Consider a phospholipid bilayer membrane consisting of a mixture of 90% uncharge

Question

Consider a phospholipid bilayer membrane consisting of a mixture of 90% uncharged lipid and 10% of singly charged acid lipid. Assume 0.75 nm2 surface area per lipid head group, and assume further that the charged lipids are uniformly distributed and immobile. The membrane is in contact with an aqueous solution of NaCl at 25 C. The salt concentration is 88 mM .

Calculate the areal charge density (i.e. charge per unit surface area) of the membrane.

Calculate the Debye length.

Calculate the electrostatic potential at the surface of the membrane.

Explanation / Answer

Based on the given data,

The membrane has

Surface area per lipid head group = 0.75 nm2

a)

The areal charge density of the membrane is as follows:

The total moles of lipid = n

Charged lipid = n/10

The total surface area of the lipid = n×0.75 nm2

Charge on lipid = (ne)/10

Therefore, the charge per unit surface area =

= ne / (10× n × 0.75 nm2)

= 0.133 nm2

= (0.133× 1.6×10-19) / (10-18)

= 0.0212 c/m2

Thus, the charge density of the membrane is 0.0212 c/m2.

b)

Debye length is 3×10-2 nm

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