Neurons process and encode information by generating sequences of action potentials. For all spiking neurons, the encoding of single-neuron computations into sequences of spikes is biophysically determined by the cell's action-potential-generating mechanism. It has recently been discovered that apparently minor modifications of this mechanism can qualitatively change the nature of neuronal encoding. Here we quantitatively analyse the dynamics of action potential initiation in cortical neurons in vivo, in vitro and in computational models. Unexpectedly, key features of the initiation dynamics of cortical neuron action potentials--their rapid initiation and variable onset potential--are outside the range of behaviours described by the classical Hodgkin-Huxley theory. We propose a new model based on the cooperative activation of sodium channels that reproduces the observed dynamics of action potential initiation. This new model predicts that Hodgkin-Huxley-type dynamics of action potential initiation can be induced by artificially decreasing the effective density of sodium channels. In vitro experiments confirm this prediction, supporting the hypothesis that cooperative sodium channel activation underlies the dynamics of action potential initiation in cortical neurons.