aMD: a possible solution to sampling issues in bilayer simulations

Liquid-liquid phase co-existence in lipids have been observed since 1970s. There is a wealth of experimental data, however, deciphering the molecular details has been a challenge.

Ever since “Lipid raft” hypothesis gained prominence, many computationalists are trying to understand the content and structure of ordered and disordered phases of lipid mixtures.

Why is this relevant?
Several proteins (GPI-anchored proteins, cytochrome C) are known to partition into ordered phases. Also, the ordered phases are known to regulate the activity of certain proteins. There are studies that suggest the order/disorder of plasma membranes can be used to detect apoptosis (Detection of apoptosis through the lipid order of the outer plasma membrane leaflet).

However, here is the  problem:
The lateral diffusion coefficient of lipids is in the order of 10^-7 cm^2/s, which means, in a 100ns simulation (which might take weeks), a lipid molecule will cover an area of 12nm^2 (which is much lesser than the size of a typical “lipid raft”).

What is the solution?

  • Run really, really long simulations on really, really powerful machines (eg: this super-cool study on characterizing the ordered phase (7 micro seconds on Anton) –  Page on acs.org)
  • Identify a good enough sampling technique that will help sample lipid mixing degrees of freedom.


Sometime last month, I came across this paper: Enhanced Lipid Diffusion and Mixing in Accelerated Molecular Dynamics.

What is accelerated molecular dynamics (aMD)?
aMD lets you set a threshold, and adds a continuous (non-negative) bias potential to energy minima below the set threshold. So, the energy barriers above the threshold remains unaffected, while the ones above the set threshold are greatly reduced, which allows the system to sample many more conformations.

In the above figure: E is the set threshold energy . V(r) is the potential of the system concerned and alpha is an “acceleration factor”, which controls the smoothness of the landscape.

So, whenever, the potential energy falls below the set threshold, the energy is modified or biased:


The amount of bias is determined by:

How does one un-bias the potential?
Well, the authors claim that running a conventional MD simulation after sampling, helps the system relax back to the unbiased state.

Why do I think this is cool?
With this technique, the authors show a 250% increase in lipid diffusion. Even though their system size is really small and there could be size effects, the technique looks very promising.

 

Data from the paper: (Panel a) : conventional MD simulation (Panel b) data from aMD

Reference:

Accelerated Molecular Dynamics