Biophysical model of AMPA receptor trafficking and its regulation during long-term potentiation/long-term depression

miR-351-5p regulation of CPEB3 affecting aluminium-induced learning and memory impairment in SD rats

Aluminium exposure has been found to impair learning and memory abilities; however, the underlying molecular mechanisms remain unclear. In this study we conducted a double luciferase reporter assay to determine whether miR-351-5p regulates cytoplasmic polyadenylation element binding protein (CPEB) 3 mRNA. To this end, we overexpressed and inhibited miR-351-5p via stereotaxic microinjections of adeno-associated virus (AAV) into the hippocampus of Sprague Dawley rats in a sub-chronic aluminium exposure model to examine learning and memory ability using Morris water maze. Ultrastructural electron microscopy and Golgi staining were used to examine morphological changes in hippocampal neurons. In addition, we examined the levels of synaptic plasticity-related proteins (PRPs) and CPEB3 to determine the involvement of the miR-351-5P/CPEB3/PRPs pathway in aluminium neurotoxicity. Sub-chronic aluminium exposure reduced the spatial learning and memory ability of rats. Overexpression of AAV-miR-351-5P in the hippocampus aggravated the impairment of spatial learning and memory abilities of aluminium-treated rats, whereas inhibition of AAV-miR-351-5p expression alleviated it. Western blotting suggested that sub-chronic aluminium exposure increased miR-351-5p levels and reduced the expression of CPEB3 and PRPs in the hippocampus. Treatment with an AAV-miR-351-5p inhibitor partially recovered CPEB3 and PRPs. Double luciferase reporter assay results showed that CPEB3 was a direct target of miR-351-5p, while electron microscopy suggested that aluminium could damage mitochondria and synapses in the CA1 of the hippocampus. Golgi staining results indicated that aluminium could reduce the number of dendritic spines in hippocampal neurons. Inhibition of miR-351-5p restored the synaptic structure and growth of dendritic spines in the hippocampus. The involvement of the miR-351-5P/CPEB3/RPPs pathway in aluminium neurotoxicity was confirmed. Our findings suggest that inhibition of miR-351-5p can alleviate learning and memory impairments by increasing CPEB3 and PRPs.

Cellular diffusion processes in singularly perturbed domains

There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain Ω ⊂ R d containing a set of small subdomains or interior compartments U j , j = 1 , … , N (singularly-perturbed diffusion problems). The domain Ω could represent the cell membrane, the cell cytoplasm, the cell nucleus or the extracellular volume, while an individual compartment could represent a synapse, a membrane protein cluster, a biological condensate, or a quorum sensing bacterial cell. In this review we use a combination of matched asymptotic analysis and Green's function methods to solve a general type of singular boundary value problems (BVP) in 2D and 3D, in which an inhomogeneous Robin condition is imposed on each interior boundary ∂ U j . This allows us to incorporate a variety of previous studies of singularly perturbed diffusion problems into a single mathematical modeling framework. We mainly focus on steady-state solutions and the approach to steady-state, but also highlight some of the current challenges in dealing with time-dependent solutions and randomly switching processes.

Biophysical Modeling of Synaptic Plasticity

Dendritic spines are small, bulbous compartments that function as postsynaptic sites and undergo intense biochemical and biophysical activity. The role of the myriad signaling pathways that are implicated in synaptic plasticity is well studied. A recent abundance of quantitative experimental data has made the events associated with synaptic plasticity amenable to quantitative biophysical modeling. Spines are also fascinating biophysical computational units because spine geometry, signal transduction, and mechanics work in a complex feedback loop to tune synaptic plasticity. In this sense, ideas from modeling cell motility can inspire us to develop multiscale approaches for predictive modeling of synaptic plasticity. In this article, we review the key steps in postsynaptic plasticity with a specific focus on the impact of spine geometry on signaling, cytoskeleton rearrangement, and membrane mechanics. We summarize the main experimental observations and highlight how theory and computation can aid our understanding of these complex processes.

Asymptotic analysis of particle cluster formation in the presence of anchoring sites

The aggregation or clustering of proteins and other macromolecules plays an important role in the formation of large-scale molecular assemblies within cell membranes. Examples of such assemblies include lipid rafts, and postsynaptic domains (PSDs) at excitatory and inhibitory synapses in neurons. PSDs are rich in scaffolding proteins that can transiently trap transmembrane neurotransmitter receptors, thus localizing them at specific spatial positions. Hence, PSDs play a key role in determining the strength of synaptic connections and their regulation during learning and memory. Recently, a two-dimensional (2D) diffusion-mediated aggregation model of PSD formation has been developed in which the spatial locations of the clusters are determined by a set of fixed anchoring sites. The system is kept out of equilibrium by the recycling of particles between the cell membrane and interior. This results in a stationary distribution consisting of multiple clusters, whose average size can be determined using an effective mean-field description of the particle concentration around each anchored cluster. In this paper, we derive corrections to the mean-field approximation by applying the theory of diffusion in singularly perturbed domains. The latter is a powerful analytical method for solving two-dimensional (2D) and three-dimensional (3D) diffusion problems in domains where small holes or perforations have been removed from the interior. Applications range from modeling intracellular diffusion, where interior holes could represent subcellular structures such as organelles or biological condensates, to tracking the spread of chemical pollutants or heat from localized sources. In this paper, we take the bounded domain to be the cell membrane and the holes to represent anchored clusters. The analysis proceeds by partitioning the membrane into a set of inner regions around each cluster, and an outer region where mean-field interactions occur. Asymptotically matching the inner and outer stationary solutions generates an asymptotic expansion of the particle concentration, which includes higher-order corrections to mean-field theory that depend on the positions of the clusters and the boundary of the domain. Motivated by a recent study of light-activated protein oligomerization in cells, we also develop the analogous theory for cluster formation in a three-dimensional (3D) domain. The details of the asymptotic analysis differ from the 2D case due to the contrasting singularity structure of 2D and 3D Green's functions.

Synaptic logistics: Competing over shared resources

High turnover rates of synaptic proteins imply that synapses constantly need to replace their constituent building blocks. This requires sophisticated supply chains and potentially exposes synapses to shortages as they compete for limited resources. Interestingly, competition in neurons has been observed at different scales. Whether it is competition of receptors for binding sites inside a single synapse or synapses fighting for resources to grow. Here we review the implications of such competition for synaptic function and plasticity. We identify multiple mechanisms that synapses use to safeguard themselves against supply shortages and identify a fundamental neurologistic trade-off governing the sizes of reserve pools of essential synaptic building blocks.

Computational insights into mRNA and protein dynamics underlying synaptic plasticity rules

Recent advances in experimental techniques provide an unprecedented peek into the intricate molecular dynamics inside synapses and dendrites. The experimental insights into the molecular turnover revealed that such processes as diffusion, active transport, spine uptake, and local protein synthesis could dynamically modulate the copy numbers of plasticity-related molecules in synapses. Subsequently, theoretical models were designed to understand the interaction of these processes better and to explain how local synaptic plasticity cues can up or down-regulate the molecular copy numbers across synapses. In this review, we discuss the recent advances in experimental techniques and computational models to highlight how these complementary approaches can provide insight into molecular cross-talk across synapses, ultimately allowing us to develop biologically-inspired neural network models to understand brain function.

Quantifying postsynaptic receptor dynamics: insights into synaptic function

The molecular composition of presynaptic and postsynaptic neuronal terminals is dynamic, and yet long-term stabilizations in postsynaptic responses are necessary for synaptic development and long-term plasticity. The need to reconcile these concepts is further complicated by learning- and memory-related plastic changes in the molecular make-up of synapses. Advances in single-particle tracking mean that we can now quantify the number and diffusive properties of specific synaptic molecules, while statistical thermodynamics provides a framework to analyse these molecular fluctuations. In this Review, we discuss the use of these approaches to gain quantitative descriptions of the processes underlying the turnover, long-term stability and plasticity of postsynaptic receptors and show how these can help us to understand the balance between local molecular turnover and synaptic structural identity and integrity.

The JAK-STAT Signaling Pathway in Epilepsy

Epilepsy is defined as spontaneous recurrent seizures in the brain. There is increasing evidence that inflammatory mediators and immune cells are involved in epileptic seizures. As more research is done on inflammatory factors and immune cells in epilepsy, new targets for the treatment of epilepsy will be revealed. The Janus kinase-signal transducer and transcriptional activator (JAKSTAT) signaling pathway is strongly associated with many immune and inflammatory diseases, At present, more and more studies have found that the JAK-STAT pathway is involved in the development and development of epilepsy, indicating the JAK-STAT pathway's potential promise as a target in epilepsy treatment. In this review, we discuss the composition, activation, and regulation of the JAK-STAT pathway and the relationship between the JAK-STAT pathway and epilepsy. In addition, we summarize the common clinical inhibitors of JAK and STAT that we would expect to be used in epilepsy treatment in the future.

A computational model to explore how temporal stimulation patterns affect synapse plasticity

Plasticity-related proteins (PRPs), which are synthesized in a synapse activation-dependent manner, are shared by multiple synapses to a limited spatial extent for a specific period. In addition, stimulated synapses can utilize shared PRPs through synaptic tagging and capture (STC). In particular, the phenomenon by which short-lived early long-term potentiation is transformed into long-lived late long-term potentiation using shared PRPs is called “late-associativity,” which is the underlying principle of “cluster plasticity.” We hypothesized that the competitive capture of PRPs by multiple synapses modulates late-associativity and affects the fate of each synapse in terms of whether it is integrated into a synapse cluster. We tested our hypothesis by developing a computational model to simulate STC, late-associativity, and the competitive capture of PRPs. The experimental results obtained using the model revealed that the number of competing synapses, timing of stimulation to each synapse, and basal PRP level in the dendritic compartment altered the effective temporal window of STC and influenced the conditions under which late-associativity occurs. Furthermore, it is suggested that the competitive capture of PRPs results in the selection of synapses to be integrated into a synapse cluster via late-associativity.

Dendritic spine morphology regulates calcium-dependent synaptic weight change

Dendritic spines act as biochemical computational units and must adapt their responses according to their activation history. Calcium influx acts as the first signaling step during postsynaptic activation and is a determinant of synaptic weight change. Dendritic spines also come in a variety of sizes and shapes. To probe the relationship between calcium dynamics and spine morphology, we used a stochastic reaction-diffusion model of calcium dynamics in idealized and realistic geometries. We show that despite the stochastic nature of the various calcium channels, receptors, and pumps, spine size and shape can modulate calcium dynamics and subsequently synaptic weight updates in a deterministic manner. Through a series of exhaustive simulations and analyses, we found that the calcium dynamics and synaptic weight change depend on the volume-to-surface area of the spine. The relationships between calcium dynamics and spine morphology identified in idealized geometries also hold in realistic geometries, suggesting that there are geometrically determined deterministic relationships that may modulate synaptic weight change.

Spectral theory of diffusion in partially absorbing media

A probabilistic framework for studying single-particle diffusion in partially absorbing media has recently been developed in terms of an encounter-based approach. The latter computes the joint probability density (generalized propagator) for particle position X t and a Brownian functional U t that specifies the amount of time the particle is in contact with a reactive component M . Absorption occurs as soon as U t crosses a randomly distributed threshold (stopping time). Laplace transforming the propagator with respect to U t leads to a classical boundary value problem (BVP) in which the reactive component has a constant rate of absorption z , where z is the corresponding Laplace variable. Hence, a crucial step in the encounter-based approach is finding the inverse Laplace transform. In the case of a reactive boundary ∂ M , this can be achieved by solving a classical Robin BVP in terms of the spectral decomposition of a Dirichlet-to-Neumann (D-to-N) operator on ∂ M . In this paper, we develop the analogous construction in the case of a reactive substrate M . In particular, we show that the Laplace transformed propagator can be computed in terms of the spectral decomposition of a pair of D-to-N operators on ∂ M . However, inverting the Laplace transform with respect to z is considerably more involved. We illustrate the theory by considering the D-to-N operators for some simple geometries.

Modeling Receptor Motility along Advecting Lipid Membranes

This work aims to overview multiphysics mechanobiological computational models for receptor dynamics along advecting cell membranes. Continuum and statistical models of receptor motility are the two main modeling methodologies identified in reviewing the state of the art. Within the former modeling class, a further subdivision based on different biological purposes and processes of proteins’ motion is recognized; cell adhesion, cell contractility, endocytosis, and receptor relocations on advecting membranes are the most relevant biological processes identified in which receptor motility is pivotal. Numerical and/or experimental methods and approaches are highlighted in the exposure of the reviewed works provided by the literature, pertinent to the topic of the present manuscript. With a main focus on the continuum models of receptor motility, we discuss appropriate multiphyisics laws to model the mass flux of receptor proteins in the reproduction of receptor relocation and recruitment along cell membranes to describe receptor–ligand chemical interactions, and the cell’s structural response. The mass flux of receptor modeling is further supported by a discussion on the methodology utilized to evaluate the protein diffusion coefficient developed over the years.

Local accumulation times in a diffusion-trapping model of receptor dynamics at proximal axodendritic synapses

The lateral diffusion and trapping of neurotransmitter receptors within the postsynaptic membrane of a neuron play a key role in determining synaptic strength and plasticity. Trapping is mediated by the reversible binding of receptors to scaffolding proteins (slots) within a synapse. In this paper we introduce a method for analyzing the transient dynamics of proximal axodendritic synapses in a diffusion-trapping model of receptor trafficking. Given a population of spatially distributed synapses, each of which has a fixed number of slots, we calculate the rate of relaxation to the steady-state distribution of bound slots (synaptic weights) in terms of a set of local accumulation times. Assuming that the rates of exocytosis and endocytosis are sufficiently slow, we show that the steady-state synaptic weights are independent of each other (purely local). On the other hand, the local accumulation time of a given synapse depends on the number of slots and the spatial location of all the synapses, indicating a form of transient heterosynaptic plasticity. This suggests that local accumulation time measurements could provide useful information regarding the distribution of synaptic weights within a dendrite.

The needs of a synapse—How local organelles serve synaptic proteostasis

Synaptic function crucially relies on the constant supply and removal of neuronal membranes. The morphological complexity of neurons poses a significant challenge for neuronal protein transport since the machineries for protein synthesis and degradation are mainly localized in the cell soma. In response to this unique challenge, local micro‐secretory systems have evolved that are adapted to the requirements of neuronal membrane protein proteostasis. However, our knowledge of how neuronal proteins are synthesized, trafficked to membranes, and eventually replaced and degraded remains scarce. Here, we review recent insights into membrane trafficking at synaptic sites and into the contribution of local organelles and micro‐secretory pathways to synaptic function. We describe the role of endoplasmic reticulum specializations in neurons, Golgi‐related organelles, and protein complexes like retromer in the synthesis and trafficking of synaptic transmembrane proteins. We discuss the contribution of autophagy and of proteasome‐mediated and endo‐lysosomal degradation to presynaptic proteostasis and synaptic function, as well as nondegradative roles of autophagosomes and lysosomes in signaling and synapse remodeling. We conclude that the complexity of neuronal cyto‐architecture necessitates long‐distance protein transport that combines degradation with signaling functions.

Local accumulation time for diffusion in cells with gap junction coupling

In this paper we analyze the relaxation to steady state of intracellular diffusion in a pair of cells with gap-junction coupling. Gap junctions are prevalent in most animal organs and tissues, providing a direct diffusion pathway for both electrical and chemical communication between cells. Most analytical models of gap junctions focus on the steady-state diffusive flux and the associated effective diffusivity. Here we investigate the relaxation to steady state in terms of the so-called local accumulation time. The latter is commonly used to estimate the time to form a protein concentration gradient during morphogenesis. The basic idea is to treat the fractional deviation from the steady-state concentration as a cumulative distribution for the local accumulation time. One of the useful features of the local accumulation time is that it takes into account the fact that different spatial regions can relax at different rates. We consider both static and dynamic gap junction models. The former treats the gap junction as a resistive channel with effective permeability μ, whereas the latter represents the gap junction as a stochastic gate that randomly switches between an open and closed state. The local accumulation time is calculated by solving the diffusion equation in Laplace space and then taking the small-s limit. We show that the accumulation time is a monotonically increasing function of spatial position, with a jump discontinuity at the gap junction. This discontinuity vanishes in the limit μ→∞ for a static junction and β→0 for a stochastically gated junction, where β is the rate at which the gate closes. Finally, our results are generalized to the case of a linear array of cells with nearest-neighbor gap junction coupling.

Flavonoid fisetin reverses impaired hippocampal synaptic plasticity and cognitive function by regulating the function of AMPARs in a male rat model of schizophrenia

Cognitive deficits are the core feature of schizophrenia and effective treatment strategies are still missing. Previous studies have reported that fisetin promotes long-term potentiation (LTP) and cognitive function in normal rodents and other model animals of neurological diseases. The aim of this study was to assess the effect of fisetin on synaptic plasticity and cognitive deficits caused by a brief disruption of N-methyl-D-aspartate receptors (NMDARs) with dizocilpine (MK-801) during early development in rats. The cognitive performance was examined by the Morris water maze task and a fear conditioning test. Hippocampal synaptic plasticity was investigated by field potential recording. The expression of α-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid receptors (AMPARs) and cognition-related proteins was measured by western blotting. We found that intraperitoneal administration of fisetin rescued hippocampus-dependent spatial and contextual fear memory in MK-801 rats. In parallel with these behavioral results, fisetin treatment in MK-801 rats reversed the impairment of hippocampal LTP. At the molecular level, fisetin treatment selectively increased the phosphorylation and surface expression of AMPA receptor subunit 1 (GluA1) in MK-801-treated rats. Moreover, fisetin restored the phosphorylation levels of calcium-calmodulin-dependent kinaseII (CaMKII), cAMP response element-binding protein (CREB), and the extracellular signal-regulated kinase (ERK1/2) in MK-801-treated rats. Collectively, our findings demonstrate that fisetin treatment can reverse the deficits of hippocampal synaptic plasticity and memory in a male rat model of schizophrenia by restoring the phosphorylation and surface expression of AMPAR GluA1 subunit, suggesting fisetin as a promising therapeutic candidate for schizophrenia-associated cognitive deficits.

The biophysical basis underlying the maintenance of early phase long-term potentiation

The maintenance of synaptic changes resulting from long-term potentiation (LTP) is essential for brain function such as memory and learning. Different LTP phases have been associated with diverse molecular processes and pathways, and the molecular underpinnings of LTP on the short, as well as long time scales, are well established. However, the principles on the intermediate time scale of 1-6 hours that mediate the early phase of LTP (E-LTP) remain elusive. We hypothesize that the interplay between specific features of postsynaptic receptor trafficking is responsible for sustaining synaptic changes during this LTP phase. We test this hypothesis by formalizing a biophysical model that integrates several experimentally-motivated mechanisms. The model captures a wide range of experimental findings and predicts that synaptic changes are preserved for hours when the receptor dynamics are shaped by the interplay of structural changes of the spine in conjunction with increased trafficking from recycling endosomes and the cooperative binding of receptors. Furthermore, our model provides several predictions to verify our findings experimentally.

Mechanical injuries of neurons induce tau mislocalization to dendritic spines and tau-dependent synaptic dysfunction

Chronic traumatic encephalopathy (CTE) is associated with repeated traumatic brain injuries (TBI) and is characterized by cognitive decline and the presence of neurofibrillary tangles (NFTs) of the protein tau in patients' brains. Here we provide direct evidence that cell-scale mechanical deformation can elicit tau abnormalities and synaptic deficits in neurons. Using computational modeling, we find that the early pathological loci of NFTs in CTE brains are regions of high deformation during injury. The mechanical energy associated with high-strain rate deformation alone can induce tau mislocalization to dendritic spines and synaptic deficits in cultured rat hippocampal neurons. These cellular changes are mediated by tau hyperphosphorylation and can be reversed through inhibition of GSK3β and CDK5 or genetic deletion of tau. Together, these findings identify a mechanistic pathway that directly relates mechanical deformation of neurons to tau-mediated synaptic impairments and provide a possibly exploitable therapeutic pathway to combat CTE.

Molecular Crowding and Diffusion-Capture in Synapses

Cell membranes often contain domains with important physiological functions. A typical example are neuronal synapses, whose capacity to capture receptors for neurotransmitters is central to neuronal functions. Receptors diffuse in the membrane until they are stabilized by interactions with stable elements, the scaffold. Single particle tracking experiments demonstrated that these interactions are rather weak and that lateral diffusion is strongly impaired in the post-synaptic membrane due to molecular crowding. We investigated how the distribution of scaffolding molecules and molecular crowding affect the capture of receptors. In particle-based Monte Carlo simulations, based on experimental data of molecular diffusion and organization, crowding enhanced the receptor-scaffold interaction but reduced the capture of new molecules. The distribution of scaffolding sites in several clusters reduced crowding and fostered the exchange of molecules accelerating synaptic plasticity. Synapses could switch between two regimes, becoming more stable or more plastic depending on the internal distribution of molecules.

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The good: molecular crowding enhances the interaction receptors-scaffold

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The bad: the exchange of molecules with extrasynaptic areas is reduced by crowding

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Molecular crowding helps synapses to be stable

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Nanoclusters of scaffold sites reduce crowding effects and favor synaptic plasticity

A Theoretical Framework to Derive Simple, Firing-Rate-Dependent Mathematical Models of Synaptic Plasticity

Synaptic plasticity serves as an essential mechanism underlying cognitive processes as learning and memory. For a better understanding detailed theoretical models combine experimental underpinnings of synaptic plasticity and match experimental results. However, these models are mathematically complex impeding the comprehensive investigation of their link to cognitive processes generally executed on the neuronal network level. Here, we derive a mathematical framework enabling the simplification of such detailed models of synaptic plasticity facilitating further mathematical analyses. By this framework we obtain a compact, firing-rate-dependent mathematical formulation, which includes the essential dynamics of the detailed model and, thus, of experimentally verified properties of synaptic plasticity. Amongst others, by testing our framework by abstracting the dynamics of two well-established calcium-dependent synaptic plasticity models, we derived that the synaptic changes depend on the square of the presynaptic firing rate, which is in contrast to previous assumptions. Thus, the here-presented framework enables the derivation of biologically plausible but simple mathematical models of synaptic plasticity allowing to analyze the underlying dependencies of synaptic dynamics from neuronal properties such as the firing rate and to investigate their implications in complex neuronal networks.

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.

Competition for synaptic building blocks shapes synaptic plasticity

Changes in the efficacies of synapses are thought to be the neurobiological basis of learning and memory. The efficacy of a synapse depends on its current number of neurotransmitter receptors. Recent experiments have shown that these receptors are highly dynamic, moving back and forth between synapses on time scales of seconds and minutes. This suggests spontaneous fluctuations in synaptic efficacies and a competition of nearby synapses for available receptors. Here we propose a mathematical model of this competition of synapses for neurotransmitter receptors from a local dendritic pool. Using minimal assumptions, the model produces a fast multiplicative scaling behavior of synapses. Furthermore, the model explains a transient form of heterosynaptic plasticity and predicts that its amount is inversely related to the size of the local receptor pool. Overall, our model reveals logistical tradeoffs during the induction of synaptic plasticity due to the rapid exchange of neurotransmitter receptors between synapses.

Functional organization of postsynaptic glutamate receptors

Glutamate receptors are the most abundant excitatory neurotransmitter receptors in the brain, responsible for mediating the vast majority of excitatory transmission in neuronal networks. The AMPA- and NMDA-type ionotropic glutamate receptors (iGluRs) are ligand-gated ion channels that mediate the fast synaptic responses, while metabotropic glutamate receptors (mGluRs) are coupled to downstream signaling cascades that act on much slower timescales. These functionally distinct receptor sub-types are co-expressed at individual synapses, allowing for the precise temporal modulation of postsynaptic excitability and plasticity. Intriguingly, these receptors are differentially distributed with respect to the presynaptic release site. While iGluRs are enriched in the core of the synapse directly opposing the release site, mGluRs reside preferentially at the border of the synapse. As such, to understand the differential contribution of these receptors to synaptic transmission, it is important to not only consider their signaling properties, but also the mechanisms that control the spatial segregation of these receptor types within synapses. In this review, we will focus on the mechanisms that control the organization of glutamate receptors at the postsynaptic membrane with respect to the release site, and discuss how this organization could regulate synapse physiology.

AMPA receptor trafficking and its role in heterosynaptic plasticity

Historically, long-term potentiation (LTP) and long-term depression (LTD), the best-characterized forms of long-term synaptic plasticity, are viewed as experience-dependent and input-specific processes. However, cumulative experimental and theoretical data have demonstrated that LTP and LTD can promote compensatory alterations in non-stimulated synapses. In this work, we have developed a computational model of a tridimensional spiny dendritic segment to investigate the role of AMPA receptor (AMPAR) trafficking during synaptic plasticity at specific synapses and its consequences for the populations of AMPAR at nearby synapses. Our results demonstrated that the mechanisms of AMPAR trafficking involved with LTP and LTD can promote heterosynaptic plasticity at non-stimulated synapses. These alterations are compensatory and arise from molecular competition. Moreover, the heterosynaptic changes observed in our model can modulate further activity-driven inductions of synaptic plasticity.

Eye movement desensitization and reprocessing as a treatment for PTSD: current neurobiological theories and a new hypothesis

Eye movement desensitization and reprocessing (EMDR), a form of psychotherapy for individuals with post-traumatic stress disorder (PTSD), has long been a controversial topic, hampered in part by a lack of understanding of the neural mechanisms that contribute to its remedial effect. Here, we review current theories describing EMDR's potential neurobiological mechanisms of action involving working memory, interhemispheric communication, de-arousal, and memory reconsolidation. We then discuss recent studies describing the temporal and spatial aspects of smooth pursuit and predictive saccades, which resemble those made during EMDR, and their neural correlates within the default mode network (DMN) and cerebellum. We hypothesize that if the production of bilateral predictive eye movements is supportive of DMN and cerebellum activation, then therapies that shift the brain towards this state correspondingly would benefit the processes regulated by these structures (i.e., memory retrieval, relaxation, and associative learning), all of which are essential components for PTSD recovery. We propose that the timing of sensory stimulation may be relevant to treatment effect and could be adapted across different patients depending on their baseline saccade metrics. Empirical data in support of this model are reviewed and experimental predictions are discussed.

Self-crowding of AMPA receptors in the excitatory postsynaptic density can effectuate anomalous receptor sub-diffusion

AMPA receptors (AMPARs) and their associations with auxiliary transmembrane proteins are bulky structures with large steric-exclusion volumes. Hence, self-crowding of AMPARs, depending on the local density, may affect their lateral diffusion in the postsynaptic membrane as well as in the highly crowded postsynaptic density (PSD) at excitatory synapses. Earlier theoretical studies considered only the roles of transmembrane obstacles and the AMPAR-binding submembranous scaffold proteins in shaping receptor diffusion within PSD. Using lattice model of diffusion, the present study investigates the additional impacts of self-crowding on the anomalousity and effective diffusion coefficient (D_eff) of AMPAR diffusion. A recursive algorithm for avoiding false self-blocking during diffusion simulation is also proposed. The findings suggest that high density of AMPARs in the obstacle-free membrane itself engenders strongly anomalous diffusion and severe decline in D_eff. Adding transmembrane obstacles to the membrane accentuates the anomalousity arising from self-crowding due to the reduced free diffusion space. Contrarily, enhanced AMPAR-scaffold binding, either through increase in binding strength or scaffold density or both, ameliorates the anomalousity resulting from self-crowding. However, binding has differential impacts on D_eff depending on the receptor density. Increase in binding causes consistent decrease in D_eff for low and moderate receptor density. For high density, binding increases D_eff as long as it reduces anomalousity associated with intense self-crowding. Given a sufficiently strong binding condition when diffusion acquires normal behavior, further increase in binding causes decrease in D_eff. Supporting earlier experimental observations are mentioned and implications of present findings to the experimental observations on AMPAR diffusion are also drawn.

The transmembrane AMPA receptors (AMPARs) prominently exhibit lateral diffusion in the postsynaptic membrane at excitatory synapses. Steric obstructions to AMPAR diffusion due to the crowd of other relatively static transmembrane proteins and binding of AMPARs to the submembranous scaffold proteins in the specialized region of postsynaptic density (PSD) are well known to retard receptor diffusion, which causes receptor trapping and accumulation within PSD. However, AMPARs are significantly bulky structures and may also obstruct their own diffusion paths in the presence of their high density. It is shown here that intense self-crowding of AMPARs may lead to highly obstructed and confined receptor diffusion even in the obstacle-free medium, and the presence of other obstacles further aggravates this effect. AMPAR-scaffold binding reduces confined diffusion arising from self-crowding and strong binding engenders normal diffusion even at high receptor density. However, it overall causes reduction in the effective diffusion coefficient of the receptor diffusion.

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 lattice model of synaptic membrane protein domains

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

Understanding the role of synaptopodin and the spine apparatus in Hebbian synaptic plasticity - New perspectives and the need for computational modeling

Synaptopodin (SP) is a proline-rich actin-associated protein essential for the formation of a spine apparatus (SA) in dendritic spines. The SA consists of stacks of smooth endoplasmic reticulum (sER) contiguous with the meshwork of somatodendritic ER. Spines of SP-deficient mice contain sER but no SA, demonstrating that SP is necessary for the assembly of ER cisterns into the more complex SA organelle. Although the SA was described decades ago, its function was difficult to investigate and remained elusive, in part because reliable markers for the SA were missing. After SP was identified as an essential component and a reliable marker of the SA, a role of SP/SA in hippocampal synaptic plasticity could be firmly established using loss-of-function approaches. Further studies revealed that SP/SA participate in the regulation of Ca²⁺-dependent spine-specific Hebbian plasticity and in activity-dependent changes in the spine actin cytoskeleton. In this review we are summarizing recent progress made on SP/SA in Hebbian plasticity and discuss open questions such as causality, spatiotemporal dynamics and complementarity of SP/SA-dependent mechanisms. We are proposing that computational modeling of spine Ca²⁺-signaling and actin remodeling pathways could address some of these issues and could indicate future research directions. Moreover, reaction-diffusion simulations could help to identify key feedforward and feedback regulatory motifs regulating the switch between an LTP and an LTD signaling module in SP/SA-containing spines, thus helping to find a unified view of SP/SA action in Hebbian plasticity.

Residence times of receptors in dendritic spines analyzed by stochastic simulations in empirical domains

Analysis of high-density superresolution imaging of receptors reveals the organization of dendrites at nanoscale resolution. We present here an apparently novel method that uses local statistics extracted from short-range trajectories for the simulations of long-range trajectories in empirical live cell images. Based on these empirical simulations, we compute the residence time of a receptor in dendritic spines that accounts for receptors' local interactions and geometrical membrane organization. We report here that depending on the type of the spine, the residence time varies from 1 to 5 min. Moreover, we show that there exists transient organized structures, previously described as potential wells that can regulate the trafficking of receptors to dendritic spine: the simulation results suggest that receptor trafficking is regulated by transient structures.

Self-assembly and plasticity of synaptic domains through a reaction-diffusion mechanism

Signal transmission across chemical synapses relies crucially on neurotransmitter receptor molecules, concentrated in postsynaptic membrane domains along with scaffold and other postsynaptic molecules. The strength of the transmitted signal depends on the number of receptor molecules in postsynaptic domains, and activity-induced variation in the receptor number is one of the mechanisms of postsynaptic plasticity. Recent experiments have demonstrated that the reaction and diffusion properties of receptors and scaffolds at the membrane, alone, yield spontaneous formation of receptor-scaffold domains of the stable characteristic size observed in neurons. On the basis of these experiments we develop a model describing synaptic receptor domains in terms of the underlying reaction-diffusion processes. Our model predicts that the spontaneous formation of receptor-scaffold domains of the stable characteristic size observed in experiments depends on a few key reactions between receptors and scaffolds. Furthermore, our model suggests novel mechanisms for the alignment of pre- and postsynaptic domains and for short-term postsynaptic plasticity in receptor number. We predict that synaptic receptor domains localize in membrane regions with an increased receptor diffusion coefficient or a decreased scaffold diffusion coefficient. Similarly, we find that activity-dependent increases or decreases in receptor or scaffold diffusion yield a transient increase in the number of receptor molecules concentrated in postsynaptic domains. Thus, the proposed reaction-diffusion model puts forth a coherent set of biophysical mechanisms for the formation, stability, and plasticity of molecular domains on the postsynaptic membrane.

Shape-induced asymmetric diffusion in dendritic spines allows efficient synaptic AMPA receptor trapping

Dendritic spines are the primary postsynaptic sites of excitatory neurotransmission in the brain. They exhibit a remarkable morphological variety, ranging from thin protrusions, to stubby shapes, to bulbous mushroom shapes. The remodeling of spines is thought to regulate the strength of the synaptic connection, which depends vitally on the number and the spatial distribution of AMPA-type glutamate receptors (AMPARs). We present numerical and analytical analyses demonstrating that this shape strongly affects AMPAR diffusion. We report a pronounced suppression of the receptor exit rate out of spines with decreasing neck radius. Thus, mushroomlike spines become highly effective at retaining receptors in the spine head. Moreover, we show that the postsynaptic density further enhances receptor trapping, particularly in mushroomlike spines local exocytosis in the spine head, in contrast to release at the base, provides rapid and specific regulatory control of AMPAR concentration at synapses.

How to scale down postsynaptic strength

Synaptic scaling is a form of synaptic plasticity that contributes to the homeostatic regulation of neuronal activity both in vitro and in vivo, by bidirectionally and proportionally adjusting postsynaptic AMPA receptor (AMPAR) abundance to compensate for chronic perturbations in activity. This proportional regulation of synaptic strength allows synaptic scaling to normalize activity without disrupting the synapse-specific differences in strength thought to underlie memory storage, but how such proportional scaling of synaptic strength is accomplished at the biophysical level is unknown. Here we addressed this question in cultured rat visual cortical pyramidal neurons. We used photoactivation and fluorescence recovery after photobleaching of fluorescently tagged AMPAR to show that scaling down, but not up, decreases the steady-state accumulation of synaptic AMPAR by increasing the rate at which they unbind from and exit the postsynaptic density (Koff). This increase in Koff was not diffusion limited, was independent of AMPAR endocytosis, and was prevented by a scaffold manipulation that specifically blocks scaling down, suggesting that it is accomplished through enhanced dissociation of AMPAR from synaptic scaffold tethers. Finally, simulations show that increasing Koff decreases synaptic strength multiplicatively, by reducing the fractional occupancy of available scaffold "slots." These data demonstrate that scaling down is accomplished through a regulated increase in Koff, which in turn reduces the fractional occupancy of synaptic scaffolds to proportionally reduce synaptic strength.

Control of flux by narrow passages and hidden targets in cellular biology

Critical biological processes, such as synaptic plasticity and transmission, activation of genes by transcription factors, or double-strained DNA break repair, are controlled by diffusion in structures that have both large and small spatial scales. These may be small binding sites inside or on the surface of the cell, or narrow passages between subcellular compartments. The great disparity in spatial scales is the key to controlling cell function by structure. We report here recent progress on resolving analytical and numerical difficulties in extracting properties from experimental data, from biophysical models, and from Brownian dynamics simulations of diffusion in multi-scale structures. This progress is achieved by developing an analytical approximation methodology for solving the model equations. The reported results are applied to analysis and simulations of subcellular processes and to the quantification of their biological functions.

Melanocortin-4 receptor regulates hippocampal synaptic plasticity through a protein kinase A-dependent mechanism

Learning and memory require orchestrated regulation of both structural and functional synaptic plasticity in the hippocampus. While a neuropeptide alpha-melanocyte-stimulating hormone, α-MSH, has been implicated in memory acquisition and retention, the functional role of its cognate receptor, melanocortin-4 receptor (MC4R), in hippocampal-dependent synaptic plasticity has not been explored. In this study, we report that activation of MC4R enhances synaptic plasticity through the regulation of dendritic spine morphology and abundance of AMPA receptors. We show that activation of postsynaptic MC4R increases the number of mature dendritic spines and enhances surface expression of AMPA receptor subunit GluA1, resulting in synaptic accumulation of GluA1-containing AMPA receptors. Moreover, MC4R stimulates surface GluA1 trafficking through phosphorylation of GluA1 at Ser845 in a Gα(s)-cAMP/PKA-dependent manner. Blockade of protein kinase A (PKA) signaling abolishes the MC4R-mediated enhancement of neurotransmission and hippocampal long-term potentiation. Importantly, in vivo application of MC4R agonists increases LTP in the mouse hippocampal CA1 region. These findings reveal that MC4R in the hippocampus plays a critical role in the regulation of structural and functional plasticity.

A stochastic signaling network mediates the probabilistic induction of cerebellar long-term depression

Many cellular processes involve a small number of molecules and undergo stochastic fluctuations in their levels of activity. Cerebellar long-term depression (LTD) is a form of synaptic plasticity expressed as a reduction in the number of synaptic AMPA receptors (AMPARs) in Purkinje cells. We developed a stochastic model of the LTD signaling network, including a PKC-ERK-cPLA(2) positive feedback loop and mechanisms of AMPAR trafficking, and tuned the model to replicate calcium uncaging experiments. The signaling network activity in single synapses switches between two discrete stable states (LTD and non-LTD) in a probabilistic manner. The stochasticity of the signaling network causes threshold dithering and allows at the macroscopic level for many different and stable mean magnitudes of depression. The probability of LTD occurrence in a single spine is only modulated by the concentration and duration of the signal used to trigger it, and inputs with the same magnitude can give rise to two different responses; there is no threshold for the input signal. The stochasticity is intrinsic to the signaling network and not mostly dependent on noise in the calcium input signal, as has been suggested previously. The activities of the ultrasensitive ERK and of cPLA(2) undergo strong stochastic fluctuations. Conversely, PKC, which acts as a noise filter, is more constantly activated. Systematic variation of the biochemical population size demonstrates that threshold dithering and the absence of spontaneous LTD depend critically on the number of molecules in a spine, indicating constraints on spine size in Purkinje cells.

Unified quantitative model of AMPA receptor trafficking at synapses

Trafficking of AMPA receptors (AMPARs) plays a key role in synaptic transmission. However, a general framework integrating the two major mechanisms regulating AMPAR delivery at postsynapses (i.e., surface diffusion and internal recycling) is lacking. To this aim, we built a model based on numerical trajectories of individual AMPARs, including free diffusion in the extrasynaptic space, confinement in the synapse, and trapping at the postsynaptic density (PSD) through reversible interactions with scaffold proteins. The AMPAR/scaffold kinetic rates were adjusted by comparing computer simulations to single-particle tracking and fluorescence recovery after photobleaching experiments in primary neurons, in different conditions of synapse density and maturation. The model predicts that the steady-state AMPAR number at synapses is bidirectionally controlled by AMPAR/scaffold binding affinity and PSD size. To reveal the impact of recycling processes in basal conditions and upon synaptic potentiation or depression, spatially and temporally defined exocytic and endocytic events were introduced. The model predicts that local recycling of AMPARs close to the PSD, coupled to short-range surface diffusion, provides rapid control of AMPAR number at synapses. In contrast, because of long-range diffusion limitations, extrasynaptic recycling is intrinsically slower and less synapse-specific. Thus, by discriminating the relative contributions of AMPAR diffusion, trapping, and recycling events on spatial and temporal bases, this model provides unique insights on the dynamic regulation of synaptic strength.

A role for α-adducin (ADD-1) in nematode and human memory

Identifying molecular mechanisms that underlie learning and memory is one of the major challenges in neuroscience. Taken the advantages of the nematode Caenorhabditis elegans, we investigated α-adducin (add-1) in aversive olfactory associative learning and memory. Loss of add-1 function selectively impaired short- and long-term memory without causing acquisition, sensory, or motor deficits. We showed that α-adducin is required for consolidation of synaptic plasticity, for sustained synaptic increase of AMPA-type glutamate receptor (GLR-1) content and altered GLR-1 turnover dynamics. ADD-1, in a splice-form- and tissue-specific manner, controlled the storage of memories presumably through actin-capping activity. In support of the C. elegans results, genetic variability of the human ADD1 gene was significantly associated with episodic memory performance in healthy young subjects. Finally, human ADD1 expression in nematodes restored loss of C. elegans add-1 gene function. Taken together, our findings support a role for α-adducin in memory from nematodes to humans. Studying the molecular and genetic underpinnings of memory across distinct species may be helpful in the development of novel strategies to treat memory-related diseases.

Diffusion laws in dendritic spines

Dendritic spines are small protrusions on a neuronal dendrite that are the main locus of excitatory synaptic connections. Although their geometry is variable over time and along the dendrite, they typically consist of a relatively large head connected to the dendritic shaft by a narrow cylindrical neck. The surface of the head is connected smoothly by a funnel or non-smoothly to the narrow neck, whose end absorbs the particles at the dendrite. We demonstrate here how the geometry of the neuronal spine can control diffusion and ultimately synaptic processes. We show that the mean residence time of a Brownian particle, such as an ion or molecule inside the spine, and of a receptor on its membrane, prior to absorption at the dendritic shaft depends strongly on the curvature of the connection of the spine head to the neck and on the neck's length. The analytical results solve the narrow escape problem for domains with long narrow necks.

Lateral organization of the postsynaptic density

Fast excitatory synaptic transmission is mediated by AMPA-type glutamate receptors (AMPARs). It is widely accepted that the number of AMPARs in the postsynaptic density (PSD) critically determines the efficiency of synaptic transmission, but an unappreciated aspect of synapse organization is the lateral positioning of AMPARs within the PSD, that is, their distribution across the face of a single synapse. Receptor lateral positioning is important in a number of processes, most notably because alignment with presynaptic release sites heavily influences the probability of receptor activation. In this review, we summarize current understanding of the mechanisms that dynamically control the subsynaptic positioning of AMPARs. This field is still at early stages, but the recent wave of developments in super-resolution microscopy, synapse tomography, and computational modeling now enable the study of lateral protein distribution and dynamics within the nanometer-scale boundaries of the PSD. We discuss data available measuring the lateral distribution of glutamate receptors and scaffold proteins within the PSD, and discuss potential mechanisms that might give rise to these patterns. Elucidating the mechanisms that underlie the lateral organization of the PSD will be critical to improve our understanding of synaptic processes whose disruption may be unexpectedly important in neurological disorders. This article is part of a Special Issue entitled Membrane Trafficking and Cytoskeletal Dynamics in 'Neuronal Function'.

Regulation of dendrite arborization by substrate stiffness is mediated by glutamate receptors

Brain injury or disease can initiate changes in local or global stiffness of brain tissue. While stiffness of the extracellular environment is known to affect the morphology and function of many cell types, little is known about how the dendrites of neurons respond to changes in brain stiffness. To assess how extracellular stiffness affects dendrite morphology, we took biomaterial and biomedical engineering approaches. We cultured mixed and pure hippocampal neurons on hydrogels composed of polyacrylamide (PA) of varying stiffnesses to mimic the effects of extracellular matrix stiffness on dendrite morphology. The majority of investigations of cortical and spinal cord neurons on soft hydrogels examined branching at early time points (days in vitro (DIV) 2-7), an important distinction from our study, where we include later time points that encompass the peak of branching (DIV 10-12). At DIV 12, dendrite branching was altered by stiffness for both pure and mixed neuronal cultures. Furthermore, we treated hippocampal cultures with glutamate receptor antagonists and with astrocyte-conditioned media. Blocking AMPA and NMDA receptors affected the changes in dendrite branching seen at varying rigidities. Moreover, extracellular factors secreted by astrocytes also change dendrite branching seen at varying rigidities. Thus, astrocytes and ionotropic glutamate receptors contribute to mechanosensing.

Quantifying the effects of elastic collisions and non-covalent binding on glutamate receptor trafficking in the post-synaptic density

One mechanism of information storage in neurons is believed to be determined by the strength of synaptic contacts. The strength of an excitatory synapse is partially due to the concentration of a particular type of ionotropic glutamate receptor (AMPAR) in the post-synaptic density (PSD). AMPAR concentration in the PSD has to be plastic, to allow the storage of new memories; but it also has to be stable to preserve important information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which AMPAR can enter, leave and remain in the synapse are unclear. We used Monte Carlo simulations to determine the influence of PSD structure and activity in maintaining homeostatic concentrations of AMPARs in the synapse. We found that, the high concentration and excluded volume caused by PSD molecules result in molecular crowding. Diffusion of AMPAR in the PSD under such conditions is anomalous. Anomalous diffusion of AMPAR results in retention of these receptors inside the PSD for periods ranging from minutes to several hours in the absence of strong binding of receptors to PSD molecules. Trapping of receptors in the PSD by crowding effects was very sensitive to the concentration of PSD molecules, showing a switch-like behavior for retention of receptors. Non-covalent binding of AMPAR to anchored PSD molecules allowed the synapse to become well-mixed, resulting in normal diffusion of AMPAR. Binding also allowed the exchange of receptors in and out of the PSD. We propose that molecular crowding is an important biophysical mechanism to maintain homeostatic synaptic concentrations of AMPARs in the PSD without the need of energetically expensive biochemical reactions. In this context, binding of AMPAR with PSD molecules could collaborate with crowding to maintain synaptic homeostasis but could also allow synaptic plasticity by increasing the exchange of these receptors with the surrounding extra-synaptic membrane.

One of the most accepted theories of information storage in neurons is that it is partially localized in the strength of synaptic contacts. Evidence suggests that at the cellular level, in combination with other cellular mechanisms, this is implemented by increasing or decreasing the concentration of a particular type of membrane molecules. Two opposing mechanisms have to coexist in synapses to allow them to store information. On one hand, synapses have to be flexible, to allow the storage of new memories. On the other hand, synapses have to be stable to preserve previously learned information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which molecules can enter, leave and remain in the synapse are unclear. Our modeling work uses fundamental biophysical principles to quantify the effects of molecular collisions and biochemical reactions. Our results show that molecular collisions alone, between the diffusing proteins with anchored molecules in the synapse, can replicate known experimental results. Molecular collision in combination with biochemical binding can be fundamental biophysical principles used by synapses for the formation and preservation of memories.

Brownian diffusion of AMPA receptors is sufficient to explain fast onset of LTP

BACKGROUND

Long-Term Potentiation (LTP) of synapses is thought to be due in part to a change in AMPA Receptor trafficking leading to an increase in the number of AMPA Receptors at the synapse. LTP onset occurs within seconds after the induction signal. A particle-based stochastic simulation software is used to investigate the effect of Brownian diffusion of glutamate receptors on receptor incorporation into the synaptic specialisation and the time-course of LTP expression. The model of the dendritic spine includes receptors diffusing within the membrane, scaffold molecules within the synaptic specialisation capable of binding receptors and a molecular picket-fence surrounding the synaptic membrane area, all features found within the biological system.

RESULTS

During simulations, receptors accumulate rapidly at the post-synaptic density (PSD) from the extra-synaptic membrane under a number of biologically observed conditions. The time of half-saturation, t1/2, defined as the time-point at which half the available scaffold proteins are occupied with receptors, is found to be 710 ms. Different scaffold distributions are shown to have little effect on this time-course. Decreasing the probability of escape of receptors from the PSD domain, thus localising receptors closer to the scaffold proteins, substantially decreases t1/2. A decrease of escape probability from 1 to 0 brings about a non-linear decrease in t1/2 from 710 ms to 390 ms. Release-location of receptors within the spine is found to affect the initial rate of receptor incorporation. We simulate three possible sources of receptors: (i) receptors distributed within the spine extra-synaptic membrane; (ii) receptors from exocytotic vesicles released to the synaptic spine; and (iii) receptors entering the spine from the dendritic shaft through the spine neck. Receptors released from exocytotic vesicles initially accumulate faster than receptors released from the other two sources. A model of glutamate release and glutamate-receptor interaction shows that newly inserted receptors make a substantial contribution to a glutamate evoked response within the observed time-frame.

CONCLUSIONS

Fast accumulation of AMPA Receptors is consistent with experimentally observed fast onset of LTP expression.

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.

Cellular transport and membrane dynamics of the glycine receptor

Regulation of synaptic transmission is essential to tune individual-to-network neuronal activity. One way to modulate synaptic strength is to regulate neurotransmitter receptor numbers at postsynaptic sites. This can be achieved either through plasma membrane insertion of receptors derived from intracellular vesicle pools, a process depending on active cytoskeleton transport, or through surface membrane removal via endocytosis. In parallel, lateral diffusion events along the plasma membrane allow the exchange of receptor molecules between synaptic and extrasynaptic compartments, contributing to synaptic strength regulation. In recent years, results obtained from several groups studying glycine receptor (GlyR) trafficking and dynamics shed light on the regulation of synaptic GlyR density. Here, we review (i) proteins and mechanisms involved in GlyR cytoskeletal transport, (ii) the diffusion dynamics of GlyR and of its scaffolding protein gephyrin that control receptor numbers, and its relationship with synaptic plasticity, and (iii) adaptative changes in GlyR diffusion in response to global activity modifications, as a homeostatic mechanism.

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.

A dynamic corral model of receptor trafficking at a synapse

The postsynaptic density (PSD) is a cytoskeletal specialization within the postsynaptic membrane of a neuron that helps to concentrate and organize neurotransmitter receptors at a chemical synapse. The total number of receptors within the PSD, which is a major factor in determining the physiological strength or weight of a synapse, fluctuates due to the surface diffusion of receptors into and out of the PSD, and the interactions of receptors with scaffolding proteins and cytoskeletal elements within the PSD. In this article, we present a stochastic model of protein receptor trafficking at the PSD that takes into account these various processes. The PSD is treated as a stochastically gated corral, which contributes a source of extrinsic or environmental noise that supplements the intrinsic noise arising from small receptor numbers. Using a combination of stochastic analysis and Monte Carlo simulations, we determine the time-dependent variation in the mean and variance of synaptic receptor numbers for a variety of initial conditions that simulate fluorescence recovery after photobleaching experiments, and indicate how such data might be used to infer certain properties of the PSD.