Hodgkin and Huxley's seminal neuron model describes the propagation of voltage spikes in axons, but it cannot explain certain full-neuron features crucial for understanding the neural code. We consider channel current fluctuations in a trisection of the Hodgkin-Huxley model, allowing an analytic-mechanistic explanation of these features and yielding consistently excellent matches with in vivo recordings of cerebellar Purkinje neurons, which we use as model systems. This shows that the neuronal encoding is described conclusively by a soft-thresholding function having just three parameters. © 2021 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.