Finer grid searches were undertaken in the vicinity of the parameter sets yielding the lowest-energy designs. Once the number of helices in the bundle and the layer type were chosen, the Crick equation parameters were sampled on a grid, backbone conformations were generated, and Rosetta sequence design calculations were carried out. We explored the design of helix bundles with two-layer, three-layer, or five-layer geometries and different numbers of helices surrounding the supercoil axis. Because of the coupling between ω 0 and ω 1, two-layer designs are left-handed (ω 0 negative), three-layer designs are right-handed (ω 0 positive), and five-layer designs are untwisted (ω 0 close to zero) ( 3). We refer to these three cases as two-layer, three-layer, and five-layer designs, respectively, corresponding to the number of distinct helix-helix–interacting layers that must be designed.
Spectrum bundles full#
Third, if ω 1 is kept at exactly 100°, after 18 residues the helix has completed five full turns (1800°). Second, if ω 1 is reduced to 98.2°, after 11 residues the helix has completed three full turns (1080°) ( 8). First, if ω 1 is increased to 102.85° from the ideal value of 100.0°, after seven residues the helix has completed two full turns (720°). There are three repeating geometries that require deviation of less than 3° from an ideal unstrained helix. Repeating backbone geometries are good targets for design because there are fewer distinct side-chain packing problems to be solved. Hence, supercoil (ω 0) and helical (ω 1) twist are coupled ( fig. As shown in the supplementary materials ( 12), successive Cα atoms rotate about the α-helical axis by ~(ω 0 + ω 1), and the protein backbone is strained when this sum deviates from the value of 100° found in ideal helices (which have ω 0 = 0° and ω 1 = 100°) ( fig. The Crick coiled-coil equation parameters for a bundle of n helices are ω 0, the supercoil twist ω 1, the α-helical twist R 0, the supercoil radius φ 1, φ 2, …, φ n, the phases of the individual helices and z 2, …, z n, their offsets along the superhelical axis relative to the first helix ( 2, 11, 12). Here we combine parametric backbone generation with the Rosetta protein-design methodology ( 10) to generate more complex and stable protein structures. The few structure-based efforts have used parametric equations first derived by Francis Crick ( 2) to design peptides that form right-handed coiled coils ( 8) or bind carbon nanotubes ( 9).
Most studies have used sequence-based approaches, focusing on choosing optimal amino acids at core positions of the coiled-coil heptad repeat ( 5– 7). Coiled coils consisting of two or more a helices supercoiled around a central axis play important roles in biology, and their simplicity and regularity have inspired peptide-design efforts ( 1– 4).
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