Asymmetric membranes and PMF

GROMACS version: 2021.3
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Dear All,

I am trying to simulate interactions of an extremely hydrophobic molecule with model bilayer membranes. The molecule tends to orient in the membrane such that most (or whole) of it remains in the hydrophobic region of the membrane (interacting with lipid tails or remaining in the interleaflet space). I would like to study how the molecule interacts with different bilayer membranes by varying composition of the membrane lipids. Going through literature, people have generally addressed this by using umbrella sampling to move the molecule from outside to the centre (or other side) of the membrane and compare the PMFs. These studies have used symmetric bilayer membranes (the inner and outer membrane leaflets have the same lipid composition). My desired experimental setup is different because I would like to study permeation in an asymmetric membrane (outer and inner membrane leaflets having different compositions). Since the number of membrane compositions to simulate is about 6, performing US will be extremely costly due to the size of system (the MARTINI CG system reaches around 100K beads due to the large size, approx. 200 beads, of the molecule).

Instead of using US, is there a less computationally expensive way to achieve this (such as TI, ABF, metadynamics, etc.)? The goal here is to just have relative strengths of interaction between the molecule and the different asymmetric membranes to identify which one is more favorable than another.

Thanks,
Raman

The accelerated weight histogram method is often faster than US.
See:
https://manual.gromacs.org/current/reference-manual/special/awh.html
and a tutorial and webinar linked here:
https://www.gromacs.org/topic/awh-pmf.html

Dear Dr. Hess,

Thank you for the suggestion. I searched but couldn’t find any paper where AWH is used for membrane permeation of solutes. Honestly, that wasn’t a very exhaustive search. Could you please point towards some papers, if there are any, where AWH is used in membrane permeation studies.

Thanks,
Raman

Here is a paper:
https://www.nature.com/articles/s41467-022-29272-x

Dear Dr. Hess,

Thank you for the pointer.

Regards,
RPS

Hi, just saw this thread.

While the paper is interesting, it also deals with the permeation of small molecules.

In my opinion, a macromolecule is very unlikely to go in or out using only the distance between the CoM of the molecule and the nearest point in the bilayer (i.e. the difference in z-coordinate).

The choice of collective variable(s) here is probably more significant than the sampling method that is applied to it/them. (Comparison between sampling methods generally makes sense only when the CV is sufficient to achieve reversible sampling).

I would certainly start with a PMF using the z-coordinate, because one should always try first what is simpler.

But if not enough, there may be other variables to consider to model the shape of the bilayer. I’d check for existing implementations with PLUMED or other modified versions of GROMACS, and see which ones are computationally efficient enough for your system.

Alternatively, if you’re open to consider other codes this this variable is available for NAMD (it is provided in Colvars, which is also available for GROMACS but unfortunately relies on code native to NAMD at the moment). This paper introduces the CV and validates it against macroscopic membrane mechanics. It scales very well even for CG or atomistic bilayers larger than the one you’re treating.

Giacomo

If the molecule can reside completely within the hydrophobic region of the membrane it is not that large. In addition a coarse-grained force field smooths interactions, computes fewer interactions and allows for larger timesteps, which together makes sampling orders of magnitude faster. So I think there is a reasonable chance that one can obtain a good PMF with a simple reaction coordinate.

Smaller bilayers (e.g. 10x10 nm^2) don’t have enough room to deform, so local deformations are often ignored. But membrane bending becomes much more important for larger bilayers (> 30x30 nm^2), and it can influence the definition of the collective variable. This free-energy cost is reproduced about as equally well by CG and atomistic models.

From what @rpsingh wrote, this is probably an elongated molecule that lies flat along the bilayer midplane while covering a sizeable area (200 CG beads).

Giacomo

I don’t think the size of the membrane has a strong effect. Most users of GROMACS would use a cylinder reference group for the membrane which only covers the environment close to the molecule being pulled.