  Brains can process sensory information from different modalities at
astonishing speed, this is surprising as already the integration of inputs
through the membrane causes a delayed response. Neuronal recordings in vitro
reveal a possible explanation for the fast processing through an advancement of
the output firing rates of individual neurons with respect to the input, a
concept which we refer to as prospective coding. The underlying mechanisms of
prospective coding, however, is not completely understood. We propose a
mechanistic explanation for individual neurons advancing their output on the
level of single action potentials and instantaneous firing rates. Using the
Hodgkin-Huxley model, we show that the spike generation mechanism can be the
source for prospective (advanced) or retrospective (delayed) responses with
respect the underlying somatic voltage. A simplified Hodgkin-Huxley model
identifies the sodium inactivation as a source for the prospective firing,
controlling the timing of the neuron's output as a function the voltage and its
derivative. We also consider a slower spike-frequency adaptation as a
mechanisms that generates prospective firings to inputs that undergo slow
temporal modulations. In general, we show that adaptation processes at
different time scales can cause advanced neuronal responses to time varying
inputs that are modulated on the corresponding time scales.
