[gmx-users] Binding energy of membrane protein to the membrane lipids

sojovictor sojovictor at gmail.com
Sun Feb 23 16:36:54 CET 2014

Dear all,

I would like to find the difference in the energy of binding or insertion of
a protein into two different types of phospholipid membranes (plus water and
ions). i.e., my hypothesis is that the energy should be lower with one type
of membrane than with the other.

I have considered an alchemical transformation from one system to the other,
gradually replacing a lipid with the other one, but I've been unable to find
any example of people switching off something as large as a protein; all the
examples I find are of ligands, single aminoacid residues, or solutes, much
smaller particles than what I'm attempting. This makes me wonder whether
what I'm planning even makes sense, or if such a simulation would never
converge or give reliable results due to the large vacuum in the middle of
the membrane created upon switching off the protein.

Taking guidance from Mobley,Chodera & Dill's 2006 paper on J.Chem.Phys., and
from Justin Lemkul's tutorial, I've devised the following, potentially
impossible, thermodynamic cycle:

Clockwise from the top left, I would do this in seven steps:
1) (Position?)Restrain the protein in the first membrane.
2) Decouple coulombic interactions in the protein (I assume annihilating
would not be a good idea here).
3) Decouple Lennard-Jones interactions in the protein. This will leave me
with a system that is effectively equivalent to an independent
fully-restrained/non-interacting protein, and a free membrane.
4) Change membrane to the second type, keeping both interactions off and
protein restriction on.
5) Switch on Lennard-Jones interactions.
6) Switch on coulombic interactions.
7) Remove protein restriction.

I believe it wouldn't be necessary to calculate energies for the protein in
solution, since my interest is not the free energy of binding to one
membrane, but the change that would be experienced upon changing from one
membrane to the other.

Now, my initial impression is that this would not work, but I can't think of
anything better, so I'd very much welcome input.

Alternatively, I have considered umbrella sampling: I would pull the protein
out of one of the membranes, separately do the same with the other membrane,
and see what's the difference, but I can't think of anything I could keep as
the reference system for the centre of mass (the membrane does not seem to
be a good idea).

In general, any advice on how to proceed with this calculation, a reference
to the literature, or wild guesses, would be very welcome!

Thanks, all.

Victor Sojo

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