# Root Mean Square Error of Neural Spike Train Sequence Matching with Optogenetics

## TL;DR

This paper analyzes the accuracy of neural spike train matching in optogenetics by deriving and verifying the root mean square error between target and stimulated spike sequences, providing insights into timing distortion.

## Contribution

It introduces a mathematical framework for quantifying spike train matching error in optogenetics, including a closed-form expression for expected distortion at low firing rates.

## Key findings

- Derived a closed-form expression for expected RMS error.
- Verified theoretical results with simulations.
- Provides a tool for assessing neural stimulation accuracy.

## Abstract

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 uses a simple optogenetic model to compare the timing distortion between a randomly-generated target spike sequence and an externally-stimulated neuron spike sequence. The distortion is measured by filtering each sequence and finding the root mean square error between the two filter outputs. The expected distortion is derived in closed form when the target sequence generation rate is sufficiently low. Derivations are verified via simulations.