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Implicit membrane model

Membrane environment significantly influences the membrane protein structure. So, prediction of correct structure of membrane proteins demands consideration of the membrane environment. One of the simplest membrane representations is the so-called implicit membrane. Such a model, based on ASP treatment of protein-environment interaction (Eisenberg & McLachlan, 1986), has been developed in our laboratory.

Membrane representation

Potential energy function: E=EECEPP/2+ESOLV+EΔφ, Intraprotein: (Némethy et al., 1983) Protein–solvent: , σi — solvent accessible surface area for atom; ASPi — atomic solvation parameter for atom i (ASPs for environments of different polarity were described in (Nolde et al., 1997, Efremov et al., 1999cd)).

Transmembrane electrostatic potential:
,
where Δφ is the transmembrane potential; D — thickness of the membrane; q_i and z_i are the partial charge and the coordinate of atom i, respectively; F is the Faraday constant.

Method: Variable-temperature Monte Carlo simulations with energy minimization in dihedral angles conformational space (Efremov et al., 2000, 2001a, Nolde et al., 2000, Volynskii et al., 2000).

Algorithm

Starting conformation of peptide/protein in folded or random coil form arbitrarily placed in with respect to the hydrophobic layer of the membrane. Then, several consequtive MC runs with different number of varying angles (high number at first runs and low at last stages) with energy minimization on each step are carried out. The starting structure of each MC conformational search is the lowest-energy one, obtained at the previous runs.

Using of this membrane model permits prediction of the mode of binding and delineation of residues important for interaction with the membrane.

Testing of the implicit membrane model

Model peptides: poly-Leu, LA and LK

The proposed solvation model needs to be tested in calculations of systems for which experimental data on the structure in membrane-like media (lipid vesicles, micelles, etc.) are available. A comparison of the theoretical calculations with experimental data would make it possible to determine how adequately the model of the membrane reproduces the real behavior of a peptide in the lipid bilayer and to refine the parameters of the model (e.g., weighting factors for the solvation term in the expression for the total energy of the system, the contribution of long-range electrostatic interactions, etc.). The simplest test systems were the model peptides with different behavior in membrane. These are:

1. 20-mer poly-L-leucine — peptide immersed in membrane in α-helical conformation;
2. peptide LK (sequence KLLKKLLKLLKKLLKKLKKLLKKL) — this peptide forms α-helix on the membrane surface;
3. peptide LA (sequence KKKKKALALALALAWALALALALAL) — charged N-terminus of this peptide is localized on the membrane surface, while hydrophobic C-terminus is buried into the non-polar region of lipid tails.

Hydrophobic peptide in unordered starting conformation. Poly-Leu

Evolution of the peptide structure during the MC procedure. Starting conformation before (1) and after (2) energy minimization and lowest energy conformations obtained with the interval of ~5000 MC steps (3–5). Non polar membrane layer is hatched. As seen from the figure, during MC simulation the peptide localizes in the non-polar phase of the system and adopts a helical conformation.

Low energy conformations of poly-Leu in the implicit membrane. Energy distributions for each class of structures are presented over the corresponding conformation. The lowest energy state of the peptide is always situated in the hydrophobic layer. Solvation of the C-terminus of the peptide costs only 1 kcal/mol of the conformational energy. So, we can propose that these two groups can exist simultaneously.

Thus, the simulation results for poly-Leu are in a good agreement with the experimental data. The next step of testing is more complex — analysis of peptides with nonuniform polar properties.

Hydrophobic peptide with polar termini: peptide LA

Starting (insert) and low-energy (1–5 bottom panels) states of LA-peptide in implicit membrane. The figure illustrates that in this case transmembrane orientation of the peptide is significantly favorable. Simulation results are completely validated by the solid-state NMR experiments.

Amphiphilic peptide LK

Results of simulations of LK peptide in implicit membrane are shown on the above figures. In the low-energy conformations the peptide forms a peripheral α-helix. All polar side chains are exposed to polar phase of the system, while the non-polar ones are buried into the hydrophobic layer.

So, application of the membrane model to study a variety of membrane peptides represents its general features such as, promotion of α-helix formation in the membrane environment, ability to predict the mode of membrane binding, etc.

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