Determination of the shape and curvature of nonplanar lipid bilayers that are bent in a single plane in molecular dynamics simulations

The curvature of biological membranes is known to be an important influence on important phenomena such as membrane fusion, endocytosis, and the functioning of integral membrane proteins. There is a growing demand for analytical tools that are able accommodate molecular dynamics trajectories of significantly curved lipid bilayers. In this work, an algorithm for determining the shape and curvature of a nonplanar lipid bilayer in molecular dynamics simulations is proposed. The algorithm calculates the coordinates of the midline and the curvature of the bilayer as well as the local normal to it at any point on the membrane, which is bent arbitrarily in a single plane and is topologically equivalent to an infinite bilayer. The algorithm is implemented as a C++ program and tested by exploring the molecular dynamic trajectories of a highly curved meander-like asymmetric lipid bilayer. The algorithm is general enough to allow it to be easily applied to other geometries of nonplanar membrane systems.