Fig 1.
Features of electrostatic potential due to the lipid bilayers in the membrane.
(a) Electrostatic potential as a function of depth and analytical fit. (b) Comparison of electrostatic potential in a 0.1 M salt solution and that calculated by Yu et al. in pure water. [45] Comparison of electrostatic potential as a function of membrane depth for (c) different lipid head groups and (d) lipid tail lengths.
Fig 2.
Coulomb electrostatic energy due to the lipid bilayers in the membrane.
(a) Membrane-dependent electrostatics potential: The energy increases when entering the bilayer and at close atom pair distances. Green arrows indicate the direction of increasing energy. (b) Dependence of the dielectric constant ε on fraction of hydration fhyd and atom-pair distance ri,j. The different dielectric constants are colored from low (dark blue) to high (yellow). (c) Variation of the membrane dielectric-dependent electrostatics energy as a function of fractional hydration fhyd and atom-pair distance ri,j. Each grid point corresponds to an energy calculated for point charges with opposing signs, and the energy varies from strong (dark blue) to weak (yellow).
Fig 3.
Values of and
with different scales.
(a) Comparison of calculated using F19 and F23 relative to the experimental values from MF and WW scales. The MF
for D−1 and E−1 are estimated by extrapolation of a linear fit of the other WW data points. (b) Comparison of
calculated using F23 and IMM1 relative to F19.
Fig 4.
Test1: Orientation of polyalanine and WALP peptides.
(a) Predicted tilt angle of polyalanine as a function of the number of residues. The polyalanine is named AAx, where x represents the number of residues. (b) Predicted tilt angle of WALP peptides as a function of the number of residues. The WALP peptides are presented as WALPx, where x represents the number of residues. Peptides for which experimental results are available are presented by filled markers, and those for which simulated data is available are shown by unfilled markers.
Fig 5.
Test2: Orientation of TM and adsorbed peptides.
(a) Predicted tilt angle of TM peptides compared with experimental measurements. (b) Predicted tilt angle of adsorbed membrane peptides and compared with experimental measurements.
Fig 6.
Per-residue F23 energy calculated at native, F23 and F19 calculated tilt angles.
(a) F23 per-residue total energy (REU), (b) per-residue transfer energy to the bilayer, and (c) per-residue electrostatic energy due to the lipid layer at native (black hashed), F23 (red) and F19 (blue) calculated tilt angles. Right: Sum of all residues.
Fig 7.
Test3: ΔΔGmutation of alanine to all other residues.
Predicted ΔΔGmutation and experimental measurements for (a) OmpLA and (b) Pagp protein. For the experimental values of ΔΔGmutation for D−1 and E−1 for OmpLA, we have used their extrapolated MF scale values as described in Methods section. Since the experimental based on the MF hydrophobicity, was measured at a pH of 3.8, where some of the Asp and Glu are in their protonated states, we removed them while calculating the slope and correlation coefficient of the best-fit lines (dashed lines) for the predictions relative to experimental values. The black line is the y = x line. The red and blue dashed lines are linear best-fit lines for values predicted by F23 and F19, respectively. The equations for the best-fit lines for F23 and F19 are shown in red and blue, respectively.
Fig 8.
Test4: ΔΔGins of polyleucines.
ΔΔGins is the energy difference between the lowest energy orientation of the peptide in the lipid bilayer phase and that in the aqueous phase. ΔΔGins is a measure of the affinity of a folded protein to be in the membrane phase relative to the aqueous phase. Predicted ΔΔGins are compared with experimental and values calculated by MD simulations.
Fig 9.
Test 5: Sequence recovery of membrane proteins.
Plots show the fraction of native amino acids recovered on the y-axis and the fraction of amino acid types with individual recovery rates greater than 0.05 on the x-axis. An accurate energy function would have a high sequence recovery rate both overall and for the individual amino acid types. The results are shown for all positions in panel (a), buried (in filled circles) vs. surface-exposed(in open circles) positions in (b), lipid-exposed positions in (c), and water exposed in (d).
Fig 10.
Distribution of residue divergence in the redesigned membrane proteins.
Plots show the difference in log-likelihood (D) and KL-divergence (DKL) of designed residue distribution relative to the native sequences. 204 MPs are redesigned with fix-bb and membrane orientation using the (a) F19 and (b) F23 energy functions. A positive divergence indicates that an amino acid is over-enriched, whereas a negative indicates that an amino acid is under-enriched. Values are given on a logarithmic scale. An amino acid composition pie chart for the sequence designed by each energy function is also shown in the bottom left-hand corner of the divergence plots. The color red is for non-polar, blue is for aromatic, violet is for polar, yellow is for charge, and green is for special residues.
Fig 11.
Redesigned membrane proteins exhibit native-like sequences.
(a-c) Confusion matrices presenting probability distribution (pi|r) of design residues i replacing a native residue r by F23 energy function. (d-f) Confusion matrices presenting probability distribution (pi|r) of design residues i replacing a native residue r by F19 energy function. (g-i) Per-residue perplexity (ppr) by F19 and F23 energy functions. In the confusion matrices, black denotes the highest (1.0), and light peach denotes the lowest (0.0) probabilities respectively. The criteria to distinguish between the membrane region is based on relative hydration in the membrane (fhyd) and geometry of the water-exposed pore of the protein (fpore). [44] Lipid: fhyd < 0.25, fpore < 0.50; Interface: fhyd ∈ [0.25, 0.75), fpore < 0.50; Aqueous: fhyd > 0.75, fpore > 0.50.
Fig 12.
Summary of F19 and F23 performance on MP benchmark tests.
Darker boxes show better performances.