Customized version of Gromacs for simulating lipid mixtures
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Biological membranes are complex mixtures. They may contain dozens of different types of phospholipids, sphingolipids, and sterols, along with a great diversity of proteins. We would like to better understand how different types of lipids are distributed in bilayer mixtures: Are they mixed randomly? Do they cluster together with other lipids of similar type? Do they preferentially surround proteins that are somehow “best fits” to their structures?

We are trying to answer these questions using computer simulations of mixed-lipid bilayers. In these simulations, every molecule is represented by a set of points, each representing the position of one atom (or one methylene or methyl group). Forces between these atoms or groups can be approximated from a combination of experimental and theoretical sources, and (using classical mechanics as an approximation) the computer can generate a molecular dynamics (MD) trajectory showing how the arrangements of a set of interacting molecules evolves over time. For a set of ~100 lipids and ~3000 water molecules, it takes about one day to calculate a trajectory one nanosecond long. Unfortunately, lipid distributions don't change much during one nanosecond – it takes about a microsecond (one thousand nanoseconds) to start to see any non-random arrangements of lipids take shape.

We have focused much of our recent effort on finding a way around this problem. A postdoc from the group (Jason de Joannis) developed a code that we call GIMLi. Within this code, each lipid can adopt either of two structures; the computer uses an algorithm called configuration-bias Monte Carlo (CBMC) to allow the lipid to switch from one structure to the other in such a way as to maintain a thermally equilibrated distribution. We have found that (depending on the specifics of the mixture involved), adding CBMC moves to an MD trajectory can lead to an apparently equilibrated lateral distribution in just a few nanoseconds.

What have we learned from GIMLi simulations? We find that for a lipid bilayer in the disordered “Liquid Crystalline” phase, lipids with the same head-groups but with tail lengths that differ by 4 carbons in both chains show very close to a random lateral distribution. In contrast, in the more ordered “Gel” phase, shorter-tail lipids tend to cluster together. We also have observed the enrichment of shorter-tail lipids at the edges of bilayer ribbons, but found no significant preference associated with local curvature properties in a strongly buckled bilayer.


Snapshots from GIMLi simulations showing distributions of DMPC (with 14-carbon tails, with head-group shown in dark blue and tails in light blue) and DDPC (with 10-carbon tails, head-group depicted in orange and tails in red) in a cross-section of a bilayer ribbon (top) and a strongly curved bilayer (bottom).  Solvent is omitted for clarity.

Simulations of a range of systems containing lipid mixtures are in progress: “bicelles”, in which very short-tailed lipids stabilize bilayer edges to produce disk, ribbon, and porous sheets; the distribution of long and short lipids near transmembrane peptides; and the mixing behavior of saturated and monounsaturated-tail lipids in the presence and absence of cholesterol.

The GIMLi code employs the “isomolar semi-grand canonical ensemble”, which means that the simulation is performed at constant temperature, constant number of lipids, and constant ∆µ, i.e. constant difference in chemical potential between the two lipids. An advantage of using this ensemble is that any two systems with the same ∆µ at the same temperature can be considered at equilibrium with each other with respect to the exchange of lipids of different types. We are exploiting this property in working towards calculating equilibrium phase diagrams of lipid mixtures. By analyzing the structures produced during the simulations, we can gain insight into the driving forces behind the separation of different lipids into separate domains. By comparing our results with experimental phase diagrams, we can validate and perhaps improve the models (force-fields) that we and other researchers use to represent lipids.

A major challenge for the future is to extend our methods to allow study of mixtures of lipids with different head-groups. The specificity of polar head-group site interactions with each other and with solvent makes it difficult to perform Monte Carlo mutations of head-groups. Some new strategies are being considered to address this problem.



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