We will do 3_membrane in the tutorial files

• https://www.sciencedirect.com/science/article/pii/S0006349508704193

• https://www.sciencedirect.com/science/article/pii/S0006349508707100

• https://doi.org/10.1529/biophysj.107.122945

• topol.top looks like this:

; Include forcefield parameters

#include "amber99sb-ildn.ff/forcefield.itp"

; bonded and non-bonded parameters for lipid

#include "../lipid21.ff/ffnonbonded.lipid21.itp"

#include "../lipid21.ff/ffbonded.lipid21.itp"

; moleculetype definition of POPC lipid

#include "../itps/popc.itp"

; Include water topology

#include "amber99sb-ildn.ff/tip3p.itp"

; Include topology for ions

#include "amber99sb-ildn.ff/ions.itp"

[ system ]

; Name

Protein

[ molecules ]

; Compound        #mols

POPC               128

SOL                 5736

• The major difference between water box and membrane box is the pressure coupling part.

  • Membrane is not isotropic. Most natural choice for memrbane is semi-isotropic pressure coupling (Pxx = Pyy and Pzz are independent).

  • By setting Pxx = Pyy = 1 bar and Pzz = 1 bar, we can simulate zero surface tension.

; pressure coupling     

Pcoupl                   = c-rescale

Pcoupltype               = semiisotropic

nstpcouple               = -1

; Time constant (ps), compressibility (1/bar) and reference P (bar)

tau-p                    = 1.0

compressibility          = 4.5e-5 4.5e-5

ref-p                    = 1      1

• Using all.1ns.xtc trajectory file, we can compare the diffusion coefficients of water and lipid molecules.

  • Obviously, water diffusion is much faster.

• Homework: calculate the diffusion coefficients of water and lipid by using gmx msd.

• 
  

• In the ∆G calculation for a water-water pair, the reaction coordinate was the distance between the water pair.

• In this case, the reaction coordinate is the z-position of a water molecule with respect to the center of mass of the membrane.

Umbrella sampling

• First, we need to generate the index file

  • • We will just select the first water molecule. The selection will not change the results. All water molecules are equal!

    • There are 128 POPC molecules. Thus, the residue index of the first water molecules will be 129.

gmx make_ndx -f topol.tpr -o pull.ndx

ri 129

q

• • • Caution: The initial distance between chosen water molecules must be smaller than half of the box. Otherwise, it violated PBC.

    • The groups will look like this:

  0 System              : 34360 atoms

  1 Other               : 17152 atoms

  2 POPC                : 17152 atoms

  3 Water               : 17208 atoms

  4 SOL                 : 17208 atoms

  5 non-Water           : 17152 atoms

  6 r_129               :     3 atoms

Perform simulation in each window

• 10 Å window

  • See PULL section in pull.10.mdp

; COM PULLING          

pull                     = yes

; Cylinder radius for dynamic reaction force groups (nm)

pull-pbc-ref-prev-step-com = yes

pull-nstxout             = 50

pull-nstfout             = 50

pull-ngroups             = 2

pull-ncoords             = 1

pull-group1-name         = POPC

pull-group1-pbcatom      = 1

pull-group2-name         = r_129

pull-coord1-type         = umbrella

pull-coord1-geometry     = direction

pull-coord1-vec          = 0 0 1

pull-coord1-groups       = 1 2

pull-coord1-dim          = N N Y

pull-coord1-init         = 1.0         ; the equilibrium length of spring is 10 Å

pull-coord1-k            = 1000        ; spring constant in kJ/mol nm

• • Generate pull.10.tpr for gmx mdrun

    • gmx grompp -c 2.pdb -f pull.10.mdp -n pull.ndx -o pull.10.tpr -t state.cpt

      • -t state.cpt: use information from the check point file.

  • Perform MDRUN for 1 ns

    • gmx mdrun -s pull.10.tpr -nt 4 -gpu_id 0 -cpi -noappend -deffnm pull.10 -nsteps 500000

      • pullx files contain the length of spring

      • pullf files contain the force on the spring (F = -kx)

  • Repeat same things for other windows. For example, 0, 2, 4, 6, 8 , 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34 Å

  • It will take much longer than the water box. Adjust the simulation time considering your computer.