Random dispersion in excitatory synapse response

The excitatory synaptic function is subject to a huge amount of researches and fairly all the structural elements of the synapse are investigated to determine their specific contribution to the response. A model of an excitatory (hippocampal) synapse, based on time discretized Langevin equations (time-step = 40 fs), was introduced to describe the Brownian motion of Glutamate molecules (GLUTs) within the synaptic cleft and their binding to postsynaptic receptors. The binding has been computed by the introduction of a binding probability related to the hits of GLUTs on receptor binding sites. This model has been utilized in computer simulations aimed to describe the random dispersion of the synaptic response, evaluated from the dispersion of the peak amplitude of the excitatory post-synaptic current. The results of the simulation, presented here, have been used to find a reliable numerical quantity for the unknown value of the binding probability. Moreover, the same results have shown that the coefficient of variation decreases when the number of postsynaptic receptors increases, all the other parameters of the process being unchanged. Due to its possible relationships with the learning and memory, this last finding seems to furnish an important clue for understanding the basic mechanisms of the brain activity.     

A Brownian simulation model of glutamate synaptic diffusion in the femtosecond time scale

 To gain a better understanding of the elementary unit of synaptic communication between hippocampal neurons, we simulated the release of glutamate from a single pre-synaptic vesicle and its diffusion into the synaptic cleft. Diffusion of glutamate was simulated by a Brownian model based on Langevin equations. The model was implemented for parallel computer simulation and tested under different conditions of glutamate release and different geometrical and physical characteristics of the synaptic cleft. All the tested parameters have shown to be important for the synaptic responses. The results show that the synaptic transmission efficacy is influenced by many different geometrical parameters and, as a consequence, the quality of the excitatory post-synaptic response can be very different in the same synapse. The variability in the quantal response found by several authors can also be explained by physical parameters other than by variations in the quantal content of the synaptic vesicle as proposed by these authors. Received: 6 October 1999 / Accepted: 29 February 2000     

Variability of neurotransmitter concentration and nonsaturation of postsynaptic AMPA receptors at synapses in hippocampal cultures and slices

To understand the elementary unit of synaptic communication between CNS neurons, one must know what causes the variability of quantal postsynaptic currents and whether unitary packets of transmitter saturate postsynaptic receptors. We studied single excitatory synapses between hippocampal neurons in culture. Focal glutamate application at individual postsynaptic sites evoked currents (I(glu)) with little variability compared with quantal excitatory postsynaptic currents (EPSCs). The maximal I(glu) was >2-fold larger than the median EPSC. Thus, variations in [glu]cleft are the main source of variability in EPSC size, and glutamate receptors are generally far from saturation during quantal transmission. This conclusion was verified by molecular antagonism experiments in hippocampal cultures and slices. The general lack of glutamate receptor saturation leaves room for increases in [glu]cleft as a mechanism for synaptic plasticity.     

The effects of geometrical parameters on synaptic transmission: a Monte Carlo simulation study

Monte Carlo simulations of transmitter diffusion and its interactions with postsynaptic receptors have been used to study properties of quantal responses at central synapses. Fast synaptic responses characteristic of those recorded at glycinergic junctions on the teleost Mauthner cell (time to peak approximately 0.3-0.4 ms and decay time constant approximately 3-6 ms) served as the initial reference, and smaller contacts with fewer postsynaptic receptors were also modeled. Consistent with experimental findings, diffusion, simulated using a random walk algorithm and assuming a diffusion coefficient of 0.5-1.0 x 10(-5) cm2 s(-1), was sufficiently fast to account for transmitter removal from the synaptic cleft. Transmitter-receptor interactions were modeled as a two-step binding process, with the double-bound state having opened and closed conformations. Addition of a third binding step only slightly decreased response amplitude but significantly slowed both its rising and decay phases. The model allowed us to assess the sources of response variability and the likelihood of postsynaptic saturation as functions of multiple kinetic and spatial parameters. The method of nonstationary fluctuation analysis, typically used to estimate the number of functional channels at a synapse and single channel current, proved unreliable, presumably because the receptors in the postsynaptic matrix are not uniformly exposed to the same profile of transmitter concentration. Thus, the time course of the probability of channel opening most likely varies among receptors. Finally, possible substrates for phenomena of synaptic plasticity, such as long-term potentiation, were explored, including the diameter of the contact zone, defined by the region of pre- and postsynaptic apposition, the number and distribution of the receptors, and the degree of vesicle filling. Surprisingly, response amplitude is quite sensitive to the size of the receptor-free annulus surrounding the receptor cluster, such that expansion of the contact zone could produce an appreciable increase in quantal size, normally attributed to either the presence of more receptors or the release of more transmitter molecules.     

Modelling zinc changes at the hippocampal mossy fiber synaptic cleft

Zinc, a transition metal existing in very high concentrations in the hippocampal mossy fibers from CA3 area, is assumed to be co-released with glutamate and to have a neuromodulatory role at the corresponding synapses. The synaptic action of zinc is determined both by the spatiotemporal characteristics of the zinc release process and by the kinetics of zinc binding to sites located in the cleft area, as well as by their concentrations. This work addresses total, free and complexed zinc concentration changes, in an individual synaptic cleft, following single, short and long periods of evoked zinc release. The results estimate the magnitude and time course of the concentrations of zinc complexes, assuming that the dynamics of the release processes are similar to those of glutamate. It is also considered that, for the cleft zinc concentrations used in the model (≤ 1 μM), there is no postsynaptic zinc entry. For this reason, all released zinc ends up being reuptaken in a process that is several orders of magnitude slower than that of release and has thus a much smaller amplitude. The time derivative of the total zinc concentration in the cleft is represented by the difference between two alpha functions, corresponding to the released and uptaken components. These include specific parameters that were chosen assuming zinc and glutamate co-release, with similar time courses. The peak amplitudes of free zinc in the cleft were selected based on previously reported experimental cleft zinc concentration changes evoked by single and multiple stimulation protocols. The results suggest that following a low amount of zinc release, similar to that associated with one or a few stimuli, zinc clearance is mainly mediated by zinc binding to the high-affinity sites on the NMDA receptors and to the low-affinity sites on the highly abundant GLAST glutamate transporters. In the case of higher zinc release brought about by a larger group of stimuli, most zinc binding occurs essentially to the GLAST transporters, having the corresponding zinc complex a maximum concentration that is more than one order of magnitude larger than that for the high and low affinity NMDA sites. The other zinc complexes considered in the model, namely those formed with sites on the AMPA receptors, calcium and K_ATP channels and with ATP molecules, have much smaller contributions to the synaptic zinc clearance.     

Spillover of glutamate onto synaptic AMPA receptors enhances fast transmission at a cerebellar synapse

Diffusion of glutamate from the synaptic cleft can activate high-affinity receptors, but is not thought to contribute to fast AMPA receptor-mediated transmission. Here, we show that single AMPA receptor EPSCs at the cerebellar mossy fiber-granule cell connection are mediated by both direct release of glutamate and rapid diffusion of glutamate from neighboring synapses. Immunogold localization revealed that AMPA receptors are located exclusively in postsynaptic densities, indicating that spillover of glutamate occurs between synaptic contacts. Spillover currents contributed half the synaptic charge and exhibited little trial-to-trial variability. We propose that spillover of glutamate improves transmission efficacy by both increasing the amplitude and duration of the EPSP and reducing fluctuations arising from the probabilistic nature of transmitter release.     

A Brownian model of glutamate diffusion in excitatory synapses of hippocampus

We simulated the diffusion of glutamate, following the release of a single vesicle from a pre-synaptic terminal, in the synaptic cleft by using a Brownian diffusion model based on Langevin equations. The synaptic concentration time course and the time course of quantal excitatory post-synaptic current have been analyzed. The results showed that they depend on the number of receptors located at post-synaptic membrane. Their time course are dependent both on the total number of the post-synaptic receptors and on the eccentricity of the pre-synaptic glutamate vesicle.     

Effect of filaments within the synaptic cleft on the response of excitatory synapses simulated by computer experiments

Mathematical models of the excitatory synapse are furnishing valuable information about the synaptic response. Based on Brownian-diffusion of glutamate molecules, a synapse model was utilized to investigate the synaptic response on a femto-second time scale by the use of a parallel computer. In particular, the presence of fibrils crossing the synaptic cleft was simulated, which could have a role in shaping the brain activity. To this aim the model of synapse was modified by considering trans-synaptic filaments with diameters ranging from 7 nm to 3 nm, disposed on a grid with spacing of 14 nm or 8 nm. The simulation demonstrated that the presence of filaments induced an increase in the synaptic response, most likely linked to an increment in the probability of encounter between glutamate molecules and receptors. The increase was small - from 5 to 20%, but metabolic and functional considerations provide substantive hints about the importance of these small changes for brain activity. Moreover, it was shown that the presence of filaments made more stable the response of the synapse to random variations of pre-synaptic elements. Originated by these computational results, some inferences about the biological bases of mind diseases such as autism, mental retardation and schizophrenia, are reported in the Discussion.     

Modeling the effect of glutamate diffusion and uptake on NMDA and non-NMDA receptor saturation.

One- and two-dimensional models of glutamate diffusion, uptake, and binding in the synaptic cleft were developed to determine if the release of single vesicles of glutamate would saturate NMDA and non-NMDA receptors. Ranges of parameter values were used in the simulations to determine the conditions when saturation could occur. Single vesicles of glutamate did not saturate NMDA receptors unless diffusion was very slow and the number of glutamate molecules in a vesicle was large. However, the release of eight vesicles at 400 Hz caused NMDA receptor saturation for all parameter values tested. Glutamate uptake was found to reduce NMDA receptor saturation, but the effect was smaller than that of changes in the diffusion coefficient or in the number of glutamate molecules in a vesicle. Non-NMDA receptors were not saturated unless diffusion was very slow and the number of glutamate molecules in a vesicle was large. The release of eight vesicles at 400 Hz caused significant non-NMDA receptor desensitization. The results suggest that NMDA and non-NMDA receptors are not saturated by single vesicles of glutamate under usual conditions, and that tetanic input, of the type typically used to induce long-term potentiation, will increase calcium influx by increasing receptor binding as well as by reducing voltage-dependent block of NMDA receptors.     

Clearance of glutamate inside the synapse and beyond.

The heated debate over the level of postsynaptic receptor occupancy by transmitter has not been extinguished - indeed, new evidence is fanning the flames. Recent experiments using two-photon microscopy suggest that the concentration of glutamate in the synaptic cleft does not attain levels previously suggested. In contrast, recordings from glial cells and studies of extrasynaptic receptor activation indicate that significant quantities of glutamate escape from the cleft following exocytosis. Determining the amount of glutamate efflux from the synaptic cleft and the distance it diffuses is critical to issues of synaptic specificity and the induction of synaptic plasticity.     

Control of Cleft Glutamate Concentration and Glutamate Spill-Out by Perisynaptic Glia: Uptake and Diffusion Barriers

Most glutamatergic synapses in the mammalian central nervous system are covered by thin astroglial processes that exert a dual action on synaptically released glutamate: they form physical barriers that oppose diffusion and they carry specific transporters that remove glutamate from the extracellular space. The present study was undertaken to investigate the dual action of glia by means of computer simulation. A realistic synapse model based on electron microscope data and Monte Carlo algorithms were used for this purpose. Results show (1) that physical obstacles formed by glial processes delay glutamate exit from the cleft and (2) that this effect is efficiently counteracted by glutamate uptake. Thus, depending on transporter densities, the presence of perisynaptic glia may result in increased or decreased glutamate transient in the synaptic cleft. Changes in temporal profiles of cleft glutamate concentration induced by glia differentially impact the response of the various synaptic and perisynaptic receptor subtypes. In particular, GluN2B- and GluN2C-NMDA receptor responses are strongly modified while GluN2A-NMDA receptor responses are almost unaffected. Thus, variations in glial transporter expression may allow differential tuning of NMDA receptors according to their subunit composition. In addition, simulation data suggest that the sink effect generated by transporters accumulation in the vicinity of the release site is the main mechanism limiting glutamate spill-out. Physical obstacles formed by glial processes play a comparatively minor role.     

Activation of presynaptic ionotropic glutamate receptors stimulates GABA release from hippocampal and cortical nerve terminals in rats

One of the pathways implicated in a fine-tuning control of neurosecretory process is the activation of presynaptic receptors. The present study was focused on the role of presynaptic glutamate receptor activation in the regulation of inhibitory synaptic transmission in the rat hippocampus and cortex. We aimed to clarify what types of ionotropic glutamate receptors are involved in the modulation of GABA secretion, and what mechanism underlies this modulation. We have revealed that specific agonists of kainate and NMDA receptors, kainate and NMDA, like glutamate, induced the release of [3H]GABA from hippocampal and cortical nerve terminals suggesting the involvement of both types in the regulation of GABAergic transmission. Our results indicate preferential involvement of vesicular, but not cytosolic, pool in response to glutamate receptor activation. This is based on the finding that NO-711 (a specific inhibitor of plasma membrane GABA transporters), fails to attenuate [3H]GABA release. We have concluded that presynaptic glutamate receptor-induced modulation of the strength of synaptic response is due to increasing the release probability of synaptic vesicles.     

The Influence of Synaptic Size on AMPA Receptor Activation: A Monte Carlo Model

Physiological and electron microscope studies have shown that synapses are functionally and morphologically heterogeneous and that variations in size of synaptic junctions are related to characteristics such as release probability and density of postsynaptic AMPA receptors. The present article focuses on how these morphological variations impact synaptic transmission. We based our study on Monte Carlo computational simulations of simplified model synapses whose morphological features have been extracted from hundreds of actual synaptic junctions reconstructed by three-dimensional electron microscopy. We have examined the effects that parameters such as synaptic size or density of AMPA receptors have on the number of receptors that open after release of a single synaptic vesicle. Our results indicate that the maximum number of receptors that will open after the release of a single synaptic vesicle may show a ten-fold variation in the whole population of synapses. When individual synapses are considered, there is also a stochastical variability that is maximal in small synapses with low numbers of receptors. The number of postsynaptic receptors and the size of the synaptic junction are the most influential parameters, while the packing density of receptors or the concentration of extrasynaptic transporters have little or no influence on the opening of AMPA receptors.     

Fast removal of synaptic glutamate by postsynaptic transporters

Glutamate transporters are believed to remove glutamate from the synaptic cleft only slowly because they cycle slowly. However, we show that when glutamate binds to postsynaptic transporters at the cerebellar climbing fiber synapse, it evokes a conformation change and inward current that reflect glutamate removal from the synaptic cleft within a few milliseconds, a time scale much faster than the overall cycle time. Contrary to present models, glutamate removal does not require binding of an extracellular proton, and the time course of transporter anion conductance activation differs from that of glutamate removal. The charge movement associated with glutamate removal is consistent with the majority of synaptically released glutamate being removed from the synaptic cleft by postsynaptic transporters.     

Molecular characteristics of glutamate receptors in the mammalian brain

Summary The strong excitatory activity of L-glutamic acid on central nervous system neurons is thought to be produced by interaction of this amino acid with specific neuronal plasma membrane receptors. The binding of L-glutamate to these surface receptors brings about an increase in membrane permeability to Na⁺ and Ca²⁺ ions presumably through direct activation of ion channels linked to the membrane receptors. The studies described in this paper represent attempts to define the subcellular distribution and pharmacological properties of the recognition site for L-glutamic acid in brain neuronal preparations, to isolate and explore the molecular characteristics of the receptor recognition site, and, finally, to demonstrate the activation of Na⁺ channels in synaptic membranes following the interaction of glutamate with its receptors.Radioligand binding assays with L-[³H] glutamic acid have been used to demonstrate a relative enrichment of these glutamate recognition sites in isolated synaptic plasma membranes. The specific binding of L-[³H] glutamate to these membrane sites exhibits rapid association and dissociation kinetics and rather complex equilibrium binding kinetics. The glutamate binding macromolecule from synaptic membranes has been solubilized and purified and was shown to be a small molecular weight glycoprotein (M_T 13 000). This protein tends to form aggregates which have higher specific activity at low concentrations of glutamate than the M_T 13 000 protein has. The overall affinity of the purified protein is lower than that of the high affinity sites in the membrane. Nevertheless, the purified protein exhibits pharmacological characteristics very similar to those of the membrane binding sites. On the basis of its pharmacological properties this protein belongs in the category of the physiologic glutamate preferring receptors.By means of differential solubilization of membrane proteins with Na-cholate, it was shown that this recognition site is an intrinsic synaptic membrane protein whose binding activity is enhanced rather than diminished by cholate extraction of the synaptic membranes. The role of membrane constituents in regulating the binding activity of this protein has been explored and a possible modulation of glutamate binding by membrane gangliosides has been demonstrated. Finally, this glutamate binding glycoprotein is a metalloprotein whose activity is dependent on the integrity of its metallic (Fe) center. This is a clear distinguishing characteristic of this protein vis-à-vis the glutamate transport carriers.The presence of functional glutamate receptors in synaptosomes and resealed synaptic plasma membranes has also been documented by the demonstration of glutamate-activated Na⁺ flux across the membrane of these preparations. The bidirectionality, temperature independence, and apparent desensitization of this stimulated flux following exposure to high concentrations of glutamate are properties indicative of a receptor-initiated ion channel activation. It would appear, then, that the synaptic membrane preparations provide a very useful system for the study of both recognition and effector function of the glutamate receptor complex.     

Re-examination of the determinants of synaptic strength from the perspective of superresolution imaging

Synaptic strength is thought to be determined by the number of presynaptic release sites, release probability and postsynaptic response to quantal release. Changes in these parameters are directly relevant to synaptic plasticity. However, our understanding of these determinants as they relate to synaptic function has been reformed by recent work on nanoscale organizations of synaptic proteins. Specifically, release probability is distributed heterogeneously among multiple release sites within a single active zone, and the quantal postsynaptic response depends strongly on the local distribution of receptors around the release site. These nanoscale characteristics reveal a new deeper layer of modulation of synaptic transmission and plasticity.     

Glutamate Binding to the GluN2B Subunit Controls Surface Trafficking of N-Methyl-D-aspartate (NMDA) Receptors

Trafficking of NMDA receptors to the surface of neurons and to synapses is critical for proper brain function and activity-dependent plasticity. Recent evidence suggests that surface trafficking of other ionotropic glutamate receptors requires ligand binding for exit from the endoplasmic reticulum. Here, we show that glutamate binding to GluN2 is required for trafficking of NMDA receptors to the cell surface. We expressed a panel of GluN2B ligand binding mutants in heterologous cells with GluN1 or in rat cultured neurons and found that surface expression correlates with glutamate efficacy. Such a correlation was found even in the presence of dominant negative dynamin to inhibit endocytosis and surface expression correlated with Golgi localization, indicating differences in forward trafficking. Co-expression of wild type GluN2B did not enhance surface expression of the mutants, suggesting that glutamate must bind to both GluN2 subunits in a tetramer and that surface expression is limited by the least avid of the two glutamate binding sites. Surface trafficking of a constitutively closed cleft GluN2B was indistinguishable from that of wild type, suggesting that glutamate concentrations are typically not limiting for forward trafficking. YFP-GluN2B expressed in hippocampal neurons from GluN2B(-/-) mice rescued synaptic accumulation at similar levels to wild type. Under these conditions, surface synaptic accumulation of YFP-GluN2B mutants also correlated with apparent glutamate affinity. Altogether, these results indicate that glutamate controls forward trafficking of NMDA receptors to the cell surface and to synapses and raise the intriguing idea that NMDA receptors may be functional at intracellular sites.     

Analytical description of the activation of multi-state receptors by continuous neurotransmitter signals at brain synapses.

Chemical synaptic transmission is a fundamental component of interneuronal communications in the central nervous system (CNS). Discharge of a presynaptic vesicle containing a few thousand molecules (a quantum) of neurotransmitter into the synaptic cleft generates a transmitter concentration signal that drives postsynaptic ion-channel receptors. These receptors exhibit multiple states, with state transition kinetics dependent on neurotransmitter concentration. Here, a novel and simple analytical approach for describing gating of multi-state receptors by signals with complex continuous time courses is used to describe the generation of glutamate-mediated quantal postsynaptic responses at brain synapses. The neurotransmitter signal, experienced by multi-state N-methyl-D-aspartate (NMDA)- and L-alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionate (AMPA)-type glutamate receptors at specific points in a synaptic cleft, is approximated by a series of step functions of different intensity and duration and used to drive a Markovian, multi-state kinetic scheme that describes receptor gating. Occupancy vectors at any point in time can be computed interatively from the occupancy vectors at the times of steps in transmitter concentration. Multi-state kinetic schemes for both the low-affinity AMPA subtype of glutamate receptor and for the high-affinity NMDA subtype are considered, and expected NMDA and AMPA components of synaptic currents are calculated. The amplitude of quantal responses mediated by postsynaptic receptor clusters having specific spatial distributions relative to foci of quantal neurotransmitter release is then calculated and related to the displacement between the center of the postsynaptic receptor cluster and the focus of synaptic vesicle discharge. Using this approach we show that the spatial relation between the focus of release and the center of the postsynaptic receptor cluster affects synaptic efficacy. We also show how variation in this relation contributes to variation in synaptic current amplitudes.