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.     

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.     

A single vesicular glutamate transporter is sufficient to fill a synaptic vesicle

Quantal size is the postsynaptic response to the release of a single synaptic vesicle and is determined in part by the amount of transmitter within that vesicle. At glutamatergic synapses, the vesicular glutamate transporter (VGLUT) fills vesicles with glutamate. While elevated VGLUT expression increases quantal size, the minimum number of transporters required to fill a vesicle is unknown. In Drosophila DVGLUT mutants, reduced transporter levels lead to a dose-dependent reduction in the frequency of spontaneous quantal release with no change in quantal size. Quantal frequency is not limited by vesicle number or impaired exocytosis. This suggests that a single functional unit of transporter is both necessary and sufficient to fill a vesicle to completion and that vesicles without DVGLUT are empty. Consistent with the presence of empty vesicles, at dvglut mutant synapses synaptic vesicles are smaller, suggesting that vesicle filling and/or transporter level is an important determinant of vesicle size.     

Effects of AMPARs trafficking and glutamate-receptors binding probability on stochastic variability of EPSC

Mathematical models of the excitatory synapse are providing valuable information about the synaptic response. The effects of several synaptic components on EPSC variability have been tested by computer simulation. Our model, based on Brownian diffusion of glutamate in the synaptic cleft, is basically the same we have used in previous papers but parameters have been upgraded according to the new experimental findings. The presence of filaments into the synaptic cleft and the number and the ratio of AMPA and NMDA receptors have been the main parameters upgraded. A different way of computing the binding probability of glutamate molecules to receptors by means of geometrical considerations has been also used. The obtained results were more precise and they suggested that the new elements can play a significant role in the stochastic variability of the synaptic response. Nevertheless, new problems arise concerning the value of the lower limit of the binding probability.     

Ectopic release of synaptic vesicles

Exocytosis of synaptic vesicles is generally assumed to occur only at ultrastructurally defined presynaptic active zones. If release is restricted to these sites, receptors not located within the synaptic cleft must be activated by transmitter that diffuses out of the cleft or not be activated at all. Here we report that AMPA receptor-mediated quantal events resulting from climbing fiber release are observed in Bergmann glial cells in the cerebellar cortex. These quantal events are not coincident with quanta recorded in neighboring Purkinje cells which receive input from the same climbing fiber. As Bergmann glial membranes are excluded from the synaptic cleft, we propose that exocytosis can occur from climbing fiber release sites located directly across from Bergmann glial membranes. Such ectopic release may account for the majority of the Bergmann glial AMPA response evoked by climbing fiber stimulation.     

Vesicular Monogamy?

Vesicular neurotransmitter transporters package transmitter into the lumen of synaptic vesicles for quantal release. However, the number of transporters that localize to each vesicle is not known. In this issue of Neuron, a study by Daniels et al. using the Drosophila neuromuscular junction and mutations of the vesicular glutamate transporter suggests that one transporter may suffice to fill each vesicle.     

Localization effects of acetylcholine release from a synaptic vesicle at the neuromuscular junction.

A two-dimensional compartment model devised for the appropriate representation of the transient process of the spontaneous generation of miniature endplate current (MEPC) at the neuromuscular junction is applied for clarifying the biochemical significance of the quantal release mechanism of acetylcholine (ACh), a typical neurotransmitter, in the synaptic chemical transmission process. The simulation analysis with the model demonstrates that the localization of the ACh release due to the fusion of a synaptic vesicle with the presynaptic membrane has significant effects on the amplitude of MEPC and that the stronger effects are caused with the smaller diffusion coefficients of ACh in the cleft. The sharpest and highest response of MEPC is achieved when the release area is about 4 times to the natural release through the narrow pore. On the other hand, the actual localization corresponding to the natural release of ACh makes the amplitude of MEPC higher by a factor about 2.5 compared with that in the most extended release of ACh examined, implying that the natural release mechanism works as an amplifier of the MEPC with the fixed amount of ACh available.     

Neurotransmitter release: the dark side of the vacuolar-H+ATPase

Vacuolar-H⁺ATPase (V-ATPase) is a complex enzyme with numerous subunits organized in two domains. The membrane domain V0 contains a proteolipid hexameric ring that translocates protons when ATP is hydrolysed by the catalytic cytoplasmic sector (V1). In nerve terminals, V-ATPase generates an electrochemical proton gradient that is acid and positive inside synaptic vesicles. It is used by specific neurotransmitter-proton antiporters to accumulate neurotransmitters inside their storage organelles. During synaptic activity, neurotransmitters are released from synaptic vesicles docked at specialized portions of the presynaptic plasma membrane, the active zones. A fusion pore opens that allows the neurotransmitter to be released from the synaptic vesicle lumen into the synaptic cleft. We briefly review experimental data suggesting that the membrane domain of V-ATPase could be such a fusion pore.We also discuss the functional implications for quantal neurotransmitter release of the sequential use of the same V-ATPase membrane domain in two different events, neurotransmitter accumulation in synaptic vesicles first, and then release from these organelles during synaptic activity.     

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.     

Hydrodynamic flow in a synaptic cleft during exocytosis

It is shown that exocytosis in a chemical synapse may be accompanied by “microjet” formation due to the overpressure that exists in the vesicles. This mechanism may take place either at complete fusion of a vesicle with the presynaptic membrane or in the so-called kiss-and-run mode of neurotransmitter release. A simple hydrodynamic model of the viscous incompressible flow arising in the synaptic cleft is suggested. The occurrence of hydrodynamic flow (microjet) leads to more efficient transport of neurotransmitter than in the case of classical diffusive transport.     

Estimating synaptic parameters from mean, variance, and covariance in trains of synaptic responses

Fluctuation analysis of synaptic transmission using the variance-mean approach has been restricted in the past to steady-state responses. Here we extend this method to short repetitive trains of synaptic responses, during which the response amplitudes are not stationary. We consider intervals between trains, long enough so that the system is in the same average state at the beginning of each train. This allows analysis of ensemble means and variances for each response in a train separately. Thus, modifications in synaptic efficacy during short-term plasticity can be attributed to changes in synaptic parameters. In addition, we provide practical guidelines for the analysis of the covariance between successive responses in trains. Explicit algorithms to estimate synaptic parameters are derived and tested by Monte Carlo simulations on the basis of a binomial model of synaptic transmission, allowing for quantal variability, heterogeneity in the release probability, and postsynaptic receptor saturation and desensitization. We find that the combined analysis of variance and covariance is advantageous in yielding an estimate for the number of release sites, which is independent of heterogeneity in the release probability under certain conditions. Furthermore, it allows one to calculate the apparent quantal size for each response in a sequence of stimuli.     

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.     

Modeling of slow glutamate diffusion and AMPA receptor activation in the cerebellar glomerulus

Synaptic conductances are influenced markedly by the geometry of the space surrounding the synapse since the transient glutamate concentration in the synaptic cleft is determined by this geometry. Our paper is an attempt to understand the reasons for slow glutamate diffusion in the cerebellar glomerulus, a structure situated around the enlarged mossy fiber terminal in the cerebellum and surrounded by a glial sheath. For this purpose, analytical expressions for glutamate diffusion in the glomerulus were considered in models with two-, three-, and fractional two-three-dimensional (2D-3D) geometry with an absorbing boundary. The time course of average glutamate concentration in the synaptic cleft of the mossy fiber-granule cell connection was calculated for both direct release of glutamate from the same synaptic unit, and for cumulative spillover of glutamate from neighboring release sites. Several kinetic schemes were examined, and the parameters of the diffusion models were estimated by identifying theoretical activation of AMPA receptors with direct release and spillover components of published experimental AMPA receptor-mediated EPSCs. For model selection, the correspondence of simulated paired-pulse ratio and EPSC increase after prevention of desensitization to experimental values were also taken into consideration. Our results suggest at least a 7- to 10-fold lower apparent diffusion coefficient of glutamate in the porous medium of the glomerulus than in water. The modeling of glutamate diffusion in the 2D-3D geometry gives the best fit of experimental EPSCs. We show that it could be only partly explained by normal diffusion of glutamate in the complex geometry of the glomerulus. We assume that anomalous diffusion of glutamate occurs in the glomerulus. A good match of experimental estimations and theoretical parameters, obtained in the simulations that use an approximation of anomalous diffusion by a solution for fractional Brownian motion, confirms our assumption.     

Transmitter concentration profiles in the synaptic cleft: an analytical model of release and diffusion.

A three-dimensional model for release and diffusion of glutamate in the synaptic cleft was developed and solved analytically. The model consists of a source function describing transmitter release from the vesicle and a diffusion function describing the spread of transmitter in the cleft. Concentration profiles of transmitter at the postsynaptic side were calculated for different transmitter concentrations in a vesicle, release scenarios, and diffusion coefficients. From the concentration profiles the receptor occupancy could be determined using alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor kinetics. It turned out that saturation of receptors and sufficiently fast currents could only be obtained if the diffusion coefficient was one order of magnitude lower than generally assumed, and if the postsynaptic receptors formed clusters with a diameter of roughly 100 nm directly opposite the release sites. Under these circumstances the gradient of the transmitter concentration at the postsynaptic membrane outside the receptor clusters was steep, with minimal cross-talk among neighboring receptor clusters. These findings suggest that for each release site a corresponding receptor aggregate exists, subdividing an individual synapse into independent functional subunits without the need for specific lateral diffusion barriers.     

Computational modeling predicts ephemeral acidic microdomains in the glutamatergic synaptic cleft

At chemical synapses, synaptic vesicles release their acidic contents into the cleft, leading to the expectation that the cleft should acidify. However, fluorescent pH probes targeted to the cleft of conventional glutamatergic synapses in both fruit flies and mice reveal cleft alkalinization rather than acidification. Here, using a reaction-diffusion scheme, we modeled pH dynamics at the Drosophila neuromuscular junction as glutamate, ATP, and protons (H⁺) were released into the cleft. The model incorporates bicarbonate and phosphate buffering systems as well as plasma membrane calcium-ATPase activity and predicts substantial cleft acidification but only for fractions of a millisecond after neurotransmitter release. Thereafter, the cleft rapidly alkalinizes and remains alkaline for over 100 ms because the plasma membrane calcium-ATPase removes H⁺ from the cleft in exchange for calcium ions from adjacent pre- and postsynaptic compartments, thus recapitulating the empirical data. The extent of synaptic vesicle loading and time course of exocytosis have little influence on the magnitude of acidification. Phosphate but not bicarbonate buffering is effective at suppressing the magnitude and time course of the acid spike, whereas both buffering systems are effective at suppressing cleft alkalinization. The small volume of the cleft levies a powerful influence on the magnitude of alkalinization and its time course. Structural features that open the cleft to adjacent spaces appear to be essential for alleviating the extent of pH transients accompanying neurotransmission.     

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.     

The neurotransmitter cycle and quantal size

Changes in the response to release of a single synaptic vesicle have generally been attributed to postsynaptic modification of receptor sensitivity, but considerable evidence now demonstrates that alterations in vesicle filling also contribute to changes in quantal size. Receptors are not saturated at many synapses, and changes in the amount of transmitter per vesicle contribute to the physiological regulation of release. On the other hand, the presynaptic factors that determine quantal size remain poorly understood. Aside from regulation of the fusion pore, these mechanisms fall into two general categories: those that affect the accumulation of transmitter inside a vesicle and those that affect vesicle size. This review will summarize current understanding of the neurotransmitter cycle and indicate basic, unanswered questions about the presynaptic regulation of quantal size.