Dynamic observer: ion channel measurement beyond voltage clamp

To date, the gold standard for characterizing neuronsand assessing the action of drugs on them are voltageclamp protocols in patch clamp recordings [1]. How-ever, it is now clear that the classical procedure, wheremeasurements performed using constant voltage stepsand channel blockers are averaged over several cells,does not typically allow the construction of accurateHodgkin-Huxley type models [2]. Here we propose togo beyond the classical procedure and rely on optimizedstimulation patterns to isolate the effect of different ionchannels.We represent stimulation patterns as clamped cubicsplines defined by a number of support points. Cubicsplines can approximate steps or sinusoids, as well asarbitrary shapes; clamped splines avoid discontinuitiesaround the endpoints. To measure the degree to whicha given pattern can isolate the contribution of one chan-nel, a reference neuron is detuned in two different ways.The first detuned neuron has one set of parametersincreased by a certain factor, while in the second a dif-ferent set of parameters is similarly detuned. Theseparation power of a stimulation pattern for these twosets of parameters is then defined as the ratio of thedivergence factors of the two detuned neurons, whichare defined as the sum of squared errors between thereference and detuned trans-membrane currents. Opti-mal patterns are constructed by adjusting the supportpoints to maximize this ratio, typically through a combi-nation of a genetic algorithm for exploring the searchspace, and gradient descent for fine-tuning.We show that for many parameters pairs in a Hodg-kin-Huxley model, there are stimulation patterns whichyield a clear dissociation between the effects of theselected parameters. Figure 1 shows a typicaldissociation between g