# Xds nonisomorphism

xds_nonisomorphism[1] is a program that analyzes data sets stored in unmerged reflection files (typically called XDS_ASCII.HKL) as written by XDS. It implements the method of Brehm and Diederichs (2014) and theory of Diederichs (2017). Its purpose is the identification of non-isomorphous (i.e. dissimilar or less well related) data sets among other, more similar data sets. As a consequence of running xds_nonisomorphism, one may choose to only merge the most isomorphous (similar) data sets, and to discard the non-isomorphous ones - or to analyze these separately.

The assumption is that several data sets exist, and that these should be merged with XSCALE. The program therefore reads the names of the XDS_ASCII.HKL files from XSCALE.INP . The latter file, and the XDS_ASCII.HKL listed after each INPUT_FILE= line in XSCALE.INP must exist. The program reads the files in the order given, and produces tables with pairwise statistics.

In particular, for each pair it determines

- the CC* values (Karplus & Diederichs (2012). Science 336, 1030–1033) from the CC1/2 of the data sets (using the σ-τ method of Assmann
*et al.*, J. Appl. Cryst. (2016). 49, 1021–1028), and - the pairwise (Pearson's) correlation coefficients.

As given by equation 2 of Diederichs (2017), the ratio between the latter quantity and the product of the CC* values of a pair is a measure of the non-isomorphism - for isomorphous data, that ratio is 1.

The method requires data sets with internal multiplicity, and mutual overlap (common reflections). Angles (calculated as the inverse cosine of the ratio) are expressed in degrees. Less than 10° may be considered good isomorphism, 90° means highly non-isomorphous (i.e. completely unrelated) datasets. After the analysis, the program produces a 3D representation of the arrangement of data sets such that their distances in 3D try to reproduce the angles (please note that this is a completely different representation from that of xscale_isocluster!).

xds_nonisomorphism prints a short help text if the -h option is used.