The Price of a Spike: Energy per Bit in Neuronal Signalling

How much metabolic energy does a neuron spend to transmit one bit of information in a spike? Sodium entry per action potential is 4.33 pmol/cm2 for the squid giant axon (Hodgkin and Huxley 1952; range 3.5-5.0) and 1.3474 pmol/cm2 for mammalian cortical neurons (1.3 times the capacitive minimum of 1.0364 pmol/cm2; Alle et al. 2009, range from entry ratios 1.2-2.0). Restoring that sodium via the Na/K ATPase (3 Na+ per ATP) at an in-vivo ATP hydrolysis free energy of 50 kJ/mol costs 7.2167e-8 J per cm2 per action potential in squid and 2.2456e-8 J per cm2 in cortex. For stated reference geometries (a 1 cm segment of 500 um squid axon; a cortical pyramidal neuron of 25,000 um2) one action potential costs 1.1336e-8 J and 5.6140e-12 J. A timing code with 1 ms jitter in a 100 ms mean interspike interval carries 6.64 bits per spike (range 2.00-8.64; measured cortical anchor 4.3 bits per spike, Kayser et al. 2010). Energy per bit is 8.4499e-13 J for the cortical neuron, 2.85e8 times the Landauer floor at 310 K and about 3004 times a stated silicon switching energy (2.8125e-16 J, companion deposit 10.5281/zenodo.24102536), and 1.7062e-9 J per bit for the squid segment. Combined sensitivity extremes span 2.16e-13 to 2.07e-11 J per bit for cortex, and the figure is a lower bound excluding synaptic and resting costs. Model calculations are labelled SIMULATED, NOT MEASURED. The deposit includes the paper PDF and Markdown, the computation script (compute.py) that produces every number in the paper, and its outputs (results.json, results.txt).