Molecular recognition and packing frustration in a helical protein
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).