The Slow Depolarization Following Individual Spikes in Thin, Unmyelinated Axons in Mammalian Cortex

Abstract

An important goal in neuroscience is to understand how neuronal excitability is controlled. Therefore, Gardner-Medwin's 1972 discovery, that cerebellar parallel fibers were more excitable up to 100 ms after individual action potentials, could have had great impact. If this long-lasting effect were due to intrinsic membrane mechanisms causing a depolarizing after-potential (DAP) this was an important finding. However, that hypothesis met resistance because the use of K + sensitive electrodes showed that synchronous activation, as commonly used in excitability tests, increased extracellular K + concentration sufficiently to explain much of the hyperexcitability. It is still controversial because intra-axonal recordings, which could have settled the debate, have not been made from parallel fibers or other axons of similar calibers. If it had not been for the fact that such thin axons are, by far, the most common axon type in cortical areas and control almost all glutamate release, it would be tempting to ignore them until an appropriate intra-axonal recording technique is invented. I will go through the literature that, taken together, supports the hypothesis that a DAP is an intrinsic membrane mechanism in cerebellar parallel fibers and hippocampal Schaffer collaterals. It is most likely due to a well-controlled process that stops the fast repolarization at a membrane potential positive to resting membrane potential, leaving the membrane more excitable for ~100 ms during a slow, passive discharge of the membrane capacitance. The DAP helps reduce failures but can also cause uncontrolled bursting if it is not properly controlled. The voltage at which the fast repolarization stops, and the DAP starts, is close the activation range of both Na + and Ca 2+ voltage activated channels and is therefore essential for neuronal function.

Cerebral cortical communication overshadows computational energy-use, but these combine to predict synapse number

“…Using a firing-rate of 1 Hz and 1.5 · 10 10 neurons/cortex, a bottom up calculation for the excitatory postsynaptic ionflux per AP per cortex yields 0.10 W. The linear relationship between firing rate and energy consumption has a substantial baseline energy consumption of 1.09 W (y-axis intercept). Apparently resting axon conductance (25) is required for a resting potential and stable behavior (26). In the case of the dendrite, computational costs are zero at zero firing rate, a theoretical limit result which, as argued earlier, is a nonsense practical situation.…”

“…If other ions contribute, we just assume that their energetic costs eventually translate into Na + and K + gradients. The axonal resting conductance uses the recent result of 50 kΩ cm 2 (25). With our surface area of 21.8 • 10 6 cm 2 (includes axonal boutons, see Plasma membrane leak is a major energy expenditure, 22% of ATP-W here compared to 13% in (11).…”

“…If other ions contribute, we just assume that their energetic costs eventually translate into Na + and K + gradients. The axonal resting conductance uses the recent result of 50 kΩ cm 2 (25). With our surface area of 21.8 · 10 6 cm 2 (includes axonal boutons, see Table S6), this produces a total conductance of 436 S. The driving voltage for each ion is determined by subtracting the appropriate Nernst potential from the assumed resting membrane potential of −66 mV.…”

Communication consumes 35 times more energy than computation in the human cortex, but both costs are needed to predict synapse number

“…If other ions contribute, we just assume that their energetic costs eventually translate into Na + and K + gradients. The axonal resting conductance uses the recent result of 50 kω cm 2 (23). With our surface area of 21.8 • 10 6 cm 2 (includes axonal boutons; SI Appendix, Table S6), this produces a total conductance of 436 S. The driving voltage for each ion is determined by subtracting the appropriate Nernst potential from the assumed resting membrane potential of −66 mV.…”

“…Using a firing rate of 1 Hz and 1.5 • 10 10 neurons per cortex, a bottom-up calculation for the excitatory postsynaptic ion flux per AP per cortex yields 0.10 W. The linear relationship between firing rate and energy consumption has a substantial baseline energy consumption of 1.09 W (y-axis intercept). Apparently resting axon conductance (23) is required for a resting potential and stable behavior (24). In the case of the dendrite, computational costs are zero at zero firing rate, a theoretical limit result which, as argued earlier, is a nonsense practical situation.…”