A model of bidirectional synaptic plasticity: from signaling network to channel conductance

Genetic mechanisms for impaired synaptic plasticity in schizophrenia revealed by computational modeling

Schizophrenia phenotypes are suggestive of impaired cortical plasticity in the disease, but the mechanisms of these deficits are unknown. Genomic association studies have implicated a large number of genes that regulate neuromodulation and plasticity, indicating that the plasticity deficits have a genetic origin. Here, we used biochemically detailed computational modeling of postsynaptic plasticity to investigate how schizophrenia-associated genes regulate long-term potentiation (LTP) and depression (LTD). We combined our model with data from postmortem RNA expression studies (CommonMind gene-expression datasets) to assess the consequences of altered expression of plasticity-regulating genes for the amplitude of LTP and LTD. Our results show that the expression alterations observed post mortem, especially those in the anterior cingulate cortex, lead to impaired protein kinase A (PKA)-pathway-mediated LTP in synapses containing GluR1 receptors. We validated these findings using a genotyped electroencephalogram (EEG) dataset where polygenic risk scores for synaptic and ion channel-encoding genes as well as modulation of visual evoked potentials were determined for 286 healthy controls. Our results provide a possible genetic mechanism for plasticity impairments in schizophrenia, which can lead to improved understanding and, ultimately, treatment of the disorder.

A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics

Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either (1) top-down and interpretable, but not flexible enough to account for experimental data, or (2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit to data. To avoid the shortcomings of these approaches, we present a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to predict plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model also predicts that in vivo-like spike timing irregularity strongly shapes plasticity outcome. This geometrical readout modelling approach can be readily applied to other excitatory or inhibitory synapses to discover their synaptic plasticity rules.

Computational modeling of AMPK and mTOR crosstalk in glutamatergic synapse calcium signaling

Neuronal energy consumption is vital for information processing and memory formation in synapses. The brain consists of just 2% of the human body's mass, but consumes almost 20% of the body's energy budget. Most of this energy is attributed to active transport in ion signaling, with calcium being the canonical second messenger of synaptic transmission. Here, we develop a computational model of synaptic signaling resulting in the activation of two protein kinases critical in metabolic regulation and cell fate, AMP-Activated protein kinase (AMPK) and mammalian target of rapamycin (mTOR) and investigate the effect of glutamate stimulus frequency on their dynamics. Our model predicts that frequencies of glutamate stimulus over 10 Hz perturb AMPK and mTOR oscillations at higher magnitudes by up to 36% and change the area under curve (AUC) by 5%. This dynamic difference in AMPK and mTOR activation trajectories potentially differentiates high frequency stimulus bursts from basal neuronal signaling leading to a downstream change in synaptic plasticity. Further, we also investigate the crosstalk between insulin receptor and calcium signaling on AMPK and mTOR activation and predict that the pathways demonstrate multistability dependent on strength of insulin signaling and metabolic consumption rate. Our predictions have implications for improving our understanding of neuronal metabolism, synaptic pruning, and synaptic plasticity.

Genetic mechanisms for impaired synaptic plasticity in schizophrenia revealed by computational modelling

Schizophrenia phenotypes are suggestive of impaired cortical plasticity in the disease, but the mechanisms of these deficits are unknown. Genomic association studies have implicated a large number of genes that regulate neuromodulation and plasticity, indicating that the plasticity deficits have a genetic origin. Here, we used biochemically detailed computational modelling of post-synaptic plasticity to investigate how schizophrenia-associated genes regulate long-term potentiation (LTP) and depression (LTD). We combined our model with data from post-mortem mRNA expression studies (CommonMind gene-expression datasets) to assess the consequences of altered expression of plasticity-regulating genes for the amplitude of LTP and LTD. Our results show that the expression alterations observed post mortem, especially those in anterior cingulate cortex, lead to impaired PKA-pathway-mediated LTP in synapses containing GluR1 receptors. We validated these findings using a genotyped EEG dataset where polygenic risk scores for synaptic and ion channel-encoding genes as well as modulation of visual evoked potentials (VEP) were determined for 286 healthy controls. Our results provide a possible genetic mechanism for plasticity impairments in schizophrenia, which can lead to improved understanding and, ultimately, treatment of the disorder.

Synaptic Plasticity Abnormalities in Fetal Alcohol Spectrum Disorders

The brain's ability to strengthen or weaken synaptic connections is often termed synaptic plasticity. It has been shown to function in brain remodeling following different types of brain damage (e.g., drugs of abuse, alcohol use disorders, neurodegenerative diseases, and inflammatory conditions). Although synaptic plasticity mechanisms have been extensively studied, how neural plasticity can influence neurobehavioral abnormalities in alcohol use disorders (AUDs) is far from being completely understood. Alcohol use during pregnancy and its harmful effects on the developing offspring are major public health, social, and economic challenges. The significant attribute of prenatal alcohol exposure on offspring is damage to the central nervous system (CNS), causing a range of synaptic structural, functional, and behavioral impairments, collectively called fetal alcohol spectrum disorder (FASD). Although the synaptic mechanisms in FASD are limited, emerging evidence suggests that FASD pathogenesis involves altering a set of molecules involved in neurotransmission, myelination, and neuroinflammation. These studies identify several immediate and long-lasting changes using many molecular approaches that are essential for synaptic plasticity and cognitive function. Therefore, they can offer potential synaptic targets for the many neurobehavioral abnormalities observed in FASD. In this review, we discuss the substantial research progress in different aspects of synaptic and molecular changes that can shed light on the mechanism of synaptic dysfunction in FASD. Increasing our understanding of the synaptic changes in FASD will significantly advance our knowledge and could provide a basis for finding novel therapeutic targets and innovative treatment strategies.

Combining hypothesis- and data-driven neuroscience modeling in FAIR workflows

Modeling in neuroscience occurs at the intersection of different points of view and approaches. Typically, hypothesis-driven modeling brings a question into focus so that a model is constructed to investigate a specific hypothesis about how the system works or why certain phenomena are observed. Data-driven modeling, on the other hand, follows a more unbiased approach, with model construction informed by the computationally intensive use of data. At the same time, researchers employ models at different biological scales and at different levels of abstraction. Combining these models while validating them against experimental data increases understanding of the multiscale brain. However, a lack of interoperability, transparency, and reusability of both models and the workflows used to construct them creates barriers for the integration of models representing different biological scales and built using different modeling philosophies. We argue that the same imperatives that drive resources and policy for data - such as the FAIR (Findable, Accessible, Interoperable, Reusable) principles - also support the integration of different modeling approaches. The FAIR principles require that data be shared in formats that are Findable, Accessible, Interoperable, and Reusable. Applying these principles to models and modeling workflows, as well as the data used to constrain and validate them, would allow researchers to find, reuse, question, validate, and extend published models, regardless of whether they are implemented phenomenologically or mechanistically, as a few equations or as a multiscale, hierarchical system. To illustrate these ideas, we use a classical synaptic plasticity model, the Bienenstock-Cooper-Munro rule, as an example due to its long history, different levels of abstraction, and implementation at many scales.

Dominant role of adult neurogenesis-induced structural heterogeneities in driving plasticity heterogeneity in dentate gyrus granule cells

Neurons and synapses manifest pronounced variability in the amount of plasticity induced by identical activity patterns. The mechanisms underlying such plasticity heterogeneity, which have been implicated in context‐specific resource allocation during encoding, have remained unexplored. Here, we employed a systematic physiologically constrained parametric search to identify the cellular mechanisms behind plasticity heterogeneity in dentate gyrus granule cells. We used heterogeneous model populations to ensure that our conclusions were not biased by parametric choices in a single hand‐tuned model. We found that each of intrinsic, synaptic, and structural heterogeneities independently yielded heterogeneities in synaptic plasticity profiles obtained with two different induction protocols. However, among the disparate forms of neural‐circuit heterogeneities, our analyses demonstrated the dominance of neurogenesis‐induced structural heterogeneities in driving plasticity heterogeneity in granule cells. We found that strong relationships between neuronal intrinsic excitability and plasticity emerged only when adult neurogenesis‐induced heterogeneities in neural structure were accounted for. Importantly, our analyses showed that it was not imperative that the manifestation of neural‐circuit heterogeneities must translate to heterogeneities in plasticity profiles. Specifically, despite the expression of heterogeneities in structural, synaptic, and intrinsic neuronal properties, similar plasticity profiles were attainable across all models through synergistic interactions among these heterogeneities. We assessed the parametric combinations required for the manifestation of such degeneracy in the expression of plasticity profiles. We found that immature cells showed physiological plasticity profiles despite receiving afferent inputs with weak synaptic strengths. Thus, the high intrinsic excitability of immature granule cells was sufficient to counterbalance their low excitatory drive in the expression of plasticity profile degeneracy. Together, our analyses demonstrate that disparate forms of neural‐circuit heterogeneities could mechanistically drive plasticity heterogeneity, but also caution against treating neural‐circuit heterogeneities as proxies for plasticity heterogeneity. Our study emphasizes the need for quantitatively characterizing the relationship between neural‐circuit and plasticity heterogeneities across brain regions.

Rapid eye movement sleep deprivation impairs neuronal plasticity and reduces hippocampal neuronal arborization in male albino rats: Noradrenaline is involved in the process

Rapid eye movement sleep (REMS) favors brain development and memory, while it is decreased in neurodegenerative diseases. REMS deprivation (REMSD) affects several physiological processes including memory consolidation; however, its detailed mechanism(s) of action was unknown. REMS reduces, while REMSD elevates noradrenaline (NA) level in the brain; the latter induces several deficiencies and disorders, including changes in neuronal cytomorphology and apoptosis. Therefore, we proposed that REMS- and REMSD-associated modulation of NA level might affect neuronal plasticity and affect brain functions. Male albino rats were REMS deprived by flower-pot method for 6 days, and its effects were compared with home cage and large platform controls as well as post-REMSD recovered and REMS-deprived prazosin (α1-adrenoceptor antagonist)-treated rats. We observed that REMSD reduced CA1 and CA3 neuronal dendritic length, branching, arborization, and spine density, while length of active zone and expressions of pre- as well as post-synaptic proteins were increased as compared to controls; interestingly, prazosin prevented most of the effects in vivo. Studies on primary culture of neurons from chick embryo brain confirmed that NA at lower concentration(s) induced neuronal branching and arborization, while higher doses were destructive. The findings support our contention that REMSD adversely affects neuronal plasticity, branching, and synaptic scaffold, which explain the underlying cytoarchitectural basis of REMSD-associated patho-physio-behavioral changes. Consolidation of findings of this study along with that of our previous reports suggest that the neuronal disintegration could be due to either withdrawal of direct protective and proliferative role of low dose of NA or indirect effect of high dose of NA or both.

Long-term depression-related tau phosphorylation is enhanced by methylene blue in healthy rat hippocampus

BACKGROUND

The present study examined whether inhibition of guanylate cyclase (GC) is associated with the plasticity-related microtubule-stabilizing protein tau phosphorylation in the dentate gyrus (DG) of hippocampal formation.

METHODS

To address this issue, methylene blue (MB 50 μM) or saline was infused into the DG starting from the induction of long-term potentiation (LTP) or depression (LTD) for 1 h. Then, protein phosphatase 1 alpha (PP1α), glycogen synthase kinase 3 beta (GSK3β), and tau total and phosphorylated protein levels were measured in these hippocampi using western blotting. LTP and LTD were induced by application of high- and low-frequency stimulation protocols (HFS and LFS), respectively. 5-min averages of the excitatory postsynaptic potential (EPSP) slopes and population spike amplitudes at the end of recording were averaged to measure the magnitude of LTP or LTD.

RESULTS

Low-frequency stimulation protocols was unable to phosphorylate thr¹⁸¹ and thr²³¹epitopes of tau, but possessed kinase activity similar to the HFS in phosphorylation of ser³⁹⁶ and ser⁴¹⁶ epitopes. MB infusion during LTD induction attenuated LTD, prevented EPSP/spike dissociation and increased tau phosphorylation at ser³⁹⁶ and ser⁴¹⁶ epitopes, without changing tau phosphorylation at thr¹⁸¹ and thr²³¹ epitopes. Neither LTP nor LTP-related tau phosphorylation state was changed by MB infusion.

CONCLUSION

Although MB can benefit to stabilize the balance between LTP and LTD, and to fix the increased spike wave discharges, it might trigger deregulation of tau phosphorylation, leading to the development of Alzheimer's disease by a mechanism that goes awry during induction of LTD. Thereby detailed studies to reveal more precise evidence for the use of MB in this disease are needed.

Energy Consumption and Entropy Production in a Stochastic Formulation of BCM Learning

In a series of previous studies, we provided a stochastic description of a theory of synaptic plasticity. This theory, called BCM from the names of the three authors, has been formulated in two ways: the original formulation, where the plasticity threshold is defined as the square of the time-averaged neuronal activity, and a newer formulation, where the plasticity threshold is defined as the time average of the square of the neuronal activity. The newest formulation of the BCM rule of synaptic activity has interesting statistical properties, derived from a risk (or energy) function, the minimization of which leads to seeking of interesting projections in high-dimensional space. Moreover, these two rules, if implemented by a chemical master equation approach, show another interesting difference: the original rule satisfies the detailed balance, whereas the other not. Based on this different behavior, we found a continuous parameterization between these two rules. This parameterization shows a minimum that corresponds to maximum negative eigenvalues of the Jacobian matrix. In addition, the newest rule, due to the fact that it is in a nonequilibrium steady state (NESS), shows a higher level of plasticity than the original rule. This higher level of plasticity has to be interpreted in the framework of open thermodynamical systems and we show that entropy production and energy consumption in the newest rule are both less than in the original BCM rule.

A unified computational model for cortical post-synaptic plasticity

Signalling pathways leading to post-synaptic plasticity have been examined in many types of experimental studies, but a unified picture on how multiple biochemical pathways collectively shape neocortical plasticity is missing. We built a biochemically detailed model of post-synaptic plasticity describing CaMKII, PKA, and PKC pathways and their contribution to synaptic potentiation or depression. We developed a statistical AMPA-receptor-tetramer model, which permits the estimation of the AMPA-receptor-mediated maximal synaptic conductance based on numbers of GluR1s and GluR2s predicted by the biochemical signalling model. We show that our model reproduces neuromodulator-gated spike-timing-dependent plasticity as observed in the visual cortex and can be fit to data from many cortical areas, uncovering the biochemical contributions of the pathways pinpointed by the underlying experimental studies. Our model explains the dependence of different forms of plasticity on the availability of different proteins and can be used for the study of mental disorder-associated impairments of cortical plasticity.

Multi-scale modeling of the circadian modulation of learning and memory

We propose a multi-scale model to explain the time-of-day effects on learning and memory. We specifically model the circadian variation of hippocampus (HC) dependent long-term potentiation (LTP), depression (LTD), and the fear conditioning paradigm in amygdala. The model we built has both Goodwin type circadian gene regulatory network (GRN) and the conductance model of Morris-Lecar (ML) type to explain the spontaneous firing patterns (SFR) in suprachiasmatic nucleus (SCN). In the conductance model, we also include N-Methyl-D-aspartic acid receptor (NMDAR) to study the circadian dependent changes in LTP/LTD in hippocampus and include both NMDAR and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR) dynamics to explain the circadian modulation of fear conditioning paradigm in memory acquisition, recall, and extinction as seen in amygdala. Our multi-scale model captures the essential dynamics seen in the experiments and strongly supports the circadian time-of-the-day effects on learning and memory.

Intracellular calcium stores mediate metaplasticity at hippocampal dendritic spines

Key points

Calcium (Ca²⁺) entry mediated by NMDA receptors is considered central to the induction of activity‐dependent synaptic plasticity in hippocampal area CA1; this description does not, however, take into account the potential contribution of endoplasmic reticulum (ER) Ca²⁺ stores.

The ER has a heterogeneous distribution in CA1 dendritic spines, and may introduce localized functional differences in Ca²⁺ signalling between synapses, as suggested by experiments on metabotropic receptor‐dependent long‐term depression.

A physiologically detailed computational model of Ca²⁺ dynamics at a CA3–CA1 excitatory synapse characterizes the contribution of spine ER via metabotropic signalling during plasticity induction protocols.

ER Ca²⁺ release via IP₃ receptors modulates NMDA receptor‐dependent plasticity in a graded manner, to selectively promote synaptic depression with relatively diminished effect on LTP induction; this may temper further strengthening at the stronger synapses which are preferentially associated with ER‐containing spines.

Acquisition of spine ER may thus represent a local, biophysically plausible ‘metaplastic switch’ at potentiated CA1 synapses, contributing to the plasticity–stability balance in neural circuits.

Abstract

Long‐term plasticity mediated by NMDA receptors supports input‐specific, Hebbian forms of learning at excitatory CA3–CA1 connections in the hippocampus. There exists an additional layer of stabilizing mechanisms that act globally as well as locally over multiple time scales to ensure that plasticity occurs in a constrained manner. Here, we investigated the role of calcium (Ca²⁺) stores associated with the endoplasmic reticulum (ER) in the local regulation of plasticity at individual CA1 synapses. Our study was spurred by (1) the curious observation that ER is sparsely distributed in dendritic spines, but over‐represented in larger spines that are likely to have undergone activity‐dependent strengthening, and (2) evidence suggesting that ER motility at synapses can be rapid, and accompany activity‐regulated spine remodelling. We constructed a physiologically realistic computational model of an ER‐bearing CA1 spine, and examined how IP₃‐sensitive Ca²⁺ stores affect spine Ca²⁺ dynamics during activity patterns mimicking the induction of long‐term potentiation and long‐term depression (LTD). Our results suggest that the presence of ER modulates NMDA receptor‐dependent plasticity in a graded manner that selectively enhances LTD induction. We propose that ER may locally tune Ca²⁺‐based plasticity, providing a braking mechanism to mitigate runaway strengthening at potentiated synapses. Our study provides a biophysically accurate description of postsynaptic Ca²⁺ regulation, and suggests that ER in the spine may promote the re‐use of hippocampal synapses with saturated strengths.

Calcium (Ca²⁺) entry mediated by NMDA receptors is considered central to the induction of activity‐dependent synaptic plasticity in hippocampal area CA1; this description does not, however, take into account the potential contribution of endoplasmic reticulum (ER) Ca²⁺ stores.

The ER has a heterogeneous distribution in CA1 dendritic spines, and may introduce localized functional differences in Ca²⁺ signalling between synapses, as suggested by experiments on metabotropic receptor‐dependent long‐term depression.

A physiologically detailed computational model of Ca²⁺ dynamics at a CA3–CA1 excitatory synapse characterizes the contribution of spine ER via metabotropic signalling during plasticity induction protocols.

ER Ca²⁺ release via IP₃ receptors modulates NMDA receptor‐dependent plasticity in a graded manner, to selectively promote synaptic depression with relatively diminished effect on LTP induction; this may temper further strengthening at the stronger synapses which are preferentially associated with ER‐containing spines.

Acquisition of spine ER may thus represent a local, biophysically plausible ‘metaplastic switch’ at potentiated CA1 synapses, contributing to the plasticity–stability balance in neural circuits.

Computer Modeling of Alzheimer's Disease-Simulations of Synaptic Plasticity and Memory in the CA3-CA1 Hippocampal Formation Microcircuit

This paper aims to present computer modeling of synaptic plasticity and memory in the CA3-CA1 hippocampal formation microcircuit. The computer simulations showed a comparison of a pathological model in which Alzheimer's disease (AD) was simulated by synaptic degradation in the hippocampus and control model (healthy) of CA3-CA1 networks with modification of weights for the memory. There were statistically higher spike values of both CA1 and CA3 pyramidal cells in the control model than in the pathological model (p = 0.0042 for CA1 and p = 0.0033 for CA3). A similar outcome was achieved for frequency (p = 0.0002 for CA1 and p = 0.0001 for CA3). The entropy of pyramidal cells of the healthy CA3 network seemed to be significantly higher than that of AD (p = 0.0304). We need to study a lot of physiological parameters and their combinations of the CA3-CA1 hippocampal formation microcircuit to understand AD. High statistically correlations were obtained between memory, spikes and synaptic deletion in both CA1 and CA3 cells.

Remembering to Forget: A Dual Role for Sleep Oscillations in Memory Consolidation and Forgetting

It has been known since the time of patient H. M. and Karl Lashley's equipotentiality studies that the hippocampus and cortex serve mnestic functions. Current memory models maintain that these two brain structures accomplish unique, but interactive, memory functions. Specifically, most modeling suggests that memories are rapidly acquired during waking experience by the hippocampus, before being later consolidated into the cortex for long-term storage. Sleep has been shown to be critical for the transfer and consolidation of memories in the cortex. Like memory consolidation, a role for sleep in adaptive forgetting has both historical precedent, as Francis Crick suggested in 1983 that sleep was for "reverse-learning," and recent empirical support. In this article I review the evidence indicating that the same brain activity involved in sleep replay associated memory consolidation is responsible for sleep-dependent forgetting. In reviewing the literature, it became clear that both a cellular mechanism for systems consolidation and an agreed upon general, as well as cellular, mechanism for sleep-dependent forgetting is seldom discussed or is lacking. I advocate here for a candidate cellular systems consolidation mechanism wherein changes in calcium kinetics and the activation of consolidative signaling cascades arise from the triple phase locking of non-rapid eye movement sleep (NREMS) slow oscillation, sleep spindle and sharp-wave ripple rhythms. I go on to speculatively consider several sleep stage specific forgetting mechanisms and conclude by discussing a notional function of NREM-rapid eye movement sleep (REMS) cycling. The discussed model argues that the cyclical organization of sleep functions to first lay down and edit and then stabilize and integrate engrams. All things considered, it is increasingly clear that hallmark sleep stage rhythms, including several NREMS oscillations and the REMS hippocampal theta rhythm, serve the dual function of enabling simultaneous memory consolidation and adaptive forgetting. Specifically, the same sleep rhythms that consolidate new memories, in the cortex and hippocampus, simultaneously organize the adaptive forgetting of older memories in these brain regions.

Calcineurin and Its Role in Synaptic Transmission

Calcineurin (CaN) is a serine/threonine phosphatase widely expressed in different cell types and structures including neurons and synapses. The most studied role of CaN is its involvement in the functioning of postsynaptic structures of central synapses. The role of CaN in the presynaptic structures of central and peripheral synapses is less understood, although it has generated a considerable interest and is a subject of a growing number of studies. The regulatory role of CaN in synaptic vesicle endocytosis in the synapse terminals is actively studied. In recent years, new targets of CaN have been identified and its role in the regulation of enzymes and neurotransmitter secretion in peripheral neuromuscular junctions has been revealed. CaN is the only phosphatase that requires calcium and calmodulin for activation. In this review, we present details of CaN molecular structure and give a detailed description of possible mechanisms of CaN activation involving calcium, enzymes, and endogenous and exogenous inhibitors. Known and newly discovered CaN targets at pre- and postsynaptic levels are described. CaN activity in synaptic structures is discussed in terms of functional involvement of this phosphatase in synaptic transmission and neurotransmitter release.

Assessing the Effects of Opioids on Pathological Memory by a Computational Model

Introduction:

Opioids hijack learning and memory formation mechanisms of brain and induce a pathological memory in the hippocampus. This effect is mainly mediated by modifications in glutamatergic system. Speaking more precisely, Opioids presence in a synapse inhibits blockage of N-Methyl-D-Aspartate Receptor (NMDAR) by Mg²⁺, enhances conductance of NMDAR and thus, induces false Long-Term Potentiation (LTP).

Methods:

Based on experimental observations of different researchers, we developed a mathematical model for a pyramidal neuron of the hippocampus to study this false LTP. The model contains a spine of the pyramidal neuron with NMDAR, α-Amino-3-hydroxy-5-Methyl-4-isoxazole Propionic Acid Receptors (AMPARs), and Voltage-Gated Calcium Channels (VGCCs). The model also describes Calmodulin-dependent protein Kinase II (CaMKII) and AMPAR phosphorylation processes which are assumed to be the indicators of LTP induction in the synapse.

Results:

Simulation results indicate that the effect of inhibition of blockage of NMDARs by Mg²⁺ on the false LTP is not as crucial as the effect of NMDAR’s conductance modification by opioids. We also observed that activation of VGCCs has a dominant role in inducing pathological LTP.

Conclusion:

Our results confirm that preventing this pathological LTP is possible by three different mechanisms: 1. By decreasing NMDAR’s conductance; and 2. By attenuating VGCC’s mediated current; and 3. By enhancing glutamate clearance rate from the synapse.

LTP or LTD? Modeling the Influence of Stress on Synaptic Plasticity

In cognitive memory, long-term potentiation (LTP) has been shown to occur when presynaptic and postsynaptic activities are highly correlated and glucocorticoid concentrations are in an optimal (i.e., low normal) range. In all other conditions, LTP is attenuated or even long-term depression (LTD) occurs. In this paper, we focus on NMDA receptor (NMDA-R)-dependent LTP and LTD, two processes involving various molecular mechanisms. To understand which of these mechanisms are indispensable for explaining the experimental evidence reported in the literature, we here propose a parsimonious model of NMDA-R-dependent synaptic plasticity. Central to this model are two processes. First, AMPA receptor-subunit trafficking; and second, glucocorticoid-dependent modifications of the brain-derived neurotrophic factor (BDNF)-receptor system. In 2008, we have published a core model, which contained the first process, while in the current paper we present an extended model, which also includes the second process. Using the extended model, we could show that stress attenuates LTP, while it enhances LTD. These simulation results are in agreement with experimental findings from other labs. In 2013, surprising experimental evidence showed that the GluA1 C-tail is unnecessary for LTP. When using our core model in its original form, our simulations already predicted that there would be no requirement for the GluA1 C-tail for LTP, allowing to eliminate a redundant mechanism from our model. In summary, we present a mathematical model that displays reduced complexity and is useful for explaining when and how LTP or LTD occurs at synapses during cognitive memory formation.

Computational modeling of opioid-induced synaptic plasticity in hippocampus

According to a broad range of research, opioids consumption can lead to pathological memory formation. Experimental observations suggested that hippocampal glutamatergic synapses play an indispensable role in forming such a pathological memory. It has been suggested that memory formation at the synaptic level is developed through LTP induction. Here, we attempt to computationally indicate how morphine induces pathological LTP at hippocampal CA3-CA1 synapses. Then, based on simulations, we will suggest how one can prevent this type of pathological LTP. To this purpose, a detailed computational model is presented, which consists of one pyramidal neuron and one interneuron both from CA3, one CA1 pyramidal neuron, and one astrocyte. Based on experimental findings morphine affects the hippocampal neurons in three primary ways: 1) disinhibitory mechanism of interneurons in CA3, 2) enhancement of NMDARs current by μ Opioid Receptor (μOR) activation and 3) by attenuation of astrocytic glutamate reuptake ability. By utilizing these effects, simulations were implemented. Our results indicate that morphine can induce LTP by all aforementioned possible mechanisms. Based on our simulation results, attenuation of pathologic LTP achieved mainly by stimulation of astrocytic glutamate transporters, down-regulation of the astrocytic metabotropic glutamate receptors (mGlurs) or by applying NMDAR’s antagonist. Based on our observations, we suggest that astrocyte has a dominant role in forming addiction-related memories. This finding may help researchers in exploring drug actions for preventing relapse.

Direct Current-Induced Calcium Trafficking in Different Neuronal Preparations

The influence of direct current (DC) stimulation on radioactive calcium trafficking in sciatic nerve in vivo and in vitro, spinal cord, and synaptosomes was investigated. The exposure to DC enhanced calcium redistribution in all of these preparations. The effect was dependent on the strength of the stimulation and extended beyond the phase of exposure to DC. The DC-induced increase in calcium sequestration by synaptosomes was significantly reduced by cobalt and rupture of synaptosomes by osmotic shock. Although both anodal and cathodal currents were effective, the experiments with two electrodes of different areas revealed that cathodal stimulation exerted stronger effect. The exposure to DC induced not only relocation but also redistribution of calcium within segments of the sciatic nerve. Enzymatic removal of sialic acid by preincubation of synaptosomes with neuroaminidase, or carrying out the experiments in sodium-free environment, amplified DC-induced calcium accumulation.

Early-life seizures alter synaptic calcium-permeable AMPA receptor function and plasticity

Calcium (Ca²⁺)-mediated⁴ signaling pathways are critical to synaptic plasticity. In adults, the NMDA glutamate receptor (NMDAR) represents a major route for activity-dependent synaptic Ca²⁺ entry. However, during neonatal development, when synaptic plasticity is particularly high, many AMPA glutamate receptors (AMPARs) are also permeable to Ca²⁺ (CP-AMPAR) due to low GluA2 subunit expression, providing an additional route for activity- and glutamate-dependent Ca²⁺ influx and subsequent signaling. Therefore, altered hippocampal Ca²⁺ signaling may represent an age-specific pathogenic mechanism. We thus aimed to assess Ca²⁺ responses 48h after hypoxia-induced neonatal seizures (HS) in postnatal day (P)10 rats, a post-seizure time point at which we previously reported LTP attenuation. We found that Ca²⁺ responses were higher in brain slices from post-HS rats than in controls and that this increase was CP-AMPAR-dependent. To determine whether synaptic CP-AMPAR expression was also altered post-HS, we assessed the expression of GluA2 at hippocampal synapses and the expression of long-term depression (LTD), which has been linked to the presence of synaptic GluA2. Here we report a decrease 48h after HS in synaptic GluA2 expression at synapses and LTD in hippocampal CA1. Given the potentially critical role of AMPAR trafficking in disease progression, we aimed to establish whether post-seizure in vivo AMPAR antagonist treatment prevented the enhanced Ca²⁺ responses, changes in GluA2 synaptic expression, and diminished LTD. We found that NBQX treatment prevents all three of these post-seizure consequences, further supporting a critical role for AMPARs as an age-specific therapeutic target.

Calcium dynamics predict direction of synaptic plasticity in striatal spiny projection neurons

The striatum is a major site of learning and memory formation for sensorimotor and cognitive association. One of the mechanisms used by the brain for memory storage is synaptic plasticity - the long-lasting, activity-dependent change in synaptic strength. All forms of synaptic plasticity require an elevation in intracellular calcium, and a common hypothesis is that the amplitude and duration of calcium transients can determine the direction of synaptic plasticity. The utility of this hypothesis in the striatum is unclear in part because dopamine is required for striatal plasticity and in part because of the diversity in stimulation protocols. To test whether calcium can predict plasticity direction, we developed a calcium-based plasticity rule using a spiny projection neuron model with sophisticated calcium dynamics including calcium diffusion, buffering and pump extrusion. We utilized three spike timing-dependent plasticity (STDP) induction protocols, in which postsynaptic potentials are paired with precisely timed action potentials and the timing of such pairing determines whether potentiation or depression will occur. Results show that despite the variation in calcium dynamics, a single, calcium-based plasticity rule, which explicitly considers duration of calcium elevations, can explain the direction of synaptic weight change for all three STDP protocols. Additional simulations show that the plasticity rule correctly predicts the NMDA receptor dependence of long-term potentiation and the L-type channel dependence of long-term depression. By utilizing realistic calcium dynamics, the model reveals mechanisms controlling synaptic plasticity direction, and shows that the dynamics of calcium, not just calcium amplitude, are crucial for synaptic plasticity.

Systems biology of synaptic plasticity: a review on N-methyl-D-aspartate receptor mediated biochemical pathways and related mathematical models

Synaptic plasticity, an emergent property of synaptic networks, has shown strong correlation to one of the essential functions of the brain, memory formation. Through understanding synaptic plasticity, we hope to discover the modulators and mechanisms that trigger memory formation. In this paper, we first review the well understood modulators and mechanisms underlying N-methyl-D-aspartate receptor dependent synaptic plasticity, a major form of synaptic plasticity in hippocampus, and then comment on the key mathematical modelling approaches available in the literature to understand synaptic plasticity as the integration of the established functionalities of synaptic components.

Modeling intracellular signaling underlying striatal function in health and disease

Striatum, which is the input nucleus of the basal ganglia, integrates cortical and thalamic glutamatergic inputs with dopaminergic afferents from the substantia nigra pars compacta. The combination of dopamine and glutamate strongly modulates molecular and cellular properties of striatal neurons and the strength of corticostriatal synapses. These actions are performed via intracellular signaling networks, containing several intertwined feedback loops. Understanding the role of dopamine and other neuromodulators requires the development of quantitative dynamical models for describing the intracellular signaling, in order to provide precise unambiguous descriptions and quantitative predictions. Building such models requires integration of data from multiple data sources containing information regarding the molecular interactions, the strength of these interactions, and the subcellular localization of the molecules. Due to the uncertainty, variability, and sparseness of these data, parameter estimation techniques are critical for inferring or constraining the unknown parameters, and sensitivity analysis evaluates which parameters are most critical for a given observed macroscopic behavior. Here, we briefly review the modeling approaches and tools that have been used to investigate biochemical signaling in the striatum, along with some of the models built around striatum. We also suggest a future direction for the development of such models from the, now becoming abundant, high-throughput data.

Molecular mechanisms underlying neuronal synaptic plasticity: systems biology meets computational neuroscience in the wilds of synaptic plasticity

Interactions among signaling pathways that are activated by transmembrane receptors produce complex networks and emergent dynamical behaviors that are implicated in synaptic plasticity. Temporal dynamics and spatial aspects are critical determinants of cell responses such as synaptic plasticity, although the mapping between spatiotemporal activity pattern and direction of synaptic plasticity is not completely understood. Computational modeling of neuronal signaling pathways has significantly contributed to understanding signaling pathways underlying synaptic plasticity. Spatial models of signaling pathways in hippocampal neurons have revealed mechanisms underlying the spatial distribution of extracellular signal-related kinase (ERK) activation in hippocampal neurons. Other spatial models have demonstrated that the major role of anchoring proteins in striatal and hippocampal synaptic plasticity is to place molecules near their activators. Simulations of yet other models have revealed that the spatial distribution of synaptic plasticity may differ for potentiation versus depression. In general, the most significant advances have been made by interactive modeling and experiments; thus, an interdisciplinary approach should be applied to investigate critical issues in neuronal signaling pathways. These issues include identifying which transmembrane receptors are key for activating ERK in neurons, and the crucial targets of kinases that produce long-lasting synaptic plasticity. Although the number of computer programs for computationally efficient simulation of large reaction-diffusion networks is increasing, parameter estimation and sensitivity analysis in these spatial models remain more difficult than in single compartment models. Advances in live cell imaging coupled with further software development will continue to accelerate the development of spatial models of synaptic plasticity.

Signaling pathways involved in striatal synaptic plasticity are sensitive to temporal pattern and exhibit spatial specificity

The basal ganglia is a brain region critically involved in reinforcement learning and motor control. Synaptic plasticity in the striatum of the basal ganglia is a cellular mechanism implicated in learning and neuronal information processing. Therefore, understanding how different spatio-temporal patterns of synaptic input select for different types of plasticity is key to understanding learning mechanisms. In striatal medium spiny projection neurons (MSPN), both long term potentiation (LTP) and long term depression (LTD) require an elevation in intracellular calcium concentration; however, it is unknown how the post-synaptic neuron discriminates between different patterns of calcium influx. Using computer modeling, we investigate the hypothesis that temporal pattern of stimulation can select for either endocannabinoid production (for LTD) or protein kinase C (PKC) activation (for LTP) in striatal MSPNs. We implement a stochastic model of the post-synaptic signaling pathways in a dendrite with one or more diffusionally coupled spines. The model is validated by comparison to experiments measuring endocannabinoid-dependent depolarization induced suppression of inhibition. Using the validated model, simulations demonstrate that theta burst stimulation, which produces LTP, increases the activation of PKC as compared to 20 Hz stimulation, which produces LTD. The model prediction that PKC activation is required for theta burst LTP is confirmed experimentally. Using the ratio of PKC to endocannabinoid production as an index of plasticity direction, model simulations demonstrate that LTP exhibits spine level spatial specificity, whereas LTD is more diffuse. These results suggest that spatio-temporal control of striatal information processing employs these Gq coupled pathways.

Role of sensory input distribution and intrinsic connectivity in lateral amygdala during auditory fear conditioning: a computational study

We propose a novel reduced-order neuronal network modeling framework that includes an enhanced firing rate model and a corresponding synaptic calcium-based synaptic learning rule. Specifically, we propose enhancements to the Wilson-Cowan firing-rate neuron model that permit full spike-frequency adaptation seen in biological lateral amygdala (LA) neurons, while being sufficiently general to accommodate other spike-frequency patterns. We also report a technique to incorporate calcium-dependent plasticity in the synapses of the network using a regression scheme to link firing rate to postsynaptic calcium. Together, the single-cell model and the synaptic learning scheme constitute a general framework to develop computationally efficient neuronal networks that employ biologically realistic synaptic learning. The reduced-order modeling framework was validated using a previously reported biophysical conductance-based neuronal network model of a rodent LA that modeled features of Pavlovian conditioning and extinction of auditory fear (Li et al., 2009). The framework was then used to develop a larger LA network model to investigate the roles of tone and shock distributions and of intrinsic connectivity in auditory fear learning. The model suggested combinations of tone and shock densities that would provide experimental estimates of tone responsive and conditioned cell proportions. Furthermore, it provided several insights including how intrinsic connectivity might help distribute sensory inputs to produce conditioned responses in cells that do not directly receive both tone and shock inputs, and how a balance between potentiation of excitation and inhibition prevents stimulus generalization during fear learning.

Learning Invariance from Natural Images Inspired by Observations in the Primary Visual Cortex

The human visual system has the remarkable ability to largely recognize objects invariant of their position, rotation, and scale. A good interpretation of neurobiological findings involves a computational model that simulates signal processing of the visual cortex. In part, this is likely achieved step by step from early to late areas of visual perception. While several algorithms have been proposed for learning feature detectors, only few studies at hand cover the issue of biologically plausible learning of such invariance. In this study, a set of Hebbian learning rules based on calcium dynamics and homeostatic regulations of single neurons is proposed. Their performance is verified within a simple model of the primary visual cortex to learn so-called complex cells, based on a sequence of static images. As a result, the learned complex-cell responses are largely invariant to phase and position.

Postsynaptic signal transduction models for long-term potentiation and depression

More than a hundred biochemical species, activated by neurotransmitters binding to transmembrane receptors, are important in long-term potentiation (LTP) and long-term depression (LTD). To investigate which species and interactions are critical for synaptic plasticity, many computational postsynaptic signal transduction models have been developed. The models range from simple models with a single reversible reaction to detailed models with several hundred kinetic reactions. In this study, more than a hundred models are reviewed, and their features are compared and contrasted so that similarities and differences are more readily apparent. The models are classified according to the type of synaptic plasticity that is modeled (LTP or LTD) and whether they include diffusion or electrophysiological phenomena. Other characteristics that discriminate the models include the phase of synaptic plasticity modeled (induction, expression, or maintenance) and the simulation method used (deterministic or stochastic). We find that models are becoming increasingly sophisticated, by including stochastic properties, integrating with electrophysiological properties of entire neurons, or incorporating diffusion of signaling molecules. Simpler models continue to be developed because they are computationally efficient and allow theoretical analysis. The more complex models permit investigation of mechanisms underlying specific properties and experimental verification of model predictions. Nonetheless, it is difficult to fully comprehend the evolution of these models because (1) several models are not described in detail in the publications, (2) only a few models are provided in existing model databases, and (3) comparison to previous models is lacking. We conclude that the value of these models for understanding molecular mechanisms of synaptic plasticity is increasing and will be enhanced further with more complete descriptions and sharing of the published models.

Interplay of the magnitude and time-course of postsynaptic Ca2+ concentration in producing spike timing-dependent plasticity

Synaptic strength can be modified by the relative timing of pre- and postsynaptic activity, a phenomenon termed spike timing-dependent plasticity (STDP). Studies of neurons in the hippocampus and in other regions have found that when presynaptic activity occurs within a narrow time window, typically 10 or 20 ms, before postsynaptic activity, long-term potentiation (LTP) is induced, while if presynaptic activity occurs within a similar time window after postsynaptic activity, long-term depression (LTD) results. The mechanisms underlying these modifications are not completely understood, although there is strong evidence that the postsynaptic Ca (2+) concentration plays a central role. Some previous modeling of STDP has focused on the dynamics of the postsynaptic Ca (2+) concentration, while other work has studied biophysical mechanisms of how a synapse can exist in, and switch between, different states corresponding to LTP and LTD. Building on previous work in these two areas we have developed the first low level STDP model of a tristable biochemical system that incorporates induction and maintenance of both LTP and LTD. Our model is able to explain the STDP observed in hippocampal neurons in response to pre- and postsynaptic pulse pairs, using only parameters derived from previous work and without the need for parameter fine-tuning. Our results also give insight into how and why the time course of the postsynaptic Ca (2+) concentration can lead to either LTP or LTD, and suggest that voltage dependent calcium channels play a key role.

Burst-induced anti-Hebbian depression acts through short-term synaptic dynamics to cancel redundant sensory signals

Weakly electric fish can enhance the detection and localization of important signals such as those of prey in part by cancellation of redundant spatially diffuse electric signals due to, e.g., their tail bending. The cancellation mechanism is based on descending input, conveyed by parallel fibers emanating from cerebellar granule cells, that produces a negative image of the global low-frequency signals in pyramidal cells within the first-order electrosensory region, the electrosensory lateral line lobe (ELL). Here we demonstrate that the parallel fiber synaptic input to ELL pyramidal cell undergoes long-term depression (LTD) whenever both parallel fiber afferents and their target cells are stimulated to produce paired burst discharges. Paired large bursts (4-4) induce robust LTD over pre-post delays of up to +/-50 ms, whereas smaller bursts (2-2) induce weaker LTD. Single spikes (either presynaptic or postsynaptic) paired with bursts did not induce LTD. Tetanic presynaptic stimulation was also ineffective in inducing LTD. Thus, we have demonstrated a form of anti-Hebbian LTD that depends on the temporal correlation of burst discharge. We then demonstrated that the burst-induced LTD is postsynaptic and requires the NR2B subunit of the NMDA receptor, elevation of postsynaptic Ca(2+), and activation of CaMKIIbeta. A model incorporating local inhibitory circuitry and previously identified short-term presynaptic potentiation of the parallel fiber synapses further suggests that the combination of burst-induced LTD, presynaptic potentiation, and local inhibition may be sufficient to explain the generation of the negative image and cancellation of redundant sensory input by ELL pyramidal cells.

Temporal sensitivity of protein kinase a activation in late-phase long term potentiation

Protein kinases play critical roles in learning and memory and in long term potentiation (LTP), a form of synaptic plasticity. The induction of late-phase LTP (L-LTP) in the CA1 region of the hippocampus requires several kinases, including CaMKII and PKA, which are activated by calcium-dependent signaling processes and other intracellular signaling pathways. The requirement for PKA is limited to L-LTP induced using spaced stimuli, but not massed stimuli. To investigate this temporal sensitivity of PKA, a computational biochemical model of L-LTP induction in CA1 pyramidal neurons was developed. The model describes the interactions of calcium and cAMP signaling pathways and is based on published biochemical measurements of two key synaptic signaling molecules, PKA and CaMKII. The model is stimulated using four 100 Hz tetani separated by 3 sec (massed) or 300 sec (spaced), identical to experimental L-LTP induction protocols. Simulations show that spaced stimulation activates more PKA than massed stimulation, and makes a key experimental prediction, that L-LTP is PKA-dependent for intervals larger than 60 sec. Experimental measurements of L-LTP demonstrate that intervals of 80 sec, but not 40 sec, produce PKA-dependent L-LTP, thereby confirming the model prediction. Examination of CaMKII reveals that its temporal sensitivity is opposite that of PKA, suggesting that PKA is required after spaced stimulation to compensate for a decrease in CaMKII. In addition to explaining the temporal sensitivity of PKA, these simulations suggest that the use of several kinases for memory storage allows each to respond optimally to different temporal patterns.

The hippocampus is a part of the cerebral cortex intimately involved in learning and memory behavior. A common cellular model of learning is a long lasting form of long term potentiation (L-LTP) in the hippocampus, because it shares several characteristics with learning. For example, both learning and long term potentiation exhibit sensitivity to temporal patterns of synaptic inputs and share common intracellular events such as activation of specific intracellular signaling pathways. Therefore, understanding the pivotal molecules in the intracellular signaling pathways underlying temporal sensitivity of L-LTP in the hippocampus may illuminate mechanisms underlying learning. We developed a computational model to evaluate whether the signaling pathways leading to activation of the two critical enzymes: protein kinase A and calcium-calmodulin-dependent kinase II are sufficient to explain the experimentally observed temporal sensitivity. Indeed, the simulations demonstrate that these enzymes exhibit different temporal sensitivities, and make a key experimental prediction, that L-LTP is dependent on protein kinase A for intervals larger than 60 sec. Measurements of hippocampal L-LTP confirm this prediction, demonstrating the value of a systems biology approach to computational neuroscience.

A kinetic model of dopamine- and calcium-dependent striatal synaptic plasticity

Corticostriatal synapse plasticity of medium spiny neurons is regulated by glutamate input from the cortex and dopamine input from the substantia nigra. While cortical stimulation alone results in long-term depression (LTD), the combination with dopamine switches LTD to long-term potentiation (LTP), which is known as dopamine-dependent plasticity. LTP is also induced by cortical stimulation in magnesium-free solution, which leads to massive calcium influx through NMDA-type receptors and is regarded as calcium-dependent plasticity. Signaling cascades in the corticostriatal spines are currently under investigation. However, because of the existence of multiple excitatory and inhibitory pathways with loops, the mechanisms regulating the two types of plasticity remain poorly understood. A signaling pathway model of spines that express D1-type dopamine receptors was constructed to analyze the dynamic mechanisms of dopamine- and calcium-dependent plasticity. The model incorporated all major signaling molecules, including dopamine- and cyclic AMP-regulated phosphoprotein with a molecular weight of 32 kDa (DARPP32), as well as AMPA receptor trafficking in the post-synaptic membrane. Simulations with dopamine and calcium inputs reproduced dopamine- and calcium-dependent plasticity. Further in silico experiments revealed that the positive feedback loop consisted of protein kinase A (PKA), protein phosphatase 2A (PP2A), and the phosphorylation site at threonine 75 of DARPP-32 (Thr75) served as the major switch for inducing LTD and LTP. Calcium input modulated this loop through the PP2B (phosphatase 2B)-CK1 (casein kinase 1)-Cdk5 (cyclin-dependent kinase 5)-Thr75 pathway and PP2A, whereas calcium and dopamine input activated the loop via PKA activation by cyclic AMP (cAMP). The positive feedback loop displayed robust bi-stable responses following changes in the reaction parameters. Increased basal dopamine levels disrupted this dopamine-dependent plasticity. The present model elucidated the mechanisms involved in bidirectional regulation of corticostriatal synapses and will allow for further exploration into causes and therapies for dysfunctions such as drug addiction.

Recent brain imaging and neurophysiological studies suggest that the striatum, the start of the basal ganglia circuit, plays a major role in value-based decision making and behavioral disorders such as drug addiction. The plasticity of synaptic input from the cerebral cortex to output neurons of the striatum, which are medium spiny neurons, depends on interactions between glutamate input from the cortex and dopaminergic input from the midbrain. It also links sensory and cognitive states in the cortex with reward-oriented action outputs. The mechanisms involved in molecular cascades that transmit glutamate and dopamine inputs to changes in postsynaptic glutamate receptors are very complex and it is difficult to intuitively understand the mechanism. Therefore, a biochemical network model was constructed, and computer simulations were performed. The model reproduced dopamine-dependent and calcium-dependent forms of long-term depression (LTD) and potentiation (LTP) of corticostriatal synapses. Further in silico experiments revealed that a positive feedback loop formed by proteins, the protein specifically expressed in the striatum, served as the major switch for inducing LTD and LTP. This model could allow us to understand dynamic constraints in reward-dependent learning, as well as causes and therapies of dopamine-related disorders such as drug addiction.

Positive and negative symptoms in schizophrenia: the NMDA receptor hypofunction hypothesis, neuregulin/ErbB4 and synapse regression

Carlsson has put forward the hypothesis that the positive and negative symptoms of schizophrenia are due to failure of mesolimbic and mesocortical projections consequent on hypofunction of the glutamate N-methyl-d-aspartate (NMDA) receptor. The hypothesis has been recently emphasized in this Journal that the loss of synaptic spines with NMDA receptors, which can be precipitated by stress, can explain the emergence of positive symptoms such as hallucinations and that this synapse regression involves molecules such as neuregulin and its receptor ErbB4 that have been implicated in schizophrenia. In this essay these two hypotheses are brought together in a single scheme in which emphasis is placed on the molecular pathways from neuregulin/ErbB4, to modulation of the NMDA receptors, subsequent changes in the synaptic spine's cytoskeletal apparatus and so regression of the spines. It is suggested that identification of the molecular constituents of this pathway will allow synthesis of suitable substances for removing the hypofunction of NMDA receptors and so the phenotypic consequences that flow from this hypofunction.

Toward a microscopic model of bidirectional synaptic plasticity

We show that a 2-step phospho/dephosphorylation cycle for the alpha-amino-3-hydroxy-5-methyl-4-isoxazole proprionic acid receptor (AMPAR), as used in in vivo learning experiments to assess long-term potentiation (LTP) induction and establishment, exhibits bistability for a wide range of parameters, consistent with values derived from biological literature. The AMPAR model we propose, hence, is a candidate for memory storage and switching behavior at a molecular-microscopic level. Furthermore, the stochastic formulation of the deterministic model leads to a mesoscopic interpretation by considering the effect of enzymatic fluctuations on the Michelis-Menten average dynamics. Under suitable hypotheses, this leads to a stochastic dynamical system with multiplicative noise whose probability density evolves according to a Fokker-Planck equation in the Stratonovich sense. In this approach, the probability density associated with each AMPAR phosphorylation state allows one to compute the probability of any concentration value, whereas the Michaelis-Menten equations consider the average concentration dynamics. We show that bistable dynamics are robust for multiplicative stochastic perturbations and that the presence of both noise and bistability simulates LTP and long-term depression (LTD) behavior. Interestingly, the LTP part of this model has been experimentally verified as a result of in vivo, one-trial inhibitory avoidance learning protocol in rats, that produced the same changes in hippocampal AMPARs phosphorylation state as observed with in vitro induction of LTP with high-frequency stimulation (HFS). A consequence of this model is the possibility of characterizing a molecular switch with a defined biochemical set of reactions showing bistability and bidirectionality. Thus, this 3-enzymes-based biophysical model can predict LTP as well as LTD and their transition rates. The theoretical results can be, in principle, validated by in vitro and in vivo experiments, such as fluorescence measurements and electrophysiological recordings at multiple scales, from molecules to neurons. A further consequence is that the bistable regime occurs only within certain parametric windows, which may simulate a "history-dependent threshold". This effect might be related to the Bienenstock-Cooper-Munro theory of synaptic plasticity.

Translational switch for long-term maintenance of synaptic plasticity

Memory can last a lifetime, yet synaptic contacts that contribute to the storage of memory are composed of proteins that have much shorter lifetimes. A physiological model of memory formation, long-term potentiation (LTP), has a late protein-synthesis-dependent phase (L-LTP) that can last for many hours in slices or even for days in vivo. Could the activity-dependent synthesis of new proteins account for the persistence of L-LTP and memory? Here, we examine the proposal that a self-sustaining regulation of translation can form a bistable switch that can persistently regulate the on-site synthesis of plasticity-related proteins. We show that an alpha CaMKII-CPEB1 molecular pair can operate as a bistable switch. Our results imply that L-LTP should produce an increase in the total amount of alpha CaMKII at potentiated synapses. This study also proposes an explanation for why the application of protein synthesis and alphaCaMKII inhibitors at the induction and maintenance phases of L-LTP result in very different outcomes.

Coupled phosphatase and kinase switches produce the tristability required for long-term potentiation and long-term depression

Studies of long-term potentiation (LTP) and long-term depression (LTD) strongly suggest that individual synapses can be bidirectionally modified. A central question is the biochemical mechanisms that make LTP and LTD persistent. Previous theoretical models have proposed that the autophosphorylation properties of CaMKII could underlie a bistable molecular switch that maintains LTP, and there is experimental support for this mechanism. In contrast, there has been comparatively little theoretical or experimental work regarding the mechanisms that maintain LTD. Several lines of evidence indicate that LTD is not simply a reversal of previous LTP but rather involves separate biochemical reactions. These findings indicate that a minimal model of the synapse must involve a tristable system. Here, we describe a phosphatase (PP2A) switch, which together with a kinase switch form a tristable system. PP2A can be activated by a Ca(2+)-dependent process but can also be phosphorylated and inactivated by CaMKII. When dephosphorylated, PP2A can dephosphorylate itself. We show that these properties can lead to a persistent increase in PP2A during LTD (as reported experimentally), thus forming a phosphatase switch. We show that the coupled PP2A and CaMKII switches lead to a tristable system in which the kinase activity is high in the LTP state; the PP2A activity is high in the LTD state, and neither activity is high in the basal state. Our results provide an explanation for the recent finding that inhibition of PP2A prevents LTD induction.

STDP in a bistable synapse model based on CaMKII and associated signaling pathways

The calcium/calmodulin-dependent protein kinase II (CaMKII) plays a key role in the induction of long-term postsynaptic modifications following calcium entry. Experiments suggest that these long-term synaptic changes are all-or-none switch-like events between discrete states. The biochemical network involving CaMKII and its regulating protein signaling cascade has been hypothesized to durably maintain the evoked synaptic state in the form of a bistable switch. However, it is still unclear whether experimental LTP/LTD protocols lead to corresponding transitions between the two states in realistic models of such a network. We present a detailed biochemical model of the CaMKII autophosphorylation and the protein signaling cascade governing the CaMKII dephosphorylation. As previously shown, two stable states of the CaMKII phosphorylation level exist at resting intracellular calcium concentration, and high calcium transients can switch the system from the weakly phosphorylated (DOWN) to the highly phosphorylated (UP) state of the CaMKII (similar to a LTP event). We show here that increased CaMKII dephosphorylation activity at intermediate Ca(2+) concentrations can lead to switching from the UP to the DOWN state (similar to a LTD event). This can be achieved if protein phosphatase activity promoting CaMKII dephosphorylation activates at lower Ca(2+) levels than kinase activity. Finally, it is shown that the CaMKII system can qualitatively reproduce results of plasticity outcomes in response to spike-timing dependent plasticity (STDP) and presynaptic stimulation protocols. This shows that the CaMKII protein network can account for both induction, through LTP/LTD-like transitions, and storage, due to its bistability, of synaptic changes.

A new principle for information storage in an enzymatic pathway model

Strong experimental evidence indicates that protein kinase and phosphatase (KP) cycles are critical to both the induction and maintenance of activity-dependent modifications in neurons. However, their contribution to information storage remains controversial, despite impressive modeling efforts. For instance, plasticity models based on KP cycles do not account for the maintenance of plastic modifications. Moreover, bistable KP cycle models that display memory fail to capture essential features of information storage: rapid onset, bidirectional control, graded amplitude, and finite lifetimes. Here, we show in a biophysical model that upstream activation of KP cycles, a ubiquitous mechanism, is sufficient to provide information storage with realistic induction and maintenance properties: plastic modifications are rapid, bidirectional, and graded, with finite lifetimes that are compatible with animal and human memory. The maintenance of plastic modifications relies on negligible reaction rates in basal conditions and thus depends on enzyme nonlinearity and activation properties of the activity-dependent KP cycle. Moreover, we show that information coding and memory maintenance are robust to stochastic fluctuations inherent to the molecular nature of activity-dependent KP cycle operation. This model provides a new principle for information storage where plasticity and memory emerge from a single dynamic process whose rate is controlled by neuronal activity. This principle strongly departs from the long-standing view that memory reflects stable steady states in biological systems, and offers a new perspective on memory in animals and humans.

Qualitative and Quantitative Analyses of Protein Phosphorylation in Naive and Stimulated Mouse Synaptosomal Preparations

Activity-dependent protein phosphorylation is a highly dynamic yet tightly regulated process essential for cellular signaling. Although recognized as critical for neuronal functions, the extent and stoichiometry of phosphorylation in brain cells remain undetermined. In this study, we resolved activity-dependent changes in phosphorylation stoichiometry at specific sites in distinct subcellular compartments of brain cells. Following highly sensitive phosphopeptide enrichment using immobilized metal affinity chromatography and mass spectrometry, we isolated and identified 974 unique phosphorylation sites on 499 proteins, many of which are novel. To further explore the significance of specific phosphorylation sites, we used isobaric peptide labels and determined the absolute quantity of both phosphorylated and non-phosphorylated peptides of candidate phosphoproteins and estimated phosphorylation stoichiometry. The analyses of phosphorylation dynamics using differentially stimulated synaptic terminal preparations revealed activity-dependent changes in phosphorylation stoichiometry of target proteins. Using this method, we were able to differentiate between distinct isoforms of Ca2+/calmodulin-dependent protein kinase (CaMKII) and identify a novel activity-regulated phosphorylation site on the glutamate receptor subunit GluR1. Together these data illustrate that mass spectrometry-based methods can be used to determine activity-dependent changes in phosphorylation stoichiometry on candidate phosphopeptides following large scale phosphoproteome analysis of brain tissue.

Synaptic Democracy in Active Dendrites

Given the extensive attenuation that can occur along dendritic cables, location within the dendritic tree might appear to be a dominant factor in determining the impact of a synapse on the postsynaptic response. By this reasoning, distal synapses should have a smaller effect than proximal ones. However, experimental evidence from several types of neurons, such as CA1 pyramidal cells, indicates that a compensatory strengthening of synapses counteracts the effect of location on synaptic efficacy. A form of spike-timing-dependent plasticity (STDP), called anti-STDP, combined with non-Hebbian activity-dependent plasticity can account for the equalization of synaptic efficacies. This result, obtained originally in models with unbranched passive cables, also arises in multi-compartment models with branched and active dendrites that feature backpropagating action potentials, including models with CA1 pyramidal morphologies. Additionally, when dendrites support the local generation of action potentials, anti-STDP prevents runaway dendritic spiking and locally balances the numbers of dendritic and backpropagating action potentials. Thus in multiple ways, anti-STDP eliminates the location dependence of synapses and allows Hebbian plasticity to operate in a more “democratic” manner.

Age-related enhancement of a protein synthesis-dependent late phase of LTP induced by low frequency paired-pulse stimulation in hippocampus

Protein synthesis-dependent late phase of LTP (L-LTP) is typically induced by repeated high-frequency stimulation (HFS). This form of L-LTP is reduced in the aged animal and is positively correlated with age-related memory loss. Here we report a novel form of protein synthesis-dependent late phase of LTP in the CA1 region of hippocampus induced by a brief 1-Hz paired-pulse stimulation (PP-1 Hz, 1 min). In contrast to L-LTP induced by HFS, the late phase of PP-1 Hz LTP does not exist in young adult animals. Rather, it emerges and becomes enhanced in an age-related way. Thus, in 1.5- to 2-mo-old mice, a brief PP-1 Hz stimulation induces only a short lasting LTP, decaying to baseline in about 90 min. By contrast, PP-1 Hz stimulation induces an enduring and protein synthesis dependent LTP in 12- to 18-mo-old mice. The PP-1 Hz-induced L-LTP is dependent on NMDA receptor activation, requires voltage-dependent calcium channels, and is modulated by dopamine D1/D5 receptors. Because memory ability declines with aging, the age-related enhancement of L-LTP induced by PP-1 Hz stimulation indicates that this form of L-LTP appears to be inversely correlated with memory ability.

The 5-HT- and FMRFa-activated signaling pathways interact at the level of the Erk MAPK cascade: potential inhibitory constraints on memory formation

The sensorimotor synapse of Aplysia exhibits long-term facilitation (LTF) and long-term depression (LTD) elicited by the neuromodulator serotonin (5-HT) and the peptide Phe-Met-Arg-Phe-NH(2), respectively. 5-HT-induced LTF engages extracellular-regulated kinase (Erk) and CREB1, whereas FMRFa-induced LTD engages p38 MAPK (mitogen-activated protein kinase) and CREB2. The interaction of the 5-HT and FMRFa pathways was recently investigated in Aplysia at the level of gene expression. However, little is known about crosstalk of these pathways at the level of the second messenger cascades. We investigated the potential interaction of the 5-HT and FMRFa pathways at the level of the Erk cascade. We found that FMRFa inhibited basal Erk activity through p38 MAPK. FMRFa also inhibited 5-HT-induced phosphorylation of Erk and nuclear accumulation of phospho-ERK, suggesting that FMRFa may place inhibitory constraints on memory formation through regulation of the Erk MAPK cascade.