Problems

1.1. Assume that a section of squid axon membrane has a capacitance of 1 |F/cm2, a resting potential of Vm = -70 mV, and a dielectric constant of 8. Neglect the presence of transmembrane proteins.

a. Calculate the pressure of electrostatic origin acting on the membrane. Assume a parallel-plate capacitor structure. Give your answer both in dyne/cm2 and in psi.

b. Calculate the electric field within the membrane in V/cm (assume it is uniform).

1.2. A cylindrical dendrite is modeled by a cylinder of passive membrane with radius r = 0.5 |im, and length L = 200 |im. An excitatory synapse at the distal end can be considered to be an ideal voltage source, Vs(t). The proximal end joins a neuron cell body (soma) with a large radius, which can be considered a short-circuit across the membrane of the dendrite. The membrane has a net passive conductance of GM = 2 x 10-4 S/cm2. CM = 2 x 10-7 F/cm2, the axoplasm resistivity is pi = 60 Qcm. Let ro = 0 for simplicity.

a. Find the cable parameters for the dendrite: cm F/cm, gm S/cm, ri Q/cm.

b. Find Zo(jra), the dendrite t, its break frequency, fb = 1/2, and its dc space constant, X, in |im.

c. Find the steady-state short-circuit current at the soma, given Vs = 10 mV depolarization at the distal end of the dendrite model.

1.3. Every time a squid giant axon conducts an action potential, 3.5 pmol/cm2 of Na+ enter the axon, and 3.5 pM/cm2 exit the axon.

a. Calculate the minimum metabolic energy in calories needed by the ion pump to restore the ionic balance over 100 cm of 1-mm-diameter axon, per action potential. Assume the resting transmembrane potential is Vm = 0.07 V, and the steady-state concentrations are [Na+]in = 0.05 M, [Na+]out = 0.460 M, [K+]in = 0.40 M, [K+]out = 0.01 M.

b. What is the steady-state energy, in calories, stored in the electric field over the 100 cm length of 1-mm-diameter axon? Assume CM = 1 ^F/cm2.

1.4. Consider the lumped-parameter circuit model for 1 cm2 of nerve axon membrane shown in Figure P1.4.

Outside axon -

Vl T

Vm Vo ltmeter

Inside axon

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