Density maps

The experimental density map for a cryoEM experiment itself corresponds to a 3-D numpy.ndarray that contains the value of the density at different voxels. It is the location of the voxels themselves that encodes how these density values map onto the spatial information of the biomolecule. This information on the grid of the density map is stored in a separate class (gridclass) in HARP.

gridclass

class harp.density.gridclass (origin, dxyz, nxyz, *args, **kwargs)

A gridclass object stores the grid defining the voxel locations for a density map.

Attributes

Variable	Descrption
`self.origin`	`numpy.ndarray` A 1-D `double` array of size 3 containing the Cartesian coordinates of the lower corner of the grid.
`self.dxyz`	`numpy.ndarray` A 1-D `double` array of size 3 containing the rectilinear spacing between each grid point along all Cartesian axes.
`self.nxyz`	`numpy.ndarray` A 1-D `double` array of size 3 containing the number of grid points in each Cartesian direction

Functions

The functions associated with gridclass are

Function	Descrption
`self.xyzmin`	Returns the Cartesian coordinates of the lower corner of the grid (i.e., `self.origin`). Input: None. Output A `numpy.ndarray` of `double` values, of size 3.
`self.xyzmax`	Returns the Cartesian coordinates of the upper corner of the grid (i.e., the one diagonally opposite `self.origin`). Input: None. Output A `numpy.ndarray` of `double` values, of size 3.
`self.com`	Returns the Cartesian coordinates of the center-of-mass of the grid (not weighted by the density). Input: None. Output A `numpy.ndarray` of `double` values, of size 3.
`self.grid_ijk()`	Returns an array of the indices of the grid. Input: None. Output: A `tuple` of `gx`, `gy`, and `gy`, which are 1-D `numpy.ndarray`s of `int` values, of size `self.nxyz[0]`, `self.nxyz[1]` and `self.nxyz[2]`, which are the number of gridpoints in the x-, y- and z-direction respectively.
`self.grid_xyz`	Returns an array of the Cartesian coordinates corresponding to the indices of the grid. Input: None. Output: A `tuple` of `gx`, `gy`, and `gy`, which are 1-D `numpy.ndarray`s of `double` values, of size `self.nxyz[0]`, `self.nxyz[1]` and `self.nxyz[2]`, which are the number of gridpoints in the x-, y- and z-direction respectively.

load

harp.density.load (fname)

This function loads cryoEM densities and the associated grid (file format suffixes supported are .map, .MAP, .mrc, .MRC, .map.gz, and .MAP.gz).

Arguments

Variable	Descrption
`fname`	`string` The file-name for the cryoEM density map.

Output

Variable	Descrption
`grid`	`gridclass` The grid of voxel locations of the cryoEM density map.
`density`	`numpy.ndarray` A 3-D array of `double` values corresponding to the density values at specific voxels corresponding to `grid`.

x2i

harp.density.x2i (grid, point)

This function transforms a point in Cartesian coordinates to the grid indices based on a particular grid.

Arguments

Variable	Descrption
`grid`	`gridclass` The cryoEM grid which the Cartesian coordinates will be transformed with respect to.
`point`	`numpy.ndarray` An array of `double` values of size 3, containing the Cartesian coordinates of the point.

Output

Variable	Descrption
`point`	`numpy.ndarray` An array of `int` values of size 3, containing the grid indices of the point.

i2x

harp.density.i2x (grid, point)

This function transforms a point in grid indices to Cartesian coordinates based on a particular grid.

Arguments

Variable	Descrption
`grid`	`gridclass` The cryoEM grid which the grid indices will be transformed with respect to.
`point`	`numpy.ndarray` An array of `int` values of size 3, containing the grid indices of the point.

Output

Variable	Descrption
`point`	`numpy.ndarray` An array of `double` values of size 3, containing the Cartesian coordinates of the point.

subgrid_center

harp.density.subgrid_center (grid, centerxyz, halfwidthxyz)

This function defines and returns a cubic subgrid within a specific gridclass object centered at the specified point and with a specified half-width in every direction from that point.

Arguments

Variable	Descrption
`grid`	`gridclass` The cryoEM grid in which the subgrid will be defined
`centerxyz`	`numpy.ndarray` An array of `double` values of size 3, containing the Cartesian coordinates of the center of the subgrid.
`halfwidthxyz`	`numpy.ndarray` An array of `double` values of size 3, containing the halfwidths of the subgrid from the center (in \(\unicode{x212B}\)).

Output

Variable	Descrption
`grid`	A `gridclass` object containing the defined subgrid.

subgrid_extract

harp.density.subgrid_extract (grid, data, subgrid)

This function extracts the cryoEM density from a map for the voxels corresponding to a cubic subgrid within a specific grid.

Arguments

Variable	Descrption
`grid`	`gridclass` The cryoEM grid associated with the cryoEM map.
`data`	`numpy.ndarray` The cryoEM density values defined at the voxel locations in `grid`.
`subgrid`	`gridclass` The subgrid defined on `grid` for which the densities will be extracted.

Output

Variable	Descrption
`data`	`numpy.ndarray` The cryoEM density values defined at the voxel locations in `subgrid`.

trim_density_to_mol

harp.density.trim_density_to_mol (grid, data, mol, pad = 8.)

This function finds the box that emcompasses the atomic coordinates of a specific molecular model on the grid for a specified density map and returns a trimmed grid and associated density map corresponding to this box. The trimmed box may additionally be padded isotropically by a constant value using periodic boundary condtions. This truncation is particularly useful for maps where only a small region has been used to build a model (which commonly occurs for molecules with high rotational symmetry) as it greatly reduces the computational cost of HARP calculations in these cases.

Arguments

Variable	Descrption
`grid`	`gridclass` The cryoEM grid associated with the cryoEM map.
`data`	`numpy.ndarray` The cryoEM density values defined at the voxel locations in `grid`.
`mol`	`harp.molecule.atomcollection` The molecular model that is built using part of the the cryoEM densities in `data` at voxel locations specified in `grid`.
`pad`	`double` A constant length (in \(\unicode{x212B}\)) that is added to the box encompassing `mol` that is padded using peridic boundary conditions. The default value is 8.

Output

Variable	Descrption
`grid`	`gridclass` The grid trimmed to the box around `mol`.
`data`	`numpy.ndarray` The cryoEM densities at the voxel locations specified by the trimmed `grid`.