  This paper uses a simple optogenetic model to compare the timing distortion
between a randomly-generated target spike sequence and an externally-stimulated
neuron spike sequence. Optogenetics is an emerging field of neuroscience where
neurons are genetically modified to express light-sensitive receptors that
enable external control over when the neurons fire. Given the prominence of
neuronal signaling within the brain and throughout the body, optogenetics has
significant potential to improve the understanding of the nervous system and to
develop treatments for neurological diseases. This paper primarily considers
two different distortion measures. The first measure is the delay in
externally-stimulated spikes. The second measure is the root mean square error
between the filtered outputs of the target and stimulated spike sequences. The
mean and the distribution of the distortion is derived in closed form when the
target sequence generation rate is sufficiently low. All derived results are
supported with simulations. This work is a step towards an analytical model to
predict whether different spike trains were observed from the same stimulus,
and the broader goal of understanding the quantity and reliability of
information that can be carried by neurons.
