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

Catherine E Morris,Vladimir E Bondarenko,Bela Joos,John E Lewis,Michael R Markham

doi:10.1371/journal.pone.0196508

Catherine E Morris, Vladimir E Bondarenko + Show 3 more

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https://doi.org/10.1371/journal.pone.0196508

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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.

Highlights

Analysis of mammalian brain energetics identifies electrical signaling as the major consumer of ATP with molecular processes underlying synaptic transmission incurring the highest costs [1,2,3]
In the context of the electric organ discharge (EOD)-linked O2-consumption reported by Lewis et al [6], these results strongly suggest that the electrocytes themselves are energetically efficient devices and that a greater fraction of global cost of EOD production can be attributed to presynaptic processes than to supporting electrocyte ion homeostasis
The two core questions driving the current study are broadly applicable to excitable cells in general: 1) what mechanisms enable sustained high-frequency firing? and, 2) what are the relative contributions of membrane excitability, synaptic processes, and organismal-level processes to the metabolic costs of high-frequency firing? The electric organ discharge of Eigenmannia is a powerful and accessible system where experimental work on the physiology of EOD production and computational modeling of these physiological processes can form a synergistic and mutually informative approach to answering these questions

Summary

Introduction

Analysis of mammalian brain energetics identifies electrical signaling as the major consumer of ATP with molecular processes underlying synaptic transmission incurring the highest costs [1,2,3]. Changes in ion concentrations due to synaptic inputs and action potentials (APs) are reversed by the action of energy-consuming ion pumps. This direct link allows energy consumption to be estimated from Na+-entry [1, 4] which drives the 3Na+/2K+-ATPase activity (at 1 ATP/3 Na+ expelled). Under the low-firing frequency conditions (4 Hz) typical of mammalian cortex, Na+ (and Ca+2) entry through postsynaptic receptor channels is estimated to be much larger than that through AP-related voltage-dependent Na+ (Nav) channels. Synaptic processes are thought to dominate energetic costs in these conditions, but whether this is the case for other firing regimes is not known

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