A model for studying the energetics of sustained high frequency firing

Abstract

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.

Convergent patterns of evolution of mitochondrial oxidative phosphorylation (OXPHOS) genes in electric fishes

“…The foundation of this metabolic adaptation lies in the capacity of mitochondria to supply enough energy to maintain these novel functions at a cellular level [4]. Bioelectrogenesis, or the ability to send and receive electric signals, is an example of a complex sensory system that requires a considerable amount of energy [5][6][7]. Therefore, it serves as an excellent system to investigate molecular adaptations to elevated metabolic burden associated with novel phenotypes.…”

Neural Optimization: Understanding Trade-offs with Pareto Theory

“…• [38] ** Using a computational model of the electric fish's organ discharge, the authors showed that with an increase in frequency, the energetic costs of APs rise superlinearly while the synaptic costs remain constant. This potentially predicts channel densities across fish.…”

“…Electric organ discharge in the weakly electric fish: The genus Eigenmannia uses a specialized electric organ to produce discharges at a near-constant rate between 200 and 600 Hz, both for electrosensing and communication. Based on biophysical models, Joos and colleagues [38] showed that the energetic cost per spike, estimated from the sodium current flow, increases superlinearly with firing rate (Figure 2a). Na + expulsion through the Na + /K + pump constitutes a large part of the energy demand of spiking [39], yet the quantification of metabolic cost is complex [27,40] and other processes contribute [41].…”

“…Figure2: Energetic cost of sustained high-frequency firing in a model of the weakly electric fish Eigenmannia electric organ (data from[38]), stimulated via postsynaptic acetylcholine receptor (AChR) activation (regular pulse-trains with a constant background conductance). (a) Resulting energy consumption of the electric organ discharge (EOD) estimated from the total entry of sodium ions per action potential into the cell (Na +entry/AP * 10 9 , y-axis).…”