Questions about STDP as a General Model of Synaptic Plasticity

A dendritic mechanism for balancing synaptic flexibility and stability

Biological and artificial neural networks learn by modifying synaptic weights, but it is unclear how these systems retain previous knowledge and also acquire new information. Here, we show that cortical pyramidal neurons can solve this plasticity-versus-stability dilemma by differentially regulating synaptic plasticity at distinct dendritic compartments. Oblique dendrites of adult mouse layer 5 cortical pyramidal neurons selectively receive monosynaptic thalamic input, integrate linearly, and lack burst-timing synaptic potentiation. In contrast, basal dendrites, which do not receive thalamic input, exhibit conventional NMDA receptor (NMDAR)-mediated supralinear integration and synaptic potentiation. Congruently, spiny synapses on oblique branches show decreased structural plasticity in vivo. The selective decline in NMDAR activity and expression at synapses on oblique dendrites is controlled by a critical period of visual experience. Our results demonstrate a biological mechanism for how single neurons can safeguard a set of inputs from ongoing plasticity by altering synaptic properties at distinct dendritic domains.

The spike-timing-dependent plasticity of VIP interneurons in motor cortex

The plasticity of inhibitory interneurons (INs) plays an important role in the organization and maintenance of cortical microcircuits. Given the many different IN types, there is an even greater diversity in synapse-type-specific plasticity learning rules at excitatory to excitatory (E→I), I→E, and I→I synapses. I→I synapses play a key disinhibitory role in cortical circuits. Because they typically target other INs, vasoactive intestinal peptide (VIP) INs are often featured in I→I→E disinhibition, which upregulates activity in nearby excitatory neurons. VIP IN dysregulation may thus lead to neuropathologies such as epilepsy. In spite of the important activity regulatory role of VIP INs, their long-term plasticity has not been described. Therefore, we characterized the phenomenology of spike-timing-dependent plasticity (STDP) at inputs and outputs of genetically defined VIP INs. Using a combination of whole-cell recording, 2-photon microscopy, and optogenetics, we explored I→I STDP at layer 2/3 (L2/3) VIP IN outputs onto L5 Martinotti cells (MCs) and basket cells (BCs). We found that VIP IN→MC synapses underwent causal long-term depression (LTD) that was presynaptically expressed. VIP IN→BC connections, however, did not undergo any detectable plasticity. Conversely, using extracellular stimulation, we explored E→I STDP at inputs to VIP INs which revealed long-term potentiation (LTP) for both causal and acausal timings. Taken together, our results demonstrate that VIP INs possess synapse-type-specific learning rules at their inputs and outputs. This suggests the possibility of harnessing VIP IN long-term plasticity to control activity-related neuropathologies such as epilepsy.

Synaptic plasticity through a naturalistic lens

From the myriad of studies on neuronal plasticity, investigating its underlying molecular mechanisms up to its behavioral relevance, a very complex landscape has emerged. Recent efforts have been achieved toward more naturalistic investigations as an attempt to better capture the synaptic plasticity underpinning of learning and memory, which has been fostered by the development of in vivo electrophysiological and imaging tools. In this review, we examine these naturalistic investigations, by devoting a first part to synaptic plasticity rules issued from naturalistic in vivo-like activity patterns. We next give an overview of the novel tools, which enable an increased spatio-temporal specificity for detecting and manipulating plasticity expressed at individual spines up to neuronal circuit level during behavior. Finally, we put particular emphasis on works considering brain-body communication loops and macroscale contributors to synaptic plasticity, such as body internal states and brain energy metabolism.

BTSP, not STDP, Drives Shifts in Hippocampal Representations During Familiarization

Synaptic plasticity is widely thought to support memory storage in the brain, but the rules determining impactful synaptic changes in-vivo are not known. We considered the trial-by-trial shifting dynamics of hippocampal place fields (PFs) as an indicator of ongoing plasticity during memory formation. By implementing different plasticity rules in computational models of spiking place cells and comparing to experimentally measured PFs from mice navigating familiar and novel environments, we found that Behavioral-Timescale-Synaptic-Plasticity (BTSP), rather than Hebbian Spike-Timing-Dependent-Plasticity, is the principal mechanism governing PF shifting dynamics. BTSP-triggering events are rare, but more frequent during novel experiences. During exploration, their probability is dynamic: it decays after PF onset, but continually drives a population-level representational drift. Finally, our results show that BTSP occurs in CA3 but is less frequent and phenomenologically different than in CA1. Overall, our study provides a new framework to understand how synaptic plasticity shapes neuronal representations during learning.

Sequence anticipation and spike-timing-dependent plasticity emerge from a predictive learning rule

Intelligent behavior depends on the brain's ability to anticipate future events. However, the learning rules that enable neurons to predict and fire ahead of sensory inputs remain largely unknown. We propose a plasticity rule based on predictive processing, where the neuron learns a low-rank model of the synaptic input dynamics in its membrane potential. Neurons thereby amplify those synapses that maximally predict other synaptic inputs based on their temporal relations, which provide a solution to an optimization problem that can be implemented at the single-neuron level using only local information. Consequently, neurons learn sequences over long timescales and shift their spikes towards the first inputs in a sequence. We show that this mechanism can explain the development of anticipatory signalling and recall in a recurrent network. Furthermore, we demonstrate that the learning rule gives rise to several experimentally observed STDP (spike-timing-dependent plasticity) mechanisms. These findings suggest prediction as a guiding principle to orchestrate learning and synaptic plasticity in single neurons.

The study of plasticity has always been about gradients

The experimental study of learning and plasticity has always been driven by an implicit question: how can physiological changes be adaptive and improve performance? For example, in Hebbian plasticity only synapses from presynaptic neurons that were active are changed, avoiding useless changes. Similarly, in dopamine-gated learning synapse changes depend on reward or lack thereof and do not change when everything is predictable. Within machine learning we can make the question of which changes are adaptive concrete: performance improves when changes correlate with the gradient of an objective function quantifying performance. This result is general for any system that improves through small changes. As such, physiology has always implicitly been seeking mechanisms that allow the brain to approximate gradients. Coming from this perspective we review the existing literature on plasticity-related mechanisms, and we show how these mechanisms relate to gradient estimation. We argue that gradients are a unifying idea to explain the many facets of neuronal plasticity.

Where is the error? Hierarchical predictive coding through dendritic error computation

Top-down feedback in cortex is critical for guiding sensory processing, which has prominently been formalized in the theory of hierarchical predictive coding (hPC). However, experimental evidence for error units, which are central to the theory, is inconclusive and it remains unclear how hPC can be implemented with spiking neurons. To address this, we connect hPC to existing work on efficient coding in balanced networks with lateral inhibition and predictive computation at apical dendrites. Together, this work points to an efficient implementation of hPC with spiking neurons, where prediction errors are computed not in separate units, but locally in dendritic compartments. We then discuss the correspondence of this model to experimentally observed connectivity patterns, plasticity, and dynamics in cortex.

Subcortical glutamatergic inputs exhibit a Hebbian form of long-term potentiation in the dentate gyrus

The hippocampus receives glutamatergic and GABAergic inputs from subcortical regions. Despite the important roles of these subcortical inputs in the regulation of hippocampal circuit, it has not been explored whether associative activation of the subcorticohippocampal pathway induces Hebbian plasticity of subcortical inputs. Here, we demonstrate that the hypothalamic supramammillary nucleus (SuM) to the dentate granule cell (GC) synapses, which co-release glutamate and GABA, undergo associative long-term potentiation (LTP) of glutamatergic, but not GABAergic, co-transmission. This LTP is induced by pairing of SuM inputs with GC spikes. We found that this Hebbian LTP is input-specific, requires NMDA receptors and CaMKII activation, and is expressed postsynaptically. By the net increase in excitatory drive of SuM inputs following LTP induction, associative inputs of SuM and the perforant path effectively discharge GCs. Our results highlight the important role of associative plasticity at SuM-GC synapses in the regulation of dentate gyrus activity and for the encoding of SuM-related information.

A calcium-based plasticity model for predicting long-term potentiation and depression in the neocortex

Pyramidal cells (PCs) form the backbone of the layered structure of the neocortex, and plasticity of their synapses is thought to underlie learning in the brain. However, such long-term synaptic changes have been experimentally characterized between only a few types of PCs, posing a significant barrier for studying neocortical learning mechanisms. Here we introduce a model of synaptic plasticity based on data-constrained postsynaptic calcium dynamics, and show in a neocortical microcircuit model that a single parameter set is sufficient to unify the available experimental findings on long-term potentiation (LTP) and long-term depression (LTD) of PC connections. In particular, we find that the diverse plasticity outcomes across the different PC types can be explained by cell-type-specific synaptic physiology, cell morphology and innervation patterns, without requiring type-specific plasticity. Generalizing the model to in vivo extracellular calcium concentrations, we predict qualitatively different plasticity dynamics from those observed in vitro. This work provides a first comprehensive null model for LTP/LTD between neocortical PC types in vivo, and an open framework for further developing models of cortical synaptic plasticity.

Dendritic Excitability and Synaptic Plasticity In Vitro and In Vivo

Much of our understanding of dendritic and synaptic physiology comes from in vitro experimentation, where the afforded mechanical stability and convenience of applying drugs allowed patch-clamping based recording techniques to investigate ion channel distributions, their gating kinetics, and to uncover dendritic integrative and synaptic plasticity rules. However, with current efforts to study these questions in vivo, there is a great need to translate existing knowledge between in vitro and in vivo experimental conditions. In this review, we identify discrepancies between in vitro and in vivo ionic composition of extracellular media and discuss how changes in ionic composition alter dendritic excitability and plasticity induction. Here, we argue that under physiological in vivo ionic conditions, dendrites are expected to be more excitable and the threshold for synaptic plasticity induction to be lowered. Consequently, the plasticity rules described in vitro vary significantly from those implemented in vivo.

Local dendritic balance enables learning of efficient representations in networks of spiking neurons

How can neural networks learn to efficiently represent complex and high-dimensional inputs via local plasticity mechanisms? Classical models of representation learning assume that feedforward weights are learned via pairwise Hebbian-like plasticity. Here, we show that pairwise Hebbian-like plasticity works only under unrealistic requirements on neural dynamics and input statistics. To overcome these limitations, we derive from first principles a learning scheme based on voltage-dependent synaptic plasticity rules. Here, recurrent connections learn to locally balance feedforward input in individual dendritic compartments and thereby can modulate synaptic plasticity to learn efficient representations. We demonstrate in simulations that this learning scheme works robustly even for complex high-dimensional inputs and with inhibitory transmission delays, where Hebbian-like plasticity fails. Our results draw a direct connection between dendritic excitatory-inhibitory balance and voltage-dependent synaptic plasticity as observed in vivo and suggest that both are crucial for representation learning.

Plasticity of olfactory bulb inputs mediated by dendritic NMDA-spikes in rodent piriform cortex

The piriform cortex (PCx) is essential for learning of odor information. The current view postulates that odor learning in the PCx is mainly due to plasticity in intracortical (IC) synapses, while odor information from the olfactory bulb carried via the lateral olfactory tract (LOT) is ‘hardwired.’ Here, we revisit this notion by studying location- and pathway-dependent plasticity rules. We find that in contrast to the prevailing view, synaptic and optogenetically activated LOT synapses undergo strong and robust long-term potentiation (LTP) mediated by only a few local NMDA-spikes delivered at theta frequency, while global spike timing-dependent plasticity (STDP) protocols failed to induce LTP in these distal synapses. In contrast, IC synapses in apical and basal dendrites undergo plasticity with both NMDA-spikes and STDP protocols but to a smaller extent compared with LOT synapses. These results are consistent with a self-potentiating mechanism of odor information via NMDA-spikes that can form branch-specific memory traces of odors that can further associate with contextual IC information via STDP mechanisms to provide cognitive and emotional value to odors.

Dendritic Branch-constrained N-Methyl-d-Aspartate Receptor-mediated Spikes Drive Synaptic Plasticity in Hippocampal CA3 Pyramidal Cells

N-methyl-d-aspartate receptor-mediated ( spikes can be causally linked to the induction of synaptic long-term potentiation (LTP) in hippocampal and cortical pyramidal cells. However, it is unclear if they regulate plasticity at a local or global scale in the dendritic tree. Here, we used dendritic patch-clamp recordings and calcium imaging to investigate the integrative properties of single dendrites of hippocampal CA3 cells. We show that local hyperpolarization of a single dendritic segment prevents NMDA spikes, their associated calcium transients, as well as LTP in a branch-specific manner. This result provides direct, causal evidence that the single dendritic branch can operate as a functional unit in regulating CA3 pyramidal cell plasticity.

Distinct place cell dynamics in CA1 and CA3 encode experience in new environments

When exploring new environments animals form spatial memories that are updated with experience and retrieved upon re-exposure to the same environment. The hippocampus is thought to support these memory processes, but how this is achieved by different subnetworks such as CA1 and CA3 remains unclear. To understand how hippocampal spatial representations emerge and evolve during familiarization, we performed 2-photon calcium imaging in mice running in new virtual environments and compared the trial-to-trial dynamics of place cells in CA1 and CA3 over days. We find that place fields in CA1 emerge rapidly but tend to shift backwards from trial-to-trial and remap upon re-exposure to the environment a day later. In contrast, place fields in CA3 emerge gradually but show more stable trial-to-trial and day-to-day dynamics. These results reflect different roles in CA1 and CA3 in spatial memory processing during familiarization to new environments and constrain the potential mechanisms that support them.

Effects of memristive synapse radiation interactions on learning in spiking neural networks

This study uses advanced modeling and simulation to explore the effects of external events such as radiation interactions on the synaptic devices in an electronic spiking neural network. Specifically, the networks are trained using the spike-timing-dependent plasticity (STDP) learning rule to recognize spatio-temporal patterns (STPs) representing 25 and 100-pixel characters. Memristive synapses based on a TiO2 non-linear drift model designed in Verilog-A are utilized, with STDP learning behavior achieved through bi-phasic pre- and post-synaptic action potentials. The models are modified to include experimentally observed state-altering and ionizing radiation effects on the device. It is found that radiation interactions tend to make the connection between afferents stronger by increasing the conductance of synapses overall, subsequently distorting the STDP learning curve. In the absence of consistent STPs, these effects accumulate over time and make the synaptic weight evolutions unstable. With STPs at lower flux intensities, the network can recover and relearn with constant training. However, higher flux can overwhelm the leaky integrate-and-fire post-synaptic neuron circuits and reduce stability of the network.

A Model for R(t) Elements and R(t) -Based Spike-Timing-Dependent Plasticity With Basic Circuit Examples

Spike-timing-dependent plasticity (STDP) is a fundamental synaptic learning rule observed in biology that leads to numerous behavioral and cognitive outcomes. Emulating STDP in electronic spiking neural networks with high-density memristive synapses is, therefore, of significant interest. While one popular method involves pulse-shaping the spiking neuron output voltages, an alternative approach is outlined in this article. The proposed STDP implementation uses time-varying dynamic resistance [ R ( t )] elements to achieve local synaptic learning from spike-pair STDP, spike triplet STDP, and firing rates. The R ( t ) elements are connected to each neuron circuit, thereby maintaining synaptic density and leveraging voltage division as a means of altering synaptic weight (memristor voltage). Example R ( t ) elements with their corresponding behaviors are demonstrated through simulation. A three-input-two-output network using single-memristor synaptic connections and R ( t ) elements is also simulated. Network-level effects, such as nonspecific synaptic plasticity, are discussed. Finally, spatiotemporal pattern recognition (STPR) using R ( t ) elements is demonstrated in simulation.

Synaptic Plasticity in Cortical Inhibitory Neurons: What Mechanisms May Help to Balance Synaptic Weight Changes?

Inhibitory neurons play a fundamental role in the normal operation of neuronal networks. Diverse types of inhibitory neurons serve vital functions in cortical networks, such as balancing excitation and taming excessive activity, organizing neuronal activity in spatial and temporal patterns, and shaping response selectivity. Serving these, and a multitude of other functions effectively requires fine-tuning of inhibition, mediated by synaptic plasticity. Plasticity of inhibitory systems can be mediated by changes at inhibitory synapses and/or by changes at excitatory synapses at inhibitory neurons. In this review, we consider that latter locus: plasticity at excitatory synapses to inhibitory neurons. Despite the fact that plasticity of excitatory synaptic transmission to interneurons has been studied in much less detail than in pyramids and other excitatory cells, an abundance of forms and mechanisms of plasticity have been observed in interneurons. Specific requirements and rules for induction, while exhibiting a broad diversity, could correlate with distinct sources of excitatory inputs and distinct types of inhibitory neurons. One common requirement for the induction of plasticity is the rise of intracellular calcium, which could be mediated by a variety of ligand-gated, voltage-dependent, and intrinsic mechanisms. The majority of the investigated forms of plasticity can be classified as Hebbian-type associative plasticity. Hebbian-type learning rules mediate adaptive changes of synaptic transmission. However, these rules also introduce intrinsic positive feedback on synaptic weight changes, making plastic synapses and learning networks prone to runaway dynamics. Because real inhibitory neurons do not express runaway dynamics, additional plasticity mechanisms that counteract imbalances introduced by Hebbian-type rules must exist. We argue that weight-dependent heterosynaptic plasticity has a number of characteristics that make it an ideal candidate mechanism to achieve homeostatic regulation of synaptic weight changes at excitatory synapses to inhibitory neurons.

Hebbian and non-Hebbian timing-dependent plasticity in the hippocampal CA3 region

The timing between synaptic inputs has been proposed to play a role in the induction of plastic changes that enable neural circuits to store information. In the case of spike timing-dependent plasticity (STDP), this relates to the interval between a synaptic input and a postsynaptic spike, thus providing a conceptual link to the Hebb learning rule. Experiments have documented STDP in many synapses and brain regions, and computational models have tested its utility in many neural network functions. However, questions remain about whether timing plays a role in plasticity during natural activity, and whether it can function in information storage. The present study used imaging with voltage sensitive dye to investigate the effectiveness of input timing in the plasticity of responses in the CA3 region of hippocampal slices. Plasticity was induced by sequential dual-site stimulation at 10 ms intervals of either synaptic inputs and cell bodies (synaptic-somatic induction) or of two sets of synaptic inputs (synaptic-synaptic induction). Both protocols potentiated responses, with greater potentiation of responses to the first stimulation of the sequence than the second. Neither of these protocols induced depression. Synaptic-somatic stimulation was much more effective than synaptic-synaptic stimulation in evoking somatic action potentials, but both protocols potentiated responses equally well. This suggests that sequential dual-site stimulation can potentiate equally well with very different degrees of somatic action potential firing. With synaptic-somatic induction, potentiation was focused at the sites of stimulation. In contrast, with synaptic-synaptic induction, the distribution of potentiation varied greatly. Changes in the spatial distribution of responses indicated that sequential dual-site stimulation functions poorly in the storage of activity patterns. These results suggest that in the hippocampal CA3 region, timed sequential activation of two inputs is less effective than theta bursts, both in the induction of LTP and in the storage of information.

Tonic GABAA Conductance Favors Spike-Timing-Dependent over Theta-Burst-Induced Long-Term Potentiation in the Hippocampus

Synaptic plasticity is triggered by different patterns of network activity. Here, we investigated how LTP in CA3-CA1 synapses induced by different stimulation patterns is affected by tonic GABA_A conductances in rat hippocampal slices. Spike-timing-dependent LTP was induced by pairing Schaffer collateral stimulation with antidromic stimulation of CA1 pyramidal neurons. Theta-burst-induced LTP was induced by theta-burst stimulation of Schaffer collaterals. We mimicked increased tonic GABA_A conductance by bath application of 30 μm GABA. Surprisingly, tonic GABA_A conductance selectively suppressed theta-burst-induced LTP but not spike-timing-dependent LTP. We combined whole-cell patch-clamp electrophysiology, two-photon Ca²⁺ imaging, glutamate uncaging, and mathematical modeling to dissect the mechanisms underlying these differential effects of tonic GABA_A conductance. We found that Ca²⁺ transients during pairing of an action potential with an EPSP were less sensitive to tonic GABA_A conductance-induced shunting inhibition than Ca²⁺ transients induced by EPSP burst. Our results may explain how different forms of memory are affected by increasing tonic GABA_A conductances under physiological or pathologic conditions, as well as under the influence of substances that target extrasynaptic GABA_A receptors (e.g., neurosteroids, sedatives, antiepileptic drugs, and alcohol).SIGNIFICANCE STATEMENT Brain activity is associated with neuronal firing and synaptic signaling among neurons. Synaptic plasticity represents a mechanism for learning and memory. However, some neurotransmitters that escape the synaptic cleft or are released by astrocytes can target extrasynaptic receptors. Extrasynaptic GABA_A receptors mediate tonic conductances that reduce the excitability of neurons by shunting. This results in the decreased ability for neurons to fire action potentials, but when action potentials are successfully triggered, tonic conductances are unable to reduce them significantly. As such, tonic GABA_A conductances have minimal effects on spike-timing-dependent synaptic plasticity while strongly attenuating the plasticity evoked by EPSP bursts. Our findings shed light on how changes in tonic conductances can selectively affect different forms of learning and memory.

Coincidence Detection within the Excitable Rat Olfactory Bulb Granule Cell Spines

In the mammalian olfactory bulb, the inhibitory axonless granule cells (GCs) feature reciprocal synapses that interconnect them with the principal neurons of the bulb, mitral, and tufted cells. These synapses are located within large excitable spines that can generate local action potentials (APs) upon synaptic input ("spine spike"). Moreover, GCs can fire global APs that propagate throughout the dendrite. Strikingly, local postsynaptic Ca²⁺ entry summates mostly linearly with Ca²⁺ entry due to coincident global APs generated by glomerular stimulation, although some underlying conductances should be inactivated. We investigated this phenomenon by constructing a compartmental GC model to simulate the pairing of local and global signals as a function of their temporal separation Δt. These simulations yield strongly sublinear summation of spine Ca²⁺ entry for the case of perfect coincidence Δt = 0 ms. Summation efficiency (SE) sharply rises for both positive and negative Δt. The SE reduction for coincident signals depends on the presence of voltage-gated Na⁺ channels in the spine head, while NMDARs are not essential. We experimentally validated the simulated SE in slices of juvenile rat brain (both sexes) by pairing two-photon uncaging of glutamate at spines and APs evoked by somatic current injection at various intervals Δt while imaging spine Ca²⁺ signals. Finally, the latencies of synaptically evoked global APs and EPSPs were found to correspond to Δt ≈ 10 ms, explaining the observed approximately linear summation of synaptic local and global signals. Our results provide additional evidence for the existence of the GC spine spike.SIGNIFICANCE STATEMENT Here we investigate the interaction of local synaptic inputs and global activation of a neuron by a backpropagating action potential within a dendritic spine with respect to local Ca²⁺ signaling. Our system of interest, the reciprocal spine of the olfactory bulb granule cell, is known to feature a special processing mode, namely, a synaptically triggered action potential that is restricted to the spine head. Therefore, coincidence detection of local and global signals follows different rules than in more conventional synapses. We unravel these rules using both simulations and experiments and find that signals coincident within ≈±7 ms around 0 ms result in sublinear summation of Ca²⁺ entry because of synaptic activation of voltage-gated Na⁺ channels within the spine.

Compensatory Relearning Following Stroke: Cellular and Plasticity Mechanisms in Rodents

von Monakow’s theory of diaschisis states the functional ‘standstill’ of intact brain regions that are remote from a damaged area, often implied in recovery of function. Accordingly, neural plasticity and activity patterns related to recovery are also occurring at the same regions. Recovery relies on plasticity in the periinfarct and homotopic contralesional regions and involves relearning to perform movements. Seeking evidence for a relearning mechanism following stroke, we found that rodents display many features that resemble classical learning and memory mechanisms. Compensatory relearning is likely to be accompanied by gradual shaping of these regions and pathways, with participating neurons progressively adapting cortico-striato-thalamic activity and synaptic strengths at different cortico-thalamic loops – adapting function relayed by the striatum. Motor cortex functional maps are progressively reinforced and shaped by these loops as the striatum searches for different functional actions. Several cortical and striatal cellular mechanisms that influence motor learning may also influence post-stroke compensatory relearning. Future research should focus on how different neuromodulatory systems could act before, during or after rehabilitation to improve stroke recovery.

Bridging the gap between striatal plasticity and learning

The striatum, the main input nucleus of the basal ganglia, controls goal-directed behavior and procedural learning. Striatal projection neurons integrate glutamatergic inputs from cortex and thalamus together with neuromodulatory systems, and are subjected to plasticity. Striatal projection neurons exhibit bidirectional plasticity (LTP and LTD) when exposed to Hebbian paradigms. Importantly, correlative and even causal links between procedural learning and striatal plasticity have recently been shown. This short review summarizes the current view on striatal plasticity (with a focus on spike-timing-dependent plasticity), recent studies aiming at bridging in vivo skill acquisition and striatal plasticity, the temporal credit-assignment problem, and the gaps that remain to be filled.

Dendritic solutions to the credit assignment problem

Guaranteeing that synaptic plasticity leads to effective learning requires a means for assigning credit to each neuron for its contribution to behavior. The 'credit assignment problem' refers to the fact that credit assignment is non-trivial in hierarchical networks with multiple stages of processing. One difficulty is that if credit signals are integrated with other inputs, then it is hard for synaptic plasticity rules to distinguish credit-related activity from non-credit-related activity. A potential solution is to use the spatial layout and non-linear properties of dendrites to distinguish credit signals from other inputs. In cortical pyramidal neurons, evidence hints that top-down feedback signals are integrated in the distal apical dendrites and have a distinct impact on spike-firing and synaptic plasticity. This suggests that the distal apical dendrites of pyramidal neurons help the brain to solve the credit assignment problem.

Beyond STDP-towards diverse and functionally relevant plasticity rules

Synaptic plasticity, induced by the close temporal association of two neural signals, supports associative forms of learning. However, the millisecond timescales for association often do not match the much longer delays for behaviorally relevant signals that supervise learning. In particular, information about the behavioral outcome of neural activity can be delayed, leading to a problem of temporal credit assignment. Recent studies suggest that synaptic plasticity can have temporal rules that not only accommodate the delays relevant to the circuit, but also be precisely tuned to the behavior the circuit supports. These discoveries highlight the diversity of plasticity rules, whose temporal requirements may depend on circuit delays and the contingencies of behavior.

Effect of inhibitory spike-timing-dependent plasticity on fast sparsely synchronized rhythms in a small-world neuronal network

We consider the Watts-Strogatz small-world network (SWN) consisting of inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP, fast sparsely synchronized rhythms, associated with diverse cognitive functions, were found to appear in a range of large noise intensities for fixed strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP on fast sparse synchronization (FSS) by varying the noise intensity D. We employ an asymmetric anti-Hebbian time window for the iSTDP update rule [which is in contrast to the Hebbian time window for the excitatory STDP (eSTDP)]. Depending on values of D, population-averaged values of saturated synaptic inhibition strengths are potentiated [long-term potentiation (LTP)] or depressed [long-term depression (LTD)] in comparison with the initial mean value, and dispersions from the mean values of LTP/LTD are much increased when compared with the initial dispersion, independently of D. In most cases of LTD where the effect of mean LTD is dominant in comparison with the effect of dispersion, good synchronization (with higher spiking measure) is found to get better via LTD, while bad synchronization (with lower spiking measure) is found to get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). Emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, we also investigate the effects of network architecture on FSS by changing the rewiring probability p of the SWN in the presence of iSTDP.

Robustness of STDP to spike timing jitter

In Hebbian plasticity, neural circuits adjust their synaptic weights depending on patterned firing. Spike-timing-dependent plasticity (STDP), a synaptic Hebbian learning rule, relies on the order and timing of the paired activities in pre- and postsynaptic neurons. Classically, in ex vivo experiments, STDP is assessed with deterministic (constant) spike timings and time intervals between successive pairings, thus exhibiting a regularity that differs from biological variability. Hence, STDP emergence from noisy inputs as occurring in in vivo-like firing remains unresolved. Here, we used noisy STDP pairings where the spike timing and/or interval between pairings were jittered. We explored with electrophysiology and mathematical modeling, the impact of jitter on three forms of STDP at corticostriatal synapses: NMDAR-LTP, endocannabinoid-LTD and endocannabinoid-LTP. We found that NMDAR-LTP was highly fragile to jitter, whereas endocannabinoid-plasticity appeared more resistant. When the frequency or number of pairings was increased, NMDAR-LTP became more robust and could be expressed despite strong jittering. Our results identify endocannabinoid-plasticity as a robust form of STDP, whereas the sensitivity to jitter of NMDAR-LTP varies with activity frequency. This provides new insights into the mechanisms at play during the different phases of learning and memory and the emergence of Hebbian plasticity in in vivo-like activity.

Dynamic Hebbian Cross-Correlation Learning Resolves the Spike Timing Dependent Plasticity Conundrum

Spike Timing-Dependent Plasticity has been found to assume many different forms. The classic STDP curve, with one potentiating and one depressing window, is only one of many possible curves that describe synaptic learning using the STDP mechanism. It has been shown experimentally that STDP curves may contain multiple LTP and LTD windows of variable width, and even inverted windows. The underlying STDP mechanism that is capable of producing such an extensive, and apparently incompatible, range of learning curves is still under investigation. In this paper, it is shown that STDP originates from a combination of two dynamic Hebbian cross-correlations of local activity at the synapse. The correlation of the presynaptic activity with the local postsynaptic activity is a robust and reliable indicator of the discrepancy between the presynaptic neuron and the postsynaptic neuron's activity. The second correlation is between the local postsynaptic activity with dendritic activity which is a good indicator of matching local synaptic and dendritic activity. We show that this simple time-independent learning rule can give rise to many forms of the STDP learning curve. The rule regulates synaptic strength without the need for spike matching or other supervisory learning mechanisms. Local differences in dendritic activity at the synapse greatly affect the cross-correlation difference which determines the relative contributions of different neural activity sources. Dendritic activity due to nearby synapses, action potentials, both forward and back-propagating, as well as inhibitory synapses will dynamically modify the local activity at the synapse, and the resulting STDP learning rule. The dynamic Hebbian learning rule ensures furthermore, that the resulting synaptic strength is dynamically stable, and that interactions between synapses do not result in local instabilities. The rule clearly demonstrates that synapses function as independent localized computational entities, each contributing to the global activity, not in a simply linear fashion, but in a manner that is appropriate to achieve local and global stability of the neuron and the entire dendritic structure.

Glutamatergic synapses are structurally and biochemically complex because of multiple plasticity processes: long-term potentiation, long-term depression, short-term potentiation and scaling

Synapses are complex because they perform multiple functions, including at least six mechanistically different forms of plasticity. Here, I comment on recent developments regarding these processes. (i) Short-term potentiation (STP), a Hebbian process that requires small amounts of synaptic input, appears to make strong contributions to some forms of working memory. (ii) The rules for long-term potentiation (LTP) induction in CA3 have been clarified: induction does not depend obligatorily on backpropagating sodium spikes but, rather, on dendritic branch-specific N-methyl-d-aspartate (NMDA) spikes. (iii) Late LTP, a process that requires a dopamine signal (and is therefore neoHebbian), is mediated by trans-synaptic growth of the synapse, a growth that occurs about an hour after LTP induction. (iv) LTD processes are complex and include both homosynaptic and heterosynaptic forms. (v) Synaptic scaling produced by changes in activity levels are not primarily cell-autonomous, but rather depend on network activity. (vi) The evidence for distance-dependent scaling along the primary dendrite is firm, and a plausible structural-based mechanism is suggested.Ideas about the mechanisms of synaptic function need to take into consideration newly emerging data about synaptic structure. Recent super-resolution studies indicate that glutamatergic synapses are modular (module size 70-80 nm), as predicted by theoretical work. Modules are trans-synaptic structures and have high concentrations of postsynaptic density-95 (PSD-95) and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor. These modules function as quasi-independent loci of AMPA-mediated transmission and may be independently modifiable, suggesting a new understanding of quantal transmission.This article is part of the themed issue 'Integrating Hebbian and homeostatic plasticity.'

Modeling somatic and dendritic spike mediated plasticity at the single neuron and network level

Synaptic plasticity is thought to be the principal neuronal mechanism underlying learning. Models of plastic networks typically combine point neurons with spike-timing-dependent plasticity (STDP) as the learning rule. However, a point neuron does not capture the local non-linear processing of synaptic inputs allowed for by dendrites. Furthermore, experimental evidence suggests that STDP is not the only learning rule available to neurons. By implementing biophysically realistic neuron models, we study how dendrites enable multiple synaptic plasticity mechanisms to coexist in a single cell. In these models, we compare the conditions for STDP and for synaptic strengthening by local dendritic spikes. We also explore how the connectivity between two cells is affected by these plasticity rules and by different synaptic distributions. Finally, we show that how memory retention during associative learning can be prolonged in networks of neurons by including dendrites.

Synaptic plasticity is the neuronal mechanism underlying learning. Here the authors construct biophysical models of pyramidal neurons that reproduce observed plasticity gradients along the dendrite and show that dendritic spike dependent LTP which is predominant in distal sections can prolong memory retention.

Modelling plasticity in dendrites: from single cells to networks

One of the key questions in neuroscience is how our brain self-organises to efficiently process information. To answer this question, we need to understand the underlying mechanisms of plasticity and their role in shaping synaptic connectivity. Theoretical neuroscience typically investigates plasticity on the level of neural networks. Neural network models often consist of point neurons, completely neglecting neuronal morphology for reasons of simplicity. However, during the past decades it became increasingly clear that inputs are locally processed in the dendrites before they reach the cell body. Dendritic properties enable local interactions between synapses and location-dependent modulations of inputs, rendering the position of synapses on dendrites highly important. These insights changed our view of neurons, such that we now think of them as small networks of nearly independent subunits instead of a simple point. Here, we propose that understanding how the brain processes information strongly requires that we consider the following properties: which plasticity mechanisms are present in the dendrites and how do they enable the self-organisation of synapses across the dendritic tree for efficient information processing? Ultimately, dendritic plasticity mechanisms can be studied in networks of neurons with dendrites, possibly uncovering unknown mechanisms that shape the connectivity in our brains.

Anisomorphic cortical reorganization in asymmetric sensorineural hearing loss

Acoustic trauma or inner ear disease may predominantly injure one ear, causing asymmetric sensorineural hearing loss (SNHL). While characteristic frequency (CF) map plasticity of primary auditory cortex (AI) contralateral to the injured ear has been detailed, there is no study that also evaluates ipsilateral AI to compare cortical reorganization across both hemispheres. We assess whether the normal isomorphic mirror-image relationship between the two hemispheres is maintained or disrupted in mild-to-moderate asymmetric SNHL of adult squirrel monkeys. At week 24 after induction of acoustic injury to the right ear, functional organization of the two hemispheres differs in direction and magnitude of interaural CF difference, percentage of recording sites with spectrally nonoverlapping binaural activation, and the concurrence of peripheral and central activation thresholds. The emergence of this anisomorphic cortical reorganization of the two hemispheres is replicated by simulation based on spike timing-dependent plasticity, where 1) AI input from the contralateral ear is dominant, 2) reestablishment of relatively shorter contralateral ear input timing drives reorganization, and 3) only AI contralateral to the injured ear undergoes major realignment of interaural frequency maps that evolve over months. Asymmetric SNHL disrupts isomorphic organization between the two hemispheres and results in relative local hemispheric autonomy, potentially impairing performance of tasks that require binaural input alignment or interhemispheric processing.NEW & NOTEWORTHY Mild-to-moderate hearing loss in one ear and essentially normal hearing in the other triggers cortical reorganization that is different in the two hemispheres. Asymmetry of cochlea sensitivities does not simply propagate to the two auditory cortices in mirror-image fashion. The resulting anisomorphic cortical reorganization may be a neurophysiological basis of clinical deficits in asymmetric hearing loss, such as difficulty with hearing in noise, impaired spatial hearing, and accelerated decline of the poorer ear.

Coexistence of Multiple Types of Synaptic Plasticity in Individual Hippocampal CA1 Pyramidal Neurons

Understanding learning and memory mechanisms is an important goal in neuroscience. To gain insights into the underlying cellular mechanisms for memory formation, synaptic plasticity processes are studied with various techniques in different brain regions. A valid model to scrutinize different ways to enhance or decrease synaptic transmission is recording of long-term potentiation (LTP) or long-term depression (LTD). At the single cell level, spike timing-dependent plasticity (STDP) protocols have emerged as a powerful tool to investigate synaptic plasticity with stimulation paradigms that also likely occur during memory formation in vivo. Such kind of plasticity can be induced by different STDP paradigms with multiple repeat numbers and stimulation patterns. They subsequently recruit or activate different molecular pathways and neuromodulators for induction and expression of STDP. Dopamine (DA) and brain-derived neurotrophic factor (BDNF) have been recently shown to be important modulators for hippocampal STDP at Schaffer collateral (SC)-CA1 synapses and are activated exclusively by distinguishable STDP paradigms. Distinct types of parallel synaptic plasticity in a given neuron depend on specific subcellular molecular prerequisites. Since the basal and apical dendrites of CA1 pyramidal neurons are known to be heterogeneous, and distance-dependent dendritic gradients for specific receptors and ion channels are described, the dendrites might provide domain specific locations for multiple types of synaptic plasticity in the same neuron. In addition to the distinct signaling and expression mechanisms of various types of LTP and LTD, activation of these different types of plasticity might depend on background brain activity states. In this article, we will discuss some ideas why multiple forms of synaptic plasticity can simultaneously and independently coexist and can contribute so effectively to increasing the efficacy of memory storage and processing capacity of the brain. We hypothesize that resolving the subcellular location of t-LTP and t-LTD mechanisms that are regulated by distinct neuromodulator systems will be essential to reach a more cohesive understanding of synaptic plasticity in memory formation.

Learning by stimulation avoidance: A principle to control spiking neural networks dynamics

Learning based on networks of real neurons, and learning based on biologically inspired models of neural networks, have yet to find general learning rules leading to widespread applications. In this paper, we argue for the existence of a principle allowing to steer the dynamics of a biologically inspired neural network. Using carefully timed external stimulation, the network can be driven towards a desired dynamical state. We term this principle "Learning by Stimulation Avoidance" (LSA). We demonstrate through simulation that the minimal sufficient conditions leading to LSA in artificial networks are also sufficient to reproduce learning results similar to those obtained in biological neurons by Shahaf and Marom, and in addition explains synaptic pruning. We examined the underlying mechanism by simulating a small network of 3 neurons, then scaled it up to a hundred neurons. We show that LSA has a higher explanatory power than existing hypotheses about the response of biological neural networks to external simulation, and can be used as a learning rule for an embodied application: learning of wall avoidance by a simulated robot. In other works, reinforcement learning with spiking networks can be obtained through global reward signals akin simulating the dopamine system; we believe that this is the first project demonstrating sensory-motor learning with random spiking networks through Hebbian learning relying on environmental conditions without a separate reward system.

Dendritic NMDA spikes are necessary for timing-dependent associative LTP in CA3 pyramidal cells

The computational repertoire of neurons is enhanced by regenerative electrical signals initiated in dendrites. These events, referred to as dendritic spikes, can act as cell-intrinsic amplifiers of synaptic input. Among these signals, dendritic NMDA spikes are of interest in light of their correlation with synaptic LTP induction. Because it is not possible to block NMDA spikes pharmacologically while maintaining NMDA receptors available to initiate synaptic plasticity, it remains unclear whether NMDA spikes alone can trigger LTP. Here we use dendritic recordings and calcium imaging to analyse the role of NMDA spikes in associative LTP in CA3 pyramidal cells. We show that NMDA spikes produce regenerative branch-specific calcium transients. Decreasing the probability of NMDA spikes reduces LTP, whereas increasing their probability enhances LTP. NMDA spikes and LTP occur without back-propagating action potentials. However, action potentials can facilitate LTP induction by promoting NMDA spikes. Thus, NMDA spikes are necessary and sufficient to produce the critical postsynaptic depolarization required for associative LTP in CA3 pyramidal cells.

Cellular and System Biology of Memory: Timing, Molecules, and Beyond

The storage of information in the mammalian nervous systems is dependent on a delicate balance between change and stability of neuronal networks. The induction and maintenance of processes that lead to changes in synaptic strength to a multistep process which can lead to long-lasting changes, which starts and ends with a highly choreographed and perfectly timed dance of molecules in different cell types of the central nervous system. This is accompanied by synchronization of specific networks, resulting in the generation of characteristic "macroscopic" rhythmic electrical fields, whose characteristic frequencies correspond to certain activity and information-processing states of the brain. Molecular events and macroscopic fields influence each other reciprocally. We review here cellular processes of synaptic plasticity, particularly functional and structural changes, and focus on timing events that are important for the initial memory acquisition, as well as mechanisms of short- and long-term memory storage. Then, we cover the importance of epigenetic events on the long-time range. Furthermore, we consider how brain rhythms at the network level participate in processes of information storage and by what means they participating in it. Finally, we examine memory consolidation at the system level during processes of sleep.

Spike-Based Bayesian-Hebbian Learning of Temporal Sequences

Many cognitive and motor functions are enabled by the temporal representation and processing of stimuli, but it remains an open issue how neocortical microcircuits can reliably encode and replay such sequences of information. To better understand this, a modular attractor memory network is proposed in which meta-stable sequential attractor transitions are learned through changes to synaptic weights and intrinsic excitabilities via the spike-based Bayesian Confidence Propagation Neural Network (BCPNN) learning rule. We find that the formation of distributed memories, embodied by increased periods of firing in pools of excitatory neurons, together with asymmetrical associations between these distinct network states, can be acquired through plasticity. The model’s feasibility is demonstrated using simulations of adaptive exponential integrate-and-fire model neurons (AdEx). We show that the learning and speed of sequence replay depends on a confluence of biophysically relevant parameters including stimulus duration, level of background noise, ratio of synaptic currents, and strengths of short-term depression and adaptation. Moreover, sequence elements are shown to flexibly participate multiple times in the sequence, suggesting that spiking attractor networks of this type can support an efficient combinatorial code. The model provides a principled approach towards understanding how multiple interacting plasticity mechanisms can coordinate hetero-associative learning in unison.

From one moment to the next, in an ever-changing world, and awash in a deluge of sensory data, the brain fluidly guides our actions throughout an astonishing variety of tasks. Processing this ongoing bombardment of information is a fundamental problem faced by its underlying neural circuits. Given that the structure of our actions along with the organization of the environment in which they are performed can be intuitively decomposed into sequences of simpler patterns, an encoding strategy reflecting the temporal nature of these patterns should offer an efficient approach for assembling more complex memories and behaviors. We present a model that demonstrates how activity could propagate through recurrent cortical microcircuits as a result of a learning rule based on neurobiologically plausible time courses and dynamics. The model predicts that the interaction between several learning and dynamical processes constitute a compound mnemonic engram that can flexibly generate sequential step-wise increases of activity within neural populations.

Large-Scale Simulations of Plastic Neural Networks on Neuromorphic Hardware

SpiNNaker is a digital, neuromorphic architecture designed for simulating large-scale spiking neural networks at speeds close to biological real-time. Rather than using bespoke analog or digital hardware, the basic computational unit of a SpiNNaker system is a general-purpose ARM processor, allowing it to be programmed to simulate a wide variety of neuron and synapse models. This flexibility is particularly valuable in the study of biological plasticity phenomena. A recently proposed learning rule based on the Bayesian Confidence Propagation Neural Network (BCPNN) paradigm offers a generic framework for modeling the interaction of different plasticity mechanisms using spiking neurons. However, it can be computationally expensive to simulate large networks with BCPNN learning since it requires multiple state variables for each synapse, each of which needs to be updated every simulation time-step. We discuss the trade-offs in efficiency and accuracy involved in developing an event-based BCPNN implementation for SpiNNaker based on an analytical solution to the BCPNN equations, and detail the steps taken to fit this within the limited computational and memory resources of the SpiNNaker architecture. We demonstrate this learning rule by learning temporal sequences of neural activity within a recurrent attractor network which we simulate at scales of up to 2.0 × 104 neurons and 5.1 × 107 plastic synapses: the largest plastic neural network ever to be simulated on neuromorphic hardware. We also run a comparable simulation on a Cray XC-30 supercomputer system and find that, if it is to match the run-time of our SpiNNaker simulation, the super computer system uses approximately 45× more power. This suggests that cheaper, more power efficient neuromorphic systems are becoming useful discovery tools in the study of plasticity in large-scale brain models.

A general homeostatic principle following lesion induced dendritic remodeling

INTRODUCTION

Neuronal death and subsequent denervation of target areas are hallmarks of many neurological disorders. Denervated neurons lose part of their dendritic tree, and are considered "atrophic", i.e. pathologically altered and damaged. The functional consequences of this phenomenon are poorly understood.

RESULTS

Using computational modelling of 3D-reconstructed granule cells we show that denervation-induced dendritic atrophy also subserves homeostatic functions: By shortening their dendritic tree, granule cells compensate for the loss of inputs by a precise adjustment of excitability. As a consequence, surviving afferents are able to activate the cells, thereby allowing information to flow again through the denervated area. In addition, action potentials backpropagating from the soma to the synapses are enhanced specifically in reorganized portions of the dendritic arbor, resulting in their increased synaptic plasticity. These two observations generalize to any given dendritic tree undergoing structural changes.

CONCLUSIONS

Structural homeostatic plasticity, i.e. homeostatic dendritic remodeling, is operating in long-term denervated neurons to achieve functional homeostasis.

Implementation of a spike-based perceptron learning rule using TiO2-x memristors

Synaptic plasticity plays a crucial role in allowing neural networks to learn and adapt to various input environments. Neuromorphic systems need to implement plastic synapses to obtain basic "cognitive" capabilities such as learning. One promising and scalable approach for implementing neuromorphic synapses is to use nano-scale memristors as synaptic elements. In this paper we propose a hybrid CMOS-memristor system comprising CMOS neurons interconnected through TiO2-x memristors, and spike-based learning circuits that modulate the conductance of the memristive synapse elements according to a spike-based Perceptron plasticity rule. We highlight a number of advantages for using this spike-based plasticity rule as compared to other forms of spike timing dependent plasticity (STDP) rules. We provide experimental proof-of-concept results with two silicon neurons connected through a memristive synapse that show how the CMOS plasticity circuits can induce stable changes in memristor conductances, giving rise to increased synaptic strength after a potentiation episode and to decreased strength after a depression episode.

A reconfigurable on-line learning spiking neuromorphic processor comprising 256 neurons and 128K synapses

Implementing compact, low-power artificial neural processing systems with real-time on-line learning abilities is still an open challenge. In this paper we present a full-custom mixed-signal VLSI device with neuromorphic learning circuits that emulate the biophysics of real spiking neurons and dynamic synapses for exploring the properties of computational neuroscience models and for building brain-inspired computing systems. The proposed architecture allows the on-chip configuration of a wide range of network connectivities, including recurrent and deep networks, with short-term and long-term plasticity. The device comprises 128 K analog synapse and 256 neuron circuits with biologically plausible dynamics and bi-stable spike-based plasticity mechanisms that endow it with on-line learning abilities. In addition to the analog circuits, the device comprises also asynchronous digital logic circuits for setting different synapse and neuron properties as well as different network configurations. This prototype device, fabricated using a 180 nm 1P6M CMOS process, occupies an area of 51.4 mm(2), and consumes approximately 4 mW for typical experiments, for example involving attractor networks. Here we describe the details of the overall architecture and of the individual circuits and present experimental results that showcase its potential. By supporting a wide range of cortical-like computational modules comprising plasticity mechanisms, this device will enable the realization of intelligent autonomous systems with on-line learning capabilities.

Dynamic stability of sequential stimulus representations in adapting neuronal networks

The ability to acquire and maintain appropriate representations of time-varying, sequential stimulus events is a fundamental feature of neocortical circuits and a necessary first step toward more specialized information processing. The dynamical properties of such representations depend on the current state of the circuit, which is determined primarily by the ongoing, internally generated activity, setting the ground state from which input-specific transformations emerge. Here, we begin by demonstrating that timing-dependent synaptic plasticity mechanisms have an important role to play in the active maintenance of an ongoing dynamics characterized by asynchronous and irregular firing, closely resembling cortical activity in vivo. Incoming stimuli, acting as perturbations of the local balance of excitation and inhibition, require fast adaptive responses to prevent the development of unstable activity regimes, such as those characterized by a high degree of population-wide synchrony. We establish a link between such pathological network activity, which is circumvented by the action of plasticity, and a reduced computational capacity. Additionally, we demonstrate that the action of plasticity shapes and stabilizes the transient network states exhibited in the presence of sequentially presented stimulus events, allowing the development of adequate and discernible stimulus representations. The main feature responsible for the increased discriminability of stimulus-driven population responses in plastic networks is shown to be the decorrelating action of inhibitory plasticity and the consequent maintenance of the asynchronous irregular dynamic regime both for ongoing activity and stimulus-driven responses, whereas excitatory plasticity is shown to play only a marginal role.

Synaptic and nonsynaptic plasticity approximating probabilistic inference

Learning and memory operations in neural circuits are believed to involve molecular cascades of synaptic and nonsynaptic changes that lead to a diverse repertoire of dynamical phenomena at higher levels of processing. Hebbian and homeostatic plasticity, neuromodulation, and intrinsic excitability all conspire to form and maintain memories. But it is still unclear how these seemingly redundant mechanisms could jointly orchestrate learning in a more unified system. To this end, a Hebbian learning rule for spiking neurons inspired by Bayesian statistics is proposed. In this model, synaptic weights and intrinsic currents are adapted on-line upon arrival of single spikes, which initiate a cascade of temporally interacting memory traces that locally estimate probabilities associated with relative neuronal activation levels. Trace dynamics enable synaptic learning to readily demonstrate a spike-timing dependence, stably return to a set-point over long time scales, and remain competitive despite this stability. Beyond unsupervised learning, linking the traces with an external plasticity-modulating signal enables spike-based reinforcement learning. At the postsynaptic neuron, the traces are represented by an activity-dependent ion channel that is shown to regulate the input received by a postsynaptic cell and generate intrinsic graded persistent firing levels. We show how spike-based Hebbian-Bayesian learning can be performed in a simulated inference task using integrate-and-fire (IAF) neurons that are Poisson-firing and background-driven, similar to the preferred regime of cortical neurons. Our results support the view that neurons can represent information in the form of probability distributions, and that probabilistic inference could be a functional by-product of coupled synaptic and nonsynaptic mechanisms operating over several timescales. The model provides a biophysical realization of Bayesian computation by reconciling several observed neural phenomena whose functional effects are only partially understood in concert.

Shaping synaptic learning by the duration of postsynaptic action potential in a new STDP model

Single spikes and their timing matter in changing synaptic efficacy, which is known as spike-timing-dependent plasticity (STDP). Most previous studies treated spikes as all-or-none events, and considered their duration and magnitude as negligible. Here we explore the effects of action potential (AP) duration on synaptic plasticity in a simplified model neuron using computer simulations. We propose a novel STDP model that depresses synapses using an AP duration dependent LTD window and induces potentiation of synaptic strength when presynaptic spikes arrive before and during a postsynaptic AP (dSTDP). We demonstrate that AP duration is another key factor for insensitizing the postsynaptic neural firing and for controlling the shape of synaptic weight distribution. Extended AP durations produce a wide unimodal weight distribution that resembles the ones reported experimentally and make the postsynaptic neuron tranquil when disturbed by poisson noise spike trains, while equivalently sensitive to the synchronized. Our results suggest that the impact of AP duration, modeled here as an AP-dependent STDP window, on synaptic plasticity can be dramatic and should motivate future STDP studies.

Modulation of human corticospinal excitability by paired associative stimulation

Paired Associative Stimulation (PAS) has come to prominence as a potential therapeutic intervention for the treatment of brain injury/disease, and as an experimental method with which to investigate Hebbian principles of neural plasticity in humans. Prototypically, a single electrical stimulus is directed to a peripheral nerve in advance of transcranial magnetic stimulation (TMS) delivered to the contralateral primary motor cortex (M1). Repeated pairing of the stimuli (i.e., association) over an extended period may increase or decrease the excitability of corticospinal projections from M1, in manner that depends on the interstimulus interval (ISI). It has been suggested that these effects represent a form of associative long-term potentiation (LTP) and depression (LTD) that bears resemblance to spike-timing dependent plasticity (STDP) as it has been elaborated in animal models. With a large body of empirical evidence having emerged since the cardinal features of PAS were first described, and in light of the variations from the original protocols that have been implemented, it is opportune to consider whether the phenomenology of PAS remains consistent with the characteristic features that were initially disclosed. This assessment necessarily has bearing upon interpretation of the effects of PAS in relation to the specific cellular pathways that are putatively engaged, including those that adhere to the rules of STDP. The balance of evidence suggests that the mechanisms that contribute to the LTP- and LTD-type responses to PAS differ depending on the precise nature of the induction protocol that is used. In addition to emphasizing the requirement for additional explanatory models, in the present analysis we highlight the key features of the PAS phenomenology that require interpretation.

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.

Numerical modelling of plasticity induced by transcranial magnetic stimulation

We use neural field theory and spike-timing dependent plasticity to make a simple but biophysically reasonable model of long-term plasticity changes in the cortex due to transcranial magnetic stimulation (TMS). We show how common TMS protocols can be captured and studied within existing neural field theory. Specifically, we look at repetitive TMS protocols such as theta burst stimulation and paired-pulse protocols. Continuous repetitive protocols result mostly in depression, but intermittent repetitive protocols in potentiation. A paired pulse protocol results in depression at short ( < ∼ 10 ms) and long ( > ∼ 100 ms) interstimulus intervals, but potentiation for mid-range intervals. The model is sensitive to the choice of neural populations that are driven by the TMS pulses, and to the parameters that describe plasticity, which may aid interpretation of the high variability in existing experimental results. Driving excitatory populations results in greater plasticity changes than driving inhibitory populations. Modelling also shows the merit in optimizing a TMS protocol based on an individual's electroencephalogram. Moreover, the model can be used to make predictions about protocols that may lead to improvements in repetitive TMS outcomes.