Some theory

Lipid order parameters quantify the degree of ordering in lipid membranes. They can be obtained from both experimental measurements and simulations, making them quite useful.

The order parameter $S$ in atomistic simulations can be calculated as:

$S=\frac{1}{2}⟨3{\cos }^2\theta -1⟩$

where $\theta$ is the angle between the C-H bond vector and the bilayer normal, and the angular brackets represent molecular and temporal ensemble averages. The order parameter for atomistic systems is usually reported as the negative of this calculated value, $-S$ (often denoted as $-S_{CH}$ or $-S_{CD}$). Higher positive values of $-S$ indicate more ordered membrane structures. $-S$ of 0 corresponds to a disordered membrane.

For coarse-grained systems, the order parameter can be calculated using the same equation. However, here $\theta$ corresponds to the angle between the vector connecting two consecutive beads of the lipid and the bilayer normal. Using this definition, the order parameter $S$ increases as the membrane structure becomes more ordered. $S$ of 0 corresponds to a disordered membrane. For coarse-grained systems, the order parameter is usually reported directly as $S$ to facilitate comparison with the atomistic $-S$ (which follows the same trend).