Saturation in excitatory synapses of hippocampus investigated by computer simulations

Heterogeneity of glutamatergic synapses: cellular mechanisms and network consequences

Chemical synapses are commonly known as a structurally and functionally highly diverse class of cell-cell contacts specialized to mediate communication between neurons. They represent the smallest "computational" unit of the brain and are typically divided into excitatory and inhibitory as well as modulatory categories. These categories are subdivided into diverse types, each representing a different structure-function repertoire that in turn are thought to endow neuronal networks with distinct computational properties. The diversity of structure and function found among a given category of synapses is referred to as heterogeneity. The main building blocks for this heterogeneity are synaptic vesicles, the active zone, the synaptic cleft, the postsynaptic density, and glial processes associated with the synapse. Each of these five structural modules entails a distinct repertoire of functions, and their combination specifies the range of functional heterogeneity at mammalian excitatory synapses, which are the focus of this review. We describe synapse heterogeneity that is manifested on different levels of complexity ranging from the cellular morphology of the pre- and postsynaptic cells toward the expression of different protein isoforms at individual release sites. We attempt to define the range of structural building blocks that are used to vary the basic functional repertoire of excitatory synaptic contacts and discuss sources and general mechanisms of synapse heterogeneity. Finally, we explore the possible impact of synapse heterogeneity on neuronal network function.

The glutamatergic synapse: a complex machinery for information processing

Being the most abundant synaptic type, the glutamatergic synapse is responsible for the larger part of the brain's information processing. Despite the conceptual simplicity of the basic mechanism of synaptic transmission, the glutamatergic synapse shows a large variation in the response to the presynaptic release of the neurotransmitter. This variability is observed not only among different synapses but also in the same single synapse. The synaptic response variability is due to several mechanisms of control of the information transferred among the neurons and suggests that the glutamatergic synapse is not a simple bridge for the transfer of information but plays an important role in its elaboration and management. The control of the synaptic information is operated at pre, post, and extrasynaptic sites in a sort of cooperation between the pre and postsynaptic neurons which also involves the activity of other neurons. The interaction between the different mechanisms of control is extremely complicated and its complete functionality is far from being fully understood. The present review, although not exhaustively, is intended to outline the most important of these mechanisms and their complexity, the understanding of which will be among the most intriguing challenges of future neuroscience.

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.

Glutamate-AMPAR interaction in a model of synaptic transmission

Over the last several years we have investigated the excitatory synaptic response by means of a mathematical model based on a detailed description of the synapse geometry, the Brownian motion of Glutamate molecules and their binding to postsynaptic receptors. Recently, the basic model has been modified for the numbers, the size and the 3D structure of receptors according to new data from the literature. Some results of simulations performed with the updated model are shown here. They were aimed to study the synaptic response in relation to the binding probability, to the probable height of the receptors in the synaptic cleft, and to the space-time distribution of Glutamate/Receptor collisions. A first series of simulations permitted to determine a possible range of values for the binding probability of Glutamate to receptors. Other simulations, investigating the changes induced on the synaptic response by the variations of the height of AMPA receptors in synaptic cleft, allowed to identify the height producing the higher amplitude peak of the mEPSCs. Finally, two new statistical descriptors for analyzing the synaptic response were presented. The first is based on the study of the space distribution of the number of Glutamate/Receptor collisions. Simulations investigating the effects of an increasing eccentricity of the releasing vesicle allowed assessing this method. The second one considers the inter-collision times between Glutamate molecules and binding sites. The results of some of the last simulations demonstrated its capacity to highlight the subtleties and the randomness underlying the activation of the receptors. This article is part of a Special Issue entitled Neural Coding 2012.

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.

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.

Parametric spectral analysis of nonstationary fluctuations of excitatory synaptic currents

We assessed on Monte-Carlo simulated excitatory post-synaptic currents the ability of autoregressive (AR)-model fitting to evaluate their fluctuations. AR-model fitting consists of a linear filter describing the process that generates the fluctuations when driven with a white noise. Its fluctuations provide a filtered version of the signal and have a spectral density depending on the properties of the linear filter. When the spectra of the non-stationary fluctuations of excitatory post-synaptic currents were estimated by fitting AR-models to the segments of current fluctuations, assumed to be stationary and independent, the parameter and spectral estimates were scattered. The scatter was much reduced if the time-variant AR-models were fitted using stochastic adaptive estimators (Kalman, recursive least squares and least mean squares). The ability of time-variant AR-models to accurately fit the current fluctuations was monitored by comparing the fluctuations with predicted fluctuations, and by evaluating the model-learning rate. The median frequency of current fluctuations, which could be rapidly tracked and estimated from the individual quantal events (either Monte-Carlo simulated or recorded from pyramidal neurons of rat hippocampus), rose during the rise phase, before declining to a lower steady-state level during the decay phase of quantal event, whereas the variance showed a broad peak. The closing rate of AMPA channels directly affects the steady-state median frequency, whereas the transient peak can be modulated by a variety of factors-number of molecules released, ability of glutamate molecules to re-enter the synaptic cleft, diffusion constant of glutamate in the cleft and opening rate of AMPA channels. In each case, the effect on the amplitude and decay time of mEPSCs and on the current fluctuations differs. Each factor thus leaves its own kinetic fingerprint arguing that the contribution of such factors can be inferred from the combined kinetic properties of individual mEPSCs.

Monte Carlo simulation of release of vesicular content in neuroendocrine cells

The release of transmitter from the vesicle, its diffusion through the fusion pore, and the cleft and its interaction with the carbon electrode were simulated using the Monte Carlo method. According to the simulation the transmitter release is largely determined by geometric factors--the ratio of the fusion pore cross-sectional and vesicular areas, if the diffusion constant is as in the aqueous solution--but the speed of transmitter dissociation from the gel matrix plays an important role during the rise phase of release. Transmitter is not depleted near the entrance to the fusion pore and there is no cleft-to-vesicle feedback, but the depletion becomes evident if the diffusion constant is reduced, especially if the pore is wide. In general, the time course of amperometric currents closely resembles the time course of the simulated transmitter concentration in the cleft and the time course of release. Surprisingly, even a tenfold change of the electrode efficiency has only a marginal effect on the amplitude or the time course of amperometric currents. Greater electrode efficiency however lowers the cleft concentration, but only if the cleft is narrow. As the cleft widens the current amplitudes diminish and rise times lengthen, but the decay times are less affected. Moreover, the amplitude dependence of the rise and decay times becomes steeper as the cleft widens and/or as the release kinetics slows. Finally, lower diffusion constant of transmitter in the narrow cleft does not further prolong the amperometric currents, whose slow time course reflects slow release kinetics.

Multisynaptic activity in a pyramidal neuron model and neural code

The highly irregular firing of mammalian cortical pyramidal neurons is one of the most striking observation of the brain activity. This result affects greatly the discussion on the neural code, i.e. how the brain codes information transmitted along the different cortical stages. In fact it seems to be in favor of one of the two main hypotheses about this issue, named the rate code. But the supporters of the contrasting hypothesis, the temporal code, consider this evidence inconclusive. We discuss here a leaky integrate-and-fire model of a hippocampal pyramidal neuron intended to be biologically sound to investigate the genesis of the irregular pyramidal firing and to give useful information about the coding problem. To this aim, the complete set of excitatory and inhibitory synapses impinging on such a neuron has been taken into account. The firing activity of the neuron model has been studied by computer simulation both in basic conditions and allowing brief periods of over-stimulation in specific regions of its synaptic constellation. Our results show neuronal firing conditions similar to those observed in experimental investigations on pyramidal cortical neurons. In particular, the variation coefficient (CV) computed from the inter-spike intervals (ISIs) in our simulations for basic conditions is close to the unity as that computed from experimental data. Our simulation shows also different behaviors in firing sequences for different frequencies of stimulation.

The mammalian central nervous synaptic cleft contains a high density of periodically organized complexes

Cryo-electron microscopy of vitreous section makes it possible to observe cells and tissues at high resolution in a close-to-native state. The specimen remains hydrated; chemical fixation and staining are fully avoided. There is minimal molecular aggregation and the density observed in the image corresponds to the density in the object. Accordingly, organotypic hippocampal rat slices were vitrified under high pressure and controlled cryoprotection conditions, cryosectioned at a final thickness of approximately 70 nm and observed below -170 degrees C in a transmission electron microscope. The general aspect of the tissue compares with previous electron microscopy observations. The detailed analysis of the synapse reveals that the density of material in the synaptic cleft is high, even higher than in the cytoplasm, and that it is organized in 8.2-nm periodic transcleft complexes. Previously undescribed structures of presynaptic and postsynaptic elements are also described.