[gmx-users] confusion of forward and backward FEP in Gromacs-4.6.5

[dbaogen]

Hi all,

        I want to calculate the free energy difference for ATP-->GTP in solution, for the forward analysis, the parameters for free energy perturbation are as follows: 
free-energy              = yes
sc-alpha                 = 0.3
sc-power                 = 1
sc-sigma                 = 0.25
sc-coul                  = no
couple-intramol          = yes
init-lambda-state        = $LAMBDA$
coul-lambdas             = 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.00 1.0 1.00 1.0 1.00 1.0 1.00 1.0 1.00 1.0 1.00 1.0 1.00 1.0 1.00 1.0 1.00 1.0 1.00 1.0
vdw-lambdas              = 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
nstdhdl                  = 50
calc-lambda-neighbors    = 1

     The calculated free energy difference is about -273 kJ/mol. In order to check the FEP convergence, backward analysis was also done. I adopt two ways to carry out backward analysis.

(1) Modify the topology file for GTP--> ATP , the parameters of free energy calculation is the same as forward analysis. And the free energy difference of backward is about 213   kJ/mol. 

（2）Using the same topology file as forward analysis. But modify the parameter settings of coul-lambdas and vdw-lambdas for free energy calculation shown as follows
free-energy              = yes
sc-alpha                 = 0.3
sc-power                 = 1
sc-sigma                 = 0.25
sc-coul                  = no
couple-intramol          = yes
init-lambda-state        = $LAMBDA$
coul-lambdas             = 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.00 0.0 0.00 0.0 0.00 0.0 0.00 0.0 0.00 0.0 0.00 0.0 0.00 0.0 0.00 0.0 0.00 0.0 0.00 0.0
vdw-lambdas              = 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.0
nstdhdl                  = 50
calc-lambda-neighbors    = 1

The calculated free energy difference is about 272 kJ/mol

Theoretically, the two ways of backward analysis is the same. And the values of free energy should be identical. Now, I am confused whether  I  misunderstand something or set the wrong parameters for FEP calculation. Would you like to give me some help？ Thanks in advance.

Best wishes
Duan Baogen

Beijing Computational Science Research Center