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. 2023 Dec 26;19(24):9077-9092.
doi: 10.1021/acs.jctc.3c00941. Epub 2023 Dec 13.

A Rigorous Framework for Calculating Protein-Protein Binding Affinities in Membranes

Marharyta Blazhynska  1 , James C Gumbart  2 , Haochuan Chen  1 , Emad Tajkhorshid  3   4 , Benoît Roux  5   6 , Christophe Chipot  1   3   5   7
Affiliations

A Rigorous Framework for Calculating Protein-Protein Binding Affinities in Membranes

Marharyta Blazhynska et al. J Chem Theory Comput. .

Abstract

Calculating the binding free energy of integral transmembrane (TM) proteins is crucial for understanding the mechanisms by which they recognize one another and reversibly associate. The glycophorin A (GpA) homodimer, composed of two α-helical segments, has long served as a model system for studying TM protein reversible association. The present work establishes a methodological framework for calculating the binding affinity of the GpA homodimer in the heterogeneous environment of a membrane. Our investigation carefully considered a variety of protocols, including the appropriate choice of the force field, rigorous standardization reflecting the experimental conditions, sampling algorithm, anisotropic environment, and collective variables, to accurately describe GpA dimerization via molecular dynamics-based approaches. Specifically, two strategies were explored: (i) an unrestrained potential mean force (PMF) calculation, which merely enhances sampling along the separation of the two binding partners without any restraint, and (ii) a so-called "geometrical route", whereby the α-helices are progressively separated with imposed restraints on their orientational, positional, and conformational degrees of freedom to accelerate convergence. Our simulations reveal that the simplified, unrestrained PMF approach is inadequate for the description of GpA dimerization. Instead, the geometrical route, tailored specifically to GpA in a membrane environment, yields excellent agreement with experimental data within a reasonable computational time. A dimerization free energy of -10.7 kcal/mol is obtained, in fairly good agreement with available experimental data. The geometrical route further helps elucidate how environmental forces drive association before helical interactions stabilize it. Our simulations also brought to light a distinct, long-lived spatial arrangement that potentially serves as an intermediate state during dimer formation. The methodological advances in the generalized geometrical route provide a powerful tool for accurate and efficient binding-affinity calculations of intricate TM protein complexes in inhomogeneous environments.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1.
Figure 1.
GpA69–97 dimer in a POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine) lipid bilayer (left). The scheme of the reference coordinates is used to define the orientational and positional restraints where H1 and H2 correspond to the symmetric α-helices. In the geometrical route, the H1 helix is pinned to the origin of the simulation box and is prevented from tumbling. The dashed line between two red balls represents the COM distance in the cylindrical coordinate frame of reference. The azimuthal angle, ϕ, relates to the position of H2 with respect to H1. The Euler angles (roll angle Θ, pitch angle Φ, and yaw angle Ψ) determine the relative orientation of H2 with respect to H1 (right).
Figure 2.
Figure 2.
GpA reversible association in unrestrained-separation PMF calculations under different computational conditions A–G detailed in Table 3. The molecular image in each panel depicts a snapshot of the molecular structure corresponding to the minima of the PMF, where H1 and H2 helices are colored blue and red, respectively.
Figure 3.
Figure 3.
(A) Normalized physical separation PMF of the GpA homodimer in POPC obtained within the geometrical route simulation at 1300 ns. (B) ΔGint corresponds to the energy interaction components obtained from the partition of the physical separation PMF into helix–helix electrostatic (blue), helix–helix vdW (green), helix–helix (sum of electrostatic and vdW interactions) (red), and sum of electrostatic and vdW interactions of helix–solvent contributions (maroon). The solvent includes the POPC lipid bilayer, water, sodium, and chloride ions.
Figure 4.
Figure 4.
(A) Pair distribution function of the residue pairs. (B) The residues that form the interhelical contacts during the association of GpA helices. (C) Contact map obtained with a 15 Å cutoff during the separation PMF calculation following the geometrical route. Black squares indicate the same residue pairs as mentioned in (B), while red squares represent the GxxxG motif. The contact-map analysis was conducted with the MDAnalysis module available in Python.,
Figure 5.
Figure 5.
(A) Time evolution of the overall bilayer thickness of the system (black) and local bilayer thickness within a distance of 16 Å from helix H2 (red) during the separation PMF simulations. Snapshots of the rearrangement of the selected phosphorus atoms (shown in pink and cyan balls) (B) at the beginning of the simulation, (C) at the moment of separation, and (D) after reversible association.
Figure 6.
Figure 6.
(A) The observed intermediate state is shown in transparent mode, and the native state is shown in solid colors. Ω corresponds to the crossing angle between two helices. (B) θ corresponds to the tilt angle. In analyses C and D, the curves of the native state are shown in black and of the intermediate state in red. (C) RMSD of the backbone of the entire complex in 1 μs-equilibrium simulation. (D) Time evolution of their buried molecular surface areas (BSA). (E) Time evolution of the crossing angle Ω (black and red curves correspond to the native and the intermediate states) and averaged tilt angle θ between two helices (green and cyan curves correspond to the native and the intermediate states) in 1 μs-equilibrium simulations.
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