Cable Energy Function of Cortical Axons: Equivalent Formulas

Cortical neurons generally have rich morphologies in dendrite arbor and axonal branches, which make it difficulty in estimate energy consumption during action potential (AP) propagation in neuronal communication. It is an unsolved issue in driving general analytical equations to estimate energy cost for those axons and dendrites with different terminations. Most previous energy calculations of AP-related metabolic cost are still based on the Na + -counting method. Here, we apply principles of physics and mathematical analysis to construct several forms of cable energy function of AP conduction along axons with different boundary conditions. These derived energy equations extend Hodgkin-Huxley theory and prove to be highly more accurate in estimation the energy consumption during AP propagation along cortical axons and dendrites with any kind of ion channels than that using the Na + -counting method.\n\nSummaryAccurate energy estimation of action potential conduction along axons with different complex terminal conditions is an unsolved issue. We have applied principles of physics and mathematical analysis to derive several forms of cable energy function of action potential conduction along cortical axons with different boundary conditions, and we have proved that these functions are equivalent. The energy calculations of action potential metabolic cost by using our cable energy function is proved to be highly accurate than that based on the Na + -counting method. This mathematical framework allows us to estimate the energy used by AP propagation along cortical axons and dendrites with any kind of ion channels more accurately than that using the Na + -counting method. Accurate calculation of energy consumption of AP conduction may be crucial in the estimation of energy expenditure, from subcellular to whole-brain level. In addition, the analytical formula of energy calculation is valuable in investigating the key factors that influence energy consumption and reveal trade-offs between energetic constraints and neural coding efficiency for individual neurons with rich morphology structures.