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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. An 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 pre-synaptic membrane is simulated.