Methods and Definitions
Each protein is considered as rigid body that freely floats in a hydrophobic slab of adjustable thickness.
Orientation of the protein was determined by minimizing its transfer energy, ΔGtransfer, with respect to d, z0, Θ and φ variables in a coordinate system whose axis Z coincides with the bilayer normal:
Figure 1. Schematic representation of a transmembrane protein in a hydrophobic slab.
d, shift along the bilayer normal; D, hydrophobic thickness (D=2z0); φ, rotation angle; τ, tilt angle.
Longitudinal axes of TM proteins are calculated as vector averages of TM segment vectors.
These proteins do not span the membrane. Maximal membrane penetration depths (D) is used instead of the hydrophobic thickness. The longitudinal axis is defined as an axis that provides minimal moment of inertia. Transfer energies of peripheral proteins are calculated without considering ligands, except for lipid clamps, photosynthetic reaction centers and light-harvesting complexes.
Anisotropic Solvent Model of the Lipid Bilayer
Figure 2. (A)
Profiles of hydrogen bonding donor (α) and acceptor (β) capacity, solvatochromic dipolarity/polarizability parameter (π*), dielectric constant (ε), dielectric function F(ε), and volume fraction of non-polar media (HDC) along the membrane normal. Polarity parameters were calculated using distributions along the membrane normal of volume fractions of lipid components obtained by X-ray and neutron scattering for fluid DOPC bilayer (B
, Kucerka et al., 2008 Biophys. J. 95: 2356-2367).
Membrane interface or "midpolar region" (8-20Å from the membrane center) is characterized by the steep gradient of all polarity parameters whose values depend on lipid composition.
Transfer free energy of the molecule from water to the lipid bilayer is calculated in accordance with a new solvation model developed for the anisotropic environment (i.e. the lipid bilayer):
is an atomic solvation parameter of atom type i (expressed in cal mol-1
is the solvent accessible surface area of atom i, ηS→wat
is a dipolar solvation parameter (expressed in cal mol-1
is a dipole moment of a group l
ASA-dependent first-shell contribution to the transfer free energy (vdW, H-bonds, solvent entropy) is described by the dependence of atomic solvation parameters σi
on macroscopic dielectric constant of a solvent (ε), solvent hydrogen bonding acidity (α) and basicity (β) parameters:
Long-range electrostatic contribution to the transfer free energy is described by the dependence of dipolar solvation parameters ηS→wati
on macroscopic solvatochromic dipolarity/polarizability parameter π*:
Energy of an ionizable group in neutral state is described as:
Born electrostatic energy for ions:
The preferential solvation of protein groups in water-lipid mixture was also taken into account.
Transfer free energies of amino-acid residues in model bilayers vs. "statistical energies" in helical TM proteins
Calculated transfer free energy profiles (solid lines) of Trp residue in TM α-helix immersed in model lipid bilayers (DOPC, DOPS, DLPE) as compared with statistical distribution of lipid-exposed Trp residues in α-helical TM proteins in native membranes (dots). Energy minima are attributed to the sharp changes of polarity parameters in the "midpolar region". The widening of the "statistical energy" profiles may arise from the heterogeneous lipid composition of native membranes.
Testing of PPM 2.0 on the membrane-associated proteins demonstrated an improved accuracy but a similar computational efficiency of the method, in comparison with the previously used model (PPM 1.0).