  The electric activities of cortical pyramidal neurons are supported by
structurally stable, morphologically complex axo-dendritic trees. Anatomical
differences between axons and dendrites in regard to their length or caliber
reflect the underlying functional specializations, for input or output of
neural information, respectively. For a proper assessment of the computational
capacity of pyramidal neurons, we have analyzed an extensive dataset of
three-dimensional digital reconstructions from the NeuroMorpho.Org database,
and quantified basic dendritic or axonal morphometric measures in different
regions and layers of the mouse, rat or human cerebral cortex. Physical
estimates of the total number and type of ions involved in neuronal electric
spiking based on the obtained morphometric data, combined with energetics of
neurotransmitter release and signaling fueled by glucose consumed by the active
brain, support highly efficient cerebral computation performed at the
thermodynamically allowed Landauer limit for implementation of irreversible
logical operations. Individual proton tunneling events in voltage-sensing S4
protein $\alpha$-helices of Na$^{+}$, K$^{+}$ or Ca$^{2+}$ ion channels are
ideally suited to serve as single Landauer elementary logical operations that
are then amplified by selective ionic currents traversing the open channel
pores. This miniaturization of computational gating allows the execution of
over 1.2 zetta logical operations per second in the human cerebral cortex
without combusting the brain by the released heat.
