# Is it possible to compute isothermal area compressibility modulus in GROMACS?

GROMACS version: 2020.2
GROMACS modification: No
Is it possible to compute isothermal area compressibility in GROMACS directly?
I try to do it by computing that in excel, but I am not sure that everything is ok, so please check
To do that I get value box-x and box-y from gmx energy. and compute area per lipid X*Y/100 (my number of lipid in leaflet), so I have 0,70 nm^2 and standard error 0,01 nm^2
From there https://pubs.acs.org/doi/pdf/10.1021/acs.jpcb.6b01870
I take the mathematical formula to calculate isothermal area compressibility modulus

kB is the Boltzmann constant, T - the simulation temperature, ⟨AL⟩ the average area per lipid, and sAL the standard error of AL, nL number of lipids.

In my case
kB = 1.38064852 × 10-23 m2 kg s-2 K-1, but I have in nanometers my area per lipid so I change to
1.38064852 × 10-5 nm2 kg s-2 K-1 = 1.38064852 x 10-5 nm2 g s-2
T = 300K
= 0,69 nm^2 (69 A^2)
nL = 100 lipids (I have 100 lipid in one leaflet, my bilayer system consists of 200 lipids)
sAL = 0,01 nm^2
so:
2*1.38064852 × 10-5 nm^2 kg s^-2 K^-1 * 300 K * 0,7 nm^2
------------------------------------------------------------------------------- =
100 * (0,01 nm^2)^2

2*1.38064852 × 10-5 nm^2 kg s^-2 K^-1 * 300 K * 0,7 nm^2
------------------------------------------------------------------------------- =
100 * 0,0001 nm^4

After reduction
0,005796 kg s^-2
------------------------------------------------------------------------------- =
0,01

0,5796kg
------------- = but I must change to mNm^-1 like in article, so
s ^2

0,5796 kg * m
---------------------- =
s ^2 * m

0,5796 kg * m
---------------------- =
s ^2 * m

If:

N = kg * m * s^-2

so:

0,5796 N * m^ -1, but I must have mNm^-1, so 579,6 mN*m^-1

Do you think that is ok? Exp IACM is 180-330 for 298 K

Hi,

Firstly no, I don’t believe there is a GROMACS tool that will do this for you. Secondly, it is worth stressing that as the isothermal area compressibility calculation uses the standard deviation of the area per lipid it can take a long time for the property to converge. It is quite dependent upon the force field used too so it wouldn’t have surprised me if the result you mentioned was calculated correctly.

However, as to your calculation, I think (from a very quick look!) that you are making one error in that you need to either use the complete number of lipids (200) or to not multiple by 2. In other words, you just need to half the result you got, which happily puts you bang in the experimental range of what I assume is POPC.

Cheers

Tom

1 Like

Oh yes, you’re right, I should take a complete number of lipids in my bilayer (or not multiple by 2 like in this article https://pubs.acs.org/doi/10.1021/ct3003157). Thank you so much. Right now, my calculations are much similar to the experimental value.

Thank you so much again!