A unified model of NMDA receptor-dependent bidirectional synaptic plasticity

Synapses in the brain are bidirectionally modifiable, but the routes of induction are diverse. In various experimental paradigms, N-methyl-d-aspartate receptor-dependent long-term depression and long-term potentiation have been induced selectively by varying the membrane potential of the postsynaptic neurons during presynaptic stimulation of a constant frequency, the rate of presynaptic stimulation, and the timing of pre- and postsynaptic action potentials. In this paper, we present a mathematical embodiment of bidirectional synaptic plasticity that is able to explain diverse induction protocols with a fixed set of parameters. The key assumptions and consequences of the model can be tested experimentally; further, the model provides the foundation for a unified theory of N-methyl-d-aspartate receptor-dependent synaptic plasticity.     

A biophysically-based neuromorphic model of spike rate- and timing-dependent plasticity

Current advances in neuromorphic engineering have made it possible to emulate complex neuronal ion channel and intracellular ionic dynamics in real time using highly compact and power-efficient complementary metal-oxide-semiconductor (CMOS) analog very-large-scale-integrated circuit technology. Recently, there has been growing interest in the neuromorphic emulation of the spike-timing-dependent plasticity (STDP) Hebbian learning rule by phenomenological modeling using CMOS, memristor or other analog devices. Here, we propose a CMOS circuit implementation of a biophysically grounded neuromorphic (iono-neuromorphic) model of synaptic plasticity that is capable of capturing both the spike rate-dependent plasticity (SRDP, of the Bienenstock-Cooper-Munro or BCM type) and STDP rules. The iono-neuromorphic model reproduces bidirectional synaptic changes with NMDA receptor-dependent and intracellular calcium-mediated long-term potentiation or long-term depression assuming retrograde endocannabinoid signaling as a second coincidence detector. Changes in excitatory or inhibitory synaptic weights are registered and stored in a nonvolatile and compact digital format analogous to the discrete insertion and removal of AMPA or GABA receptor channels. The versatile Hebbian synapse device is applicable to a variety of neuroprosthesis, brain-machine interface, neurorobotics, neuromimetic computation, machine learning, and neural-inspired adaptive control problems.     

Increasing Ca2+ transients by broadening postsynaptic action potentials enhances timing-dependent synaptic depression

Repeated induction of pre- and postsynaptic action potentials (APs) at a fixed time difference leads to long-term potentiation (LTP) or long-term depression (LTD) of the synapse, depending on the temporal order of pre- and postsynaptic activity. This phenomenon of spike-timing-dependent plasticity (STDP) is believed to arise by nonlinear processes that lead to larger calcium transients (and thus LTP) when presynaptic APs precede postsynaptic APs and smaller calcium transients (and thus LTD) when postsynaptic APs precede presynaptic APs. In contrast to predictions from such calcium-peak-detector models, we show that constitutively or artificially broadened APs in layer II/III pyramidal cells of entorhinal cortex (EC) lead to an increase in the dendritic calcium transient and shift the balance of STDP toward LTD. STDP in entorhinal pyramidal cells is NMDA-receptor-dependent and modulated by the Ca(V)1Ca(2+) channel-blocker nifedipine. Results are consistent with an elaboration of the calcium-peak-detector model in which downstream signals from voltage-dependent Ca(2+) channels suppress LTP relative to LTD. Our results suggest that modulation of AP width is a potent way to adjust the rules of synaptic plasticity in the EC.     

A biophysical model of bidirectional synaptic plasticity: dependence on AMPA and NMDA receptors.

In many regions of the brain, including the mammalian cortex, the magnitude and direction of activity-dependent changes in synaptic strength depend on the frequency of presynaptic stimulation (synaptic plasticity), as well as the history of activity at those synapses (metaplasticity). We present a model of a molecular mechanism of bidirectional synaptic plasticity based on the observation that long-term synaptic potentiation (LTP) and long-term synaptic depression (LTD) correlate with the phosphorylation/dephosphorylation of sites on the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor subunit protein GluR1. The primary assumption of the model, for which there is wide experimental support, is that postsynaptic calcium concentration and consequent activation of calcium-dependent protein kinases and phosphatases are the triggers for the induction of LTP/LTD. As calcium influx through the n-methyl-d-aspartate (NMDA) receptor plays a fundamental role in the induction of LTP/LTD, changes in the properties of NMDA receptor-mediated calcium influx will dramatically affect activity-dependent synaptic plasticity (metaplasticity). We demonstrate that experimentally observed metaplasticity can be accounted for by activity-dependent regulation of NMDA receptor subunit composition and function. Our model produces a frequency-dependent LTP/LTD curve with a sliding synaptic modification threshold similar to what has been proposed theoretically by Bienenstock, Cooper, and Munro and observed experimentally.     

Synapse elimination accompanies functional plasticity in hippocampal neurons

A critical component of nervous system development is synapse elimination during early postnatal life, a process known to depend on neuronal activity. Changes in synaptic strength in the form of long-term potentiation (LTP) and long-term depression (LTD) correlate with dendritic spine enlargement or shrinkage, respectively, but whether LTD can lead to an actual separation of the synaptic structures when the spine shrinks or is lost remains unknown. Here, we addressed this issue by using concurrent imaging and electrophysiological recording of live synapses. Slices of rat hippocampus were cultured on multielectrode arrays, and the neurons were labeled with genes encoding red or green fluorescent proteins to visualize presynaptic and postsynaptic neuronal processes, respectively. LTD-inducing stimulation led to a reduction in the synaptic green and red colocalization, and, in many cases, it induced a complete separation of the presynaptic bouton from the dendritic spine. This type of synapse loss was associated with smaller initial spine size and greater synaptic depression but not spine shrinkage during LTD. All cases of synapse separation were observed without an accompanying loss of the spine during this period. We suggest that repeated low-frequency stimulation simultaneous with LTD induction is capable of restructuring synaptic contacts. Future work with this model will be able to provide critical insight into the molecular mechanisms of activity- and experience-dependent refinement of brain circuitry during development.     

AMPA receptors gate spine Ca2+ transients and spike-timing-dependent potentiation

Spike timing-dependent long-term potentiation (t-LTP) is the embodiment of Donald Hebb’s postulated rule for associative memory formation. Pre- and postsynaptic action potentials need to be precisely correlated in time to induce this form of synaptic plasticity. NMDA receptors have been proposed to detect correlated activity and to trigger synaptic plasticity. However, the slow kinetic of NMDA receptor currents is at odds with the millisecond precision of coincidence detection. Here we show that AMPA receptors are responsible for the extremely narrow time window for t-LTP induction. Furthermore, we visualized synergistic interactions between AMPA and NMDA receptors and back-propagating action potentials on the level of individual spines. Supralinear calcium signals were observed for spike timings that induced t-LTP and were most pronounced in spines well isolated from the dendrite. We conclude that AMPA receptors gate the induction of associative synaptic plasticity by regulating the temporal precision of coincidence detection.     

Long-term synaptic transformation of hippocampal CA1 gamma-aminobutyric acid synapses and the effect of anandamide.

Evidence is presented for a distinctive type of hippocampal synaptic modification [previously described for a molluscan gamma-aminobutyric acid (GABA) synapse after paired pre- and postsynaptic excitation]: transformation of GABA-mediated synaptic inhibition into synaptic excitation. This transformation persists with no further paired stimulation for 60 min or longer and is termed long-term transformation. Long-term transformation is shown to contribute to pairing-induced long-term potentiation but not to long-term potentiation induced by presynaptic stimulation alone. Further support for such mechanistic divergence is provided by pharmacologic effects on long-term transformation as well as these two forms of long-term potentiation by Cl- channel blockers, glutamate and GABA antagonists, as well as the endogenous cannabinoid ligand anandamide.     

Generalized Bienenstock-Cooper-Munro rule for spiking neurons that maximizes information transmission

Maximization of information transmission by a spiking-neuron model predicts changes of synaptic connections that depend on timing of pre- and postsynaptic spikes and on the postsynaptic membrane potential. Under the assumption of Poisson firing statistics, the synaptic update rule exhibits all of the features of the Bienenstock-Cooper-Munro rule, in particular, regimes of synaptic potentiation and depression separated by a sliding threshold. Moreover, the learning rule is also applicable to the more realistic case of neuron models with refractoriness, and is sensitive to correlations between input spikes, even in the absence of presynaptic rate modulation. The learning rule is found by maximizing the mutual information between presynaptic and postsynaptic spike trains under the constraint that the postsynaptic firing rate stays close to some target firing rate. An interpretation of the synaptic update rule in terms of homeostatic synaptic processes and spike-timing-dependent plasticity is discussed.     

Pre- and postnatal propylthiouracil-induced hypothyroidism impairs synaptic transmission and plasticity in area CA1 of the neonatal rat hippocampus

Thyroid hormones are essential for neonatal brain development. It is well established that insufficiency of thyroid hormone during critical periods of development can impair cognitive functions. The mechanisms that underlie learning deficits in hypothyroid animals, however, are not well understood. As impairments in synaptic function are likely to contribute to cognitive deficits, the current study tested whether thyroid hormone insufficiency during development would alter quantitative characteristics of synaptic function in the hippocampus. Developing rats were exposed in utero and postnatally to 0, 3, or 10 ppm propylthiouracil (PTU), a thyroid hormone synthesis inhibitor, administered in the drinking water of dams from gestation d 6 until postnatal day (PN) 30. Excitatory postsynaptic potentials and population spikes were recorded from the stratum radiatum and the pyramidal cell layer, respectively, in area CA1 of hippocampal slices from offspring between PN21 and PN30. Baseline synaptic transmission was evaluated by comparing input-output relationships between groups. Paired-pulse facilitation, paired-pulse depression, long-term potentiation, and long-term depression were recorded to examine short- and long-term synaptic plasticity. PTU reduced thyroid hormones, reduced body weight gain, and delayed eye-opening in a dose-dependent manner. Excitatory synaptic transmission was increased by developmental exposure to PTU. Thyroid hormone insufficiency was also dose-dependently associated with a reduction paired-pulse facilitation and long-term potentiation of the excitatory postsynaptic potential and elimination of paired-pulse depression of the population spike. The results indicate that thyroid hormone insufficiency compromises the functional integrity of synaptic communication in area CA1 of developing rat hippocampus and suggest that these changes may contribute to learning deficits associated with developmental hypothyroidism.     

Extracellular proteolysis by matrix metalloproteinase-9 drives dendritic spine enlargement and long-term potentiation coordinately

Persistent dendritic spine enlargement is associated with stable long-term potentiation (LTP), and the latter is thought to underlie long-lasting memories. Extracellular proteolytic remodeling of the synaptic microenvironment could be important for such plasticity, but whether or how proteolytic remodeling contributes to persistent modifications in synapse structure and function is unknown. Matrix metalloproteinase-9 (MMP-9) is an extracellular protease that is activated perisynaptically after LTP induction and required for LTP maintenance. Here, by monitoring spine size and excitatory postsynaptic potentials (EPSPs) simultaneously with combined 2-photon time-lapse imaging and whole-cell recordings from hippocampal neurons, we find that MMP-9 is both necessary and sufficient to drive spine enlargement and synaptic potentiation concomitantly. Both structural and functional MMP-driven forms of plasticity are mediated through β1-containing integrin receptors, are associated with integrin-dependent cofilin inactivation within spines, and require actin polymerization. In contrast, postsynaptic exocytosis and protein synthesis are both required for MMP-9-induced potentiation, but not for initial MMP-9-induced spine expansion. However, spine expansion becomes unstable when postsynaptic exocytosis or protein synthesis is blocked, indicating that the 2 forms of plasticity are expressed independently but require interactions between them for persistence. When MMP activity is eliminated during theta-stimulation-induced LTP, both spine enlargement and synaptic potentiation are transient. Thus, MMP-mediated extracellular remodeling during LTP has an instructive role in establishing persistent modifications in both synapse structure and function of the kind critical for learning and memory.     

Bidirectional plasticity of excitatory postsynaptic potential (EPSP)-spike coupling in CA1 hippocampal pyramidal neurons

Integration of synaptic excitation to generate an action potential (excitatory postsynaptic potential-spike coupling or E-S coupling) determines the neuronal output. Bidirectional synaptic plasticity is well established in the hippocampus, but whether active synaptic integration can display potentiation and depression remains unclear. We show here that synaptic depression is associated with an N-methyl-d-aspartate receptor-dependent and long-lasting depression of E-S coupling. E-S depression is input-specific and is expressed in the presence of gamma-aminobutyric acid type A and B receptor antagonists. In single neurons, E-S depression is observed without modification of postsynaptic passive properties. We conclude that a decrease in intrinsic excitability underlies E-S depression and is synergic with glutamatergic long-term depression.     

Heterosynaptic metaplasticity in the hippocampus in vivo: a BCM-like modifiable threshold for LTP

The homeostatic maintenance of the "modification threshold" for inducing long-term potentiation (LTP) is a fundamental feature of the Bienenstock, Cooper, and Munro (BCM) model of synaptic plasticity. In the present study, two key features of the modification threshold, its heterosynaptic expression and its regulation by postsynaptic neural activity, were tested experimentally in the dentate gyrus of awake, freely moving rats. Conditioning stimulation ranging from 10 to 1,440 brief 400-Hz trains, when applied to medial perforant path afferents, raised the threshold for LTP induction heterosynaptically in the neighboring lateral perforant path synapses. This effect recovered slowly over a 7- to 35-day period. The same conditioning paradigms, however, did not affect the reversal of long-term depression. The inhibition of LTP by medial-path conditioning stimulation was N-methyl-D-aspartate (NMDA) receptor-dependent, but antidromic stimulation of the granule cells could also inhibit lateral path LTP induction, independently of NMDA receptor activation. Increased calcium buffering is a potential mechanism underlying the altered LTP threshold, but the levels of two important calcium-binding proteins did not increase after conditioning stimulation, nor was de novo protein synthesis required for generating the threshold shift. These data confirm, in an in vivo model, two key postulates of the BCM model regarding the LTP threshold. They also provide further evidence for the broad sensitivity of synaptic plasticity mechanisms to the history of prior activity, i.e., metaplasticity.     

All-or-none potentiation at CA3-CA1 synapses

The molecular mechanisms underlying long-term potentiation in the hippocampus have received much attention because of the likely functional importance of synaptic plasticity for information storage and the development of neuronal connectivity. Surprisingly, it remains unclear whether activity modifies the strength of individual synapses in a digital (all-or-none) or analog (graded) manner. Here we characterize step-like all-or-none transitions from baseline synaptic transmission to potentiated states following protocols for inducing potentiation at putative single CA3-CA1 synaptic connections. Individual synapses appear to have all-or-none potentiation indicative of highly cooperative processes but different thresholds for undergoing potentiation. These results raise the possibility that some forms of synaptic memory may be stored in a digital manner in the brain.     

Mice deficient for prion protein exhibit normal neuronal excitability and synaptic transmission in the hippocampus.

We recorded in the CA1 region from hippocampal slices of prion protein (PrP) gene knockout mice to investigate whether the loss of the normal form of prion protein (PrPC) affects neuronal excitability as well as synaptic transmission in the central nervous system. No deficit in synaptic inhibition was found using field potential recordings because (i) responses induced by stimulation in stratum radiatum consisted of a single population spike in PrP gene knockout mice similar to that recorded from control mice and (ii) the plot of field excitatory postsynaptic potential slope versus the population spike amplitude showed no difference between the two groups of mice. Intracellular recordings also failed to detect any difference in cell excitability and the reversal potential for inhibitory postsynaptic potentials. Analysis of the kinetics of inhibitory postsynaptic current revealed no modification. Finally, we examined whether synaptic plasticity was altered and found no difference in long-term potentiation between control and PrP gene knockout mice. On the basis of our findings, we propose that the loss of the normal form of prion protein does not alter the physiology of the CA1 region of the hippocampus.     

Calcium dependent forms of synaptic plasticity in cerebellar Purkinje cells

Elevation of intracellular calcium concentration ([Ca(2+)](i)) induces several forms of long-term synaptic plasticity in cerebellar Purkinje cells (PCs). These include (1) long-term depression (LTD) at parallel fiber (PF) to PC synapses, (2) LTD at climbing fiber (CF) to PC synapses, (3) long-term potentiation (LTP) at synapses from inhibitory interneurons (rebound potentiation). The current knowledge about calcium dependency for these forms of synaptic plasticity is described in this chapter. (1) Induction of PF-LTD is dependent on elevation of [Ca(2+)](i), that derives from two distinct sources. One is through voltage-dependent calcium channel (VDCC). A CF stimulation leads to elevation of [Ca(2+)](i) due to activation of VDCCs. The other is from the internal calcium store. PFs stimulation activates metabotropic glutamate receptor subtype 1 (mGluR1). It leads to production of inositol-1,4,5-triphosphate (IP(3)) and diacylglycerol (DG) which cause calcium release from internal stores and activation of protein kinase C, respectively. The conjunctive activation of PF and CF inputs is necessary for PF-LTD. (2) LTD at CF to PC synapses (CF-LTD) is induced by the mechanisms similar to those involved in PF-LTD. CF-LTD requires elevation of [Ca(2+)](i) and activation of the mGluR1 to PKC cascade. (3) Rebound potentiation is induced by transient elevation of [Ca(2+)](i) due to activation of VDCCs or IP3-mediated calcium release from internal stores. Elevation of [Ca(2+)](i) activates calcium/ calmodulin-dependent protein kinase II and leads to persistent up-regulation of postsynaptic GABAA receptor function. At the three types of synapses described above, elevation of [Ca(2+)](i) also causes short-term depression of neurotransmitter release from presynaptic terminals. Recent studies demonstrate that transient elevation of [Ca(2+)](i) produces endocannabinoids in PCs that act retrogradely onto presynaptic terminals and suppress neurotransmitter release.     

Spontaneous transmitter release is critical for the induction of long-term and intermediate-term facilitation in Aplysia

Long-term plasticity can differ from short-term in recruiting the growth of new synaptic connections, a process that requires the participation of both the presynaptic and postsynaptic components of the synapse. How does information about synaptic plasticity spread from its site of origin to recruit the other component? The answer to this question is not known in most systems. We have investigated the possible role of spontaneous transmitter release as such a transsynaptic signal. Until recently, relatively little has been known about the functions of spontaneous release. In this paper, we report that spontaneous release is critical for the induction of a learning-related form of synaptic plasticity, long-term facilitation in Aplysia. In addition, we have found that this signaling is engaged quite early, during an intermediate-term stage that is the first stage to involve postsynaptic as well as presynaptic molecular mechanisms. In a companion paper, we show that spontaneous release from the presynaptic neuron acts as an orthograde signal to recruit the postsynaptic mechanisms of intermediate-term facilitation and initiates a cascade that can culminate in synaptic growth with additional stimulation during long-term facilitation. Spontaneous release could make a similar contribution to learning-related synaptic plasticity in mammals.     

Rapid increase in clusters of synaptophysin at onset of homosynaptic potentiation in Aplysia

Imaging studies have shown that even the earliest phases of long-term plasticity are accompanied by the rapid recruitment of synaptic components, which generally requires actin polymerization and may be one of the first steps in a program that can lead to the formation of new stable synapses during late-phase plasticity. However, most of those results come from studies of long-term potentiation in rodent hippocampus and might not generalize to other forms of synaptic plasticity or plasticity in other brain areas and species. For example, recruitment of presynaptic proteins during long-term facilitation by 5HT in Aplysia is delayed for several hours, suggesting that whereas activity-dependent forms of plasticity, such as long-term potentiation, involve rapid recruitment of presynaptic proteins, neuromodulatory forms of plasticity, such as facilitation by 5HT, involve more delayed recruitment. To begin to explore this hypothesis, we examined an activity-dependent form of plasticity, homosynaptic potentiation produced by tetanic stimulation of the presynaptic neuron in Aplysia. We found that homosynaptic potentiation involves presynaptic but not postsynaptic actin and a rapid (under 10 min) increase in the number of clusters of the presynaptic vesicle-associated protein synaptophysin. These results indicate that rapid recruitment of synaptic components is not limited to hippocampal potentiation and support the hypothesis that activity-dependent types of plasticity involve rapid recruitment of presynaptic proteins, whereas neuromodulatory types of plasticity involve more delayed recruitment.     

Initial synaptic efficacy influences induction and expression of long-term changes in transmission.

Long-term depression (LTD) of glutamatergic and electrotonic transmission can be induced at mixed synapses between eighth nerve fibers and the goldfish Mauthner (M) cell in vivo, by pairing weak presynaptic tetani with postsynaptic inhibition. This LTD can be reversed by stronger tetani that produce long-term potentiation (LTP). Moreover, the depression is more likely to occur and tends to last longer when the initial synaptic efficacy is high--that is, if the synaptic strength is first potentiated. In addition, when synaptic efficacy is initially elevated, a weak tetanization that usually results in a gradually developing potentiation instead produces no change in chemical transmission and even a depression of electrotonic coupling. Thus, the modifications in synaptic transmission caused by a certain tetanizing protocol depend upon the history of synaptic efficacy. This last concept provides an experimental basis for theoretical models concerned with pre- and postsynaptic contributions to the regulation of synaptic plasticity.