Peptide folding in membranes

The computational procedure for modeling TM α-helices was based on the following thermodynamic cycle which describes folding of peptides and proteins in membranes: (1) helix-coil transition in water; (2) transfer of folded peptide to membrane; (3) binding of coil to membrane surface; (4) insertion and folding of a peptide in membrane; and (5) helix association in membranes (Figure 3).

Figure 3. Thermodynamic cycle of α-helix folding and association in membrane. The two-state model includes: (I) α-helix folding and insertion into membrane; and (II) helix-helix association in membrane.

FMAP

The FMAP (Folding of Membrane-Associated Peptides) method for prediction of membrane-bound α-helices and their positions in membranes (transitions 1-4) was developed and implemented into the FMAP web server. FMAP was used to predict TM domains of bitopic proteins from Membranome and to generate their 3D models in the lipid bilayer.

The coordinate files of 3D models of TM α-helical domains of bitopic proteins are available for downloading individually and for the entire protein set.

FMAP server predicts formation of individually stable α-helices by peptides and proteins depending on the experimental conditions in vitro. It utilizes different physical models for the following cases:

  1. peptides in aqueous solution
  2. water-soluble protein in the molten globule state
  3. peptides in micelles
  4. peptides in the lipid bilayers
  5. TM proteins

The computational procedure includes the following steps:

  1. Calculation of free energy differences for membrane-bound α-helical and coil segments relative to coil in water for every segment of the polypeptide chain, similar to that in FRAMEWORK program (PubMed)

  2. Calculation of the lowest energy partition of polypeptide chain into α-helical and coil segments by the dynamic programming algorithm or averaging of different helix-coil partitions

  3. Generation of all-atom 3D models for predicted α-helical segments

  4. Positioning of 3D model of a predicted TM α-helices in membranes by optimizing their transfer free energy by the PPM2.0 program using an anisotropic solvent model of the lipid bilayer (PubMed)

STEP 1

Folding energy of every α-helical segment of m residues, starting from residue k is calculated as the sum of intrinsic helix stability in water and its transfer energy from water to the lipid bilayer:

Energy of helix folding in water, ΔGint,watα(k,m) is calculated as sum of main chain enthalpic (H-bonding) and conformational entropy contributions for the “host” poly-Ala chain during coil-to-helix transition, free energy differences associated with replacement of Ala by other side chains (experimental α-helix “propensities”), H-bonding, electrostatic, and hydrophobic interactions between side-chains. Empirical energies for N-cap, C-cap and the hydrophobic staple motifs are tabulated based on experimental studies of peptide stabilities in the aqueous solution.

Transfer energy of an α-helix from water to a nonpolar environment ΔGint,watα(k,m) depends on the chosen physical model. The approach for micelles and protein molten globule state is essentially the same as in our previous work (PubMed) although we have changed transfer energies to micelles to reflect recent studies.

Transfer energies for TM α-helices can be estimated using an all-atom or whole-residue approximations. For bitopic proteins we used the whole-residue transfer energy profiles along the bilayer normal for different types of residues, ΔGiα(z i )w which were pre-calculated ausing our implicit solvation model (PubMed):

Two additional terms describe the energetic penalty for the hydrophobic mismatch and the helix tilting in membrane, where D0 and D are the hydrophobic thicknesses of the lipid bilayer and helix, respectively, L is length of TM segment of the helix, ϕ is tilt angle of the helix with respect to bilayer normal, and fmism and fcross are adjustable parameters which define the corresponding contributions. Transfer energy ΔGtransferα(k,m) was optimized by grid scan with respect to three variables: zo (shift of 1st residue in the helix along membrane normal), D (hydrophobic thickness) and ϕ (tilt angle of the helix with respect to membrane.

Membrane binding energy of unfolded polypeptide chain ΔGbind(k,m) is calculated based on Wimley-White whole-residue interfacial scale.

STEP 2. was implemented as described in our previous work (PubMed).

STEP 3.

To generate all-atom 3D models of predicted α-helical segments, FMAP uses structural templates that represent a straight or a Pro-kinked helix. The allowed side-chain rotamers are automatically selected from a backbone-dependent library to minimize transfer energy in the lipid bilayer .

STEP 4.

The spatial positions of 3D models of predicted TM α-helices are defined by optimizing transfer energy from water to the lipid bilayer using an updated version of PPM program incorporated into FMAP. In addition to solvation energy, it includes a few mechanical energy terms to account for membrane deformations during penetration of α-helices into the lipid bilayer. These contributions are related to the hydrophobic mismatch and tilting of TM helices.

TMDOCK

TMDOCK web server predicts formation of parallel homodimers by transmembrane (TM) alpha-helices. The computational procedure includes the following steps:

  1. Step 1: A single TM helix is predicted and generated by FMAP

  2. Step 2: A set of different structures of the dimer is generated by “threading” target amino acid sequence through four dimeric templates (5eh4, 2zta, 2k1k and 2hac PDB entries). The target and template helices are superimosed to produce all possible helix packing arrangements. Each structure undergoes local energy minimization in space of torsion angles and rigid body variables of the helices using a modified version of ConforNMR (Lomize et al. 1992) with new force field.

  3. Step 3: Selecting set of possible structures of the homodimer based on the calculated free energy of helix association and a few supplementary parameters. The methodology and parameters for calculating this energy were previously developed and tested (Lomize et al. 2002, Lomize et al. 2004). Main components of this energy are: (a) stabilizing van der Waals interactions and H-bonds between TM helices; (b) solvation energy that describes transfer of protein atoms from lipid bilayer to the protein interior; (c) changes in conformational entropy of side chains during helix association; and (d) electrostatic interactions between helix dipoles in membrane. The contributions of interactions are averaged over different side chain conformers and therefore effectively reduced for flexible side chains.