Vito Di Maio

Stochastic fluctuations of the quantal EPSC amplitude in computer simulated excitatory synapses of hippocampus

The postsynaptic response in glutamatergic synapses of hippocampus, produced by the release of a single presynaptic vesicle, shows a large variability in amplitude not only among the synapses, but also for a single synapse. A mathematical modelling based on a Brownian motion for the diffusion of glutamate molecules and receptor binding was applied to study the possible sources of the quantal variability. Detailed, geometric and functional, descriptions of the vesicle, of the fusion pore and of the synaptic cleft were used and quantal (or miniature) EPSCs were computed. Our results show non-saturation of AMPA receptors, attributable to the small number of molecules contained in the glutamate vesicles of hippocampus. NMDA receptor saturation was obtained rarely, only in very specific instances. We concluded that the lack of AMPA saturation and intrinsic random variations in basic presynaptic elements, such as the vesicle volume and the vesicle docking position, are the main causes of the observed stochastic variability of the quantal EPSC amplitude. Only minor effects can be ascribed to postsynaptic sources.

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

Abstract. 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.

Synaptic fusion pore structure and AMPA receptor activation according to Brownian simulation of glutamate diffusion.

Abstract. The rising phase of fast, AMPA-mediated Excitatory Post Synaptic Currents (EPSCs) has a primary role in the computational ability of neurons. The structure and radial expansion velocity of the fusion pore between the vesicle and the presynaptic membrane could be important factors in determining the time course of the EPSC. We have used a Brownian simulation model for glutamate neurotransmitter diffusion to test two hypotheses on the fusion pore structure, namely, the proteinaceous pore and the purely lipidic pore. Three more hypotheses on the radial expansion velocity were also tested. The rising phases of the EPSC, computed under various conditions, were compared with experimental data from the literature. Our present results show that a proteinaceous fusion pore should produce a more marked foot at the beginning of the rising phase of the EPSC. They also confirm the hypothesis that the structure of the fusion pore and its radial expansion velocity play significant roles in shaping the fast EPSC time course.

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.

Stochastic fluctuations of the synaptic function.

The peak amplitudes of the quantal Excitatory Post Synaptic Currents in single hippocampal synapses show a large variability. Here, we present the results of a mathematical, computational investigation on the main sources of this variability. A detailed description of the synaptic cleft, rigorously based on empirically-derived parameters, was used. By using a Brownian motion model of neurotransmitter molecule diffusion, quantal EPSCs were computed by a simple kinetic schema of AMPA receptor dynamics. Our results show that the lack of saturation of AMPA receptors obtained in these conditions, combined with stochastic variations in basic presynaptic elements, such as the vesicle volume, the vesicle docking position, and the vesicle neurotransmitter concentration can explain almost the entire range of EPSC variability experimentally observed.

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.

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.

Neural code and irregular spike trains

The problem of the code used by brain to transmit information along the different cortical stages is yet unsolved. Two main hypotheses named the rate code and the temporal code have had more attention, even though the highly irregular firing of the cortical pyramidal neurons seems to be more consistent with the first hypothesis. In the present article, we present a model of cortical pyramidal neuron intended to be biologically plausible and to give more information on the neural coding problem. The model takes into account the complete set of excitatory and inhibitory inputs impinging on a pyramidal neuron and simulates the output behaviour when all the huge synaptic machinery is active. Our results show neuronal firing conditions, very similar to those observed in in vivo experiments on pyramidal cortical neurons. In particular, the variation coefficient (CV) computed for the Inter-Spike-Intervals in our computational experiments is very close to the unity and quite similar to that experimentally observed. The bias toward the rate code hypothesis is reinforced by these results.

Area perception in simple geometrical figures.

The results of experiments on visual perception of area of circles and squares are reported. Pairs of geometrical figures were presented simultaneously on an oscilloscope screen. While one of them was fixed, the other one was controlled by an experimental subject. The task of the subject was to match the area of the variable figure to the area of the fixed one. The obtained data show underestimation of the area of circle when compared with square. A mathematical model designed to explain this phenomenon is proposed here. The image function defined as a low-pass filtered (blurred) version of the figure is employed for this purpose. Then, instead of the position of the image function maxima, the position of a threshold value is used for area computation.

A model of cooperative effect of AMPA and NMDA receptors in glutamatergic synapses

Glutamatergic synapses play a pivotal role in brain excitation. The synaptic response is mediated by the activity of two receptor types (AMPA and NMDA). In the present paper we propose a model of glutamatergic synaptic activity where the fast current generated by the AMPA conductance produces a local depolarization which activates the voltage- and [Mg2+]-dependent NMDA conductance. This cooperative effect is dependent on the biophysical properties of the synaptic spine which can be considered a high input resistance specialized compartment. Herein we present results of simulations where different values of the spine resistance and of the Mg2+ concentrations determine different levels of cooperativeness between AMPA and NMDA receptors in shaping the post-synaptic response.