We apply our stochastic cell model to simulate the noisy shape of single neuronal action potentials on the basis of the nonlinear oscillatory Brusselator model. By comparison with the experimental action potentials as measured by Laurent and co-workers in the olfactory system of the locust, we conclude that at least similar to14000 ion channels in a local neuron (LN) and similar to70000 ion channels in a project neueron (PN) are responsible for the stochastic appearance of the measured action potentials. Instead of treating the stochastic gating of ionic channels as a multistate Markov process, we use a computer simulation that performs a direct count of all events of each individual reaction step on the basis of their Poisson distributions. Our stochastic analysis is independent of the particular architecture of the neuronal network.