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Objective: 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 when the neurons fire. Methods: Two different measures are studied to determine the timing distortion. 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. Results: The mean and the distribution of the distortion are derived in closed form when the target sequence generation rate is sufficiently low. The derived results are verified with simulations. Conclusion: The proposed model and distortion measures can be used to measure the deviation between neuron spike sequences that are prescribed and what can be achieved via external stimulation. Significance: 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 work is a step towards an analytical model to predict whether different spike trains were observed from the same external stimulus, and the broader goal of understanding the quantity and reliability of information that can be carried by neurons.

Distortion Distribution of Neural Spike Train Sequence Matching With Optogenetics