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Continuous distribution model for the investigation of complex molecular architectures near interfaces with scattering techniques
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10.1063/1.3661986
/content/aip/journal/jap/110/10/10.1063/1.3661986
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/10/10.1063/1.3661986

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Distribution of sub-molecular components along the membrane normal in a DMPC bilayer, as obtained from a MD simulation (Ref. 52). The overlaid DMPC molecules are drawn to scale.

Image of FIG. 2.
FIG. 2.

Possibilities of accounting for atomic positions along the normal direction z at an interface for reflectivity modeling. (A) Average positions of the five atoms of a lipid phosphate group. (B) Lumping together atomic positions into one average position as a basis of describing the phosphate distribution by a Gaussian function. (C) Approximating the associated volume V of the component atoms by a boxcar function of width l and height A b  = V/l that represents the cross-sectional area of the component. This approximation is the basis of the model developed in this work.

Image of FIG. 3.
FIG. 3.

(Color online) (A) The sum of two error functions represents an area profile A(z) of a sub-molecular component within a layered interface structure with the following parameters: l = 4 Å, V = 8 Å3, σ1 = σ2 = 1 Å. The overlaid Gaussian function has the same volume V and a width parameter σGauss ≈ 1.63 σ1. (B) Adding a second sub-molecular component with the same l, V/l, and σ1 at the common interface results in ideal volume filling, even if σ1 ≠ σ2 for the second component. For details, see text.

Image of FIG. 4.
FIG. 4.

(Color online) Validation of the model by fitting to an NAMD simulation (Ref. 51) of a DMPC bilayer (72 lipids, 6 waters/lipid; T = 315 K, initial configurations from Ref. 55) that used the CHARMM27 force field (Refs. 52–54). For details, see Supplemental Information. (A) Best-fit of the error-function based continuous distribution model with constraints (see text) to component distributions obtained from an average of 1000 configuration snapshots of the MD simulation. The overall space filling of the lipid molecules is broken down into the area profiles of individual lipid components, as indicated, for both the model (dashed black lines) and the simulation (continuous lines). Residuals shown at the top of the panel quantify the agreement between the model and the simulation data. (B) Comparison of the interfacial positions of molecular components, defined in the text, and their interfacial roughness with mean atomic positions and standard deviations from the mean obtained in the simulation. Different background gray levels indicate the projected extensions of sub-molecular lipid components. Crosses (x) on the interfaces between two sub-molecular components indicate the interfacial roughness σ of adjacent error functions determined by the fit. These parameters describe the thermally disordered distributions of neighboring molecular components. Upright crosses (+) provide the averaged locations and standard deviations from the mean of non-hydrogen atomic positions observed in the MD snapshot. For the methyl, carboxyl-glycerol, phosphate and choline components, non-hydrogen atoms are labeled. Dashed lines are guides for the eye.

Image of FIG. 5.
FIG. 5.

(Color online) Validation of the model by fitting to an NAMD simulation of a DOPC bilayer (72 lipids, 5.4 waters/lipid, T = 296 K; initial configuration from Ref. 33). Other details as given in Fig. 4 and the Supplemental Information. (A) Best-fit of the error-function based continuous distribution model with constraints to a simulation snapshot. (B) Comparison of the interfacial positions of molecular components and their interfacial roughness with mean atomic positions and standard deviations from the mean obtained in the simulation.

Image of FIG. 6.
FIG. 6.

(Color online) NR at two different solvent contrasts and structural analysis of a bilayer, deposited from floating surface monolayers with a composition, DMPS:DMPC-d54 30:70, on a thermally oxidized Si wafer. (A) Experimental data. Error bars represent 66% confidence intervals. Inset: Neutron SLD determined from the fit using the molecular distribution model. (B) Decomposition of the area profile into sub-molecular components. The PS:PC compositions in the two bilayer leaflets is distinctly different from that of the parent monolayer, particularly in the leaflet proximal to the solid substrate. Note the slight displacement of the PS with respect to the PC head groups toward the bilayer center, which illustrates the capabilities of the new model, as such shifts of molecular fragments against each other cannot be described within the conventional box model.

Image of FIG. 7.
FIG. 7.

(Color online) NR at three different solvent contrasts and structural analysis of a stBLM based upon WC14:βME 3:7 completed with DMPC-d54 (Ref. 8; details, see Supplemental Information). (A) Experimental data. Error bars represent 66% confidence intervals. Inset: Neutron SLD determined from the fit using the molecular distribution model. (B) Decomposition of the area profile into sub-molecular components. Note the high density of hydrocarbons in the proximal bilayer leaflet compared to the distal leaflet which comes about by the large content (≈ 63%) of myristyl chains associated with WC14 that pack more densely than the myristoyl chains of DMPC. The decomposition of the sub-membrane space between the bilayer and the substrate into its components, βME, oligo(ethyleneoxide) of the WC14 and water, is a unique capability of the new model and has not been possible within the limitations of conventional box models. This allows, for the first time, quantitative estimates of the area density ratio between βME and WC14 at the interface and of WC14 and free DMPC in the proximal bilayer leaflet within the self-organized tBLM structure.

Tables

Generic image for table
Table I.

Parameters of the continuous distribution model fitted to the area profiles obtained from MD simulation of a DMPC bilayer (6 waters per lipid, Fig. 4) and equivalent quantities directly determined from the MD snapshot (see text). The parameters σ refer to the interface of the respective sub-molecular component with that on the preceding row. A lipid determined from the fit was (59.50 ± 0.04) Å2 and 59.43 Å2 in the simulation.

Generic image for table
Table II.

Parameters of the continuous distribution model fitted to the area profiles obtained from MD simulation of a DOPC bilayer (5.4 water per lipid, Fig. 5) and equivalent quantities directly determined from the MD snapshot. A lipid determined from the fit was (56.53 ± 0.04) Å2 and 57.06 Å2 in the simulation.

Generic image for table
Table III.

Fit parameters for a solid supported bilayer derived using the continuous distribution model. 95.4% confidence intervals were computed using a Monte Carlo resampling technique (Ref. 9).

Generic image for table
Table IV.

Fit parameters for the sparsely tethered lipid bilayer membrane derived using the continuous distribution model. 95.4% confidence intervals were computed using a Monte Carlo resampling technique (Ref. 9).

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/content/aip/journal/jap/110/10/10.1063/1.3661986
2011-11-30
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Continuous distribution model for the investigation of complex molecular architectures near interfaces with scattering techniques
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/10/10.1063/1.3661986
10.1063/1.3661986
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