Synaptic dendritic activity modulates the single synaptic event.

Synaptic transmission is the key system for the information transfer and elaboration among neurons. Nevertheless, a synapse is not a standing alone structure but it is a part of a population of synapses inputting the information from several neurons on a specific area of the dendritic tree of a single neuron. This population consists of excitatory and inhibitory synapses the inputs of which drive the postsynaptic membrane potential in the depolarizing (excitatory synapses) or depolarizing (inhibitory synapses) direction modulating in such a way the postsynaptic membrane potential. The postsynaptic response of a single synapse depends on several biophysical factors the most important of which is the value of the membrane potential at which the response occurs. The concurrence in a specific time window of inputs by several synapses located in a specific area of the dendritic tree can, consequently, modulate the membrane potential such to severely influence the single postsynaptic response. The degree of modulation operated by the synaptic population depends on the number of synapses active, on the relative proportion between excitatory and inbibitory synapses belonging to the population and on their specific mean firing frequencies. In the present paper we show results obtained by the simulation of the activity of a single Glutamatergic excitatory synapse under the influence of two different populations composed of the same proportion of excitatory and inhibitory synapses but having two different sizes (total number of synapses). The most relevant conclusion of the present simulations is that the information transferred by the single synapse is not and independent simple transition between a pre- and a postsynaptic neuron but is the result of the cooperation of all the synapses which concurrently try to transfer the information to the postsynaptic neuron in a given time window. This cooperativeness is mainly operated by a simple mechanism of modulation of the postsynaptic membrane potential which influences the amplitude of the different components forming the postsynaptic excitatory response.

Influence of active synaptic pools on the single synaptic event.

The activity of the single synapse is the base of information processing and transmission in the brain as well as of important phenomena as the Long Term Potentiation which is the main mechanism for learning and memory. Although usually considered as independent events, the single quantum release gives variable postsynaptic responses which not only depend on the properties of the synapses but can be strongly influenced by the activity of other synapses. In the present paper we show the results of a series of computational experiments where pools of active synapses, in a compatible time window, influence the response of a single synapse of the considered pool. Moreover, our results show that the activity of the pool, by influencing the membrane potential, can be a significant factor in the NMDA unblocking from Mg2+ increasing the contribution of this receptor type to the Excitatory Post Synaptic Current. We consequently suggest that phenomena like the LTP, which depend on NMDA activation, can occur also in subthreshold conditions due to the integration of the dendritic synaptic activity.

Multisynaptic cooperation shapes single glutamatergic synapse response.

The activity of thousands of excitatory synapse in the dendritic tree produces variations of membrane potential which, while can produce the spike generation at soma (hillock), can also influence the output of a single glutamatergic synapse. We used a model of synaptic diffusion and EPSP generation to simulate the effect of different number of active synapses on the output of a single one. Our results show that, also in subthreshold conditions, the excitatory dendritic activity can influence several parameters of the single synaptic output such as its amplitude, its time course, the NMDA-component activation and consequently phenomena like STP and LTP.

Stochastic, structural and functional factors influencing AMPA and NMDA synaptic response variability: a review.

Synaptic transmission is the basic mechanism of information transfer between neurons not only in the brain, but along all the nervous system. In this review we will briefly summarize some of the main parameters that produce stochastic variability in the synaptic response. This variability produces different effects on important brain phenomena, like learning and memory, and, alterations of its basic factors can cause brain malfunctioning.

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 [Mg(2+)]-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 Mg(2+) concentrations determine different levels of cooperativeness between AMPA and NMDA receptors in shaping the post-synaptic response.

AMPA/NMDA cooperativity and integration during a single synaptic event.

Coexistence of AMPA and NMDA receptors in glutamatergic synapses leads to a cooperative effect that can be very complex. This effect is dependent on many parameters including the relative and absolute number of the two types of receptors and biophysical parameters that can vary among synapses of the same cell. Herein we simulate the AMPA/NMDA cooperativity by using different number of the two types of receptors and considering the effect of the spine resistance on the EPSC production. Our results show that the relative number of NMDA with respect to AMPA produces a different degree of cooperation which depends also on the spine resistance.

A model of dopamine regulation of glutamatergic synapse on medium size spiny neurons.

Spiny neurons of striatum receive glutamatergic synapses on dendritic spines on the neck of which project dopaminergic synapses. Dopamine modulates, by D1 type receptors, the glutamatergic synapses by inducing the phosphorylation of AMPA and NMDA receptors which produces an increased amplitude response. Herein we present a model where, in addition to phosphorylation, the direct modulation by dopamine of the spine resistance can cooperate in producing the observed effect on some of these synapses.

A model of dopamine modulated glutamatergic synapse.

The dopamine neurotransmitter regulates important neural pathways and its action in the brain is very complex. When dopaminergic neurons make synapses on spiny neurons of the striatum nucleus, they tune the responsiveness of glutamatergic synapses by means of the dopamine D1 and D2 receptors. We studied the effect of dopamine D1 receptors on glutamatergic synapse of GABAergic spiny neurons in striatum nucleus where they are located on the neck of the same spine. The action of dopamine consists essentially in promoting the phosphorylation of AMPA and NMDA receptors thus increasing the Excitatory Post Synaptic Current peak amplitude. The consequence is a cooperative effect of glutamatergic and dopaminergic synapses for the regulation of the GABAergic neuronal code. The mechanisms by which the phosphorylation induces the increase of the EPSC amplitude still remain unclear although the lack of this regulation can be involved in several pathologies as, for example, the Parkinson's disease. We tested, by computational experiments based on our model of glutamatergic synapse, three parameters of the synaptic function that could be involved in dopamine action: (a) time binding of glutamate to receptors; (b) open probability of the receptors; and (c) single receptor conductance. For different reasons, any of the three parameters could be responsible of the increased EPSC-dopamine-dependent. Our computational results were compared and discussed with experimental results found in literature. Although for our model both the open probability and the single receptor conductance can reproduce the phosphorylation effect of dopamine, we argue that the dopamine effect consists essentially in an increase of the single receptor conductance due to a 3D rearrangement of the phosphorylated receptors.

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.

The engram formation and the global oscillations of CA3.

The investigation on the conditions which cause global population oscillatory activities in neural fields, originated some years ago with reference to a kinetic theory of neural systems, as been further deepened in this paper. In particular, the genesis of sharp waves and of some rhythmic activities, such as theta and gamma rhythms, of the hippocampal CA3 field, behaviorally important for their links to learning and memory, has been analyzed with more details. To this aim, the modeling-computational framework previously devised for the study of activities in large neural fields, has been enhanced in such a way that a greater number of biological features, extended dendritic trees-in particular, could be taken into account. By using that methodology, a two-dimensional model of the entire CA3 field has been described and its activity, as it results from the several external inputs impinging on it, has been simulated. As a consequence of these investigations, some hypotheses have been elaborated about the possible function of global oscillatory activities of neural populations of Hippocampus in the engram formation.

Global rhythmic activities in hippocampal neural fields and neural coding.

Global oscillations of the neural field represent some of the most interesting expressions of the hippocampal activity, being related also to learning and memory. To study oscillatory activities of the CA3 field in theta range, a model of this sub-field of Hippocampus has been formulated. The model describes the firing activity of CA3 neuronal populations within the frame of a kinetic theory of neural systems and it has been used for computer simulations. The results show that the propagation of activities induced in the neural field by hippocampal afferents occurs only in narrow time windows confined by inhibitory barrages, whose time-course follows the theta rhythm. Moreover, during each period of a theta wave, the entire CA3 field bears a firing activity with peculiar space-time patterns, a sort of specific imprint, which can induce effects with similar patterns on brain regions driven by the hippocampal formation. The simulation has also demonstrated the ability of medial septum to influence the global activity of the CA3 pyramidal population through the control of the population of inhibitory interneurons. At last, the possible involvement of global population oscillations in neural coding has been discussed.

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.

Saturation in excitatory synapses of hippocampus investigated by computer simulations.

The standard view of the synaptic function in excitatory synapses has been deeply questioned by recent experimental data on hippocampal glutamate synapses both for possible receptor nonsaturation and for larger and non-Gaussian peak amplitude fluctuations. Our previous investigations of the mechanisms involved in the variability of the response of hippocampal glutamatergic synapses, carried out by computer simulation of simple Brownian models of glutamate diffusion, furnished initial evidence about their presynaptic character. A new, refined model, reported here, assumes a collision volume for the glutamate molecule and a more realistic description of receptors and their binding dynamics. Based on this model, conditions for AMPA and NMDA receptor saturation have been investigated and new miniature (or quantal) EPSC parameters have been computed. The results corroborate the hypothesis that the lack of AMPA and NMDA receptor saturation and the EPSC stochastic variability are attributable to the small volume of glutamatergic synaptic vesicles and hence to the small number of glutamate molecules diffusing in the cleft after a vesicle release. The investigations better characterize some not well-known elements of the synaptic structure, such as the fusion pore, and provide useful information on AMPA receptor dynamics. Indeed, a nice fit between computed EPSCs and some miniature EPSCs in recent experimental literature allowed for the computation of new transition time values among the different AMPA receptor states through a trial-and-error optimization procedure. Moreover, the model has been used to evaluate two hypotheses on the genesis of the long-term potentiation phenomenon.

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.

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

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.

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.