# Elastic Properties from lipid bilayer molecular dynamics

GROMACS version: 2018.6
GROMACS modification: No

Hello all
Is there any gromacs analysis tool present that can calculate bending modulus of a lipid bilayer?
Regards
Anirban

Hi,

I am not sure if such a functionality exists, but I guess you can utilize position restraints to ‘manually’ compute the bending modulus.

The bending modulus can be defined as coefficient of the integral of the square of the total curvature in the elastic free energy functional; so, you could in principle restrain the lipid bilayer to a given curvature (B) and perform a free energy calculation starting from some other baseline curvature (A), e.g. flat or maybe some spontaneous curvature that you already know. By comparing the free-energy difference to the curvature difference you should be able to obtain the bending modulus.

Hello @MichelePellegrino
This sounds interesting. Though I never used position restrain to fix lipid bilayer to a particular curvature. How to do that in Gromacs? Can you provide any reference?
p.s I thought to use method like height fluctuation in my case, nice reference can be found in the paper named “Determination of Biomembrane Bending Moduli in Fully Atomistic Simulations”.
Thanks and regards.
Anirban

Hi again,

I actually don’t know any specific methodology, I will check out this height fluctuation method.

There is a whole chapter in GROMACS documentation about position restraints:
https://manual.gromacs.org/documentation/current/reference-manual/functions/restraints.html

The easiest thing one can do is to restrain to absolute positions in space; however, there are other more flexible choices that I guess could be employed if the aim is to constrain the membrane to a specific curvature.

The free energy calculations are also mentioned in the documentation:
https://manual.gromacs.org/documentation/2019-rc1/reference-manual/algorithms/free-energy-calculations.html

Basically, you interpolate the Hamiltonians corresponding to two reference configuration and obtain the free energy difference via thermodynamic integration.

Thanks Michele for your suggestions. I will surely look into the references and would be great if that works!
Thank you for your time :)
Regards
Anirban