Modeling Transport of Ca2+ in Neural Synapse with Boltzmann Equation and Electrodynamics

The transport of ions such as Calcium 2+ plays a relevant role in neural synapse. Because the electric charge of neurotransmitters, Boltzmann equation as well as well-known equations of classical electrodynamics can be used to explore electrical properties of synapse. In order to accomplish this, an axes of symmetry so that the geometry of axon as a cylinder, was assumed. In essence, equation models the entry of intracellular Calcium 2+ known as voltage-gated N-type calcium channels into neurons. Inside axon ions produce waves that are responsible to produce electric interactions with synaptic vesicles as well as neurotransmitters. Thus it is expected a well-defined electrodynamics that allows to neurotransmitters to pass along cleft towards postsynaptic neuron. In this manner, current and voltage by using the Boltzmann equation have been derived. It is shown that both the Calcium 2+ ions trigger a well-defined electrodynamics for neurotransmitters.