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Demonstrations of multi-dimensional Voronoi tessellations. Division of 2D plane (A) and 3D cube (B) domains into Voronoi cells based on 12 random points and packed spheres, respectively. A 2D VT method divides a square domain Ω into twelve Voronoi polygons or 2D cells. The generator Z 1 with its yellow Voronoi region has six nearest neighbors (Z 2 to Z 7 ) with different colored Voronoi regions. A 3D rendering of polyhedral volume occupied by each atom in a representative PC (C) and CHOL (D) molecule in a lipid bilayer. The colors correspond to those assigned to different atom group as given in Fig. 1. Nearest neighbor lipids and water molecules to a beta-amyloid protein in a PC/CHOL bilayer (E) as determined from the nearestatom-neighbor list of Voro++ are also given. The polar headgroups of PC and CHOL are represented by blue and red spheres, and the non-polar groups of PC and CHOL are represented by blue and yellow lines, respectively. The protein is shown by color spheres. Scale bar = 10 Å. See Materials and methods for details. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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... denote a regular VT as non-weighted VT and a radical VT as weighted VT. In our simulations, each atom represents a generator and its van der Waals radius is considered as its weight. Examples of 2D and 3D regular VT-based VT cells are shown in Fig. 2A and B respectively. In Fig. 2A, a two-dimensional (2D) square domain Ω contains twelve randomly generated particles in black circles (N = 12). A 2D VT method divides this square domain Ω into twelve Voronoi polygons or 2D cells with blue boundaries. The generator Z 1 with its yellow Voronoi region has six nearest neighbors (Z 2 to Z 7 ...
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... denote a regular VT as non-weighted VT and a radical VT as weighted VT. In our simulations, each atom represents a generator and its van der Waals radius is considered as its weight. Examples of 2D and 3D regular VT-based VT cells are shown in Fig. 2A and B respectively. In Fig. 2A, a two-dimensional (2D) square domain Ω contains twelve randomly generated particles in black circles (N = 12). A 2D VT method divides this square domain Ω into twelve Voronoi polygons or 2D cells with blue boundaries. The generator Z 1 with its yellow Voronoi region has six nearest neighbors (Z 2 to Z 7 ) with different colored ...
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... two-dimensional (2D) square domain Ω contains twelve randomly generated particles in black circles (N = 12). A 2D VT method divides this square domain Ω into twelve Voronoi polygons or 2D cells with blue boundaries. The generator Z 1 with its yellow Voronoi region has six nearest neighbors (Z 2 to Z 7 ) with different colored Voronoi regions. In Fig. 2B, a three-dimensional (3D) cube Ω contains disperse small particles [25]. A 3D VT method divides this cube domain Ω into Voronoi polyhedra or 3D cells with flat faces as shown in Fig. 2B. In both 2D and 3D regular VT, the line or planes between two nearest particle neighbors form the 2D and 3D bisectors, respectively, of the line ...
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... 2D cells with blue boundaries. The generator Z 1 with its yellow Voronoi region has six nearest neighbors (Z 2 to Z 7 ) with different colored Voronoi regions. In Fig. 2B, a three-dimensional (3D) cube Ω contains disperse small particles [25]. A 3D VT method divides this cube domain Ω into Voronoi polyhedra or 3D cells with flat faces as shown in Fig. 2B. In both 2D and 3D regular VT, the line or planes between two nearest particle neighbors form the 2D and 3D bisectors, respectively, of the line joining these two particles. It is important to note that no two Voronoi cells overlap, except for the points on bisectors. So the VT cells span the entire domain Ω, and the sum of the volumes ...
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... of 3D VT cells of the atoms of PC and cholesterol lipids is illustrated in Fig. 2C and D, respectively. The color codes are identical to those used in Fig. 1A and B, respectively. Additionally, the first nearestneighbor lipids and water of the protein in the Aβ/PC/CHOL bilayer based on 3D VT are also demonstrated in Fig. ...
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... of 3D VT cells of the atoms of PC and cholesterol lipids is illustrated in Fig. 2C and D, respectively. The color codes are identical to those used in Fig. 1A and B, respectively. Additionally, the first nearestneighbor lipids and water of the protein in the Aβ/PC/CHOL bilayer based on 3D VT are also demonstrated in Fig. ...
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... first-order (n = 1) VT lipid shell consisted of lipid molecules that were nearest neighbors to the protein (see Fig. 2E). A nearest neighbor was determined by a lipid selection criterion that at least one atom of the lipid in the first shell must be on the nearest-atom-neighbor list of at least one protein atom. For higher-order VT lipid shells (n ≥ 2), the selection criterion was that at least one of the lipid atoms of each lipid in the nth lipid shell ...
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... to the planar bilayer surface, of the separated lipid shells, using the same color codes as the above lateral view. Only six lipid shells (n = 1 to 6) are visible. Again, because of the periodic boundary, two repeating simulation boxes along the x-direction are demonstrated. Results generated from the non-weighted VT method are shown in Fig. S2 of the Supporting ...
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... examinations of the lipid and lipid-interfacial water shells calculated from both weighted and non-weighted methods reveal that almost identical shell classifications were achieved in both methods except those at high orders (see Fig. S2 in the Supporting material). Volumetric and biophysical characterizations of these shells from both methods are given ...
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... has a "larger" free space than the tetravalent atom in PC. In CHOL, similar observations of larger volume in monovalent united atoms than in multivalent atoms, e.g., C1, C17, and C23 of ~ 35 Å 3 vs. C2 and C16 of ~ 5 Å 3 , were evident as shown in Fig. 4I. Similar atomic volume profile was found in both PC and CHOL using non-weighted VT method (Fig. S2 of the Supporting ...
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Citations
... The great advantage of VT technique is that it provides not only APL distribution beyond the average but also local structural information of the bilayer surface. 105 For instance, local disturbances caused by the direct permeation of small molecules can be identified by VT-based APL distribution. 106,107,102 To find such local disturbances, the NpT trajectories had been analyzed by a VT-based in-house Python script (powered by Python 2.7 108 and MDAnalysis 0.18.1 109 ), in which the phosphorous atom was projected to the macroscopic XY surface of the membrane, 110 while the periodic boundary conditions were also taken into account. ...
... This region is defined as the lipid insertion domain. However, in our recent studies on monomeric beta-amyloid peptide in various lipid bilayers, the lipid insertion domain was alpha-helix rich (Qiu et al., 2014;Cheng et al., 2015c). ...
We used molecular dynamics simulations to explore the effects of asymmetric transbilayer distribution of anionic phosphatidylserine (PS) lipids on the structure of a protein on the membrane surface and subsequent protein-lipid interactions. Our simulation systems consisted of an amyloidogenic, beta-sheet rich dimeric protein (D42) absorbed to the phosphatidylcholine (PC) leaflet, or protein-contact PC leaflet, of two membrane systems: a single-component PC bilayer and double PC/PS bilayers. The latter comprised of a stable but asymmetric transbilayer distribution of PS in the presence of counterions, with a 1-component PC leaflet coupled to a 1-component PS leaflet in each bilayer. The maximally asymmetric PC/PS bilayer had a non-zero transmembrane potential (TMP) difference and higher lipid order packing, whereas the symmetric PC bilayer had a zero TMP difference and lower lipid order packing under physiologically relevant conditions. Analysis of the adsorbed protein structures revealed weaker protein binding, more folding in the N-terminal domain, more aggregation of the N- and C-terminal domains and larger tilt angle of D42 on the PC leaflet surface of the PC/PS bilayer versus the PC bilayer. Also, analysis of protein-induced membrane structural disruption revealed more localized bilayer thinning in the PC/PS versus PC bilayer. Although the electric field profile in the non-protein-contact PS leaflet of the PC/PS bilayer differed significantly from that in the non-protein-contact PC leaflet of the PC bilayer, no significant difference in the electric field profile in the protein-contact PC leaflet of either bilayer was evident. We speculate that lipid packing has a larger effect on the surface adsorbed protein structure than the electric field for a maximally asymmetric PC/PS bilayer. Our results support the mechanism that the higher lipid packing in a lipid leaflet promotes stronger protein-protein but weaker protein-lipid interactions for a dimeric protein on membrane surfaces.
... However, unfolding in the LID over a wide range occurred after the UA simulation relaxation. This result suggests that the unfolding of LID in the deep inserted state was mainly attributed to the interactions of the LID with the lipid matrix during the UA relaxation similar to the observation of the partially inserted -to-fully inserted transition found in earlier studies [14,65]. In the II complex, significant changes in the average protein unfolding in the LID was found before and after the UA simulation relaxation. ...
The connection between empty intermolecular volume and gas solubility has been widely discussed. Recently, interest in this issue has increased concerning ionic liquids (ILs). In this work, we study the mixtures of gases (CO2, O2, N2, CH4) with ionic liquids ([CnMIM][NTf2], n = 2, 4, 6, 8) using molecular dynamics simulations and the Voronoi-Delaunay method for the empty volume analysis. We have shown that the gas molecules locally loosen the IL, forming an additional empty volume in the mixture. However, the CO2 molecule adds a significantly smaller empty volume compared to O2, N2, and CH4 molecules. This fact correlates with their solubility: the solubility of CO2 is higher compared to other studied gases. The distributions of dissolved molecules near different components of ionic liquids have also been studied. We showed that CO2 molecules are located closer to the anions than other gases.
A convenient way to analyse solvent structure around a solute is to use solvation shells, whereby solvent position around the solute is discretised by the size of a solvent molecule, leading to multiple shells around the solute. The two main ways to define multiple shells around a solute are either directly with respect to the solute, called solute-centric, or locally for both solute and solvent molecules alike. It might be assumed that both methods lead to solvation shells with similar properties. However, our analysis suggests otherwise. Solvation shells are analysed in a series of simulations of five pure liquids of differing polarity. Shells are defined locally working outwards from each molecule treated as a reference molecule using two methods: the cutoff at the first minimum in the radial distribution function and the parameter-free Relative Angular Distance method (RAD). The molecular properties studied are potential energy, coordination number and coordination radius. Rather than converging to bulk values, as might be expected for pure solvents, properties are found to deviate as a function of shell index. This behaviour occurs because molecules with larger coordination numbers and radius have more neighbours, which make them more likely to be connected to the reference molecule via fewer shells. The effect is amplified for RAD because of its more variable coordination radii and for water with its more open structure and stronger interactions. These findings indicate that locally defined shells should not be thought of as directly comparable to solute-centric shells or to distance. As well as showing how box size and cutoff affect the non-convergence, to restore convergence we propose a hybrid method by defining a new set of shells with boundaries at the uppermost distance of each locally derived shell.
