Computed Properties

Helanal follows the procedure of Sugeta and Miyazawa [Sugeta1967] and is based on the Fortran HELANAL implementation by [Bansal2000]. Properties are computed for a ‘window’ of four consecutive \(C_α\) atoms, and this window is then slid along the length of the helix in one-residue steps.

For each window consisting of atoms \(c_i\), \(c_{i+1}\), \(c_{i+2}\), \(c_{i+3}\), the vectors \(\mathbf{B_1}\), \(\mathbf{B_2}\), and \(\mathbf{B_3}\) joining (respectively) atoms \(c_i\) → \(c_{i+1}\), \(c_{i+1}\) → \(c_{i+2}\) and \(c_{i+2}\) → \(c_{i+3}\) are calculated, along with the vectors \(\mathbf{D_1} = \mathbf{B_1} - \mathbf{B_2}\) and \(\mathbf{D_2} = \mathbf{B_2} - \mathbf{B_3}\).

From these, the helix properties below are computed in each simulation frame. These properties are available in .results as arrays, the shape of which depends on the number of residues \(n_{res}\) (and the property being calculated). Note that each helix must contain at least 9 residues.

If multiple helices are being analysed, the results are returned as lists (of length \(n_{helices}\)) of arrays of the indicated shape.

All angles are in degrees.

Description		Shape
local_helix_directions: the normalised vector \(\mathbf{D_1}\) (or \(\mathbf{D_2}\)) for each atom \(c_{i+1}\) (or \(c_{i+2}\)). Assuming ~even spacing of the atoms, this vector will bisect the angle formed by (\(c_i,c_{i+1},c_{i+2}\)), lie approximately in the plane perpendicular to the helix axis, and point from the projected local helix centre to the atom \(c_{i+1}\).		\((n_{frames},\) \(n_{res}-2, 3)\)
local_twists: the approximate ‘twist’ of the helix between atoms \(c_{i+1}\) and \(c_{i+2}\), calculated as the angle \(θ\) between \(\mathbf{D_1}\) and \(\mathbf{D_2}\).		\((n_{frames},\) \(n_{res}-3)\)
local_nres_per_turn: the number of residues that fit in one complete turn of the helix, based on local_twist.		\((n_{frames},\) \(n_{res}-3)\)
local_origins: the projected centre of each 4-atom window, in line with atom \(c_{i+1}\). Calculated as the approximate intersection of \(\mathbf{D_1}\) and \(\mathbf{D_2}\) projected on the perpendicular plane, assuming ~even spacing of atoms.		\((n_{frames},\) \(n_{res}-2,\) \(3)\)
local_axes: the (normalised) central axis \(\mathbf{A}\) of the 4-atom window, calculated as the normal to the two vectors \(\mathbf{D_1}\) and \(\mathbf{D_2}\).		\((n_{frames},\) \(n_{res}-3,\) \(3)\)
local_heights: the ‘rise’ \(h\) of the helix (in the direction of local_axes) between atoms \(c_{i+1}\) and \(c_{i+2}\).		\((n_{frames},\) \(n_{res}-3)\)
local_bends: the angle of bending of the helix between adjacent 4-atom windows, i.e. the angle \(β\) between the local_axes \(\mathbf{A_i}\) (of atoms \(c_i,c_{i+1},c_{i+2},c_{i+3}\)) and \(\mathbf{A_{i+3}}\) (of atoms \(c_{i+3},c_{i+4},c_{i+5},c_{i+6}\)).		\((n_{frames},\) \(n_{res}-6)\)
all_bends: pair-wise matrix of angles between all pairs of local_axes.		\((n_{frames},\) \(n_{res}-3,\) \(n_{res}-3)\)
global_axis: the length-wise axis \(\mathbf{G}\) for the overall helix, pointing from the end of the helix to the start. Calculated as the vector of best fit through all local_origins.		\((n_{frames},\) \(3)\)
global_tilts: the angle \(γ\) between the global_axis \(\mathbf{G}\) and the reference axis (specified by the ref_axis option). If no axis is specified, the z-axis is used.		\((n_{frames},)\)
local_screw_angles: The cylindrical azimuthal angle \(α\) of atom \(c_{i+1}\) (in the range -pi to pi). This is measured as the angle between the ref_axis to the local_helix_directions vector \(\mathbf{D}\), when both are projected on a plane perpendicular to global_axis.		\((n_{frames},\) \(n_{res}-2)\)

A summary of the results, including mean, sample standard deviation and mean absolute deviation is also provided in results.summary.