Action potentials (APs) in the soma of central neurons exhibit a sharp, step-like onset dynamics, which facilitates the encoding of weak but rapidly changing input signals into trains of action potentials. One possibility to explain the rapid AP onset dynamics is to assume cooperative activation of sodium channels. However, there is no direct evidence for cooperativity of voltage gated sodium channels in central mammalian neurons. The fact that APs in cortical neurons are initiated in the axon and backpropagate into the soma, prompted an alternative explanation of the sharp onset of somatic APs. In the invasion scenario, the AP onset is smooth at the initiation site in the axon initial segment, but the current invading the soma before somatic sodium channels are activated produces a sharp onset of somatic APs. Here we used multicompartment neuron models to identify ranges of active and passive cell properties that are necessary to reproduce the sharp AP onset in the invasion scenario. Results of our simulations show that AP initiation in the axon is a necessary but not a sufficient condition for the sharp onset of somatic AP: for a broad range of parameters, models could reproduce distal AP initiation and backpropagation but failed to quantitatively reproduce the onset dynamics of somatic APs observed in cortical neurons. To reproduce sharp onset of somatic APs, the invasion scenario required specific combinations of active and passive cell properties. The required properties of the axon initial segment differ significantly from the currently accepted and experimentally estimated values. We conclude that factors additional to the invasion contribute to the sharp AP onset and further experiments are needed to explain the AP onset dynamics in cortical neurons.