Model the human brain as neurons (a standard estimate for the number of neurons in an…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Molecular machines, transport and bioenergetics · Molecular machines, transport and bioenergetics

Life at Thermal Energy, Ch The membrane: barrier, capacitor and pump

Problem

Model the human brain as

8.6\times10^{10}

neurons (a standard estimate for the number of neurons in an adult human brain). Take each neuron to have a steady resting sodium leak current of

100\,\mathrm{pA}

that the sodium-potassium pump must balance by moving sodium back out, at the pump's measured stoichiometry of

3

sodium ions per ATP hydrolysed. At body temperature (

T = 310\,\mathrm{K}

k_BT = 4.28\times10^{-21}\,\mathrm{J}

) one ATP supplies about

20k_BT

of free energy. ((a)) Estimate the total power the brain spends running this pump, and compare it with the brain's known total power consumption of about

20\,\mathrm{W}

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

100\,\mathrm{W}

, a figure from Chapter 1). ((b)) The chapter found that the same pump takes about

30

per cent of the power share of a neuron-sized cell of radius

10\,\mathrm{\mu m}

and mass

4.2\times10^{-12}\,\mathrm{kg}

, with brain tissue running at

14\,\mathrm{W\,kg^{-1}}

. Taking the brain's mass as

1.4\,\mathrm{kg}

, find the brain mass per neuron, and use it to explain why your whole-brain share from (a) is so much smaller than

30

per cent.

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