PubMed · 12987078
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S DRUAULT-TOUFESCO. 1952. [More on prepapillary flocculus].. https://pubmed.ncbi.nlm.nih.gov/12987078/
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Synaptic conductances are influenced markedly by the geometry of the space surrounding the synapse since the transient glutamate concentration in the synaptic cleft is determined by this geometry. Our paper is an attempt to understand the reasons for slow glutamate diffusion in the cerebellar glomerulus, a structure situated around the enlarged mossy fiber terminal in the cerebellum and surrounded by a glial sheath. For this purpose, analytical expressions for glutamate diffusion in the glomerulus were considered in models with two-, three-, and fractional two-three-dimensional (2D-3D) geometry with an absorbing boundary. The time course of average glutamate concentration in the synaptic cleft of the mossy fiber-granule cell connection was calculated for both direct release of glutamate from the same synaptic unit, and for cumulative spillover of glutamate from neighboring release sites. Several kinetic schemes were examined, and the parameters of the diffusion models were estimated by identifying theoretical activation of AMPA receptors with direct release and spillover components of published experimental AMPA receptor-mediated EPSCs. For model selection, the correspondence of simulated paired-pulse ratio and EPSC increase after prevention of desensitization to experimental values were also taken into consideration. Our results suggest at least a 7- to 10-fold lower apparent diffusion coefficient of glutamate in the porous medium of the glomerulus than in water. The modeling of glutamate diffusion in the 2D-3D geometry gives the best fit of experimental EPSCs. We show that it could be only partly explained by normal diffusion of glutamate in the complex geometry of the glomerulus. We assume that anomalous diffusion of glutamate occurs in the glomerulus. A good match of experimental estimations and theoretical parameters, obtained in the simulations that use an approximation of anomalous diffusion by a solution for fractional Brownian motion, confirms our assumption.
The length of cerebellar parallel fibers is important for information integration by the Purkinje cells. Based on the Copernican principle for analyzing the length of stochastic events, we have recently devised a stochastic method to estimate the mean length of parallel fibers within a given cerebellar region. The purpose of the present report is to provide validation of this methodology via computational simulations. We create virtual parallel fibers with known lengths and program each step of our stochastic method for computational simulation. We then compare the observed mean length obtained from our computational simulation with the known mean length of the virtual parallel fibers. In particular, we investigate the effect of cutting parallel fibers into segments during histological sectioning. Our computational results reveal an over-estimation factor ranging from 1.0 (no correction is necessary) to 2.0 as the parallel fiber segmentation becomes increasingly severe. Based on probability theory considerations, we have confirmed the existence of this over-estimation. We have further determined the cause of this over-estimation to be an artificial consequence of one of the sampling steps in our stochastic method. These results provide validation of our methodology, as well as a correction factor, which can be derived directly from the experimentally measured parameters and used to obtain the true mean length of parallel fibers. Potential applications of the stochastic method include a comparative analysis of the length of parallel fibers as an approach to gain clues about cerebellar circuit principles and function. In addition, the stochastic method may also find promising applications in other functionally important axonal systems in the brain.
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