Reconstructing dynamics from neural spike trains

The series of firing times from a neuron can be viewed as a point process. There is great interest in being able to relate these firing times to dynamical variables such as the intracellular voltage. A method has recently been proposed (T. Saner, Phys. Rev. Let., vol. 72, p. 3811, 1994) that allows the reconstruction of the full dynamics of an input to an integrate and fire (IF) device using a delay embedding of interspike intervals (ISI's). The authors show that this does not imply that the intracellular dynamics of a neuron can be reconstructed. They use a similar but physiologically more plausible IF neuron model to show that the attractor can only be reconstructed if the dynamics are "sampled" at a high frequency by the spikes. The reconstructed dynamics degrade for more physiologically plausible sampling rates.