title: Generalized Crick equations for modeling noncanonical coiled coils.
abstract: Crick envisaged the alpha-helical coiled coil to result from systematic bending of an alpha-helix such that every seventh residue was structurally equivalent, and he derived equations for the coordinates of the backbone atoms. Crick's predictions were vindicated experimentally and coiled-coil sequences were shown to have hydrophobic residues alternately spaced 3 and 4 residues apart. Nonetheless, in some coiled coils such canonical heptad repeats are interrupted by inserts of 3 or 4 residues generating decad and hendecad motifs. The supercoiling of the coiled coils varies with the sequence pattern, being left- or right-handed in purely heptad-based or hendecad-based motifs, respectively. To model coiled coils with a mixture of motifs, we describe how Crick's equations can be modified for cases where the pitch is not constant. Using the analogy of the bending of a beam, we took the tilt angle to change linearly with distance along the major helix and the pitch of a motif to be affected by neighboring motifs depending on the rigidity of the alpha-helical strands. We tested our approach by fitting the two-, three-, and four-stranded noncanonical coiled coils of GrpE, hemagglutinin, and tetrabrachion. The backbone atoms of the model and crystal structures agreed with root mean square deviations of <1.1 A.
authors.affiliation: Muscle Contraction Group, Department of Physiology, Medical School, University of Bristol, University Walk, Bristol BS8 1TD, United Kingdom. g.w.offer@bristol.ac.uk
authors.forename: Gerald
authors.initials: G
authors.lastname: Offer
authors.forename: Matthew R
authors.initials: MR
authors.lastname: Hicks
authors.forename: Derek N
authors.initials: DN
authors.lastname: Woolfson
mesh_terms: D020816:Amino Acid Motifs; D001426:Bacterial Proteins / Q000737:chemistry; D001703:Biophysics / Q000379:methods*; D006360:Heat-Shock Proteins / Q000737:chemistry; D006388:Hemagglutinins / Q000737:chemistry; D008958:Models, Molecular; D008962:Models, Theoretical; D011487:Protein Conformation; D017433:Protein Structure, Secondary; D017434:Protein Structure, Tertiary; D011506:Proteins / Q000032:analysis* / Q000737:chemistry*
chemical_list: D001426:Bacterial Proteins; C068113:GrpE protein, Bacteria; D006360:Heat-Shock Proteins; D006388:Hemagglutinins; D011506:Proteins