Fig 1.
Schematics of Im9 simulation systems.
(A) Full-length Im9 (PDB ID: 1IMQ [47]). Helices are represented as cylinders. (B-D) Combined helical wheel and cylinder representations of systems wherein H1 packs against (B) H2, (C) H4, or (D) H2, H3, and H4. For each helical wheel, the red arrow indicates the residue closest to the viewer. Energetic effects of translating H1 in the directions of the solid blue arrows are determined with the position(s) and orientation(s) of the opposing helix or helices (cylinders) fixed. To evaluate the energetic consequences of helical rotation and nonnative packing, the fragment depicted by the helical wheel is rotated (dashed arrows) to nonnative orientations with positive (+) and negative (‒) rotation angles. Residues on the helical wheels are colored differently depending on the type of amino acid: charged residues in grey, nonpolar residues in yellow, and polar residues in white.
Table 1.
Im9 simulation systems.
Fig 2.
Im9 binding free energies for H1→H2.
(A) Binding free energies, ΔGbind, for the association of H1 and H2 with native and nonnative packing angles. Nonnative configurations are generated by rotating H1 (filled black circles), or H2 (open red squares), or changing the H1-H2 crossing angle (filled blue triangles). ΔGbind is computed from the total Boltzmann-weighted H1-H2-distance-dependent population of the entire free-energy basin (thus it correlates with but is not necessarily equal to the minimum PMF value; see S1 Text). (B) PMFs here are distance-dependent free energies for the association of H1 and H2 in native (black curve) and nonnative orientations with H1 targeted to be rotated by +30° (blue curve) or −30° (red curve). Actual rotation angles sampled during the computations of these PMFs are close to the targets (S3 Fig). Standard deviations of the mean from block averaging are shown as vertical bars in (A) or shaded regions in (B). (C) Two-dimensional PMF of the H1, H2 packing angles in simulations with helical rotation but no change in H1-H2 crossing angle. Data are drawn from multiple simulations, including one started and restrained to the native orientation and twenty others with preferred nonnative packing angles in which one helix is rotated by ±10–50°. Each free energy value (bottom color scale) plotted is the minimum of the distance-dependent PMF for a given inter-helix geometry (S1 Text). White regions have no sampling. By construction, the H1-H2 distance at the minimum of PMF can be different for different rotation angles (see example in S4 Fig). It is noteworthy that the two free-energy basins exhibited here are nonetheless robustly observed at essentially the same packing angles in multiple restrained simulations wherein inter-helical distances are targeted at a given ranging from 1.0 nm to 1.3 nm (S5 Fig).
Table 2.
Binding free energies for Im9 systems in native and nonnative orientations.
Table 3.
Differences between H1 binding free energies for different Im9 helical bundles in native and nonnative orientations.
Fig 3.
Im9 binding free energies for H1→H4.
(A) Binding free energies, ΔGbind, for the association of H1 and H4 with native and nonnative packing angles generated by rotating H1 (filled black circles), or H4 (open red squares). ΔGbind is computed from multiple PMF values as in Fig 2 (S1 Text). (B) PMFs describing distance-dependent free energies for the association of H1 and H4 in native (black curve) and nonnative orientations of H4 rotated by +30° (blue curve) or −30° (red curve). Standard deviations of the mean from block averaging are shown as vertical bars (A) or shaded regions (B). (C) Two-dimensional PMF of H1 and H4 packing angles, constructed by the same procedure as that in Fig 2C (S1 Text). White regions have no sampling.
Fig 4.
Residue-specific potential energies for Im9 H1→H2 at = 1.10 nm.
(A) Lennard-Jones (filled) and electrostatic (hashed) potential energies for direct interaction of selected interfacial residue pairs from the native configuration (red) and a nonnative (blue) configuration with H1 rotated by +30°. Pairs with |ΔE| > 1 kJ/mol are circled (S1 Text). (B) Snapshot of H1 (orange) packed against H2 (blue) in the native orientation, superposed with the configuration with a nonnative +30° rotation of H1 (both helices in grey). Sidechains involved in residue pairs with |ΔE| > 1 kJ/mol, identified in (A), are shown as sticks. (C, D) Helical wheels show (C) native and (D) nonnative interactions between residues that contribute to the more favorable (red dashed lines) and more unfavorable (green dashed lines) component binding energies for nonnative than for native packing (see part A). As in Fig 1, amino acid residues on the helical wheels are color coded: grey for charged, yellow for nonpolar, and white for polar residues.
Fig 5.
Im9 potential energies by interaction type.
Average native (red) and nonnative (blue) Lennard Jones (filled) and electrostatic (hashed) energies are shown for (A) H1→H2 restrained at displacement = 1.10 nm and (B) H1→H2LH3LH4C at
= 1.04 nm. The notation for energy types is identical to that in Fig 4. Component energies shown here are for the interactions within H1, H2, or H2LH3LH4C; solvent-helix interactions (S-H1, S-H2, S-H2LH3LH4C); direct helix-helix interactions (H1-H2, H1-H2LH3LH4C); solvent-solvent interactions (S-S); and the sum of all component energies.
Fig 6.
Energetic profiles of Im9 H1 binding.
Change in free energy (PMF, ΔG), its enthalpic (ΔH) and entropic (−TΔS) components, and system volume (ΔV) for H1 binding to other molecular fragments at 300 K as a function of the displacement, d (distance), between H1 and the opposing helical bundle: H1→H2 (A, C, E, G) and H1→H2LH3LH4C (B, D, F, H). Simulation data are shown for the native orientation (red curves) and the nonnative orientation with +30° rotation of H1 (blue curves). Vertical dashed lines mark the positions of the native (red) and nonnative (blue) PMF minima. Error bars show standard deviations of the mean estimated by block averaging (S1 Text).
Fig 7.
Schematics of relative preference for native versus nonnative binding in Im9 fragments.
System identifiers are defined in Table 1. Helices are depicted as circles, covalent linkages are indicated by black bars, and the positions of native helix-helix interfaces are highlighted by red arcs. For each system, the configurations on the left and right are native and nonnative, respectively, with the nonnative rotation indicated by a red arrow. Black arrows point toward the orientation with a more favorable binding free energy, with bi-directional arrows indicating energetic equivalence and arrow thickness representing free energy differences with absolute values that are mild (≤ 6kJ/mol) or significant (≥ 10 kJ/mol). Black or grey boxes enclose, respectively, nonnative packing configurations that are significantly or mildly favored over native packing.