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In a galvanic cell setup and around each electrode in that setup, we have species that either undergo oxidation or reduction—resulting in the literal flow of electrons between the two electrodes. We can then use a voltmeter to calculate the electric potential difference between the two electrodes (using Ohm's law).
A similar situation also happens when we're doing voltammetry—fast scan or otherwise. The typical example is of dopamine. One electrode is placed in the solution containing dopamine. The other electrode can be electronically manipulated to create a certain potential difference between itself and the electrode submerged in the dopamine solution. At some point across this voltage manipulation, dopamine is oxidized to dopamine-o-quinone. There's a literal flow of electrons (two per dopamine oxidized) which then establishes a current—which then we can measure.
What's the "parallel" situation in measuring spike activity? Consider the following diagram:
What species (if any) are oxidized to provide the electrons needed to establish a current in the electrode system (which then can be used to calculate the voltage difference across the axonal membrane)? During the propagation of an action potential—where voltage gated sodium channels open—what species (again, if any) are oxidized?