A two-dimensional compartment model for the reaction-diffusion system of acetylcholine in the synaptic cleft at the neuromuscular junction

Naka, Takashi; Shiba, K.; Sakamoto, Naoto

doi:10.1016/s0303-2647(96)01659-0

Cited by 13 publications

(35 citation statements)

References 8 publications

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“…Virtually all functional models of the NMJ focus on relating the receptor conformational state to the other properties of interest (Friboulet and Thomas 1993;Jackson 1989;Madsen et al 1984;Mathie and Cull-Candy 1991;Naka and Shiba 1997;Naka and Sakamoto 2002;Rosenberry 1979;Schild 1995;Vieth and Chotani 1983;Vieth and Ciftci 1981;Wathey and Nass 1979). A good test of the integrity of a model is how well the state of the receptors can be directly or indirectly coupled to a measurable property.…”

Section: Resultsmentioning

confidence: 99%

“…A good test of the integrity of a model is how well the state of the receptors can be directly or indirectly coupled to a measurable property. Parameter values used in the simulation and their sources (Naka and Shiba 1997;Wathey and Nass 1979) are listed in Table 1.…”

Section: Resultsmentioning

confidence: 99%

“…Table 1 Parameter values used in the simulation and their sources (Naka and Shiba 1997;Wathey and Nass 1979) Name/symbol Value (units)…”

Section: D Modelmentioning

confidence: 99%

“…The loss of Ach from the gap was modeled mathematically as a reactive "sink" term. Naka and Shiba (1997) extended the works of Rosenberry, Wathey, and Friboulet into a two-dimensional space geometrically modeled as an axis-symmetrical disk. Acetylcholine simultaneously diffused transversely across the gap from the presynaptic membrane to the post-synaptic membrane, radially out of the gap, and reacted with receptors and enzyme.…”

Section: Introductionmentioning

confidence: 99%

“…However, these analytical models either do not incorporate the complete reaction kinetics, or use assumptions which simplify the geometry or spatial dimensions. The bulk of the published researches which achieve a more complete description of the NMJ diffusion-reaction processes are based on numerical solutions (Bartol 1991;Friboulet and Thomas 1993;Giniatullin 1995;Madsen et al 1984;Naka and Shiba 1997;Rosenberry 1979;Schild 1995;Wathey and Nass 1979). Finite difference discretization is one numerical technique commonly chosen to solve coupled nonlinear PDEs, which results in transforming a system of nonlinear PDEs into a system of coupled nonlinear algebraic equations.…”

Section: Introductionmentioning

confidence: 99%

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A new 3D mass diffusion–reaction model in the neuromuscular junction

et al. 2010

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A three-dimensional model of the reaction-diffusion processes of a neurotransmitter and its ligand receptor in a disk shaped volume is proposed which represents the transmission process of acetylcholine in the synaptic cleft in the neuromuscular junction. The behavior of the reaction-diffusion system is described by a three-dimensional diffusion equation with nonlinear reaction terms due to the rate processes of acetylcholine with the receptor. A new stable and accurate numerical method is used to solve the equations with Neumann boundaries in cylindrical coordinates. The simulation analysis agrees with experimental measurements of end-plate current, and agrees well with the results of the conformational state of the acetylcholine receptor as a function of time and acetylcholine concentration of earlier investigations with a smaller error compared to experiments. Asymmetric emission of acetylcholine in the synaptic cleft and the subsequent effects on open receptor population is simulated. Sensitivity of the open receptor dynamics to the changes in the diffusion parameters and neuromuscular junction volume is investigated. The effects of anisotropic diffusion and non-symmetric emission of transmitter at the presynaptic membrane is simulated.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…Table 1 Parameter values used in the simulation and their sources (Naka and Shiba 1997;Wathey and Nass 1979) Name/symbol Value (units)…”

Section: D Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A new 3D mass diffusion–reaction model in the neuromuscular junction

et al. 2010

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Improving Diffusion-Based Molecular Communication with Unanchored Enzymes

Noel

Cheung

Schober

2014

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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In this paper, we propose adding enzymes to the propagation environment of a diffusive molecular communication system as a strategy for mitigating intersymbol interference. The enzymes form reaction intermediates with information molecules and then degrade them so that they have a smaller chance of interfering with future transmissions. We present the reaction-diffusion dynamics of this proposed system and derive a lower bound expression for the expected number of molecules observed at the receiver. We justify a particle-based simulation framework, and present simulation results that show both the accuracy of our expression and the potential for enzymes to improve communication performance.

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Continuum simulations of acetylcholine diffusion with reaction-determined boundaries in neuromuscular junction models

Cheng

Suen

Radić

et al. 2007

Biophysical Chemistry

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The reaction-diffusion system of the neuromuscular junction has been modeled in 3D using the finite element package FEtk. The numerical solution of the dynamics of acetylcholine with the detailed reaction processes of acetylcholinesterases and nicotinic acetylcholine receptors has been discussed with the reaction-determined boundary conditions. The simulation results describe the detailed acetylcholine hydrolysis process, and reveal the time-dependent interconversion of the closed and open states of the acetylcholine receptors as well as the percentages of unliganded/monoliganded/diliganded states during the neuro-transmission. The finite element method has demonstrated its flexibility and robustness in modeling large biological systems.

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A two-dimensional compartment model for the reaction-diffusion system of acetylcholine in the synaptic cleft at the neuromuscular junction

Cited by 13 publications

References 8 publications

A new 3D mass diffusion–reaction model in the neuromuscular junction

A new 3D mass diffusion–reaction model in the neuromuscular junction

Improving Diffusion-Based Molecular Communication with Unanchored Enzymes

Continuum simulations of acetylcholine diffusion with reaction-determined boundaries in neuromuscular junction models

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