# NAMD free energy calculations (FEP, Alchemical)

I am trying to calculate the absolute free energy of a protein-ligand-complex using the free energy perturbation theory.

Following the alchemical route in this tutorial, I have calculated eight MD-simulations over 24 lambda values (500ps each).

1/2: Ligand in protein (Ligand restraint, forward/backward)

 Ligand ->(forward) vacuum ->(backward) protein


3/4: Ligand in water (Ligand restraint, forward/backward

 Ligand ->(forward) vacuum ->(backward) water


5/6: Ligand in protein (Ligand restraints scaled, forward/backward)

 Colvars 1 ->(forward) 0 ->(backward) 1


7/8: Ligand in water (Ligand restraints scaled, forward/backward)

 Colvars 1 ->(forward) 0 ->(backward) 1


The free energy contribution of 1/2 and 3/4 is calculated with the ParseFEP-tool. All colvar contributions were printed to the output file for each lambda value.

$\Delta G_{1/2} = -152.65 ~~~~ \Delta G_{3/4} = 152.1$

Is it sufficient to integrate the curves for each colvar and sum them up afterwards?

$\Delta G_{5/6} = 12.3 ~~~~ \Delta G_{7/8} = 1.84$

Do I have to subtract the colvar contribution from binding and solvation energy to get the absolute binding free energy?

$\Delta G = (\Delta G_{1/2} - \Delta G_{5/6}) - (\Delta G_{3/4} - \Delta G_{7/8}) = -11.1\,$kcal/mol

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