Exploration of signal transduction pathways in cerebellar long-term depression by kinetic simulation

Purkinje cell models: past, present and future

The investigation of the dynamics of Purkinje cell (PC) activity is crucial to unravel the role of the cerebellum in motor control, learning and cognitive processes. Within the cerebellar cortex (CC), these neurons receive all the incoming sensory and motor information, transform it and generate the entire cerebellar output. The relatively homogenous and repetitive structure of the CC, common to all vertebrate species, suggests a single computation mechanism shared across all PCs. While PC models have been developed since the 70's, a comprehensive review of contemporary models is currently lacking. Here, we provide an overview of PC models, ranging from the ones focused on single cell intracellular PC dynamics, through complex models which include synaptic and extrasynaptic inputs. We review how PC models can reproduce physiological activity of the neuron, including firing patterns, current and multistable dynamics, plateau potentials, calcium signaling, intrinsic and synaptic plasticity and input/output computations. We consider models focusing both on somatic and on dendritic computations. Our review provides a critical performance analysis of PC models with respect to known physiological data. We expect our synthesis to be useful in guiding future development of computational models that capture real-life PC dynamics in the context of cerebellar computations.

Physiological and Pathological Roles of the Cytohesin Family in Neurons

The cytohesin proteins, consisting of four closely related members (cytohesins-1, -2, -3, and -4), are a subfamily of the Sec7 domain-containing guanine nucleotide exchange factors for ADP ribosylation factors (Arfs), which are critical regulators of membrane trafficking and actin cytoskeleton remodeling. Recent advances in molecular biological techniques and the development of a specific pharmacological inhibitor for cytohesins, SecinH3, have revealed the functional involvement of the cytohesin-Arf pathway in diverse neuronal functions from the formation of axons and dendrites, axonal pathfinding, and synaptic vesicle recycling, to pathophysiological processes including chronic pain and neurotoxicity induced by proteins related to neurodegenerative disorders, such as amyotrophic lateral sclerosis and Alzheimer's disease. Here, we review the physiological and pathological roles of the cytohesin-Arf pathway in neurons and discuss the future directions of this research field.

Associative anticipatory learning and control of the cerebellar cortex based on the spike-timing-dependent plasticity of the parallel fiber-Purkinje cell synapses

Time delays are inevitable in the neural processing of sensorimotor systems; small delays can cause severe damage to movement accuracy and stability. It is strongly suggested that the cerebellum compensates for delays in neural signal processing and performs predictive control. Neural computational theories have explored concepts of the internal models of control objects-believed to avoid delays by providing internal feedback information-although there has been no clear relevance to neural processing. The timing-dependent plasticity of parallel fiber-Purkinje cell synapses is well known. The long-term depression of the synapse is observed when parallel fiber activation precedes climbing fiber activation within -50-300 ms, and is the greatest within 50-200 ms. This paper presents a theory that this temporal difference of 50-200 ms is the basis for an associative anticipation of as many milliseconds. Associative learning can theoretically connect an input signal to a desired signal; therefore, a 50-200 ms earlier input signal can be connected to a desired output signal through temporary asymmetric plasticity. After learning is completed, an input signal generates a desired output signal that appears 50-200 ms later. For the associative learning of temporally continuous signals, this study integrates the universal function approximation capability of the cerebellar cortex model and temporally asymmetric synaptic plasticity to create the theory of associative anticipatory learning of the cerebellum. The effective motor control of this learning is demonstrated by adaptively stabilizing an inverted pendulum with a delay similar to that done by humans.

Endothelial dysfunction due to selective insulin resistance in vascular endothelium: insights from mechanistic modeling

Previously, we have used mathematical modeling to gain mechanistic insights into insulin-stimulated glucose uptake. Phosphatidylinositol 3-kinase (PI3K)-dependent insulin signaling required for metabolic actions of insulin also regulates endothelium-dependent production of the vasodilator nitric oxide (NO). Vasodilation increases blood flow that augments direct metabolic actions of insulin in skeletal muscle. This is counterbalanced by mitogen-activated protein kinase (MAPK)-dependent insulin signaling in endothelium that promotes secretion of the vasoconstrictor endothelin-1 (ET-1). In the present study, we extended our model of metabolic insulin signaling into a dynamic model of insulin signaling in vascular endothelium that explicitly represents opposing PI3K/NO and MAPK/ET-1 pathways. Novel NO and ET-1 subsystems were developed using published and new experimental data to generate model structures/parameters. The signal-response relationships of our model with respect to insulin-stimulated NO production, ET-1 secretion, and resultant vascular tone, agree with published experimental data, independent of those used for model development. Simulations of pathological stimuli directly impairing only insulin-stimulated PI3K/Akt activity predict altered dynamics of NO and ET-1 consistent with endothelial dysfunction in insulin-resistant states. Indeed, modeling pathway-selective impairment of PI3K/Akt pathways consistent with insulin resistance caused by glucotoxicity, lipotoxicity, or inflammation predict diminished NO production and increased ET-1 secretion characteristic of diabetes and endothelial dysfunction. We conclude that our mathematical model of insulin signaling in vascular endothelium supports the hypothesis that pathway-selective insulin resistance accounts, in part, for relationships between insulin resistance and endothelial dysfunction. This may be relevant for developing novel approaches for the treatment of diabetes and its cardiovascular complications.

Electrical coupling controls dimensionality and chaotic firing of inferior olive neurons

We previously proposed, on theoretical grounds, that the cerebellum must regulate the dimensionality of its neuronal activity during motor learning and control to cope with the low firing frequency of inferior olive neurons, which form one of two major inputs to the cerebellar cortex. Such dimensionality regulation is possible via modulation of electrical coupling through the gap junctions between inferior olive neurons by inhibitory GABAergic synapses. In addition, we previously showed in simulations that intermediate coupling strengths induce chaotic firing of inferior olive neurons and increase their information carrying capacity. However, there is no in vivo experimental data supporting these two theoretical predictions. Here, we computed the levels of synchrony, dimensionality, and chaos of the inferior olive code by analyzing in vivo recordings of Purkinje cell complex spike activity in three different coupling conditions: carbenoxolone (gap junctions blocker), control, and picrotoxin (GABA-A receptor antagonist). To examine the effect of electrical coupling on dimensionality and chaotic dynamics, we first determined the physiological range of effective coupling strengths between inferior olive neurons in the three conditions using a combination of a biophysical network model of the inferior olive and a novel Bayesian model averaging approach. We found that effective coupling co-varied with synchrony and was inversely related to the dimensionality of inferior olive firing dynamics, as measured via a principal component analysis of the spike trains in each condition. Furthermore, for both the model and the data, we found an inverted U-shaped relationship between coupling strengths and complexity entropy, a measure of chaos for spiking neural data. These results are consistent with our hypothesis according to which electrical coupling regulates the dimensionality and the complexity in the inferior olive neurons in order to optimize both motor learning and control of high dimensional motor systems by the cerebellum.

Computational theory suggests that the cerebellum must decrease the dimensionality of its neuronal activity to learn and control high dimensional motor systems effectively, while being constrained by the low firing frequency of inferior olive neurons, one of the two major source of input signals to the cerebellum. We previously proposed that the cerebellum adaptively controls the dimensionality of inferior olive firing by adjusting the level of synchrony and that such control is made possible by modulating the electrical coupling strength between inferior olive neurons. Here, we developed a novel method that uses a biophysical model of the inferior olive to accurately estimate the effective coupling strengths between inferior olive neurons from in vivo recordings of spike activity in three different coupling conditions. We found that high coupling strengths induce synchronous firing and decrease the dimensionality of inferior olive firing dynamics. In contrast, intermediate coupling strengths lead to chaotic firing and increase the dimensionality of the firing dynamics. Thus, electrical coupling is a feasible mechanism to control dimensionality and chaotic firing of inferior olive neurons. In sum, our results provide insights into possible mechanisms underlying cerebellar function and, in general, a biologically plausible framework to control the dimensionality of neural coding.

Ocular Reflex Adaptation as an Experimental Model of Cerebellar Learning -- In Memory of Masao Ito -

Masao Ito proposed a cerebellar learning hypothesis with Marr and Albus in the early 1970s. He suggested that cerebellar flocculus (FL) Purkinje cells (PCs), which directly inhibit the vestibular nuclear neurons driving extraocular muscle motor neurons, adaptively control the horizontal vestibulo-ocular reflex (HVOR) through the modification of mossy and parallel fiber-mediated vestibular responsiveness by visual climbing fiber (CF) inputs. Later, it was suggested that the same FL PCs adaptively control the horizontal optokinetic response (HOKR) in the same manner through the modification of optokinetic responsiveness in rodents and rabbits. In 1982, Ito and his colleagues discovered the plasticity of long-term depression (LTD) at parallel fiber (PF)-PC synapses after conjunctive stimulation of mossy or parallel fibers with CFs. Long-term potentiation (LTP) at PF-PC synapses by weak PF stimulation alone was found later. Many lines of experimental evidence have supported their hypothesis using various experimental methods and materials for the past 50 years by many research groups. Although several controversial findings were presented regarding their hypothesis, the reasons underlying many of them were clarified. Today, their hypothesis is considered as a fundamental mechanism of cerebellar learning. Furthermore, it was found that the memory of adaptation is transferred from the FL to vestibular nuclei for consolidation by repetition of adaptation through the plasticity of vestibular nuclear neurons. In this article, after overviewing their cerebellar learning hypothesis, I discuss possible roles of LTD and LTP in gain-up and gain-down HVOR/HOKR adaptations and refer to the expansion of their hypothesis to cognitive functions.

50 Years Since the Marr, Ito, and Albus Models of the Cerebellum

Fifty years have passed since David Marr, Masao Ito, and James Albus proposed seminal models of cerebellar functions. These models share the essential concept that parallel-fiber-Purkinje-cell synapses undergo plastic changes, guided by climbing-fiber activities during sensorimotor learning. However, they differ in several important respects, including holistic versus complementary roles of the cerebellum, pattern recognition versus control as computational objectives, potentiation versus depression of synaptic plasticity, teaching signals versus error signals transmitted by climbing-fibers, sparse expansion coding by granule cells, and cerebellar internal models. In this review, we evaluate different features of the three models based on recent computational and experimental studies. While acknowledging that the three models have greatly advanced our understanding of cerebellar control mechanisms in eye movements and classical conditioning, we propose a new direction for computational frameworks of the cerebellum, that is, hierarchical reinforcement learning with multiple internal models.

Norepinephrine Facilitates Induction of Long-term Depression through β-Adrenergic Receptor at Parallel Fiber-to-Purkinje Cell Synapses in the Flocculus

The cerebellum is involved in motor learning, and long-term depression (LTD) at parallel fiber-to-Purkinje cell (PF-PC) synapses has been considered to be a primary cellular mechanism for motor learning. In addition, the contribution of norepinephrine (NE) to cerebellum-dependent learning paradigms has been reported. Thus, the roles of LTD and of NE in motor learning have been studied separately, and the relationship between the effects of NE and LTD remains unclear. Here, we examined effects of β-adrenergic receptor (β-AR) activity on the synaptic transmission and LTD at PF-PC synapses in the cerebellar flocculus. The flocculus regulates adaptation of oculomotor reflexes, and we previously reported the involvement of both LTD and β-AR in adaptation of an oculomotor reflex. Here we found that specific agonists for β-AR or NE did not directly change synaptic transmission, but lowered the threshold for LTD induction at PF-PC synapses in the flocculus. In addition, protein kinase A (PKA), which is activated downstream of β-AR, facilitated the LTD induction. Altogether, these results suggest that NE facilitates LTD induction at PF-PC synapses in the flocculus by activating PKA through β-AR.

Binding of Filamentous Actin to CaMKII as Potential Regulation Mechanism of Bidirectional Synaptic Plasticity by β CaMKII in Cerebellar Purkinje Cells

Calcium-calmodulin dependent protein kinase II (CaMKII) regulates many forms of synaptic plasticity, but little is known about its functional role during plasticity induction in the cerebellum. Experiments have indicated that the β isoform of CaMKII controls the bidirectional inversion of plasticity at parallel fibre (PF)-Purkinje cell (PC) synapses in cerebellar cortex. Because the cellular events that underlie these experimental findings are still poorly understood, we developed a simple computational model to investigate how β CaMKII regulates the direction of plasticity in cerebellar PCs. We present the first model of AMPA receptor phosphorylation that simulates the induction of long-term depression (LTD) and potentiation (LTP) at the PF-PC synapse. Our simulation results suggest that the balance of CaMKII-mediated phosphorylation and protein phosphatase 2B (PP2B)-mediated dephosphorylation of AMPA receptors can determine whether LTD or LTP occurs in cerebellar PCs. The model replicates experimental observations that indicate that β CaMKII controls the direction of plasticity at PF-PC synapses, and demonstrates that the binding of filamentous actin to CaMKII can enable the β isoform of the kinase to regulate bidirectional plasticity at these synapses.

Postsynaptic Stability and Variability Described by a Stochastic Model of Endosomal Trafficking

Neurons undergo dynamic processes of constitutive AMPA-type glutamate receptor (AMPAR) trafficking, such as the insertion and internalization of AMPARs by exocytosis and endocytosis, while stably maintaining synaptic efficacy. Studies using advanced imaging techniques have suggested that the frequency of these constitutive trafficking processes, as well as the number of AMPARs that are involved in a particular event highly fluctuate. In addition, mechanisms that trigger some forms of synaptic plasticity have been shown to include not only these processes but also additional fluctuating processes, such as the sorting of AMPARs to late endosomes (LEs). Thus, the regulation of postsynaptic AMPARs by the endosomal trafficking system appears to have superficially conflicting properties between the stability or organized control of plasticity and highly fluctuating or stochastic processes. However, it is not clear how the endosomal trafficking system reconciles and utilizes such conflicting properties. Although deterministic models have been effective to describe the stable maintenance of synaptic AMPAR numbers by constitutive recycling, as well as the involvement of endosomal trafficking in synaptic plasticity, they do not take stochasticity into account. In this study, we introduced the stochasticity into the model of each crucial machinery of the endosomal trafficking system. The specific questions we solved by our improved model are whether stability is accomplished even with a combination of fluctuating processes, and how overall variability occurs while controlling long-term synaptic depression (LTD). Our new stochastic model indeed demonstrated the stable regulation of postsynaptic AMPAR numbers at the basal state and during LTD maintenance, despite fast fluctuations in AMPAR numbers as well as high variability in the time course and amounts of LTD. In addition, our analysis suggested that the high variability arising from this stochasticity is beneficial for reproducing the relatively constant timing of LE sorting for LTD. We therefore propose that the coexistence of stability and stochasticity in the endosomal trafficking system is suitable for stable synaptic transmission and the reliable induction of synaptic plasticity, with variable properties that have been observed experimentally.

Timely regulated sorting from early to late endosomes is required to maintain cerebellar long-term depression

An important feature of long-term synaptic plasticity is the prolonged maintenance of plastic changes in synaptic transmission. The trafficking of AMPA-type glutamate receptors (AMPARs) is involved in the expression of many forms of synaptic plasticity, yet the subsequent events accomplishing the maintenance of plastic changes in synaptic AMPAR numbers are not fully understood. Here, we find that maintenance of cerebellar long-term depression results from a reduction in the number of AMPARs residing within endocytic recycling pathways. We then develop a genetically encoded, photosensitive inhibitor of late endosome sorting and use this to discover that initial maintenance of long-term depression relies on timely regulated late endosome sorting, which exhibits a threshold as well as switch-like behavior. Thus, our results indicate that recycling AMPAR numbers are reduced by a switching machinery of transient late endosome sorting, and that this process enables the transition from basal synaptic transmission to long-term depression maintenance.

Long term depression (LTD) of the cerebellum is known to be mediated by postsynaptic trafficking of glutamate receptor AMPAR. Here, Kim and colleagues show that early- to late-endosomal sorting of AMPAR represents the switch from expression to maintenance phase of cerebellar LTD.

Stochastic Induction of Long-Term Potentiation and Long-Term Depression

Long-term depression (LTD) and long-term potentiation (LTP) of granule-Purkinje cell synapses are persistent synaptic alterations induced by high and low rises of the intracellular calcium ion concentration ([Ca²⁺]), respectively. The occurrence of LTD involves the activation of a positive feedback loop formed by protein kinase C, phospholipase A₂, and the extracellular signal-regulated protein kinase pathway, and its expression comprises the reduction of the population of synaptic AMPA receptors. Recently, a stochastic computational model of these signalling processes demonstrated that, in single synapses, LTD is probabilistic and bistable. Here, we expanded this model to simulate LTP, which requires protein phosphatases and the increase in the population of synaptic AMPA receptors. Our results indicated that, in single synapses, while LTD is bistable, LTP is gradual. Ca²⁺ induced both processes stochastically. The magnitudes of the Ca²⁺ signals and the states of the signalling network regulated the likelihood of LTP and LTD and defined dynamic macroscopic Ca²⁺ thresholds for the synaptic modifications in populations of synapses according to an inverse Bienenstock, Cooper and Munro (BCM) rule or a sigmoidal function. In conclusion, our model presents a unifying mechanism that explains the macroscopic properties of LTP and LTD from their dynamics in single synapses.

Real-World-Time Simulation of Memory Consolidation in a Large-Scale Cerebellar Model

We report development of a large-scale spiking network model of the cerebellum composed of more than 1 million neurons. The model is implemented on graphics processing units (GPUs), which are dedicated hardware for parallel computing. Using 4 GPUs simultaneously, we achieve realtime simulation, in which computer simulation of cerebellar activity for 1 s completes within 1 s in the real-world time, with temporal resolution of 1 ms. This allows us to carry out a very long-term computer simulation of cerebellar activity in a practical time with millisecond temporal resolution. Using the model, we carry out computer simulation of long-term gain adaptation of optokinetic response (OKR) eye movements for 5 days aimed to study the neural mechanisms of posttraining memory consolidation. The simulation results are consistent with animal experiments and our theory of posttraining memory consolidation. These results suggest that realtime computing provides a useful means to study a very slow neural process such as memory consolidation in the brain.

Linking short tandem repeat polymorphisms with cytosine modifications in human lymphoblastoid cell lines

Inter-individual variation in cytosine modifications has been linked to complex traits in humans. Cytosine modification variation is partially controlled by single nucleotide polymorphisms (SNPs), known as modified cytosine quantitative trait loci (mQTL). However, little is known about the role of short tandem repeat polymorphisms (STRPs), a class of structural genetic variants, in regulating cytosine modifications. Utilizing the published data on the International HapMap Project lymphoblastoid cell lines (LCLs), we assessed the relationships between 721 STRPs and the modification levels of 283,540 autosomal CpG sites. Our findings suggest that, in contrast to the predominant cis-acting mode for SNP-based mQTL, STRPs are associated with cytosine modification levels in both cis-acting (local) and trans-acting (distant) modes. In local scans within the ±1 Mb windows of target CpGs, 21, 9, and 21 cis-acting STRP-based mQTL were detected in CEU (Caucasian residents from Utah, USA), YRI (Yoruba people from Ibadan, Nigeria), and the combined samples, respectively. In contrast, 139,420, 76,817, and 121,866 trans-acting STRP-based mQTL were identified in CEU, YRI, and the combined samples, respectively. A substantial proportion of CpG sites detected with local STRP-based mQTL were not associated with SNP-based mQTL, suggesting that STRPs represent an independent class of mQTL. Functionally, genetic variants neighboring CpG-associated STRPs are enriched with genome-wide association study (GWAS) loci for a variety of complex traits and diseases, including cancers, based on the National Human Genome Research Institute (NHGRI) GWAS Catalog. Therefore, elucidating these STRP-based mQTL in addition to SNP-based mQTL can provide novel insights into the genetic architectures of complex traits.

Biochemical Computation for Spine Structural Plasticity

The structural plasticity of dendritic spines is considered to be essential for various forms of synaptic plasticity, learning, and memory. The process is mediated by a complex signaling network consisting of numerous species of molecules. Furthermore, the spatiotemporal dynamics of the biochemical signaling are regulated in a complicated manner because of geometrical restrictions from the unique morphology of the dendritic branches and spines. Recent advances in optical techniques have enabled the exploration of the spatiotemporal aspects of the signal regulations in spines and dendrites and have provided many insights into the principle of the biochemical computation that underlies spine structural plasticity.

Around LTD hypothesis in motor learning

Long-term depression (LTD) at parallel fiber-Purkinje neuron synapses has been regarded as a primary cellular mechanism for motor learning. However, this hypothesis has been challenged. Demonstration of normal motor learning under LTD-suppressed conditions suggested that motor learning can occur without LTD. Synaptic plasticity mechanisms other than LTD have been found at various synapses in the cerebellum. Animals may achieve motor learning using several types of synaptic plasticity in the cerebellum including LTD.

Protein tyrosine phosphatase receptor type R is required for Purkinje cell responsiveness in cerebellar long-term depression

Background

Regulation of synaptic connectivity, including long-term depression (LTD), allows proper tuning of cellular signalling processes within brain circuitry. In the cerebellum, a key centre for motor coordination, a positive feedback loop that includes mitogen-activated protein kinases (MAPKs) is required for proper temporal control of LTD at cerebellar Purkinje cell synapses. Here we report that the tyrosine-specific MAPK-phosphatase PTPRR plays a role in coordinating the activity of this regulatory loop.

Results

LTD in the cerebellum of Ptprr^−/− mice is strongly impeded, in vitro and in vivo. Comparison of basal phospho-MAPK levels between wild-type and PTPRR deficient cerebellar slices revealed increased levels in mutants. This high basal phospho-MAPK level attenuated further increases in phospho-MAPK during chemical induction of LTD, essentially disrupting the positive feedback loop and preventing α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR) phosphorylation and endocytosis.

Conclusions

Our findings indicate an important role for PTPRR in maintaining low basal MAPK activity in Purkinje cells. This creates an optimal ‘window’ to boost MAPK activity following signals that induce LTD, which can then propagate through feed-forward signals to cause AMPAR internalization and LTD.

Nitric oxide regulates synaptic transmission between spiny projection neurons

Recurrent axon collaterals are a major means of communication between spiny projection neurons (SPNs) in the striatum and profoundly affect the function of the basal ganglia. However, little is known about the molecular and cellular mechanisms that underlie this communication. We show that intrastriatal nitric oxide (NO) signaling elevates the expression of the vesicular GABA transporter (VGAT) within recurrent collaterals of SPNs. Down-regulation of striatal NO signaling resulted in an attenuation of GABAergic signaling in SPN local collaterals, down-regulation of VGAT expression in local processes of SPNs, and impaired motor behavior. PKG1 and cAMP response element-binding protein are involved in the signal transduction that transcriptionally regulates VGAT by NO. These data suggest that transcriptional control of the vesicular GABA transporter by NO regulates GABA transmission and action selection.

Stochasticity in Ca2+ increase in spines enables robust and sensitive information coding

A dendritic spine is a very small structure (∼0.1 µm³) of a neuron that processes input timing information. Why are spines so small? Here, we provide functional reasons; the size of spines is optimal for information coding. Spines code input timing information by the probability of Ca²⁺ increases, which makes robust and sensitive information coding possible. We created a stochastic simulation model of input timing-dependent Ca²⁺ increases in a cerebellar Purkinje cell's spine. Spines used probability coding of Ca²⁺ increases rather than amplitude coding for input timing detection via stochastic facilitation by utilizing the small number of molecules in a spine volume, where information per volume appeared optimal. Probability coding of Ca²⁺ increases in a spine volume was more robust against input fluctuation and more sensitive to input numbers than amplitude coding of Ca²⁺ increases in a cell volume. Thus, stochasticity is a strategy by which neurons robustly and sensitively code information.

Long-term depression as a model of cerebellar plasticity

Long-term depression (LTD) here concerned is persistent attenuation of transmission efficiency from a bundle of parallel fibers to a Purkinje cell. Uniquely, LTD is induced by conjunctive activation of the parallel fibers and the climbing fiber that innervates that Purkinje cell. Cellular and molecular processes underlying LTD occur postsynaptically. In the 1960s, LTD was conceived as a theoretical possibility and in the 1980s, substantiated experimentally. Through further investigations using various pharmacological or genetic manipulations of LTD, a concept was formed that LTD plays a major role in learning capability of the cerebellum (referred to as "Marr-Albus-Ito hypothesis"). In this chapter, following a historical overview, recent intensive investigations of LTD are reviewed. Complex signal transduction and receptor recycling processes underlying LTD are analyzed, and roles of LTD in reflexes and voluntary movements are defined. The significance of LTD is considered from viewpoints of neural network modeling. Finally, the controversy arising from the recent finding in a few studies that whereas LTD is blocked pharmacologically or genetically, motor learning in awake behaving animals remains seemingly unchanged is examined. We conjecture how this mismatch arises, either from a methodological problem or from a network nature, and how it might be resolved.

Multiscale modeling and synaptic plasticity

Synaptic plasticity is a major convergence point for theory and computation, and the process of plasticity engages physiology, cell, and molecular biology. In its many manifestations, plasticity is at the hub of basic neuroscience questions about memory and development, as well as more medically themed questions of neural damage and recovery. As an important cellular locus of memory, synaptic plasticity has received a huge amount of experimental and theoretical attention. If computational models have tended to pick specific aspects of plasticity, such as STDP, and reduce them to an equation, some experimental studies are equally guilty of oversimplification each time they identify a new molecule and declare it to be the last word in plasticity and learning. Multiscale modeling begins with the acknowledgment that synaptic function spans many levels of signaling, and these are so tightly coupled that we risk losing essential features of plasticity if we focus exclusively on any one level. Despite the technical challenges and gaps in data for model specification, an increasing number of multiscale modeling studies have taken on key questions in plasticity. These have provided new insights, but importantly, they have opened new avenues for questioning. This review discusses a wide range of multiscale models in plasticity, including their technical landscape and their implications.

A common framework of signal processing in the induction of cerebellar LTD and cortical STDP

Cerebellar long-term depression (LTD) and cortical spike-timing-dependent synaptic plasticity (STDP) are two well-known and well-characterized types of synaptic plasticity. Induction of both types of synaptic plasticity depends on the spike timing, pairing frequency, and pairing numbers of two different sources of spiking. This implies that the induction of synaptic plasticity may share common frameworks in terms of signal processing regardless of the different signaling pathways involved in the two types of synaptic plasticity. Here we propose that both types share common frameworks of signal processing for spike-timing, pairing-frequency, and pairing-numbers detection. We developed system models of both types of synaptic plasticity and analyzed signal processing in the induction of synaptic plasticity. We found that both systems have upstream subsystems for spike-timing detection and downstream subsystems for pairing-frequency and pairing-numbers detection. The upstream systems used multiplication of signals from the feedback filters and nonlinear functions for spike-timing detection. The downstream subsystems used temporal filters with longer time constants for pairing-frequency detection and nonlinear switch-like functions for pairing-numbers detection, indicating that the downstream subsystems serve as a leaky integrate-and-fire system. Thus, our findings suggest that a common conceptual framework for the induction of synaptic plasticity exists despite the differences in molecular species and pathways.

Gating of long-term depression by Ca2+/calmodulin-dependent protein kinase II through enhanced cGMP signalling in cerebellar Purkinje cells

Long-term depression (LTD) at parallel fibre synapses on a cerebellar Purkinje cell has been regarded as a cellular basis for motor learning. Although Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) has been implicated in the LTD induction as an important Ca(2+)-sensing molecule, the underlying signalling mechanism remains unclear. Here, we attempted to explore the potential signalling pathway underlying the CaMKII involvement in LTD using a systems biology approach, combined with validation by electrophysiological and FRET imaging experiments on a rat cultured Purkinje cell. Model simulation predicted the following cascade as a candidate mechanism for the CaMKII contribution to LTD: CaMKII negatively regulates phosphodiesterase 1 (PDE1), subsequently facilitates the cGMP/protein kinase G (PKG) signalling pathway and down-regulates protein phosphatase 2A (PP-2A), thus supporting the LTD-inducing positive feedback loop consisting of mutual activation of protein kinase C (PKC) and mitogen-activated protein kinase (MAPK). This model suggestion was corroborated by whole-cell patch clamp recording experiments. In addition, FRET measurement of intracellular cGMP concentration revealed that CaMKII activation causes sustained increase of cGMP, supporting the signalling mechanism of LTD induction by CaMKII. Furthermore, we found that activation of the cGMP/PKG pathway by nitric oxide (NO) can support LTD induction without activation of CaMKII. Thus, this study clarified interaction between NO and Ca(2+)/CaMKII, two important factors required for LTD.

Long-term depression and other synaptic plasticity in the cerebellum

Cerebellar long-term depression (LTD) is a type of synaptic plasticity and has been considered as a critical cellular mechanism for motor learning. LTD occurs at excitatory synapses between parallel fibers and a Purkinje cell in the cerebellar cortex, and is expressed as reduced responsiveness to transmitter glutamate. Molecular induction mechanism of LTD has been intensively studied using culture and slice preparations, which has revealed critical roles of Ca(2+), protein kinase C and endocytosis of AMPA-type glutamate receptors. Involvement of a large number of additional molecules has also been demonstrated, and their interactions relevant to LTD mechanisms have been studied. In vivo experiments including those on mutant mice, have reported good correlation of LTD and motor learning. However, motor learning could occur with impaired LTD. A possibility that cerebellar synaptic plasticity other than LTD compensates for the defective LTD has been proposed.

Calcium as a trigger for cerebellar long-term synaptic depression

Cerebellar long-term depression (LTD) is a form of long-term synaptic plasticity that is triggered by calcium(Ca2+) signals in the postsynaptic Purkinje cell. This Ca2+comes both from IP3-mediated release from intracellular Ca2+ stores, as well as from Ca2+ influx through voltage-gated Ca2+ channels. The Ca2+ signal that triggers LTD occurs locally within dendritic spines and is due to supralinear summation of signals coming from these two Ca2+ sources. The properties of this postsynaptic Ca2+signal can explain several features of LTD, such as its associativity, synapse specificity, and dependence on thetiming of synaptic activity, and can account for the slow kinetics of LTD expression. Thus, from a Ca2+ signaling perspective, LTD is one of the best understood forms of synaptic plasticity.

The importance of stochastic signaling processes in the induction of long-term synaptic plasticity

A stochastic model of the signaling network responsible for the induction of long-term depression (LTD) at the parallel fiber to Purkinje cell synapse is described. The model includes a PKC-ERK-cPLA2 positive feedback loop and mechanisms of AMPA receptor trafficking. It was tuned to replicate calcium uncaging experiments that cause LTD. The ultrasensitive activation of ERK makes the signaling network activity bistable, causing either LTD or not. Therefore, in single synapses only two discrete stable states (LTD and non-LTD) can be expressed. The stochastic properties of the signaling network causes threshold dithering and probabilistic expression of LTD, which allows at the macroscopic level for many different and stable mean magnitudes of depression. When the volume of a single spine is simulated no thresholds for the calcium input signal are present. Such thresholds appear only when the volume of simulation is increased by a factor 100 or more and the model output is then bistable. Similarly, deterministic solutions of the same model show only bistable behavior. LTD induction requires activation of the PKC-ERK-cPLA2 positive feedback loop but this activity is not constant: the activities of ERK and of cPLA2 fluctuate strongly. This is much less the case for PKC which is more constantly activated and thereby promotes a stable output of the pathway.

Mechanisms producing time course of cerebellar long-term depression

Cerebellar long-term depression (LTD) is induced by short-lasting synaptic activities, progressively expressed, and then maintained for hours or longer. Short-lasting events, such as calcium transients, are activated and required for the induction of LTD. Further, a positive-feedback kinase loop was shown to follow the transient events and to aid the transition between LTD induction and prolonged synaptic depression. Yet, it is not entirely clear as to how LTD is maintained and how the maintenance mechanisms are activated, mainly because of a lack of experimental studies regarding this topic, while an idea has been theoretically proposed. A new analysis of the experimental results suggests that early maintenance mechanisms display a threshold behavior and that they may be of stochastic nature. This suggestion is conceptually consistent with an idea from a computational study, which postulates that other bistable switch systems are required for LTD maintenance. We thus propose that cellular mechanisms showing a threshold behavior and a stochastic nature maintain LTD, and that future experimental studies in search of such mechanisms would be an important step toward fully understanding the time course of LTD.

Putative roles for phospholipase Cη enzymes in neuronal Ca2+ signal modulation

The most recently identified PLC (phospholipase C) enzymes belong to the PLCη family. Their unique Ca2+-sensitivity and their specific appearance in neurons have attracted great attention since their discovery; however, their physiological role(s) in neurons are still yet to be established. PLCη enzymes are expressed in the neocortex, hippocampus and cerebellum. PLCη2 is also expressed at high levels in pituitary gland, pineal gland and in the retina. Driven by the specific localization of PLCη enzymes in different brain areas, in the present paper, we discuss the roles that they may play in neural processes, including differentiation, memory formation, circadian rhythm regulation, neurotransmitter/hormone release and the pathogenesis of neurodegenerative disorders associated with aberrant Ca2+ signalling, such as Alzheimer's disease.

Positive feedback in the Akt/mTOR pathway and its implications for growth signal progression in skeletal muscle cells: an analytical study

The IGF-1 mediated Akt/mTOR pathway has been recently proposed as mediator of skeletal muscle growth and a positive feedback between Akt and mTOR was suggested to induce homogeneous growth signals along the whole spatial extension of such long cells. Here we develop two biologically justified approximations which we study under the presence of four different initial conditions that describe different paradigms of IGF-1 receptor-induced Akt/mTOR activation. In first scenario the activation of the feedback cascade was assumed to be mild or protein turnover considered to be high. In turn, in the second scenario the transcriptional regulation was assumed to maintain defined levels of inactive pro-enzymes. For both scenarios, we were able to obtain closed-form formulas for growth signal progression in time and space and found that a localised initial signal maintains its Gaussian shape, but gets delocalised and exponentially degraded. Importantly, mathematical treatment of the reaction diffusion system revealed that diffusion filtered out high frequencies of spatially periodic initiator signals suggesting that the muscle cell is robust against fluctuations in spatial receptor expression or activation. However, neither scenario was consistent with the presence of stably travelling signal waves. Our study highlights the role of feedback loops in spatiotemporal signal progression and results can be applied to studies in cell proliferation, cell differentiation and cell death in other spatially extended cells.

Dynamic impact of temporal context of Ca²⁺ signals on inhibitory synaptic plasticity

Neuronal activity-dependent synaptic plasticity, a basis for learning and memory, is tightly correlated with the pattern of increase in intracellular Ca²⁺ concentration ([Ca²⁺]_i). Here, using combined application of electrophysiological experiments and systems biological simulation, we show that such a correlation dynamically changes depending on the context of [Ca²⁺]_i increase. In a cerebellar Purkinje cell, long-term potentiation of inhibitory GABA_A receptor responsiveness (called rebound potentiation; RP) was induced by [Ca²⁺]_i increase in a temporally integrative manner through sustained activation of Ca²⁺/calmodulin-dependent protein kinase II (CaMKII). However, the RP establishment was canceled by coupling of two patterns of RP-inducing [Ca²⁺]_i increase depending on the temporal sequence. Negative feedback signaling by phospho-Thr305/306 CaMKII detected the [Ca²⁺]_i context, and assisted the feedforward inhibition of CaMKII through PDE1, resulting in the RP impairment. The [Ca²⁺]_i context-dependent dynamic regulation of synaptic plasticity might contribute to the temporal refinement of information flow in neuronal networks.

Cerebellar supervised learning revisited: biophysical modeling and degrees-of-freedom control

The biophysical models of spike-timing-dependent plasticity have explored dynamics with molecular basis for such computational concepts as coincidence detection, synaptic eligibility trace, and Hebbian learning. They overall support different learning algorithms in different brain areas, especially supervised learning in the cerebellum. Because a single spine is physically very small, chemical reactions at it are essentially stochastic, and thus sensitivity-longevity dilemma exists in the synaptic memory. Here, the cascade of excitable and bistable dynamics is proposed to overcome this difficulty. All kinds of learning algorithms in different brain regions confront with difficult generalization problems. For resolution of this issue, the control of the degrees-of-freedom can be realized by changing synchronicity of neural firing. Especially, for cerebellar supervised learning, the triangle closed-loop circuit consisting of Purkinje cells, the inferior olive nucleus, and the cerebellar nucleus is proposed as a circuit to optimally control synchronous firing and degrees-of-freedom in learning.

The protein kinase Mζ network as a bistable switch to store neuronal memory

Background

Protein kinase Mζ (PKMζ), the brain-specific, atypical protein kinase C isoform, plays a key role in long-term maintenance of memory. This molecule is essential for long-term potentiation of the neuron and various modalities of learning such as spatial memory and fear conditioning. It is unknown, however, how PKMζ stores information for long periods of time despite molecular turnover.

Results

We hypothesized that PKMζ forms a bistable switch because it appears to constitute a positive feedback loop (PKMζ induces its local synthesis) part of which is ultrasensitive (PKMζ stimulates its synthesis through dual pathways). To examine this hypothesis, we modeled the biochemical network of PKMζ with realistic kinetic parameters. Bifurcation analyses of the model showed that the system maintains either the up state or the down state according to previous inputs. Furthermore, the model was able to reproduce a variety of previous experimental results regarding synaptic plasticity and learning, which suggested that it captures the essential mechanism for neuronal memory. We proposed in vitro and in vivo experiments that would critically examine the validity of the model and illuminate the pivotal role of PKMζ in synaptic plasticity and learning.

Conclusions

This study revealed bistability of the PKMζ network and supported its pivotal role in long-term storage of memory.

Modelling the molecular mechanisms of synaptic plasticity using systems biology approaches

Synaptic plasticity is thought to underlie learning and memory, but the complexity of the interactions between the ion channels, enzymes and genes that are involved in synaptic plasticity impedes a deep understanding of this phenomenon. Computer modelling has been used to investigate the information processing that is performed by the signalling pathways involved in synaptic plasticity in principal neurons of the hippocampus, striatum and cerebellum. In the past few years, new software developments that combine computational neuroscience techniques with systems biology techniques have allowed large-scale, kinetic models of the molecular mechanisms underlying long-term potentiation and long-term depression. We highlight important advancements produced by these quantitative modelling efforts and introduce promising approaches that use advancements in live-cell imaging.

Lipid signaling in cytosolic phospholipase A2alpha-cyclooxygenase-2 cascade mediates cerebellar long-term depression and motor learning

In this study, we show the crucial roles of lipid signaling in long-term depression (LTD), that is, synaptic plasticity prevailing in cerebellar Purkinje cells. In mouse brain slices, we found that cPLA(2)alpha knockout blocked LTD induction, which was rescued by replenishing arachidonic acid (AA) or prostaglandin (PG) D(2) or E(2). Moreover, cyclooxygenase (COX)-2 inhibitors block LTD, which is rescued by supplementing PGD(2)/E(2). The blockade or rescue occurs when these reagents are applied within a time window of 5-15 min following the onset of LTD-inducing stimulation. Furthermore, PGD(2)/E(2) facilitates the chemical induction of LTD by a PKC activator but is unable to rescue the LTD blocked by a PKC inhibitor. We conclude that PGD(2)/E(2) mediates LTD jointly with PKC, and suggest possible pathways for their interaction. Finally, we demonstrate in awake mice that cPLA(2)alpha deficiency or COX-2 inhibition attenuates short-term adaptation of optokinetic eye movements, supporting the view that LTD underlies motor learning.

Prediction and validation of a mechanism to control the threshold for inhibitory synaptic plasticity

Synaptic plasticity, neuronal activity-dependent sustained alteration of the efficacy of synaptic transmission, underlies learning and memory. Activation of positive-feedback signaling pathways by an increase in intracellular Ca²⁺ concentration ([Ca²⁺]_i) has been implicated in synaptic plasticity. However, the mechanism that determines the [Ca²⁺]_i threshold for inducing synaptic plasticity is elusive. Here, we developed a kinetic simulation model of inhibitory synaptic plasticity in the cerebellum, and systematically analyzed the behavior of intricate molecular networks composed of protein kinases, phosphatases, etc. The simulation showed that Ca²⁺/calmodulin-dependent protein kinase II (CaMKII), which is essential for the induction of synaptic plasticity, was persistently activated or suppressed in response to different combinations of stimuli. The sustained CaMKII activation depended on synergistic actions of two positive-feedback reactions, CaMKII autophosphorylation and CaMKII-mediated inhibition of a CaM-dependent phosphodiesterase, PDE1. The simulation predicted that PDE1-mediated feedforward inhibition of CaMKII predominantly controls the Ca²⁺ threshold, which was confirmed by electrophysiological experiments in primary cerebellar cultures. Thus, combined application of simulation and experiments revealed that the Ca²⁺ threshold for the cerebellar inhibitory synaptic plasticity is primarily determined by PDE1.

Experimental and computational aspects of signaling mechanisms of spike-timing-dependent plasticity

STDP (spike-timing-dependent synaptic plasticity) is thought to be a synaptic learning rule that embeds spike-timing information into a specific pattern of synaptic strengths in neuronal circuits, resulting in a memory. STDP consists of bidirectional long-term changes in synaptic strengths. This process includes long-term potentiation and long-term depression, which are dependent on the timing of presynaptic and postsynaptic spikings. In this review, we focus on computational aspects of signaling mechanisms that induce and maintain STDP as a key step toward the definition of a general synaptic learning rule. In addition, we discuss the temporal and spatial aspects of STDP, and the requirement of a homeostatic mechanism of STDP in vivo.

A positive feedback signal transduction loop determines timing of cerebellar long-term depression

Synaptic activity produces short-lived second messengers that ultimately yield a long-term depression (LTD) of cerebellar Purkinje cells. Here, we test the hypothesis that these brief second messenger signals are translated into long-lasting biochemical signals by a positive feedback loop that includes protein kinase C (PKC) and mitogen-activated protein kinase. Histochemical "epistasis" experiments demonstrate the reciprocal activation of these kinases, and physiological experiments--including the use of a light-activated protein kinase--demonstrate that such reciprocal activation is required for LTD. Timed application of enzyme inhibitors reveals that this positive feedback loop causes PKC to be active for more than 20 min, allowing sufficient time for LTD expression. Such regenerative mechanisms may sustain other long-lasting forms of synaptic plasticity and could be a general mechanism for prolonging signal transduction networks.

From 'understanding the brain by creating the brain' towards manipulative neuroscience

Ten years have passed since the Japanese 'Century of the Brain' was promoted, and its most notable objective, the unique 'creating the brain' approach, has led us to apply a humanoid robot as a neuroscience tool. Here, we aim to understand the brain to the extent that we can make humanoid robots solve tasks typically solved by the human brain by essentially the same principles. I postulate that this 'Understanding the Brain by Creating the Brain' approach is the only way to fully understand neural mechanisms in a rigorous sense. Several humanoid robots and their demonstrations are introduced. A theory of cerebellar internal models and a systems biology model of cerebellar synaptic plasticity is discussed. Both models are experimentally supported, but the latter is more easily verifiable while the former is still controversial. I argue that the major reason for this difference is that essential information can be experimentally manipulated in molecular and cellular neuroscience while it cannot be manipulated at the system level. I propose a new experimental paradigm, manipulative neuroscience, to overcome this difficulty and allow us to prove cause-and-effect relationships even at the system level.

Cytosolic PLA2(alpha) activation in Purkinje neurons and its role in AMPA-receptor trafficking

Cytosolic phospholipase A(2)alpha (cPLA(2)alpha) selectively releases arachidonic acid from membrane phospholipids and has been proposed to be involved in the induction of long-term depression (LTD), a form of synaptic plasticity in the cerebellum. This enzyme requires two events for its full activation: Ca(2+)-dependent translocation from the cytosol to organelle membranes in order to access phospholipids as substrates, and phosphorylation by several kinases. However, the subcellular distribution and activation of cPLA(2)alpha in Purkinje cells and the role of arachidonic acid in cerebellar LTD have not been fully elucidated. In cultured Purkinje cells, stimulation of AMPA receptors, but not metabotropic glutamate receptors, triggered translocation of cPLA(2)alpha to the somatic and dendritic Golgi compartments. This translocation required Ca(2+) influx through P-type Ca(2+) channels. AMPA plus PMA, a chemical method for inducing LTD, released arachidonic acid via phosphorylation of cPLA(2)alpha. AMPA plus PMA induced a decrease in surface GluR2 for more than 2 hours. Interestingly, this reduction was occluded by a cPLA(2)alpha-specific inhibitor. Furthermore, PMA plus arachidonic acid caused the prolonged internalization of GluR2 without activating AMPA receptors. These results suggest that cPLA(2)alpha regulates the persistent decrease in the expression of AMPA receptors, underscoring the role of cPLA(2)alpha in cerebellar LTD.

Algebraic method for the analysis of signaling crosstalk

A unified mathematical description that expresses the characteristics of whole systems is necessary for an understanding of signal transduction cascades. In this study we explore an algebraic method, named extreme signaling flow, enhanced from the concept of extreme pathway, to analyze signal transduction systems. This method enables us to represent the long-term potentiation (LTP) and the long-term depression (LTD) of hippocampal neuronal plasticity in an integrated simulation model. The model is validated by comparing the results of redundancy, reaction participation, and in silico knockout analysis with biological knowledge available from the literature. The following properties are assumed in these computational analyses: (1) LTP is fault-tolerant under network modification, (2) protein kinase C and MAPK have numerous routes to LTP induction, (3) calcium-calmodulin kinase II has a few routes to LTP induction, and (4) calcineurin has many routes to LTD induction. These results demonstrate that our approach produces an integrated framework for analyzing properties of large-scale systems with complicated signal transduction.

Ca2+ requirements for cerebellar long-term synaptic depression: role for a postsynaptic leaky integrator

Photolysis of a caged Ca(2+) compound was used to characterize the dependence of cerebellar long-term synaptic depression (LTD) on postsynaptic Ca(2+) concentration ([Ca(2+)](i)). Elevating [Ca(2+)](i) was sufficient to induce LTD without requiring any of the other signals produced by synaptic activity. A sigmoidal relationship between [Ca(2+)](i) and LTD indicated a highly cooperative triggering of LTD by Ca(2+). The duration of the rise in [Ca(2+)](i) influenced the apparent Ca(2+) affinity of LTD, and this time-dependent behavior could be described by a leaky integrator process with a time constant of 0.6 s. A computational model, based on a positive-feedback cycle that includes protein kinase C and MAP kinase, was capable of simulating these properties of Ca(2+)-triggered LTD. Disrupting this cycle experimentally also produced the predicted changes in the Ca(2+) dependence of LTD. We conclude that LTD arises from a mechanism that integrates postsynaptic Ca(2+) signals and that this integration may be produced by the positive-feedback cycle.

A propagating ERKII switch forms zones of elevated dendritic activation correlated with plasticity

Strong inputs to neurons trigger complex biochemical events leading to synaptic plasticity. These biochemical events occur at many spatial scales, ranging from submicron dendritic spines to signals that propagate hundreds of microns from dendrites to the nucleus. ERKII is an important signaling molecule that is involved in many aspects of plasticity, including local excitability, communication with the nucleus, and control of local protein synthesis. We observed that ERKII activation spreads long distances in apical dendrites of stimulated hippocampal CA1 pyramidal neurons. We combined experiments and models to show that this >100 mum spread was too large to be explained by biochemical reaction-diffusion effects. We show that two modes of calcium entry along the dendrite contribute to the extensive activation of ERKII. We predict the occurrence of feedback between biophysical events resulting in calcium entry, and biochemical events resulting in ERKII activation. This feedback causes a switch-like propagation of ERKII activation, coupled with enhanced electrical excitability, along the apical dendrite. We propose that this propagating switch forms zones on dendrites in which plasticity is facilitated.

A propagating ERKII switch forms zones of elevated dendritic activation correlated with plasticity

Strong inputs to neurons trigger complex biochemical events leading to synaptic plasticity. These biochemical events occur at many spatial scales, ranging from submicron dendritic spines to signals that propagate hundreds of microns from dendrites to the nucleus. ERKII is an important signaling molecule that is involved in many aspects of plasticity, including local excitability, communication with the nucleus, and control of local protein synthesis. We observed that ERKII activation spreads long distances in apical dendrites of stimulated hippocampal CA1 pyramidal neurons. We combined experiments and models to show that this >100 mum spread was too large to be explained by biochemical reaction-diffusion effects. We show that two modes of calcium entry along the dendrite contribute to the extensive activation of ERKII. We predict the occurrence of feedback between biophysical events resulting in calcium entry, and biochemical events resulting in ERKII activation. This feedback causes a switch-like propagation of ERKII activation, coupled with enhanced electrical excitability, along the apical dendrite. We propose that this propagating switch forms zones on dendrites in which plasticity is facilitated.

Persistent activation of protein kinase Calpha is not necessary for expression of cerebellar long-term depression

Protein kinase Calpha (PKCalpha) plays a major role in the induction of long-term depression (LTD) in a cerebellar Purkinje cell (PC). The sequential activation model for classical PKC states that PKCalpha translocates to the plasma membrane by binding Ca(++) and then becomes fully activated by binding diacylglycerol (DAG), which enables estimation of the activity by monitoring its localization. Here, we performed simultaneous electrophysiological recording and fluorescence imaging in a cultured PC expressing GFP-tagged PKCalpha. When a PC was depolarized, PKCalpha transiently translocated to the plasma membrane in a Ca(++)-dependent manner. Application of membrane permeable DAG or the blocker of DAG lipase prolonged the translocation. These results suggest that the sequential activation model is applicable to PCs. Conjunctive applications of glutamate and depolarization pulse induced LTD, but did not prolong the translocation. Thus, our results imply that persistent activation of PKCalpha is not necessary for the expression of LTD.