Numerical simulation for a neurotransmitter transport model in the axon terminal of a presynaptic neuron

Abstract

Neurotransmitters in the terminal bouton of a presynaptic neuron are stored in vesicles, which diffuse in the cytoplasm and, after a stimulation signal is received, fuse with the membrane and release its contents into the synaptic cleft. It is commonly assumed that vesicles belong to three pools whose content is gradually exploited during the stimulation. This article presents a model that relies on the assumption that the release ability is associated with the vesicle location in the bouton. As a modeling tool, partial differential equations are chosen as they allow one to express the continuous dependence of the unknown vesicle concentration on both the time and space variables. The model represents the synthesis, concentration-gradient-driven diffusion, and accumulation of vesicles as well as the release of neuroactive substances into the cleft. An initial and boundary value problem is numerically solved using the finite element method (FEM) and the simulation results are presented and discussed. Simulations were run for various assumptions concerning the parameters that govern the synthesis and diffusion processes. The obtained results are shown to be consistent with those obtained for a compartment model based on ordinary differential equations. Such studies can be helpful in gaining a deeper understanding of synaptic processes including physiological pathologies. Furthermore, such mathematical models can be useful for estimating the biological parameters that are included in a model and are hard or impossible to measure directly.

Synaptic bouton properties are tuned to best fit the prevailing firing pattern

“…Electrical signaling of neurons is often modeled as a one-dimensional process using the cable equation and compartmental one-dimensional space discretization (Hines and Carnevale, 2001). There are few approaches in cellular modeling that make use of 2D or 3D modeling techniques (Smart and McCammon, 1998; Ross et al, 2000; Meinrenken et al, 2002; Tai et al, 2003; Marpeau et al, 2009; Bielecki et al, 2010). Most commonly, stochastic models are employed to address the high complexity of three-dimensional simulations.…”

The general entity of life: a cybernetic approach

“…In such a way, the highest levels of information processing can be considered-compare Kȩpiński's studies. The information processing, for instance in the nervous system, takes place over time [108,Chapter 5], [121], so the operators that model this phenomenon mathematically are time-dependent [13][14][15][16].…”

Relations between Geometric Parameters and Numerical Simulation Accuracy in Modeling Signal Transmission in the Presynaptic Bouton

“…The above mentioned dynamical processes are often described by using differential equations [5][6][7], including−for a long time−partial ones [8][9][10]. The equation of this type can not, usually, be solved analytically, and therefore numerical methods have to be used [10][11][12][13]. In order to perform the calculations quickly and accurately, the appropriately designed mesh, in the nodes of which the calculations will be made, should be created.…”