(a) Homogeneous standard implicit solvent model: and are the dielectric constants of a protein and solvent, respectively. (b) Heterogeneous implicit membrane (dark gray area) environment: is the dielectric constant of a membrane and varies along the direction.
Three different types of dielectric continuum models for a membrane-water system are shown schematically. The direction corresponds to the direction normal to the membrane plane, and the center of the membrane is taken to be . See text for the description of the dielectric regions.
The electrostatic contribution of the solvation free energy is plotted for a monovalent spherical ion of radius as the probe ion moves across the membrane along the direction. Boxes and triangles represent the five- and three-dielectric models, although they may be difficult to distinguish. Stars ( and 80) and diamonds ( and 80) represent the two dielectric models. The different dielectric models for the membrane-water environment are described in Fig. 2.
The apparent dielectric constant curves are determined for the probe ions of three different radii (box for , triangle for , and star for ). The values of at the center of the membrane for radii 1, 2, and are 2.108, 2.258, and 2.426, respectively.
The profile function (solid line) was derived by least-squares fit to the free energy profile data of oxygen in the lipid membrane computed by explicit MD simulations show as points (data are normalized to one) (Ref. 43).
The M2 channel-lining segment from nicotinic acetylcholine receptors [PDB entry 1EQ8 (Ref. 48)] is placed in the membrane-water system which is modeled as three dielectric media (hydrocarbon interior, ester group, and the rest). The partition of the membrane-water system into different regions is based on explicit simulations (Ref. 22).
Electrostatic solvation free energies are calculated for 64 different orientations and positions of M2 by using three different apparent dielectric constant profiles (see Fig. 4), and compared with the CHARMM PBEQ results.
Solvation free energy profile of water molecule along the axis with different values of surface tension parameters (triangles for , stars for , and diamonds for ). Explicit MD simulation data are shown as filled boxes (Ref. 56).
Change in water oxygen radius (top) for in order to match the free energy profile (bottom) between our implicit membrane model (solid line) and data from explicit MD simulations (filled box). The uncorrected solvation free energy profile (dotted line) is shown for comparison.
Nonpolar profile (solid line) corrected according to the suggested change in the water oxygen radius inside the membrane as shown in Fig. 9. The original profile from Fig. 5 (dotted line) is shown for comparison.
Solvation free energy profiles of amino acid side chain analogs along the axis are shown for our implicit model GB model without the radius correction (solid line) and with the radius correction (dashed line), the two-dielectric model GBSW (Ref. 24) (empty triangle), and the explicit MD simulation results (Ref. 59) (solid line with error bar; only for methanol, acetamide, and acetic acids). We used surface tension parameters of . The arrow indicates the experimental transfer free energy from cyclohexane to water for uncharged species (Ref. 74) at 7.
component of the geometrical center of melittin over of MD simulation at for different surface tension parameters. Horizontal dotted lines indicate the experimental distribution. The shaded area corresponds to the range of the center of mass position of melittin during a molecular dynamics simulation of melittin in explicit lipid bilayers and water (Ref. 8).
Snapshots of melittin at the end of MD simulations.
The backbone RMSD (top) and the component of the center of mass (bottom) of bacteriorhodopsin from MD simulations. The surface tension parameter was set to . The bRMSD for all residues, TM residues, and non-TM residues are shown in black, dark gray, and light gray respectively. The dashed lines indicate the range of bRMSD from the explicit MD simulations of bacteriorhodopsin trimer (Ref. 69).
Free energies of transfer from the center of the membrane to bulk solvent for neutral amino acid side chain analogs are computed without the radius modification (uncorrected) and with the radius modification (corrected). They are arranged in increasing order of the solvent accessible surface area (SASA) and compared with the experimental data (Ref. 74) and results from the two-dielectric model GBSW (Refs. 24 and 26). Boldface is used in uncorrected and corrected columns to indicate the value that agrees better to experimental data.
Membrane position and transfer energy of melittin for different values of the empirical surface tension parameter . The positions of the geometric center of melittin are averaged over the last of simulations. The transfer energy is computed as the difference between the solvation energy with the implicit membrane environment and an implicit homogeneous aqueous environment for the melittin conformations sampled during the last of implicit membrane simulations.
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