A Practical Implicit Membrane Potential for NMR Structure Calculations of Membrane Proteins

Abstract

The highly anisotropic environment of the lipid bilayer membrane imposes significant constraints on the structures and functions of membrane proteins. However, NMR structure calculations typically use a simple repulsive potential that neglects the effects of solvation and electrostatics, because explicit atomic representation of the solvent and lipid molecules is computationally expensive and impractical for routine NMR-restrained calculations that start from completely extended polypeptide templates. Here, we describe the extension of a previously described implicit solvation potential, eefxPot, to include a membrane model for NMR-restrained calculations of membrane protein structures in XPLOR-NIH. The key components of eefxPot are an energy term for solvation free energy that works together with other nonbonded energy functions, a dedicated force field for conformational and nonbonded protein interaction parameters, and a membrane function that modulates the solvation free energy and dielectric screening as a function of the atomic distance from the membrane center, relative to the membrane thickness. Initial results obtained for membrane proteins with structures determined experimentally in lipid bilayer membranes show that eefxPot affords significant improvements in structural quality, accuracy, and precision. Calculations with eefxPot are straightforward to implement and can be used to both fold and refine structures, as well as to run unrestrained molecular-dynamics simulations. The potential is entirely compatible with the full range of experimental restraints measured by various techniques. Overall, it provides a useful and practical way to calculate membrane protein structures in a physically realistic environment.

Figure 1

Shape of the membrane profile function f (z) that modulates the solvation and electrostatic interactions of eefxPot. Profiles were calculated with T = 2D_C and n = 10 (black) or T = D_B and n = 7 (gray) using bilayer structure parameters for DMPC at 30°C (78) with D_B = 36.3 Å, D_HH = 35.3 Å, and 2D_C = 25.4 Å. (A) Modulation of the solvation free energy by f (z). (B) Modulation of solvent screening by f (z) and the effect of the parameter a. To see this figure in color, go online.

Figure 2

MD simulations of the experimentally determined structures of psc-3, Vpu-TM, CrgA-TM, and OmpX, performed with eefxPot or vacuum in the absence of experimental restrains. Simulations were performed at 300 K in Cartesian space. Membranes are depicted as horizontal lines separated by thickness T. (A–D) Plots of structural accuracy as a function of MD time with eefxPot (green) or vacuum (blue). Accuracy is reported as the backbone atom (N, CA, and C) RMSD to the experimental structure deposited in the PDB. (E) Structure of psc-3 in DMPC/DMPG-oriented bilayers (48) taken directly from the PDB (2MCW, pink) or after eefxPot simulation in a 25.4 Å membrane (green). (F) Structure of Vpu-TM in DOPC-oriented bilayers (49) taken directly from the PDB (1PI7, pink) or after eefxPot simulation in 28.5 Å or 25.4 Å membranes (green). (G) Structure of CrgA-TM in DOPC-oriented bilayers (50) taken directly from the PDB (2MMU, pink) or after eefxPot simulation in a 26 Å membrane (green). (H) Structure of OmpX in DMPC/DMPG nanodiscs (51) taken directly from the PDB (2M06, pink) or after eefxPot simulation in a 26 Å membrane (green). The crystal structure (57) (1QJ8, red) is shown in the membrane position derived by rigid-body orientation with solid-state NMR restraints (56). To see this figure in color, go online.

Figure 3

Structural statistics for NMR-restrained calculations. Bars represent results obtained with eefxPot (green) or REPEL (gray). (A) Agreement between structures and experimental DC restraints that were excluded from structure calculations. (B) Structural precision evaluated as the average pairwise RMSD of backbone (CA, C, and N) atoms or all heavy atoms. (C) Agreement between the structures and experimental dihedral-angle restraints used in the structure calculations. To see this figure in color, go online.

Figure 4

WHAT IF and MolProbity validation metrics of the NMR-restrained structures. Bars represent results obtained with eefxPot (green) or REPEL (gray). (A) WHAT IF validation statistics for Ramachandran plot appearance, backbone conformation, χ1/χ2 torsion angles, and protein packing quality. (B) MolProbity validation statistics for percent of residues in favored regions of the Ramachandran plot, percent of residues in disfavored regions of the Ramachandran plot, percent of residues with poor side chain torsion angles, clashscore, and overall MolProbity score. The MolProbity clashscore and MolProbity score are costs (the lower the better). To see this figure in color, go online.

Figure 5

NMR-restrained structures of psc-3 and Vpu-TM. Structures were calculated using eefxPot (green) or REPEL (gray), or taken from the PDB (pink). Membranes are depicted as horizontal lines separated by membrane thickness T = 25.4 Å. The alignment tensor (red) derived from the experimental solid-state NMR restraints has the z axis aligned parallel to the membrane normal. (A–D) Structures of psc-3 folded from an extended template (A and B) and then refined (C and D) using backbone dihedral-angle and ¹⁵N CSA restraints, or taken from the PDB (2MCW) (48). (E–H) Structures of Vpu-TM folded from an extended template using only ¹⁵N CSA restraints without backbone dihedral angles (E and F), or folded from an extended template and then refined using backbone dihedral angles and ¹⁵N CSA restraints (G and H). (I) Solid-state NMR structure of Vpu-TM (52) taken from the PDB (2GOF). To see this figure in color, go online.

Figure 6

NMR-restrained structures of fd coat protein and OmpX. Structures were calculated using eefxPot (green) or REPEL (gray), or taken from the PDB (pink). The eefxPot membrane is depicted as horizontal lines separated by the membrane thickness T. The alignment tensor (red) derived from solid-state NMR CSA restraints has the z axis aligned parallel to the membrane normal. Each ensemble is aligned to its lowest-energy structure. (A–D) Side and top views of ensembles of the 10 lowest-energy structures calculated for fd coat protein with dihedral angles and solid-state NMR ¹⁵N CSA restraints. (E) Snapshot of a structure obtained previously (64) from ED simulations of fd coat protein in all-atom lipid bilayers; lipid phosphate atoms (orange spheres) mark the membrane-water interface. (F) PDB (1MZT) structure of the fd coat protein determined with solid-state NMR CSA and DC restraints without refinement (58). (G–I) Ensembles of the 10 lowest-energy structures calculated for OmpX using solution NMR amide hydrogen distances and dihedral angles, with (G and H) or without (I) solid-state NMR ¹⁵N CSA restraints for Phe residues. The PDB structure of OmpX (2M06, pink) was determined in nanodiscs by solution NMR (51). To see this figure in color, go online.