Action Potential Energetics at the Organismal Level Reveal a Trade-Off in Efficiency at High Firing Rates

Abstract

The energetic costs of action potential (AP) production constrain the evolution of neural codes and brain networks. Cellular-level estimates of AP-related costs are typically based on voltage-dependent Na(+) currents that drive active transport by the Na(+)/K(+) ATPase to maintain the Na(+) and K(+) ion concentration gradients necessary for AP production. However, these estimates of AP cost have not been verified at the organismal level. Electric signaling in the weakly electric fish Eigenmannia virescens requires that specialized cells in an electric organ generate APs with large Na(+) currents at high rates (200-600 Hz). We measured these currents using a voltage-clamp protocol and then estimated the energetic cost at the cellular level using standard methods. We then used this energy-intensive signaling behavior to measure changes in whole-animal energetics for small changes in electric discharge rate. At low rates, the whole-animal measure of AP cost was similar to our cellular-level estimates. However, AP cost increased nonlinearly with increasing firing rates. We show, with a biophysical model, that this nonlinearity can arise from the increasing cost of maintaining AP amplitude at high rates. Our results confirm that estimates of energetic costs based on Na(+) influx are appropriate for low baseline firing rates, but that extrapolating to high firing rates may underestimate true costs in cases in which AP amplitude does not decrease. Moreover, the trade-off between energetic cost and firing rate suggests an additional constraint on the evolution of high-frequency signaling in neuronal systems.