Supplemental Material for Correlation between Length and Tilt of Lipid Tails

The goal of this section is to investigate the tilt-length correlations for the following alternative definitions of the tail director: A. Molecular directors, which characterize tilt of an entire molecule, rather than an individual tail. This approach to the director definition was taken in the earlier work [1–3]. Here, we investigate two different definitions of molecular directors (see Fig. S1a): 1. Mean tail director n m , defined as the average of the end-to-end directors −−−→ C N C 1 of individual tails of a molecule. Specifically, n m is defined as the vector pointing from C (m) N to C (m) 1 , where C (m) i is the midpoint between atoms C i of different tails of a lipid molecule. 2. Overall molecular director n P , which accounts for contributions of both the head-and tail-groups to molecular tilt. Following [3], we define n P as the vector pointing from C (m) N to the phosphorus atom in the lipid head-group. Similarly to the individual tail directors, the length L of a molecular director is defined as the distance between its end-points. B. Gyration director n g defined as the principal direction of gyration of a lipid tail corresponding to its largest radius of gyration. In the calculations of the tensor of gyration S of a hydrocarbon chain, we neglect hydrogen atoms belonging to the chain, i.e.