Calculating Electrostatic Energy of Trivalent Ion Binding to Membrane

[Oijl]

Homework Statement

Consider a phospholipid bilayer membrane consisting of a mixture of 90% uncharged lipid and 10% singly charged acid lipid. Assume 68 Å^2 surface area per lipid head group, and assume further that the charged lipids are uniformly distributed and immobile. The membrance is in contact with an aqueous solution of NaCl at 25 ˚C. The alt concentration is c = 100mM.

What is the electrostatic energy (in kT units) of binding to the membrane of a trivalent positive ion such as spermidine assuming that:

(a) binding occurs at the membrane surface?
(b) owing to steric factors the charges of the bound spermidine stay in the water 5 Å distance from the membrane surface?

Homework Equations

?

The Attempt at a Solution

The electric potential at the surface and at 5 Å must be known to find the energy of the binding, and I can find that potential. But what tells me the binding energy? I just don't know. Thanks.

 

[anathema]

Hello, thank you for your post. The electrostatic energy of binding to a membrane can be calculated using the formula: E = -qV, where E is the electrostatic energy, q is the charge of the ion, and V is the electric potential at the membrane surface or 5 Å distance from the surface. In this case, the charge of spermidine is +3, and the electric potential can be calculated using the Nernst equation for a monovalent ion: V = (RT/zF) ln (c/c0), where R is the gas constant, T is the temperature, z is the valence of the ion, F is Faraday's constant, c is the concentration of the ion at the membrane surface, and c0 is the concentration of the ion in the bulk solution.

(a) For binding at the membrane surface, the electric potential would be the same as the potential at the surface of the membrane, which can be calculated using the given information about the lipid composition and the Nernst equation. From there, you can use the above formula to calculate the electrostatic energy of binding.

(b) For binding at 5 Å distance from the surface, the electric potential would be the potential at the surface minus the potential drop due to the steric factors. This potential drop can be calculated using the Debye-Hückel equation: V = (RT/2F) ln (1 + κa), where κ is the Debye-Hückel parameter and a is the distance from the surface. From there, you can use the above formula to calculate the electrostatic energy of binding.

I hope this helps answer your question. Let me know if you need further clarification or assistance.