Umbrella sampling - WHAM analysis

GROMACS version: 2023
GROMACS modification: No

Dear all,

I am doing a WHAM analysis of an umbrella sampling of an enzyme-inhibitor complex and I have some questions.

I did SMD simulations to pull the inhibitor from the enzyme along the X-axis with pull_coord1_k = 1000 kJ mol^-1 nm^-2, at different pulling velocities 0.1, 0.05, 0.02, 0.01, 0.005 Å/ps. I got frames along the pulling axis for US sampling during 10 ns. Then, I run the wham command as:

gmx_mpi wham -it tpr-files.dat -ix pullx-files.dat -o profile_pullx -hist -unit kCal -b 1000 -min 2.375790 -max 5 -nBootstrap 100

Below is a figure of the histograms and the PMF for each pulling velocity.

At first glance, it seems that the pulling velocities of 0.1 and 0.005 Å/ps give the best histogram overlapping. The ∆G was calculated manually as the difference between the minimum and the maximum value of the PMF values (∆G = min(PMF)-max(PMF)).

1 - Does the wham command give the ∆G value directly or should it be calculated as before manually?
2 - Although the ∆G values are reasonable, these are 2x the expected value ≈ 14 kcal/mol. I am aware that this analysis can be difficult and tricky. Could you give some tips to improve this calculation?

My mdp file for the US simulations is:

title                   = Umbrella pulling simulation 
define                  = -DPOSRES_X ; Restraining the enzyme
; Run parameters
integrator              = md
dt                      = 0.002
tinit                   = 0
nsteps                  = 5000000   ; 10 ns 
nstcomm                 = 10
; Output parameters
nstxout-compressed      = 5000      ; every 10 ps
nstenergy               = 5000
; Bond parameters
constraint_algorithm    = lincs
constraints             = all-bonds
continuation            = yes
; Single-range cutoff scheme
cutoff-scheme           = Verlet
nstlist                 = 20 
ns_type                 = grid 
rlist                   = 1.4
rcoulomb                = 1.4
rvdw                    = 1.4
; PME electrostatics parameters
coulombtype             = PME
fourierspacing          = 0.12
fourier_nx              = 0
fourier_ny              = 0
fourier_nz              = 0
pme_order               = 4
ewald_rtol              = 1e-5
optimize_fft            = yes
; Berendsen temperature coupling is on in two groups
Tcoupl      = Nose-Hoover
tc_grps     = Protein   Non-Protein 
tau_t       = 1.0       1.0
ref_t       = 310       310
; Pressure coupling is on
Pcoupl          = Parrinello-Rahman 
pcoupltype      = isotropic
tau_p           = 1.0       
compressibility = 4.5e-5
ref_p           = 1.0
refcoord_scaling = com
; Generate velocities is off
gen_vel         = no 
; Periodic boundary conditions are on in all directions
pbc     = xyz
; Long-range dispersion correction
DispCorr    = EnerPres
; Pull code
pull                    = yes
pull_ncoords            = 1         ; only one reaction coordinate
pull_ngroups            = 2         ; two groups defining one reaction coordinate
pull_group1_name        = emzyme
pull_group2_name        = inhibitor
pull_coord1_type        = umbrella  ; harmonic potential
pull_coord1_geometry    = distance  ; simple distance increase
pull_coord1_dim         = Y N N
pull_coord1_groups      = 1 2
pull_coord1_start       = yes       ; define initial COM distance > 0
pull_coord1_rate        = 0.0       ; restrain in place
pull_coord1_k           = 1000      ; kJ mol^-1 nm^-2

I am considering repeating the calculations with a different pulling constant to improve the spacing of the initial configurations for the US.

Thanks in advance.