EXTENDS (CCP4: Unsupported Program)


extends - Extend Fourier maps and compute standard uncertainty of electron density.


extends mapin foo_in.map mapout foo_out.map [ xyzin foo_in.brk ]
[Key-worded input]


The program EXTENDS generates any part of a map from a map calculated by the FFT program which typically contains only one asymmetric unit.

This is a modified version of the EXTEND program that attempts to compute the standard uncertainty of the electron density.  To do this the input map must be a true difference map (i.e. of the type Fo-Fc, not nFo-(n-1)Fc) and must consist of exactly one asymmetric unit (an integral number of a.u.'s such as exactly half or an exact complete unit cell is also valid input).  Note that the program does NOT check that the input map covers an exact integral number of a.u.'s: it is the user's responsibility to ensure this.  However this will normally be the case if the FFT program has been used to prepare the input map.

The rationale for this is statistical rigour: the asymmetric unit of the map represents the true population of electron density values in the statistical sense and therefore the values of the mean and RMS deviation for the asymmetric unit can be considered to be those of the true population mean and population standard deviation respectively.  Any other subset or superset of the map that is not an integral number of asymmetric units is a sample in the statistical sense, with corresponding sample mean and sample standard deviation.

It may even be a biased sample either because the density covers only a specific region of the structure and is therefore non-representative of the map as a whole, or because when a map is extended, density values related by the map symmetry are very likely to be generated more than once.  Sample statistics, whether biased or not, are always only approximations to population statistics.

Note that the standard deviation of the density, unlike the RMS deviation of the density from its mean value, is a property of the density that does NOT change simply because a different map extent is chosen.  Most other programs that output electron density maps that do not cover an exact integral number of a.u.'s always automatically recompute both the mean and RMSD - if this is done it is then not valid to treat the RMSD in subsequent calculations as though it were the SU of the density.


The data control lines are identified by keywords. Only the first 4 letters of each keyword are necessary. Some data cards are optional. The available keywords are: XYZLIM, SYMMETRY, BORDER, FILL, KEEP and END.  They are all optional, but some must be specified if XYZIN isn't assigned.


XYZLIM <xmin> <xmax> <ymin> <ymax> <zmin> <zmax>

Output map limits in grid points or fractions of cell edge. If this card is not given XYZIN must be assigned. The program then reads the coordinates to determine the map limits.

SYMMETRY <Name> | <Number>

Followed by space group Name (e.g. P212121) or Number (e.g. 19). Symmetry is usually read from the header of the input map so this keyword is not normally needed. Use it only to change symmetry, or if no symmetry is present in the map. This is needed after certain non-CCP4 programs e.g. from Uppsala.

MAPSYM <Name> | <Number>

Inserts the specified space group symmetry operators into the output map, but does not use them for extending the map. This may be needed after `skewing' a map, since that map will have only X,Y,Z symmetry, but be careful.

BORDER <width>

<width> of border in Angstroms to add to coordinate limits.

Default = 10 Angstroms. This card is only needed if XYZLIM is not given; otherwise limits are determined from the XYZIN coordinate file.

FILL <fill>

Set map values outside borders of input map to <fill>.


Keep the input RMSD of the density.  This option should be used only for 2mFo-DFc and other types of non-difference Fouriers, i.e. with coefficients of the form nFo-(n-1)Fc.  In some cases the program can detect that a non-difference Fourier has been input and will not recompute the standard uncertainty; however it would not be wise to rely on this!

The RMSD of a 2mFo-DFc or equivalent map is completely devoid of any statistical meaning anyway: it will greatly depend on the solvent content, so comparing Fourier maps contoured at 1 sigma is nonsense (pointed out by Dale Tronrud!).

For mFo-DFc and other types of true difference Fouriers this option must be omitted so that the program is allowed to recompute the standard uncertainty.  In this case the input map must consist of exactly one asymmetric unit (an integral number of a.u.'s such as exactly half or a complete unit cell is also valid input).  This will normally be the case if the FFT program has been used to prepare the input map.

This option should also be used in the case that the input map does not cover an exact integral number of a.u.'s, but the SU of the density has been previously correctly computed, so that the correct SU is kept and copied to the output map.


Ends input.


input map (from FFT)
extended output map
input coordinates, optional unless limits not given.


The program EXTENDS is used to extend the range of Fourier map or to calculate a different part of the unit cell from that input.  Its main use is in preparing data for programs that process electron density and require an accurate value of the standard uncertainty.


Phil Evans, MRC-LMB, Cambridge (original EXTEND code)
Ian Tickle, Astex Technology, Cambridge (mods for SU calculation)


fft, mapmask


The following is an example of control data for extending a map

extends MAPIN 2fofc.map MAPOUT 2fofc-ext.map << END-extends
KEEP  ! Only for nFo-(n-1)Fc type maps.

extends MAPIN fofc.map MAPOUT fofc-ext.map << END-extends