Optogenetics, named “Breakthrough of the Decade” by Science Magazine, gives scientists the ability to directly control individual neurons with pulses of light. The technique involves genetic modification of neurons, causing them to express light-sensitive proteins called opsins. When exposed to light, opsins open an ion channel; the ion current through the channel changes the electric potential across the neuron’s membrane, causing it to fire. Optogenetics gives scientists a precise tool for probing the function of the brain, and is expected to deliver revolutionary therapies for neurological conditions.
Our paper considers signal processing for optogenetics, in which there is a desired target firing pattern for an optogenetically-modified neuron. We consider two questions related to this setup. First, neurons do not fire instantly on exposure to light, and instead require a charging time. How should we illuminate the neuron to achieve the target firing pattern? Second, some firing patterns are impossible; for example, neurons have a refractory period after firing, so spikes cannot be created too close together in time. If the target pattern can’t be created, how close can we get to the target – that is, what is the minimum distortion?
We consider two measures of distortion: delay distortion, which measures the delay of spikes between the target and generated spike trains; and filter distortion, which measures the distance (in the ℓp-norm sense) between the target and the best generated spike trains. Our results give the mean and variance of the distortion from memoryless spike trains for various refractory periods. These results establish mathematical limits for the technique, and could help neuroscientists design optogenetic experiments.
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