Morphology of voids in molecular systems. A Voronoi-Delaunay analysis of a simulated DMPC membrane

A generalized version of the Voronoi-Delaunay method is used to study relatively large intermolecular voids in a model of the hydrated DMPC bilayer, obtained from all-atom Monte Carlo simulation. Application of the original version of the method for molecular systems has been hampered by the fact that these systems geometrically represent ensembles of partially overlapping spheres of different radii. The generalized version of the method is based on using the additively weighed Voronoi diagram, representing the locus of spatial points being equally far from the surface rather than the center of the corresponding pair of atoms. This version of the Voronoi-Delaunay method can be readily used to reveal and analyze voids accessible for probes of different radii even in rather complex molecular systems. When the properties of the voids present in the simulated DMPC membrane are investigated, their shape, size, and orientation have been analyzed in detail in the different regions of the membrane located at different depths along the membrane normal axis. The characteristics of the voids are found to be different in different regions of the bilayer, namely (i) at the middle of the membrane, in the region of the hydrophobic lipid tails, (ii) in the region of the hydrophilic zwitterionic headgroups, and (iii) in the region of the bulklike water adjacent to the bilayer. The largest and oblong voids are found in the middle of the membrane, with a preferred orientation that is parallel to the bilayer normal axis. A clear correlation between the orientation of the voids and the orientation of the lipid chains is observed. In the bulk water region the fraction of the empty space is even higher than at the middle of the membrane; however, here the voids are distributed more uniformly. Finally, in the high-density region of the hydrophilic headgroups the voids are found, on average, smaller than in the other parts of the system.