Neural computation at the thermal limit
  Although several measurements and analyses support the idea that the brain is energy-optimized, there is one disturbing, contradictory observation: In theory, computation limited by thermal noise can occur as cheaply as ~$2.9\cdot 10^{-21}$ joules per bit (kTln2). Unfortunately, for a neuron the ostensible discrepancy from this minimum is startling - ignoring inhibition the discrepancy is $10^7$ times this amount and taking inhibition into account $>10^9$. Here we point out that what has been defined as neural computation is actually a combination of computation and neural communication: the communication costs, transmission from each excitatory postsynaptic activation to the S4-gating-charges of the fast Na+ channels of the initial segment (fNa's), dominate the joule-costs. Making this distinction between communication to the initial segment and computation at the initial segment (i.e., adding up of the activated fNa's) implies that the size of the average synaptic event reaching the fNa's is the size of the standard deviation of the thermal noise. Moreover, defining computation as the addition of activated fNa's, yields a biophysically plausible mechanism for approaching the desired minimum. This mechanism, requiring something like the electrical engineer's equalizer (not much more than the action potential generating conductances), only operates at threshold. This active filter modifies the last few synaptic excitations, providing barely enough energy to allow the last sub-threshold gating charge to transport. That is, the last, threshold-achieving S4-subunit activation requires an energy that matches the information being provided by the last few synaptic events, a ratio that is near kTln2 joules per bit. 
William B. Levy, Toby Berger, Ilya A. Fleidervish
q-bio.NC physics.bio-ph