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.     

Learning of Precise Spike Times with Homeostatic Membrane Potential Dependent Synaptic Plasticity

Precise spatio-temporal patterns of neuronal action potentials underly e.g. sensory representations and control of muscle activities. However, it is not known how the synaptic efficacies in the neuronal networks of the brain adapt such that they can reliably generate spikes at specific points in time. Existing activity-dependent plasticity rules like Spike-Timing-Dependent Plasticity are agnostic to the goal of learning spike times. On the other hand, the existing formal and supervised learning algorithms perform a temporally precise comparison of projected activity with the target, but there is no known biologically plausible implementation of this comparison. Here, we propose a simple and local unsupervised synaptic plasticity mechanism that is derived from the requirement of a balanced membrane potential. Since the relevant signal for synaptic change is the postsynaptic voltage rather than spike times, we call the plasticity rule Membrane Potential Dependent Plasticity (MPDP). Combining our plasticity mechanism with spike after-hyperpolarization causes a sensitivity of synaptic change to pre- and postsynaptic spike times which can reproduce Hebbian spike timing dependent plasticity for inhibitory synapses as was found in experiments. In addition, the sensitivity of MPDP to the time course of the voltage when generating a spike allows MPDP to distinguish between weak (spurious) and strong (teacher) spikes, which therefore provides a neuronal basis for the comparison of actual and target activity. For spatio-temporal input spike patterns our conceptually simple plasticity rule achieves a surprisingly high storage capacity for spike associations. The sensitivity of the MPDP to the subthreshold membrane potential during training allows robust memory retrieval after learning even in the presence of activity corrupted by noise. We propose that MPDP represents a biophysically plausible mechanism to learn temporal target activity patterns.     

Dual synaptic plasticity in the hippocampus: Hebbian and spatiotemporal learning dynamics

We assume that Hebbian learning dynamics (HLD) and spatiotemporal learning dynamics (SLD) are involved in the mechanism of synaptic plasticity in the hippocampal neurons. While HLD is driven by pre- and postsynaptic spike timings through the backpropagating action potential, SLD is evoked by presynaptic spike timings alone. Since the backpropagation attenuates as it nears the distal dendrites, we assume an extreme case as a neuron model where HLD exists only at proximal dendrites and SLD exists only at the distal dendrites. We examined how the synaptic weights change in response to three types of synaptic inputs in computer simulations. First, in response to a Poisson train having a constant mean frequency, the synaptic weights in HLD and SLD are qualitatively similar. Second, SLD responds more rapidly than HLD to synchronous input patterns, while each responds to them. Third, HLD responds more rapidly to more frequent inputs, while SLD shows fluctuating synaptic weights. These results suggest an encoding hypothesis in that a transient synchronous structure in spatiotemporal input patterns will be encoded into distal dendrites through SLD and that persistent synchrony or firing rate information will be encoded into proximal dendrites through HLD.     

Network Self-Organization Explains the Statistics and Dynamics of Synaptic Connection Strengths in Cortex

The information processing abilities of neural circuits arise from their synaptic connection patterns. Understanding the laws governing these connectivity patterns is essential for understanding brain function. The overall distribution of synaptic strengths of local excitatory connections in cortex and hippocampus is long-tailed, exhibiting a small number of synaptic connections of very large efficacy. At the same time, new synaptic connections are constantly being created and individual synaptic connection strengths show substantial fluctuations across time. It remains unclear through what mechanisms these properties of neural circuits arise and how they contribute to learning and memory. In this study we show that fundamental characteristics of excitatory synaptic connections in cortex and hippocampus can be explained as a consequence of self-organization in a recurrent network combining spike-timing-dependent plasticity (STDP), structural plasticity and different forms of homeostatic plasticity. In the network, associative synaptic plasticity in the form of STDP induces a rich-get-richer dynamics among synapses, while homeostatic mechanisms induce competition. Under distinctly different initial conditions, the ensuing self-organization produces long-tailed synaptic strength distributions matching experimental findings. We show that this self-organization can take place with a purely additive STDP mechanism and that multiplicative weight dynamics emerge as a consequence of network interactions. The observed patterns of fluctuation of synaptic strengths, including elimination and generation of synaptic connections and long-term persistence of strong connections, are consistent with the dynamics of dendritic spines found in rat hippocampus. Beyond this, the model predicts an approximately power-law scaling of the lifetimes of newly established synaptic connection strengths during development. Our results suggest that the combined action of multiple forms of neuronal plasticity plays an essential role in the formation and maintenance of cortical circuits.     

Mechanisms of association learning in the post-synaptic neurone

A general mechanism for association learning in neurones is presented based on the biochemistry and electrophysiology of synaptic receptor regions. The mechanism involves the voltage sensitive generation of second messengers in the post-synaptic neurone, and their subsequent influence on the sensitivity of the local receptor region. The mechanism is examined in detail using a computer model of the reaction dynamics of two important synaptic receptors; the adrenergic receptor and the NMDA-type glutamate receptor. The computer model simulates concentration changes of several molecules in the post-synaptic neurone following an input to a receptor. It also models changes in membrane potential caused by the cell firing, and allows for the impact of these potential changes on second messenger generation within the cell. Finally the model incorporates two possible mechanisms whereby high concentrations of second messenger can lead to long-lasting changes in receptor sensitivity. The model demonstrates an enhancement of synaptic response when previous inputs to the same receptor region have occurred when the cell was firing. Using the model, long term potentiation (LTP) of the glutamate response is demonstrated following a high frequency input to the glutamate receptor. A neurone with ten glutamate receptors is simulated and demonstrates that individual neurones should be capable of recognising patterns of input activity when those patterns have repeatedly occurred at times of major cellular activity.     

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.     

Cellular and molecular mechanisms of memory

There has been nearly a century of interest in the idea that information is encoded in the brain as specific spatio-temporal patterns of activity in distributed networks and stored as changes in the efficacy of synaptic connections on neurons that are activated during learning. The discovery and detailed report of the phenomenon generally known as long-term potentiation opened a new chapter in the study of synaptic plasticity in the vertebrate brain, and this form of synaptic plasticity has now become the dominant model in the search for the cellular bases of learning and memory. To date, the key events in the cellular and molecular mechanisms underlying synaptic plasticity are starting to be identified. They require the activation of specific receptors and of several molecular cascades to convert extracellular signals into persistent functional changes in neuronal connectivity. Accumulating evidence suggests that the rapid activation of the genetic machinery is a key mechanism underlying the enduring modification of neural networks required for the laying down of memory. The recent developments in the search for the cellular and molecular mechanisms of memory storage are reviewed.     

Synaptic protein degradation by the ubiquitin proteasome system

Synaptic plasticity -- the modulation of synaptic strength between a presynaptic terminal and a postsynaptic dendrite -- is thought to be a mechanism that underlies learning and memory. It has become increasingly clear that regulated protein synthesis is an important mechanism used to regulate the protein content of synapses that results in changes in synaptic strength. Recent experiments have highlighted a role for the opposing process, that is, regulated protein degradation via the ubiquitin-proteasome system, in synaptic plasticity. These recent findings raise exciting questions as to how proteasomal activity can regulate synapses over different temporal and spatial scales.     

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

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

A Burst-Based “Hebbian” Learning Rule at Retinogeniculate Synapses Links Retinal Waves to Activity-Dependent Refinement

Patterned spontaneous activity in the developing retina is necessary to drive synaptic refinement in the lateral geniculate nucleus (LGN). Using perforated patch recordings from neurons in LGN slices during the period of eye segregation, we examine how such burst-based activity can instruct this refinement. Retinogeniculate synapses have a novel learning rule that depends on the latencies between pre- and postsynaptic bursts on the order of one second: coincident bursts produce long-lasting synaptic enhancement, whereas non-overlapping bursts produce mild synaptic weakening. It is consistent with “Hebbian” development thought to exist at this synapse, and we demonstrate computationally that such a rule can robustly use retinal waves to drive eye segregation and retinotopic refinement. Thus, by measuring plasticity induced by natural activity patterns, synaptic learning rules can be linked directly to their larger role in instructing the patterning of neural connectivity.     

A burst-based "Hebbian" learning rule at retinogeniculate synapses links retinal waves to activity-dependent refinement

Patterned spontaneous activity in the developing retina is necessary to drive synaptic refinement in the lateral geniculate nucleus (LGN). Using perforated patch recordings from neurons in LGN slices during the period of eye segregation, we examine how such burst-based activity can instruct this refinement. Retinogeniculate synapses have a novel learning rule that depends on the latencies between pre- and postsynaptic bursts on the order of one second: coincident bursts produce long-lasting synaptic enhancement, whereas non-overlapping bursts produce mild synaptic weakening. It is consistent with “Hebbian” development thought to exist at this synapse, and we demonstrate computationally that such a rule can robustly use retinal waves to drive eye segregation and retinotopic refinement. Thus, by measuring plasticity induced by natural activity patterns, synaptic learning rules can be linked directly to their larger role in instructing the patterning of neural connectivity.     

A Novel Whole-Cell Mechanism for Long-Term Memory Enhancement

Olfactory-discrimination learning was shown to induce a profound long-lasting enhancement in the strength of excitatory and inhibitory synapses of pyramidal neurons in the piriform cortex. Notably, such enhancement was mostly pronounced in a sub-group of neurons, entailing about a quarter of the cell population. Here we first show that the prominent enhancement in the subset of cells is due to a process in which all excitatory synapses doubled their strength and that this increase was mediated by a single process in which the AMPA channel conductance was doubled. Moreover, using a neuronal-network model, we show how such a multiplicative whole-cell synaptic strengthening in a sub-group of cells that form a memory pattern, sub-serves a profound selective enhancement of this memory. Network modeling further predicts that synaptic inhibition should be modified by complex learning in a manner that much resembles synaptic excitation. Indeed, in a subset of neurons all GABA_A-receptors mediated inhibitory synapses also doubled their strength after learning. Like synaptic excitation, Synaptic inhibition is also enhanced by two-fold increase of the single channel conductance. These findings suggest that crucial learning induces a multiplicative increase in strength of all excitatory and inhibitory synapses in a subset of cells, and that such an increase can serve as a long-term whole-cell mechanism to profoundly enhance an existing Hebbian-type memory. This mechanism does not act as synaptic plasticity mechanism that underlies memory formation but rather enhances the response of already existing memory. This mechanism is cell-specific rather than synapse-specific; it modifies the channel conductance rather than the number of channels and thus has the potential to be readily induced and un-induced by whole-cell transduction mechanisms.     

A Model of Self-Organizing Head-Centered Visual Responses in Primate Parietal Areas

We present a hypothesis for how head-centered visual representations in primate parietal areas could self-organize through visually-guided learning, and test this hypothesis using a neural network model. The model consists of a competitive output layer of neurons that receives afferent synaptic connections from a population of input neurons with eye position gain modulated retinal receptive fields. The synaptic connections in the model are trained with an associative trace learning rule which has the effect of encouraging output neurons to learn to respond to subsets of input patterns that tend to occur close together in time. This network architecture and synaptic learning rule is hypothesized to promote the development of head-centered output neurons during periods of time when the head remains fixed while the eyes move. This hypothesis is demonstrated to be feasible, and each of the core model components described is tested and found to be individually necessary for successful self-organization.     

A Biophysical Model of Synaptic Delay Learning and Temporal Pattern Recognition in a Cerebellar Purkinje Cell

It has been suggested that information in the brain is encoded in temporal spike patterns which are decoded by a combination of time delays and coincidence detection. Here, we show how a multi-compartmental model of a cerebellar Purkinje cell can learn to recognise temporal parallel fibre activity patterns by adapting latencies of calcium responses after activation of metabotropic glutamate receptors (mGluRs). In each compartment of our model, the mGluR signalling cascade is represented by a set of differential equations that reflect the underlying biochemistry. Phosphorylation of the mGluRs changes the concentration of receptors which are available for activation by glutamate and thereby adjusts the time delay between mGluR stimulation and voltage response. The adaptation of a synaptic delay as opposed to a weight represents a novel non-Hebbian learning mechanism that can also implement the adaptive timing of the classically conditioned eye-blink response.     

Dynamics of memory representations in networks with novelty-facilitated synaptic plasticity

The ability to associate some stimuli while differentiating between others is an essential characteristic of biological memory. Theoretical models identify memories as attractors of neural network activity, with learning based on Hebb-like synaptic modifications. Our analysis shows that when network inputs are correlated, this mechanism results in overassociations, even up to several memories "merging" into one. To counteract this tendency, we introduce a learning mechanism that involves novelty-facilitated modifications, accentuating synaptic changes proportionally to the difference between network input and stored memories. This mechanism introduces a dependency of synaptic modifications on previously acquired memories, enabling a wide spectrum of memory associations, ranging from absolute discrimination to complete merging. The model predicts that memory representations should be sensitive to learning order, consistent with recent psychophysical studies of face recognition and electrophysiological experiments on hippocampal place cells. The proposed mechanism is compatible with a recent biological model of novelty-facilitated learning in hippocampal circuitry.     

Emotion enhances learning via norepinephrine regulation of AMPA-receptor trafficking

Emotion enhances our ability to form vivid memories of even trivial events. Norepinephrine (NE), a neuromodulator released during emotional arousal, plays a central role in the emotional regulation of memory. However, the underlying molecular mechanism remains elusive. Toward this aim, we have examined the role of NE in contextual memory formation and in the synaptic delivery of GluR1-containing alpha-amino-3-hydroxy-5-methyl-4-isoxazoleproprionic acid (AMPA)-type glutamate receptors during long-term potentiation (LTP), a candidate synaptic mechanism for learning. We found that NE, as well as emotional stress, induces phosphorylation of GluR1 at sites critical for its synaptic delivery. Phosphorylation at these sites is necessary and sufficient to lower the threshold for GluR1 synaptic incorporation during LTP. In behavioral experiments, NE can lower the threshold for memory formation in wild-type mice but not in mice carrying mutations in the GluR1 phosphorylation sites. Our results indicate that NE-driven phosphorylation of GluR1 facilitates the synaptic delivery of GluR1-containing AMPARs, lowering the threshold for LTP, thereby providing a molecular mechanism for how emotion enhances learning and memory.     

Regulation of Calpain-2 in Neurons: Implications for Synaptic Plasticity

The family of calcium-dependent neutral proteases, calpains, was discovered more than 30 years ago, but their functional roles in the nervous system under physiological or pathological conditions still remain unclear. Although calpain was proposed to participate in synaptic plasticity and in learning and memory in the early 1980s, the precise mechanism regarding its activation, its target(s) and the functional consequences of its activation have remained controversial. A major issue has been the identification of roles of the two major calpain isoforms present in the brain, calpain-1 and calpain-2, and the calcium requirement for their activation, which exceeds levels that could be reached intracellularly under conditions leading to changes in synaptic efficacy. In this review, we discussed the features of calpains that make them ideally suited to link certain patterns of presynaptic activity to the structural modifications of dendritic spines that could underlie synaptic plasticity and learning and memory. We then summarize recent findings that provide critical answers to the various questions raised by the initial hypothesis, and that further support the idea that, in brain, calpain-2 plays critical roles in developmental and adult synaptic plasticity.     

Spectral analysis of input spike trains by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) has been observed in many brain areas such as sensory cortices, where it is hypothesized to structure synaptic connections between neurons. Previous studies have demonstrated how STDP can capture spiking information at short timescales using specific input configurations, such as coincident spiking, spike patterns and oscillatory spike trains. However, the corresponding computation in the case of arbitrary input signals is still unclear. This paper provides an overarching picture of the algorithm inherent to STDP, tying together many previous results for commonly used models of pairwise STDP. For a single neuron with plastic excitatory synapses, we show how STDP performs a spectral analysis on the temporal cross-correlograms between its afferent spike trains. The postsynaptic responses and STDP learning window determine kernel functions that specify how the neuron "sees" the input correlations. We thus denote this unsupervised learning scheme as 'kernel spectral component analysis' (kSCA). In particular, the whole input correlation structure must be considered since all plastic synapses compete with each other. We find that kSCA is enhanced when weight-dependent STDP induces gradual synaptic competition. For a spiking neuron with a "linear" response and pairwise STDP alone, we find that kSCA resembles principal component analysis (PCA). However, plain STDP does not isolate correlation sources in general, e.g., when they are mixed among the input spike trains. In other words, it does not perform independent component analysis (ICA). Tuning the neuron to a single correlation source can be achieved when STDP is paired with a homeostatic mechanism that reinforces the competition between synaptic inputs. Our results suggest that neuronal networks equipped with STDP can process signals encoded in the transient spiking activity at the timescales of tens of milliseconds for usual STDP.     

Robust Short-Term Memory without Synaptic Learning

Short-term memory in the brain cannot in general be explained the way long-term memory can – as a gradual modification of synaptic weights – since it takes place too quickly. Theories based on some form of cellular bistability, however, do not seem able to account for the fact that noisy neurons can collectively store information in a robust manner. We show how a sufficiently clustered network of simple model neurons can be instantly induced into metastable states capable of retaining information for a short time (a few seconds). The mechanism is robust to different network topologies and kinds of neural model. This could constitute a viable means available to the brain for sensory and/or short-term memory with no need of synaptic learning. Relevant phenomena described by neurobiology and psychology, such as local synchronization of synaptic inputs and power-law statistics of forgetting avalanches, emerge naturally from this mechanism, and we suggest possible experiments to test its viability in more biological settings.     

Theoretical analysis of a synaptotropic dendrite growth mechanism

It is generally believed that the genome cannot encode explicit instructions to form each synaptic connection in the nervous system, but may provide general neurite growth mechanisms which will result in proper connectivity. Recent in vivo imaging has provided evidence for a synaptotropic growth mechanism, wherein synapses could influence dendrite growth by selectively stabilizing filopodia upon which they form. We undertook a theoretical investigation into the consequences of such a growth process. Discrete stochastic simulations demonstrate that the synaptotropic mechanism can result in decreased dendritic wiring length, is capable of searching for regions of high density pre-synaptic partners, and can recapitulate specific patterns of dendrite growth and connectivity. A mean-field analysis shows that growth by selective stabilization of filopodia can be approximated as a reaction-diffusion system, with a spatially varying diffusion constant that depends on the probability of synapse formation. Thus, growth will occur faster in regions of appropriate synaptic connections, and the net growth can be shown to climb a gradient of synaptic partner density. Synaptotropic growth thus presents a mechanism for the emergent development of connectivity based on local properties of the circuit elements, rather than explicit dependence on global guidance molecules or innate predetermined branching programs.