Francesco Ventriglia

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.

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.

Renal and Cardiovascular Effects of Angiotensin-Converting Enzyme Inhibitor Plus Angiotensin II Receptor Antagonist Therapy in Children With Proteinuria

OBJECTIVE. We investigated whether the combination of an angiotensin-converting enzyme inhibitor and an angiotensin II type 1 receptor antagonist offers better control of proteinuria and cardiovascular parameters without causing adverse side effects. METHODS. We enrolled 10 children (mean age: 12.3 ± 4.06 years) with proteinuria resulting from chronic renal diseases of various causes. The study consisted of 2 phases, 3 months each, for an overall 6-month observation time. During phase 1 (3 months), each child was assigned randomly to treatment with either an angiotensin-converting enzyme inhibitor or an angiotensin II type 1 receptor antagonist alone. During phase 2, each child was advanced to combination therapy with the addition of an angiotensin II type 1 receptor antagonist or an angiotensin-converting enzyme inhibitor, respectively. Renal function tests, echocardiography, and 24-hour ambulatory blood pressure monitoring were performed at the beginning of the study (time 0), at 3 months (time 1), and at 6 months (time 2). RESULTS. At time 2, proteinuria (change: −80.21 ± 10.75%), interventricular septum index (change: −13.63 ± 18.64%), posterior wall of the left ventricle index (change: −30.71 ± 20.32%), and left ventricular mass index (change: −28.33 ± 24.44%) were reduced significantly, compared with time 0 and time 1. No untoward side effects were detected during the study. CONCLUSIONS. In the short term, the combination of angiotensin-converting enzyme inhibitors and angiotensin II type 1 receptor antagonists for children with proteinuria of renal origin reduced proteinuria significantly, compared with baseline or either drug alone. Furthermore, echocardiographic studies gave evidence of reduction of left ventricular hypertrophy. Additional studies are needed to evaluate long-term results.

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.

10 – Towards a Kinetic Theory of Cortical-like Neural Fields

Publisher Summary The kinetic theory of neural fields is based fundamentally on the description of electrical properties of single neurons and on some statistical hypotheses about their connecting network. This chapter discusses the basis of this theory and its main results. It discusses a basilar, minimal set of biological neural features, except those linked to neural plasticity. Such characteristics are utilized for the construction, through statistical-physics methods, of a general mathematical model, which does not refer to particular brain regions. The chapter discusses some results of the application of the theory to cortical-like neural fields and to attention and learning. Neural systems are considered as finite regions of the three-dimensional space filled with two different types of particles. Neurons, characterized by an inner excitation corresponding to the subthreshold membrane potential, constitute a kind of motionless, solid background. They, under some conditions, emit impulses in space.

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.

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.

Saturation in excitatory synapses of hippocampus investigated by computer simulations

Abstract.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.

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.