Estimate, to one significant figure, the power the human brain spends on the sodium…

PHYSICS · Subjective · Fermi University Physics · Biophysics & Medical Physics · Molecular machines, transport and bioenergetics · Bioelectricity, the senses and the physics of the body

Forces, Machines and Signals, Ch The nerve impulse

Problem

Estimate, to one significant figure, the power the human brain spends on the sodium entry of action potentials alone, and compare it with the brain's total power consumption of about

20\,\mathrm{W}

(roughly a fifth of the body's resting metabolic rate of about

100\,\mathrm{W}

). Use these assumptions: about

9\times10^{10}

neurons in the brain; a mean firing rate of

4\,\mathrm{Hz}

per neuron; a mean axonal membrane area per neuron of

3\times10^{-4}\,\mathrm{cm^2}

(an axon roughly

1\,\mathrm{cm}

long and

1\,\mu\mathrm{m}

across); a minimum sodium entry per impulse of

6\times10^{11}

ions per

\mathrm{cm^2}

; a pump stoichiometry of

3\,\mathrm{Na^+}

extruded per ATP hydrolysed; and

\Delta G_{\rm ATP} \approx 50\,\mathrm{kJ\,mol^{-1}}

under cellular conditions.

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