A model for studying the energetics of sustained high frequency firing.

Regulating membrane potential and synaptic function contributes significantly to the energetic costs of brain signaling, but the relative costs of action potentials (APs) and synaptic transmission during high-frequency firing are unknown. The continuous high-frequency (200-600Hz) electric organ discharge (EOD) of Eigenmannia, a weakly electric fish, underlies its electrosensing and communication. EODs reflect APs fired by the muscle-derived electrocytes of the electric organ (EO). Cholinergic synapses at the excitable posterior membranes of the elongated electrocytes control AP frequency. Based on whole-fish O2 consumption, ATP demand per EOD-linked AP increases exponentially with AP frequency. Continual EOD-AP generation implies first, that ion homeostatic processes reliably counteract any dissipation of posterior membrane ENa and EK and second that high frequency synaptic activation is reliably supported. Both of these processes require energy. To facilitate an exploration of the expected energy demands of each, we modify a previous excitability model and include synaptic currents able to drive APs at frequencies as high as 600 Hz. Synaptic stimuli are modeled as pulsatile cation conductance changes, with or without a small (sustained) background conductance. Over the full species range of EOD frequencies (200-600 Hz) we calculate frequency-dependent "Na+-entry budgets" for an electrocyte AP as a surrogate for required 3Na+/2K+-ATPase activity. We find that the cost per AP of maintaining constant-amplitude APs increases nonlinearly with frequency, whereas the cost per AP for synaptic input current is essentially constant. This predicts that Na+ channel density should correlate positively with EOD frequency, whereas AChR density should be the same across fish. Importantly, calculated costs (inferred from Na+-entry through Nav and ACh channels) for electrocyte APs as frequencies rise are much less than expected from published whole-fish EOD-linked O2 consumption. For APs at increasingly high frequencies, we suggest that EOD-related costs external to electrocytes (including packaging of synaptic transmitter) substantially exceed the direct cost of electrocyte ion homeostasis