Analysis of lipid surface area in protein–membrane systems combining voronoi tessellation and monte carlo integration methods

Abstract

All-atom molecular dynamics (MD) simulation has become a powerful research tool to investigate structural and dynamical properties of biological membranes and membrane proteins. The lipid structures of simple membrane systems in recent MD simulations are in good agreement with those obtained by experiments. However, for protein-membrane systems, the complexity of protein-lipid interactions makes investigation of lipid structure difficult. Although the area per lipid is one of the essential structural properties in membrane systems, the area in protein-membrane systems cannot be computed easily by conventional approaches like the Voronoi tessellation method. To overcome this limitation, we propose a new method combining the two-dimensional Voronoi tessellation and Monte Carlo integration methods. This approach computes individual surface areas of lipid molecules not only in bulk lipids but also in proximity to membrane proteins. We apply the method to all-atom MD trajectories of the sarcoplasmic reticulum Ca(2+)-pump and the SecY protein-conducting channel. The calculated lipid surface area is in agreement with experimental values and consistent with other structural parameters of lipid bilayers. We also observe changes in the average area per lipid induced by the conformational transition of the SecY channel. Our method is particularly useful for examining equilibration of lipids around membrane proteins and for analyzing the time course of protein-lipid interactions.

Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms

“…While it is difficult to estimate the correct number of lipids in each leaflet of protein–membrane systems to avoid a mismatch in lipid packing, it has been suggested that the area per lipid mismatch up to 5% would be tolerable in membrane simulations of typical all-atom system sizes [163]. For the analysis of the area per lipid in protein–membrane systems, the Voronoi tessellation Monte Carlo integration method has been proposed [164], which also makes possible to assess equilibration of lipid bilayers by comparing the obtained area per lipid with the experimental data.…”

Characterization of 3D Voronoi tessellation nearest neighbor lipid shells provides atomistic lipid disruption profile of protein containing lipid membranes

“…Previous MC-, VT- and grid-based studies on lipid domains and lipid/protein interactions [9, 13, 22, 23] projected the atoms or the center-of-masses of lipids on the bilayer surface or xy -plane. This projection approach might introduce uncertainties in the lipid classification and averages out atomistic detail about the structure of the protein-lipid bilayer interactions.…”

“…Previous simulation studies on pure lipid bilayers have demonstrated that the time-averaged volume and surface area per lipid, membrane thickness, order parameter, and domain size of the bulk lipids compared favorably with those from experiments [12–21]. In the presence of protein, different analytical tools based on the grid-method [22], Voronoi tessellations (VT) [2], Monte Carlo (MC) Integration [10] and hybrid VT and MC integration [23] have been proposed to study protein/lipid interactions. In most cases, a two-dimensional projection of the protein and lipid atoms or molecules on the bilayer plane was used to classify the annular and non-annular lipids.…”

Bioinformatics for Membrane Lipid Simulations: Models, Computational Methods, and Web Server Tools

“…Mori and colleagues proposed a more sophisticated method for calculating the APL using Voronoi tessellation and Monte Carlo simulation [80]. Coordinates of center of mass for each lipid molecules and coordinates for protein atoms located between the maximum and minimum z-coordinates for the monolayer are projected onto the XY plane.…”