[gmx-users] Re: A question about "PEF"

Michael Brunsteiner mbx0009 at yahoo.com
Fri Dec 3 19:27:12 CET 2004

The potential of mean force is actually the free energy difference.
between the states at the two well defined endpoints of an arbitrarily 
defined reaction path.
This "reaction path" can be, for example, the path traveled by a molecule
in a solvent through a distance dz normal to a surface. The result would be 
the free energy of adsorption if z(lambda_0) is a point well away from the
surface and z(lambda_1) is the equilibrium distance of an adsorbed
molecule. Other frequently used reaction paths are the path that
an ion travels through a ion channel or the path defined by 
a rotation trhough a dihedral angle in a molecule in solution.

The, maybe confusing, name PMF comes from the fact that the PMF is 
customarily calculated as the integral of the average force as a function 
of lambda going from lambda=0 to lambda=1, which in the above case would
correspond to the two states defined by the molecule-surface distance
z(lambda_0) and z(lambda_1)
If you write the average force as <F> = <dU/dz>, put that expression
in the integral and replace z by lambda you see that this is nothing elso 
but a special case of a thermodynamic integration ... see, for example 
textbooks such as Allen, Tildeslay for more detailed explanations.

You can calculate the PMF in gromacs with the pull code. Be careful
though, in all but the newset version of Gromacs there seem to be a couple
of bugs in the pull code.


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