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.     

The Effect of STDP Temporal Kernel Structure on the Learning Dynamics of Single Excitatory and Inhibitory Synapses

Spike-Timing Dependent Plasticity (STDP) is characterized by a wide range of temporal kernels. However, much of the theoretical work has focused on a specific kernel – the “temporally asymmetric Hebbian” learning rules. Previous studies linked excitatory STDP to positive feedback that can account for the emergence of response selectivity. Inhibitory plasticity was associated with negative feedback that can balance the excitatory and inhibitory inputs. Here we study the possible computational role of the temporal structure of the STDP. We represent the STDP as a superposition of two processes: potentiation and depression. This allows us to model a wide range of experimentally observed STDP kernels, from Hebbian to anti-Hebbian, by varying a single parameter. We investigate STDP dynamics of a single excitatory or inhibitory synapse in purely feed-forward architecture. We derive a mean-field-Fokker-Planck dynamics for the synaptic weight and analyze the effect of STDP structure on the fixed points of the mean field dynamics. We find a phase transition along the Hebbian to anti-Hebbian parameter from a phase that is characterized by a unimodal distribution of the synaptic weight, in which the STDP dynamics is governed by negative feedback, to a phase with positive feedback characterized by a bimodal distribution. The critical point of this transition depends on general properties of the STDP dynamics and not on the fine details. Namely, the dynamics is affected by the pre-post correlations only via a single number that quantifies its overlap with the STDP kernel. We find that by manipulating the STDP temporal kernel, negative feedback can be induced in excitatory synapses and positive feedback in inhibitory. Moreover, there is an exact symmetry between inhibitory and excitatory plasticity, i.e., for every STDP rule of inhibitory synapse there exists an STDP rule for excitatory synapse, such that their dynamics is identical.     

Emergence of preferred firing sequences in large spiking neural networks during simulated neuronal development

Two main processes concurrently refine the nervous system over the course of development: cell death and selective synaptic pruning. We simulated large spiking neural networks (100 x 100 neurons "at birth") characterized by an early developmental phase with cell death due to excessive firing rate, followed by the onset of spike timing dependent synaptic plasticity (STDP), driven by spatiotemporal patterns of stimulation. The cell death affected the inhibitory units more than the excitatory units during the early developmental phase. The network activity showed the appearance of recurrent spatiotemporal firing patterns along the STDP phase, thus suggesting the emergence of cell assemblies from the initially randomly connected networks. Some of these patterns were detected throughout the simulation despite the activity-driven network modifications while others disappeared.     

Spike timing-dependent plasticity and memory

Spike timing-dependent plasticity (STDP) is a bidirectional form of synaptic plasticity discovered about 30 years ago and based on the relative timing of pre- and post-synaptic spiking activity with a millisecond precision. STDP is thought to be involved in the formation of memory but the millisecond-precision spike-timing required for STDP is difficult to reconcile with the much slower timescales of behavioral learning. This review therefore aims to expose and discuss recent findings about i) the multiple STDP learning rules at both excitatory and inhibitory synapses in vitro, ii) the contribution of STDP-like synaptic plasticity in the formation of memory in vivo and iii) the implementation of STDP rules in artificial neural networks and memristive devices.     

Intrinsic stability of temporally shifted spike-timing dependent plasticity

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

A neural circuit model of emotional learning using two pathways with different granularity and speed of information processing

We propose a neural circuit model of emotional learning using two pathways with different granularity and speed of information processing. In order to derive a precise time process, we utilized a spiking model neuron proposed by Izhikevich and spike-timing-dependent synaptic plasticity (STDP) of both excitatory and inhibitory synapses. We conducted computer simulations to evaluate the proposed model. We demonstrate some aspects of emotional learning from the perspective of the time process. The agreement of the results with the previous behavioral experiments suggests that the structure and learning process of the proposed model are appropriate.     

Where’s the Noise? Key Features of Spontaneous Activity and Neural Variability Arise through Learning in a Deterministic Network

Even in the absence of sensory stimulation the brain is spontaneously active. This background “noise” seems to be the dominant cause of the notoriously high trial-to-trial variability of neural recordings. Recent experimental observations have extended our knowledge of trial-to-trial variability and spontaneous activity in several directions: 1. Trial-to-trial variability systematically decreases following the onset of a sensory stimulus or the start of a motor act. 2. Spontaneous activity states in sensory cortex outline the region of evoked sensory responses. 3. Across development, spontaneous activity aligns itself with typical evoked activity patterns. 4. The spontaneous brain activity prior to the presentation of an ambiguous stimulus predicts how the stimulus will be interpreted. At present it is unclear how these observations relate to each other and how they arise in cortical circuits. Here we demonstrate that all of these phenomena can be accounted for by a deterministic self-organizing recurrent neural network model (SORN), which learns a predictive model of its sensory environment. The SORN comprises recurrently coupled populations of excitatory and inhibitory threshold units and learns via a combination of spike-timing dependent plasticity (STDP) and homeostatic plasticity mechanisms. Similar to balanced network architectures, units in the network show irregular activity and variable responses to inputs. Additionally, however, the SORN exhibits sequence learning abilities matching recent findings from visual cortex and the network’s spontaneous activity reproduces the experimental findings mentioned above. Intriguingly, the network’s behaviour is reminiscent of sampling-based probabilistic inference, suggesting that correlates of sampling-based inference can develop from the interaction of STDP and homeostasis in deterministic networks. We conclude that key observations on spontaneous brain activity and the variability of neural responses can be accounted for by a simple deterministic recurrent neural network which learns a predictive model of its sensory environment via a combination of generic neural plasticity mechanisms.     

Regulation of spike timing-dependent plasticity of olfactory inputs in mitral cells in the rat olfactory bulb

The recent history of activity input onto granule cells (GCs) in the main olfactory bulb can affect the strength of lateral inhibition, which functions to generate contrast enhancement. However, at the plasticity level, it is unknown whether and how the prior modification of lateral inhibition modulates the subsequent induction of long-lasting changes of the excitatory olfactory nerve (ON) inputs to mitral cells (MCs). Here we found that the repetitive stimulation of two distinct excitatory inputs to the GCs induced a persistent modification of lateral inhibition in MCs in opposing directions. This bidirectional modification of inhibitory inputs differentially regulated the subsequent synaptic plasticity of the excitatory ON inputs to the MCs, which was induced by the repetitive pairing of excitatory postsynaptic potentials (EPSPs) with postsynaptic bursts. The regulation of spike timing-dependent plasticity (STDP) was achieved by the regulation of the inter-spike-interval (ISI) of the postsynaptic bursts. This novel form of inhibition-dependent regulation of plasticity may contribute to the encoding or processing of olfactory information in the olfactory bulb.     

Emergence of Connectivity Motifs in Networks of Model Neurons with Short- and Long-Term Plastic Synapses

Recent experimental data from the rodent cerebral cortex and olfactory bulb indicate that specific connectivity motifs are correlated with short-term dynamics of excitatory synaptic transmission. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form predominantly unidirectional pairwise connections. The cause of these structural differences in excitatory synaptic microcircuits is unknown. We show that these connectivity motifs emerge in networks of model neurons, from the interactions between short-term synaptic dynamics (SD) and long-term spike-timing dependent plasticity (STDP). While the impact of STDP on SD was shown in simultaneous neuronal pair recordings in vitro, the mutual interactions between STDP and SD in large networks are still the subject of intense research. Our approach combines an SD phenomenological model with an STDP model that faithfully captures long-term plasticity dependence on both spike times and frequency. As a proof of concept, we first simulate and analyze recurrent networks of spiking neurons with random initial connection efficacies and where synapses are either all short-term facilitating or all depressing. For identical external inputs to the network, and as a direct consequence of internally generated activity, we find that networks with depressing synapses evolve unidirectional connectivity motifs, while networks with facilitating synapses evolve reciprocal connectivity motifs. We then show that the same results hold for heterogeneous networks, including both facilitating and depressing synapses. This does not contradict a recent theory that proposes that motifs are shaped by external inputs, but rather complements it by examining the role of both the external inputs and the internally generated network activity. Our study highlights the conditions under which SD-STDP might explain the correlation between facilitation and reciprocal connectivity motifs, as well as between depression and unidirectional motifs.     

A Nonlinear Cable Framework for Bidirectional Synaptic Plasticity

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

Calcium control of triphasic hippocampal STDP

Synaptic plasticity is believed to represent the neural correlate of mammalian learning and memory function. It has been demonstrated that changes in synaptic conductance can be induced by approximately synchronous pairings of pre- and post- synaptic action potentials delivered at low frequencies. It has also been established that NMDAr-dependent calcium influx into dendritic spines represents a critical signal for plasticity induction, and can account for this spike-timing dependent plasticity (STDP) as well as experimental data obtained using other stimulation protocols. However, subsequent empirical studies have delineated a more complex relationship between spike-timing, firing rate, stimulus duration and post-synaptic bursting in dictating changes in the conductance of hippocampal excitatory synapses. Here, we present a detailed biophysical model of single dendritic spines on a CA1 pyramidal neuron, describe the NMDAr-dependent calcium influx generated by different stimulation protocols, and construct a parsimonious model of calcium driven kinase and phosphatase dynamics that dictate the probability of stochastic transitions between binary synaptic weight states in a Markov model. We subsequently demonstrate that this approach can account for a range of empirical observations regarding the dynamics of synaptic plasticity induced by different stimulation protocols, under regimes of pharmacological blockade and metaplasticity. Finally, we highlight the strengths and weaknesses of this parsimonious, unified computational synaptic plasticity model, discuss differences between the properties of cortical and hippocampal plasticity highlighted by the experimental literature, and the manner in which further empirical and theoretical research might elucidate the cellular basis of mammalian learning and memory function.     

A neural circuit model forming semantic network with exception using spike-timing-dependent plasticity of inhibitory synapses

We propose a neural circuit model forming a semantic network with exceptions using the spike-timing-dependent plasticity (STDP) of inhibitory synapses. To evaluate the proposed model, we conducted nine types of computer simulation by combining the three STDP rules for inhibitory synapses and the three spike pairing rules. The simulation results obtained with the STDP rule for inhibitory synapses by Haas et al. [Haas, J.S., Nowotny, T., Abarbanel, H.D.I., 2006, Spike-timing-dependent plasticity of inhibitory synapses in the entorhinal cortex. J. Neurophysiol. 96, 3305–3313] are successful, whereas, the other results are unsuccessful. The results and examinations suggested that the inhibitory connection from the concept linked with an exceptional feature to the general feature is necessary for forming a semantic network with an exception.     

Role of GABAA-Mediated Inhibition and Functional Assortment of Synapses onto Individual Layer 4 Neurons in Regulating Plasticity Expression in Visual Cortex

Layer 4 (L4) of primary visual cortex (V1) is the main recipient of thalamocortical fibers from the dorsal lateral geniculate nucleus (LGN_d). Thus, it is considered the main entry point of visual information into the neocortex and the first anatomical opportunity for intracortical visual processing before information leaves L4 and reaches supra- and infragranular cortical layers. The strength of monosynaptic connections from individual L4 excitatory cells onto adjacent L4 cells (unitary connections) is highly malleable, demonstrating that the initial stage of intracortical synaptic transmission of thalamocortical information can be altered by previous activity. However, the inhibitory network within L4 of V1 may act as an internal gate for induction of excitatory synaptic plasticity, thus providing either high fidelity throughput to supragranular layers or transmittal of a modified signal subject to recent activity-dependent plasticity. To evaluate this possibility, we compared the induction of synaptic plasticity using classical extracellular stimulation protocols that recruit a combination of excitatory and inhibitory synapses with stimulation of a single excitatory neuron onto a L4 cell. In order to induce plasticity, we paired pre- and postsynaptic activity (with the onset of postsynaptic spiking leading the presynaptic activation by 10ms) using extracellular stimulation (ECS) in acute slices of primary visual cortex and comparing the outcomes with our previously published results in which an identical protocol was used to induce synaptic plasticity between individual pre- and postsynaptic L4 excitatory neurons. Our results indicate that pairing of ECS with spiking in a L4 neuron fails to induce plasticity in L4-L4 connections if synaptic inhibition is intact. However, application of a similar pairing protocol under GABA_ARs inhibition by bath application of 2μM bicuculline does induce robust synaptic plasticity, long term potentiation (LTP) or long term depression (LTD), similar to our results with pairing of pre- and postsynaptic activation between individual excitatory L4 neurons in which inhibitory connections are not activated. These results are consistent with the well-established observation that inhibition limits the capacity for induction of plasticity at excitatory synapses and that pre- and postsynaptic activation at a fixed time interval can result in a variable range of plasticity outcomes. However, in the current study by virtue of having two sets of experimental data, we have provided a new insight into these processes. By randomly mixing the assorting of individual L4 neurons according to the frequency distribution of the experimentally determined plasticity outcome distribution based on the calculated convergence of multiple individual L4 neurons onto a single postsynaptic L4 neuron, we were able to compare then actual ECS plasticity outcomes to those predicted by randomly mixing individual pairs of neurons. Interestingly, the observed plasticity profiles with ECS cannot account for the random assortment of plasticity behaviors of synaptic connections between individual cell pairs. These results suggest that connections impinging onto a single postsynaptic cell may be grouped according to plasticity states.     

Heterosynaptic LTD of hippocampal GABAergic synapses: a novel role of endocannabinoids in regulating excitability

Neuronal excitability and long-term synaptic plasticity at excitatory synapses are critically dependent on the level of inhibition, and accordingly, changes of inhibitory synaptic efficacy should have great impact on neuronal function and neural network processing. We describe here a form of activity-dependent long-term depression at hippocampal inhibitory synapses that is triggered postsynaptically via glutamate receptor activation but is expressed presynaptically. That is, glutamate released by repetitive activation of Schaffer collaterals activates group I metabotropic glutamate receptors at CA1 pyramidal cells, triggering a persistent reduction of GABA release that is mediated by endocannabinoids. This heterosynaptic form of plasticity is involved in changes of pyramidal cell excitability associated with long-term potentiation at excitatory synapses and could account for the effects of cannabinoids on learning and memory.     

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.     

Slowness: An Objective for Spike-Timing–Dependent Plasticity?

Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this “temporal stability” or “slowness” approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing–dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the “trace rule.” The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons.     

Effectively reducing sensory eye dominance with a push-pull perceptual learning protocol

Much knowledge of sensory cortical plasticity is gleaned from perceptual learning studies that improve visual performance [1-7]. Although the improvements are likely caused by modifications of excitatory and inhibitory neural networks, most studies were not primarily designed to differentiate their relative contributions. Here we designed a novel push-pull training protocol to reduce sensory eye dominance (SED), a condition that is mainly caused by unbalanced interocular inhibition [8-10]. During the training, an attention cue presented to the weak eye precedes the binocular competitive stimulation. The cue stimulates the weak eye (push) while causing interocular inhibition of the strong eye (pull). We found that this push-pull protocol reduces SED (shifts the balance toward the weak eye) and improves stereopsis more so than the push-only protocol, which solely stimulates the weak eye without inhibiting the strong eye. The stronger learning effect with the push-pull training than the push-only training underscores the crucial involvement of a putative inhibitory mechanism in sensory plasticity. The design principle of the push-pull protocol can potentially lend itself as an effective, noninvasive treatment of amblyopia.     

Mechanisms and significance of spike-timing dependent plasticity

Hebb's original postulate left two important issues unaddressed: (i) what is the effective time window between pre- and postsynaptic activity that will result in potentiation? and (ii) what is the learning rule that underlies decreases in synaptic strength? While research over the past 2 decades has addressed these questions, several studies within the past 5 years have shown that synapses undergo long-term depression (LTD) or long-term potentiation (LTP) depending on the order of activity in the pre- and postsynaptic cells. This process has been referred to as spike-timing dependent plasticity (STDP). Here we discuss the experimental data on STDP, and develop models of the mechanisms that may underlie it. Specifically, we examine whether the standard model of LTP and LTD in which high and low levels of Ca(2+) produce LTP and LTD, respectively, can also account for STDP. We conclude that the standard model can account for a type of STDP in which, counterintuitively, LTD will be observed at some intervals in which the presynaptic cell fires before the postsynaptic cell. This form of STDP will also be sensitive to parameters such as the presence of an after depolarization following an action potential. Indeed, the sensitivity of this type of STDP to experimental parameters suggests that it may not play an important physiological role in vivo. We suggest that more robust forms of STDP, which do not exhibit LTD at pre-before-post intervals, are not accounted for by the standard model, and are likely to rely on a second coincidence detector in addition to the NMDA receptor.     

Transfer of habituation in Aplysia: contribution of heterosynaptic pathways in habituation of the gill-withdrawal reflex

Habituation of the Aplysia gill-withdrawal reflex (and siphon-withdrawal reflex) has been attributed to low-frequency homosynaptic depression at central sensory-motor synapses. The recent demonstration that transfer of habituation between stimulation sites occurs in this model system has prompted the hypothesis that heterosynaptic inhibitory pathways also play a role in the mediation of habituation behavior. To test this hypothesis, the sites and mechanisms of neural plasticity which underlie transfer of habituation in Aplysia were examined. Transfer of habituation is a reduction in the reflex evoked at one stimulation site (siphon) due to repeated presentation of a stimulus to a second site (gill). Centrally mediated transfer of habituation, measured in a preparation lacking the siphon-gill peripheral nervous system (PNS), was associated with a reduced excitatory response in central motor neurons. Repeated tactile stimulation of the gill did not attenuate the gill response evoked by electrical stimulation of the branchial nerve nor the mechanoreceptor response recorded in LE sensory neurons. In contrast, repeated stimulation of siphon or gill at a site which was "off" the sensory field of a specific mechanoreceptor led to a diminution in synaptic transmission between that sensory neuron and its followers (motor neurons and inter-neurons). These data demonstrate that centrally mediated transfer of habituation results from heterosynaptic modulation of synaptic transmission at the sensory-motor (and sensory-interneuron) synapses. Therefore, habituation behavior in Aplysia is mediated through the conjoint action of homosynaptic and heterosynaptic inhibitory processes.     

Slowness: an objective for spike-timing-dependent plasticity?

Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this "temporal stability" or "slowness" approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing-dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the "trace rule." The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons.