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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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 7nm to 3nm, disposed on a grid with spacing of 14nm or 8nm. 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. [Copyright &y& Elsevier]

Abstract: 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 i mprint, 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

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. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

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. [Copyright &y& Elsevier]

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 postsynaptic 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]