed instantaneous effects in neuronal activity on application of Dopamine agonists. Specifically, an instant facilitation of neuronal excitability in the striatum can not be explained by the only indirect effect that dopamine-modulated STDP has on a neuron’s firing pattern. We therefore propose a model for synaptic transmission where the level of neuromodulator does not directly influence synaptic plasticity, but instead alters the relative firing causality between pre- and postsynaptic neurons. Through the direct effect on postsynaptic activity, our rule allows indirect modulation of the learning outcome even with unmodulated, two-factor STDP. However, it also does not prohibit joint operation together with three-factor STDP rules.     

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.     

Spiking neural networks with different reinforcement learning (RL) schemes in a multiagent setting

This paper investigates the effectiveness of spiking agents when trained with reinforcement learning (RL) in a challenging multiagent task. In particular, it explores learning through reward-modulated spike-timing dependent plasticity (STDP) and compares it to reinforcement of stochastic synaptic transmission in the general-sum game of the Iterated Prisoner's Dilemma (IPD). More specifically, a computational model is developed where we implement two spiking neural networks as two "selfish" agents learning simultaneously but independently, competing in the IPD game. The purpose of our system (or collective) is to maximise its accumulated reward in the presence of reward-driven competing agents within the collective. This can only be achieved when the agents engage in a behaviour of mutual cooperation during the IPD. Previously, we successfully applied reinforcement of stochastic synaptic transmission to the IPD game. The current study utilises reward-modulated STDP with eligibility trace and results show that the system managed to exhibit the desired behaviour by establishing mutual cooperation between the agents. It is noted that the cooperative outcome was attained after a relatively short learning period which enhanced the accumulation of reward by the system. As in our previous implementation, the successful application of the learning algorithm to the IPD becomes possible only after we extended it with additional global reinforcement signals in order to enhance competition at the neuronal level. Moreover it is also shown that learning is enhanced (as indicated by an increased IPD cooperative outcome) through: (i) strong memory for each agent (regulated by a high eligibility trace time constant) and (ii) firing irregularity produced by equipping the agents' LIF neurons with a partial somatic reset mechanism.     

A computational framework for cortical learning

Recent physiological findings have revealed that long-term adaptation of the synaptic strengths between cortical pyramidal neurons depends on the temporal order of presynaptic and postsynaptic spikes, which is called spike-timing-dependent plasticity (STDP) or temporally asymmetric Hebbian (TAH) learning. Here I prove by analytical means that a physiologically plausible variant of STDP adapts synaptic strengths such that the presynaptic spikes predict the postsynaptic spikes with minimal error. This prediction error model of STDP implies a mechanism for cortical memory: cortical tissue learns temporal spike patterns if these spike patterns are repeatedly elicited in a set of pyramidal neurons. The trained network finishes these patterns if their beginnings are presented, thereby recalling the memory. Implementations of the proposed algorithms may be useful for applications in voice recognition and computer vision.     

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.     

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.     

Mirrored STDP Implements Autoencoder Learning in a Network of Spiking Neurons

The autoencoder algorithm is a simple but powerful unsupervised method for training neural networks. Autoencoder networks can learn sparse distributed codes similar to those seen in cortical sensory areas such as visual area V1, but they can also be stacked to learn increasingly abstract representations. Several computational neuroscience models of sensory areas, including Olshausen & Field’s Sparse Coding algorithm, can be seen as autoencoder variants, and autoencoders have seen extensive use in the machine learning community. Despite their power and versatility, autoencoders have been difficult to implement in a biologically realistic fashion. The challenges include their need to calculate differences between two neuronal activities and their requirement for learning rules which lead to identical changes at feedforward and feedback connections. Here, we study a biologically realistic network of integrate-and-fire neurons with anatomical connectivity and synaptic plasticity that closely matches that observed in cortical sensory areas. Our choice of synaptic plasticity rules is inspired by recent experimental and theoretical results suggesting that learning at feedback connections may have a different form from learning at feedforward connections, and our results depend critically on this novel choice of plasticity rules. Specifically, we propose that plasticity rules at feedforward versus feedback connections are temporally opposed versions of spike-timing dependent plasticity (STDP), leading to a symmetric combined rule we call Mirrored STDP (mSTDP). We show that with mSTDP, our network follows a learning rule that approximately minimizes an autoencoder loss function. When trained with whitened natural image patches, the learned synaptic weights resemble the receptive fields seen in V1. Our results use realistic synaptic plasticity rules to show that the powerful autoencoder learning algorithm could be within the reach of real biological networks.     

Coexistence of Reward and Unsupervised Learning During the Operant Conditioning of Neural Firing Rates

A fundamental goal of neuroscience is to understand how cognitive processes, such as operant conditioning, are performed by the brain. Typical and well studied examples of operant conditioning, in which the firing rates of individual cortical neurons in monkeys are increased using rewards, provide an opportunity for insight into this. Studies of reward-modulated spike-timing-dependent plasticity (RSTDP), and of other models such as R-max, have reproduced this learning behavior, but they have assumed that no unsupervised learning is present (i.e., no learning occurs without, or independent of, rewards). We show that these models cannot elicit firing rate reinforcement while exhibiting both reward learning and ongoing, stable unsupervised learning. To fix this issue, we propose a new RSTDP model of synaptic plasticity based upon the observed effects that dopamine has on long-term potentiation and depression (LTP and LTD). We show, both analytically and through simulations, that our new model can exhibit unsupervised learning and lead to firing rate reinforcement. This requires that the strengthening of LTP by the reward signal is greater than the strengthening of LTD and that the reinforced neuron exhibits irregular firing. We show the robustness of our findings to spike-timing correlations, to the synaptic weight dependence that is assumed, and to changes in the mean reward. We also consider our model in the differential reinforcement of two nearby neurons. Our model aligns more strongly with experimental studies than previous models and makes testable predictions for future experiments.     

Stability of complex spike timing-dependent plasticity in cerebellar learning

Dynamics of spike-timing dependent synaptic plasticity are analyzed for excitatory and inhibitory synapses onto cerebellar Purkinje cells. The purpose of this study is to place theoretical constraints on candidate synaptic learning rules that determine the changes in synaptic efficacy due to pairing complex spikes with presynaptic spikes in parallel fibers and inhibitory interneurons. Constraints are derived for the timing between complex spikes and presynaptic spikes, constraints that result from the stability of the learning dynamics of the learning rule. Potential instabilities in the parallel fiber synaptic learning rule are found to be stabilized by synaptic plasticity at inhibitory synapses if the inhibitory learning rules are stable, and conditions for stability of inhibitory plasticity are given. Combining excitatory with inhibitory plasticity provides a mechanism for minimizing the overall synaptic input. Stable learning rules are shown to be able to sculpt simple-spike patterns by regulating the excitability of neurons in the inferior olive that give rise to climbing fibers.     

The Convallis Rule for Unsupervised Learning in Cortical Networks

The phenomenology and cellular mechanisms of cortical synaptic plasticity are becoming known in increasing detail, but the computational principles by which cortical plasticity enables the development of sensory representations are unclear. Here we describe a framework for cortical synaptic plasticity termed the “Convallis rule”, mathematically derived from a principle of unsupervised learning via constrained optimization. Implementation of the rule caused a recurrent cortex-like network of simulated spiking neurons to develop rate representations of real-world speech stimuli, enabling classification by a downstream linear decoder. Applied to spike patterns used in in vitro plasticity experiments, the rule reproduced multiple results including and beyond STDP. However STDP alone produced poorer learning performance. The mathematical form of the rule is consistent with a dual coincidence detector mechanism that has been suggested by experiments in several synaptic classes of juvenile neocortex. Based on this confluence of normative, phenomenological, and mechanistic evidence, we suggest that the rule may approximate a fundamental computational principle of the neocortex.     

Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) with asymmetric learning windows is commonly found in the brain and useful for a variety of spike-based computations such as input filtering and associative memory. A natural consequence of STDP is establishment of causality in the sense that a neuron learns to fire with a lag after specific presynaptic neurons have fired. The effect of STDP on synchrony is elusive because spike synchrony implies unitary spike events of different neurons rather than a causal delayed relationship between neurons. We explore how synchrony can be facilitated by STDP in oscillator networks with a pacemaker. We show that STDP with asymmetric learning windows leads to self-organization of feedforward networks starting from the pacemaker. As a result, STDP drastically facilitates frequency synchrony. Even though differences in spike times are lessened as a result of synaptic plasticity, the finite time lag remains so that perfect spike synchrony is not realized. In contrast to traditional mechanisms of large-scale synchrony based on mutual interaction of coupled neurons, the route to synchrony discovered here is enslavement of downstream neurons by upstream ones. Facilitation of such feedforward synchrony does not occur for STDP with symmetric learning windows. Action Editor: Wulfram Gerstner     

Effect of stimulus-driven pruning on the detection of spatiotemporal patterns of activity in large neural networks

Adult patterns of neuronal connectivity develop from a transient embryonic template characterized by exuberant projections to both appropriate and inappropriate target regions in a process known as synaptic pruning. Trigger signals able to induce synaptic pruning could be related to dynamic functions that depend on the timing of action potentials. We stimulated locally connected random networks of spiking neurons and observed the effect of a spike-timing-dependent synaptic plasticity (STDP)-driven pruning process on the emergence of cell assemblies. The spike trains of the simulated excitatory neurons were recorded. We searched for spatiotemporal firing patterns as potential markers of the build-up of functionally organized recurrent activity associated with spatially organized connectivity.     

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.     

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.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. II. Input selectivity—symmetry breaking

Spike-timing-dependent plasticity (STDP) is believed to structure neuronal networks by slowly changing the strengths (or weights) of the synaptic connections between neurons depending upon their spiking activity, which in turn modifies the neuronal firing dynamics. In this paper, we investigate the change in synaptic weights induced by STDP in a recurrently connected network in which the input weights are plastic but the recurrent weights are fixed. The inputs are divided into two pools with identical constant firing rates and equal within-pool spike-time correlations, but with no between-pool correlations. Our analysis uses the Poisson neuron model in order to predict the evolution of the input synaptic weights and focuses on the asymptotic weight distribution that emerges due to STDP. The learning dynamics induces a symmetry breaking for the individual neurons, namely for sufficiently strong within-pool spike-time correlation each neuron specializes to one of the input pools. We show that the presence of fixed excitatory recurrent connections between neurons induces a group symmetry-breaking effect, in which neurons tend to specialize to the same input pool. Consequently STDP generates a functional structure on the input connections of the network.     

Messages in spike timing-dependent plasticity: pros and cons

Spike-timing dependent plasticity (STDP), a synaptic modification depending on a relative timing of presynaptic and postsynaptic spikes, has fascinated researchers in the fields of neurophysiology and computational neuroscience, because it is not only conceptually simple or biologically reasonable but is also versatile in neural network simulations. The STDP rule may be valid only under specific conditions, however. We propose herein a method that could find more natural and potent rules of synaptic plasticity.     

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.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I. Input selectivity–strengthening correlated input pathways

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity. In this paper, we extend previous studies of input selectivity induced by (STDP) for single neurons to the biologically interesting case of a neuronal network with fixed recurrent connections and plastic connections from external pools of input neurons. We use a theoretical framework based on the Poisson neuron model to analytically describe the network dynamics (firing rates and spike-time correlations) and thus the evolution of the synaptic weights. This framework incorporates the time course of the post-synaptic potentials and synaptic delays. Our analysis focuses on the asymptotic states of a network stimulated by two homogeneous pools of “steady” inputs, namely Poisson spike trains which have fixed firing rates and spike-time correlations. The (STDP) model extends rate-based learning in that it can implement, at the same time, both a stabilization of the individual neuron firing rates and a slower weight specialization depending on the input spike-time correlations. When one input pathway has stronger within-pool correlations, the resulting synaptic dynamics induced by (STDP) are shown to be similar to those arising in the case of a purely feed-forward network: the weights from the more correlated inputs are potentiated at the expense of the remaining input connections.     

A Calcium-Dependent Plasticity Rule for HCN Channels Maintains Activity Homeostasis and Stable Synaptic Learning

Theoretical and computational frameworks for synaptic plasticity and learning have a long and cherished history, with few parallels within the well-established literature for plasticity of voltage-gated ion channels. In this study, we derive rules for plasticity in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, and assess the synergy between synaptic and HCN channel plasticity in establishing stability during synaptic learning. To do this, we employ a conductance-based model for the hippocampal pyramidal neuron, and incorporate synaptic plasticity through the well-established Bienenstock-Cooper-Munro (BCM)-like rule for synaptic plasticity, wherein the direction and strength of the plasticity is dependent on the concentration of calcium influx. Under this framework, we derive a rule for HCN channel plasticity to establish homeostasis in synaptically-driven firing rate, and incorporate such plasticity into our model. In demonstrating that this rule for HCN channel plasticity helps maintain firing rate homeostasis after bidirectional synaptic plasticity, we observe a linear relationship between synaptic plasticity and HCN channel plasticity for maintaining firing rate homeostasis. Motivated by this linear relationship, we derive a calcium-dependent rule for HCN-channel plasticity, and demonstrate that firing rate homeostasis is maintained in the face of synaptic plasticity when moderate and high levels of cytosolic calcium influx induced depression and potentiation of the HCN-channel conductance, respectively. Additionally, we show that such synergy between synaptic and HCN-channel plasticity enhances the stability of synaptic learning through metaplasticity in the BCM-like synaptic plasticity profile. Finally, we demonstrate that the synergistic interaction between synaptic and HCN-channel plasticity preserves robustness of information transfer across the neuron under a rate-coding schema. Our results establish specific physiological roles for experimentally observed plasticity in HCN channels accompanying synaptic plasticity in hippocampal neurons, and uncover potential links between HCN-channel plasticity and calcium influx, dynamic gain control and stable synaptic learning.     

Synaptic modifications depend on synapse location and activity: a biophysical model of STDP

In spike-timing-dependent plasticity (STDP) the synapses are potentiated or depressed depending on the temporal order and temporal difference of the pre- and post-synaptic signals. We present a biophysical model of STDP which assumes that not only the timing, but also the shapes of these signals influence the synaptic modifications. The model is based on a Hebbian learning rule which correlates the NMDA synaptic conductance with the post-synaptic signal at synaptic location as the pre- and post-synaptic quantities. As compared to a previous paper [Saudargiene, A., Porr, B., Worgotter, F., 2004. How the shape of pre- and post-synaptic signals can influence stdp: a biophysical model. Neural Comp.], here we show that this rule reproduces the generic STDP weight change curve by using real neuronal input signals and combinations of more than two (pre- and post-synaptic) spikes. We demonstrate that the shape of the STDP curve strongly depends on the shape of the depolarising membrane potentials, which induces learning. As these potentials vary at different locations of the dendritic tree, model predicts that synaptic changes are location dependent. The model is extended to account for the patterns of more than two spikes of the pre- and post-synaptic cells. The results show that STDP weight change curve is also activity dependent.