One can model some of the passive response electrical properties of an unmyelina

Question

One can model some of the passive response electrical properties of an unmyelinated axon as an electrical cable covered with defective insulation so that current flows down the interior of the axon but also leaks out of the axon - through the membrane - into the surrounding fluid. Assume that the axon consists of a cylindrical membrane filled with conducting fluid. A current of ions can travel along the axon in this fluid and can also leak out through the membrane. The inner radius of the cylinder is 5.0 microns and the membrane thickness is 8.0 nm.

(a) If the resistivity of the interior axon fluid is 2.0 ohm*m, calculate the resistance along a 1.0 cm length of axon to current flow along its length.________Mohms

(b) Ion channels through the membrane give a resistivity of the porous membrane of 3.5E7 ohm*m, calculate the resistance of the wall of a 1.0 cm length of axon to current flow across the membrane.____kohms

(c) If a resting potential difference of 70 mV is maintained across the membrane by the sodium/potassium ion pump, how much current of ions flows through the 1.0 cm length of membrane? _______nanoAmps

Explanation / Answer

a)Resistance resistivity relation is given by:

R=pL/A = 2*0.01/[3.14*5*5*10-6*10-6] = 255 MOhms

b) here A will be curved surface area and L will be thickness

R =pL/A = 3.5E7 * 8E-9 / [2*3.14*5*10-6*0.01] = 892 kOhms

c)By ohms law

i =V/R = 70mV /  892 kOhms = 7.847 × 10-8 A = 78.5 nanoAmps

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