A patch of unmyelinated axon membrane with specific capacitance depolarises from to…

PHYSICS · Multi-part · 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

A patch of unmyelinated axon membrane with specific capacitance Cm=1 μF cm−2C_m = 1\,\mu\mathrm{F\,cm^{-2}} depolarises from −70 mV-70\,\mathrm{mV} to +20 mV+20\,\mathrm{mV} during an action potential. ((a)) Find the minimum number of sodium ions that must cross each square centimetre of membrane to charge this capacitance, and the corresponding minimum number of ATP molecules consumed by the sodium-potassium pump (which exports three sodium ions per ATP hydrolysed). ((b)) For a 1 mm21\,\mathrm{mm^2} patch of this membrane, give the minimum ATP consumption in moles.

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