1. Modeling the Neuromuscular Junction
Shanae Roybal1, Edgar Ronquillo2, Ashis Nandy2, Ulises M. Ricoy1, David Torres3
Northern New Mexico University
Department of Biology, Chemistry and Environmental Science1
College of Engineering2
Department of Mathematics and Physical Science3
Results
Abstract
Chemical Reactions
Time history of average concentration of acetylcholine at postsynaptic muscle.
We use partial differential equations (PDEs) to model the neuromuscular junction (NMJ). The partial differential equations model the diffusion of the neurotransmitter acetylcholine and the reaction of acetylcholine with acetylcholinesterase. Equations also model the generation of the Michaelis ligand-substrate complex and its conversion to acylate enzyme followed by the re generation of acetylcholinesterase.
Concentration of acetylcholine
Red – highest, Blue – Lowest
Initial concentrations of reactants
Acetylcholine = .1 moles/liter
Acetylcholinesterase =.001 moles/liter
A: Acetylcholine
E: Acetylcholinesterase
AE: Michaelis ligand-substrate
acE: Acylate enzyme
The concentration of acetylcholine
is reduced through its reaction with
acetylcholinesterase.
Introduction
Equations
Time = 0 μs
Our body movements require a cascade of interactions beginning with specific commands originating in the brain, nerve impulses moving down our spinal cord, and neurotransmitter release into the neuromuscular junctions (NMJ) of striated muscles, leading to the contraction of the muscle. In our project, we focus on the neuromuscular junction. More specifically we analyze the diffusion and removal of neurotransmitters across the synaptic cleft.
Within the presynaptic terminal, there are vesicles that contain the neurotransmitter acetylcholine. Acetylcholine is a neurotransmitter made from choline and the acetyl CoA and catalyzed by choline acetyltransferase. As the nerve impulse reaches the terminal, voltage gated ion channels open allowing calcium ions to diffuse into the terminal. The rapid rise in intracellular calcium is the signal for the neurotransmitter vesicles to fuse to the membrane. Exocytosis allows the content of the vesicles to be released into the synaptic space (the space between the axon and the striated muscle). The neuromuscular junction is a specialized synapse and has various acetylcholine binding sites including acetylcholinesterase. Once the neurotransmitter binds to its receptor, the nerve impulse continues, the muscle contracts and movement follows. Acetylcholinesterase (hydrolysis enzyme) reacts with acetylcholine and reduces its concentration. If acetylcholine did not get hydrolyzed by acetylcholinesterase, the NMJ would be overstimulated and lose its function. Different levels of the enzyme will determine the levels of acetylcholine in the synapse. For example, Myathenia Gravis is treated medically with acetylcholinesterase inhibitors. Myasthenia gravis is an autoimmune neuromuscular disease that leads to fluctuating muscle weakness and fatigue. In most common cases, muscle weakness is cause by antibodies blocking acetylcholine receptors at the postsynaptic neuromuscular junction.
Conclusion
Our simulation was successful in modeling the chemistry and diffusion within a neuromuscular junction using a simplified geometry. Future plans include using more realistic geometries and an implicit method to accommodate larger time steps in the numerical solution.
Time = .54 μs
Solution method
A 2D grid (20 x 100) is constructed and concentrations of all reactants are initialized. A first-order Euler method is used to advance the equations in time. Diffusion terms are approximated using a second- order centered finite difference scheme.
Time = 1.08 μs
References
Liu D, Wang Y, and DeCoster MA (2013) Spectral Element Simulation of Reaction-Diffusion System in the Neuromuscular Junction. Journal of Applied and Computational Mathematics 2:136.
Image of neuromuscular junction
Time = 1.62 μs
Acknowledgements
We would like the acknowledge the support of the New Mexico Alliance for Participation grant.
For more Information contact:
Dr. David Torres,
Dr. Ulises Ricoy,
Time = 2.16 μs
Note the folds which increase the area on the muscle cell and the numerous vesicles.