# Read and analyse an XDS file

## Introduction

Main aim of this tutorial is to load the full content of two different XDS files in the workspace, to analyse and modify data for one of the two files, and to write the modified content into a new XDS file.

## Sample XDS file

Some sample files are stored as external data in this package. Among them there are two XDS files available with the current release. To access the files, first load the `cry` package.

    library(cry)

Next, have a look at what is included in the external-data directory of `cry`.

    datadir <- system.file("extdata",package="cry")
    all_files <- list.files(datadir)
    print(all_files)
    #>  [1] "1dei-sf.cif"               "1dei_phases.mtz"
    #>  [3] "2ol9_phases.mtz"           "3syu.cif"
    #>  [5] "6vww_xds_ascii_merged.hkl" "AMS_DATA.cif"
    #>  [7] "e-65-00i60-Isup2.rtv"      "shelxc.log"
    #>  [9] "shelxd.log"                "shelxe_i.log"
    #> [11] "shelxe_o.log"              "xds00_ascii.hkl"

The two XDS files we are interested in are “xds00_ascii.hkl” and “6vww_xds_ascii_merged.hkl”. Both files can be loaded using function `readXDS_ASCII`.

## Two types of XDS files

The `cry` function `readXDS_ASCII` can load in the R working memory both XDS reflection files produced by XDS and XSCALE. Their formats differ slightly. Let’s start by loading “xds00_ascii.hkl”, which is created by the ’CORRECT’component of XDS. The created object is a named list.

    filename <- file.path(datadir,"xds00_ascii.hkl")
    objXDS1 <- readXDS_ASCII(filename)
    class(objXDS1)
    #> [1] "list"
    names(objXDS1)
    #> [1] "processing_info" "header"          "reflections"

Each component of is either a named list, or a data frame. More specifically:

1. `processing_info`

   It’s a small named list with names `MERGE`, `FRIEDEL` and `PROFILE_FITTING`. All these components are logical variables (TRUE/FALSE). If `MERGE` is TRUE, the file has been produced by XSCALE. If `FRIEDEL` is TRUE, the Bijvoet pairs have been averaged to respect Friedel’s law. `PROFILE_FITTING` is only TRUE for files produced by XDS.

2. `header`

   This is a longer named list with components related to the diffraction experiment including for example the oscillation range, the fraction of polarization, the rough cell parameters’ estimate, etc.

3. `reflections`

   These are the experimental observations, i.e. the integrated intensity, its error, and other qualities for each triplet of Miller indices. They are included in a data frame.

    # 'reflections' is a data frame
    print(class(objXDS1$reflections))
    #> [1] "data.frame"

    # First 5 observations
    print(objXDS1$reflections[1:5,])
    #>   H K   L   IOBS SIGMA.IOBS.     XD    YD   ZD     RLP PEAK CORR   PSI
    #> 1 0 0 -35  61.77       128.4 2094.2 664.4  6.4 0.17998   92    7 62.60
    #> 2 0 0 -36 137.70       136.3 2120.2 645.5 10.3 0.18539   99    8 62.91
    #> 3 0 0 -38 -29.38       153.9 2172.7 607.6 18.0 0.19628  100   -7 63.53
    #> 4 0 0 -39 -23.68       158.5 2199.2 588.5 21.9 0.20176  100   -7 63.85
    #> 5 0 0 -40  73.30       161.0 2226.0 569.5 25.8 0.20726  100    8 64.16

A file produced by XSCALE has in general a smaller number of data columns:

    # Load the other XDS ascii file
    filename <- file.path(datadir,"6vww_xds_ascii_merged.hkl")
    objXDS2 <- readXDS_ASCII(filename,message=TRUE)
    #>
    #>  File read successfully.
    #>  There are 27951 reflections in this file.
    #>  Here is a summary of the observations:
    #>
    #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
    #>  -1.085   2.089   2.920   2.868   3.684   5.888

    # This file has been produced by XSCALE
    print(objXDS2$processing_info$MERGE)
    #> [1] TRUE

    # First 5 observations
    print(objXDS2$reflections[1:5,])
    #>   H K  L     IOBS SIGMA.IOBS.
    #> 1 0 0  4   192900       78780
    #> 2 0 0  6  1707000      694600
    #> 3 0 0  8 16670000     6782000
    #> 4 0 0 10   224900       93500
    #> 5 0 0 12  7838000     3189000

## The XDS reflections

Let us focus on the dataset produced by XSCALE. The full set of data is contained, as seen, in a data frame structure. This makes it easy to carry out the usual selection, reshaping and statistical operations normally available in R.

    # Copy reflections data for the first and
    # second dataset, to save on later typing
    refs1 <- objXDS1$reflections
    refs2 <- objXDS2$reflections

    # Check whether the set of reflections is unique

    # Dataset 1
    nrefs1 <- length(refs1[,1])
    print(nrefs1)
    #> [1] 3315
    n_unique1 <- length(unique(refs1[,1:3])[,1])
    print(n_unique1)
    #> [1] 3315

    # Dataset 2
    nrefs2 <- length(refs2[,1])
    print(nrefs2)
    #> [1] 27951
    n_unique2 <- length(unique(refs2[,1:3])[,1])
    print(n_unique2)
    #> [1] 27951

Both datasets have only one value per reflection. But the space group associated with the first dataset is P1, while the space group associated with the second dataset is P -3 1 c, belonging to the trigonal crystal system.

    # Space group of first dataset
    print(objXDS1$header$SPACE_GROUP_NUMBER)
    #> [1] 1

    # Space group of second dataset
    print(objXDS2$header$SPACE_GROUP_NUMBER)
    #> [1] 163

    # Extended Hermann-Mauguin symbol for symmetry n 163
    SG <- translate_SG(163)$msg
    print(SG)
    #> [1] "P -3 1 c"

This means that while the reflections of the second file are actually the result of averaging among multiple values of equivalent reflections (both because of multiplicity and symmetry), those of the first file derive from averaging due to multiplicity; once the symmetry for the crystal structure has been established, some of the reflections will be related by symmetry and a new unique set can be calculated after the appropriate merging.

Data selection can be carried out using conditions on the intensities, for example. Let us consider the second dataset and single out those reflections with \(\mathrm{I/sigI} > 2\).

    # Names of data columns
    names(refs2)
    #> [1] "H"           "K"           "L"           "IOBS"        "SIGMA.IOBS."

    # Selection based on I/sigI > 2
    idx <- which(refs2$IOBS/refs2$SIGMA.IOBS > 2)
    print(length(idx))  #  21579 reflections have I/sigI > 2
    #> [1] 21579

Visually, the separation between reflections with \(\mathrm{I/sigI} \leq 2\) and those with \(\mathrm{I/sigI} > 2\) can be demonstrated with a frequency histogram.

    # Create new I/sigI array
    isi <- refs2$IOBS/refs2$SIGMA.IOBS

    # Histogram
    hh <- hist(isi,breaks=30,plot=FALSE)
    cuts <- cut(hh$breaks,c(-Inf,2,Inf))
    plot(hh,main="I/sigI",xlab="I/sigI",col=cuts)

Data selection can also follow a different ordering of the data. Consider again, in dataset 2, the first 10 reflections:

    # First reflections in original data ordering
    print(refs2[1:10,])
    #>    H K  L     IOBS SIGMA.IOBS.
    #> 1  0 0  4   192900       78780
    #> 2  0 0  6  1707000      694600
    #> 3  0 0  8 16670000     6782000
    #> 4  0 0 10   224900       93500
    #> 5  0 0 12  7838000     3189000
    #> 6  0 0 14  3230000     1859000
    #> 7  0 0 16   118200       51690
    #> 8  0 0 18  2158000      878600
    #> 9  0 0 20    16970       35280
    #> 10 0 0 22   433600      181900
    #

We could, next, sort the data from the largest to the smallest value of the intensity:

    # First create the ordering index
    idx <- order(refs2$IOBS,decreasing=TRUE)

    # Now display the first 10 reflections. They correspond to the
    # 10 reflections with highest intensity
    print(refs2[idx[1:10],])
    #>       H  K  L     IOBS SIGMA.IOBS.
    #> 13    0  0 28 18660000     7591000
    #> 3     0  0  8 16670000     6782000
    #> 1081  6 -2 -8 12950000     3746000
    #> 3753 11 -3  0 12730000     3999000
    #> 3996 11 -1 -3  9507000     2552000
    #> 120   2 -1 -2  9322000     3794000
    #> 9415 17  0 15  9287000     3168000
    #> 1396  7 -3 -6  9004000     3665000
    #> 3070 10 -3 -6  8756000     1967000
    #> 1807  8 -4 -4  8733000     2939000

Or, we could sort the data according to the decreasing values of \(\mathrm{I/sigI}\):

    # Ordering index
    idx <- order(refs2$IOBS/refs2$SIGMA.IOBS,decreasing=TRUE)

    # Display first 10 highest I/sigI reflections
    print(refs2[idx[1:10],])
    #>       H  K   L    IOBS SIGMA.IOBS.
    #> 2481  9 -3  20 2202000      374000
    #> 166   2  0  17 2441000      415400
    #> 1200  6 -1 -14 2438000      416500
    #> 684   5 -2 -29 1052000      180700
    #> 2058  8 -2  31 1176000      202800
    #> 3345 10 -1  23 1599000      276000
    #> 1304  6  0  27 1944000      335900
    #> 1387  7 -3 -15 2502000      432500
    #> 1301  6  0  24 1534000      266000
    #> 1305  6  0  28 1262000      219000

To verify that the operation is correct, we can add a new column to the original `refs2` data frame and verify that the previous ordering corresponds, indeed, to decreasing values of \(\mathrm{I/sigI}\):

    # Add an I/sigI column
    refs2 <- cbind(refs2,data.frame(IsigI=refs2$IOBS/refs2$SIGMA.IOBS))

    # Now display with the order previously obtained
    print(refs2[idx[1:10],])
    #>       H  K   L    IOBS SIGMA.IOBS.    IsigI
    #> 2481  9 -3  20 2202000      374000 5.887701
    #> 166   2  0  17 2441000      415400 5.876264
    #> 1200  6 -1 -14 2438000      416500 5.853541
    #> 684   5 -2 -29 1052000      180700 5.821804
    #> 2058  8 -2  31 1176000      202800 5.798817
    #> 3345 10 -1  23 1599000      276000 5.793478
    #> 1304  6  0  27 1944000      335900 5.787437
    #> 1387  7 -3 -15 2502000      432500 5.784971
    #> 1301  6  0  24 1534000      266000 5.766917
    #> 1305  6  0  28 1262000      219000 5.762557

We can also carry out routine statistics of the values of the data frame. It is very quick, for instance, to obtain summary statistics for all the columns:

    summary(refs2)
    #>        H               K                 L                IOBS
    #>  Min.   : 0.00   Min.   :-15.000   Min.   :-62.000   Min.   : -537600
    #>  1st Qu.:15.00   1st Qu.: -8.000   1st Qu.:-28.000   1st Qu.:  202750
    #>  Median :21.00   Median : -4.000   Median :  4.000   Median :  417600
    #>  Mean   :20.15   Mean   : -5.041   Mean   :  1.997   Mean   :  635462
    #>  3rd Qu.:26.00   3rd Qu.: -2.000   3rd Qu.: 32.000   3rd Qu.:  810750
    #>  Max.   :30.00   Max.   :  0.000   Max.   : 62.000   Max.   :18660000
    #>   SIGMA.IOBS.          IsigI
    #>  Min.   :   2992   Min.   :-1.085
    #>  1st Qu.:  91430   1st Qu.: 2.089
    #>  Median : 144600   Median : 2.920
    #>  Mean   : 196604   Mean   : 2.868
    #>  3rd Qu.: 238500   3rd Qu.: 3.684
    #>  Max.   :7591000   Max.   : 5.888

## Specific types of data visualisation

The advantage of having crystallographic data imported in R is that they can be exposed to several types of data visualisation and statistical analysis available in the platform. In this section an histogram visualisation has been created for the original dataset, in which that part of the histogram corresponding to \(\mathrm{I/sigI} > 2\) is coloured differently. This is not an operation easily achievable with standard crystallographic software, but relatively easy to carry out using R.

    # Initial histogram
    mtxt <- "I/sigI and top quartile for I"
    hh <- hist(refs2$IOBS/refs2$SIGMA.IOBS,breaks=30,main=mtxt,
               xlab="I/sigI")

    # Find top quartile of I
    top_qt <- quantile(refs2$IOBS)[4]

    # Data with absolute intensity in the top quartile
    idx <- which(refs2$IOBS >= top_qt)

    # Colour portion of histogram in red
    hist(refs2$IOBS[idx]/refs2$SIGMA.IOBS[idx],breaks=30,col=2,add=TRUE)

Another useful but not easily available visualisation is with histograms where lowest or highest resolutions are highlighted in a different colour. A resolution vector with the same ordering of the original data frame must first be calculated with the `cry` function `hkl_to_reso` and this can be then used to select data with wanted resolution.

    # Cell parameters are needed to calculate resolutions
    cpars <- objXDS2$header$UNIT_CELL_CONSTANTS

    # Resolutions in angstroms. (resos has been computed previously)
    resos <- hkl_to_reso(refs2$H,refs2$K,refs2$L,cpars[1],cpars[2],cpars[3],
                         cpars[4],cpars[5],cpars[6])
    summary(resos)
    #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
    #>   1.785   2.314   3.226   3.957   4.776  49.263

    # Select high resolution data ( <= 2 angstroms)
    idx <- which(resos <= 2)

    # Now draw the histogram
    mtxt <- "I/sigI and top quartile for I"
    hh <- hist(refs2$IOBS/refs2$SIGMA.IOBS,breaks=30,main=mtxt,
               xlab="I/sigI")
    hist(refs2$IOBS[idx]/refs2$SIGMA.IOBS[idx],breaks=30,col=2,add=TRUE)

The above histogram reflects the unfortunate circumstance in structural x-ray crystallography, according to which high resolution data correspond on average to weak intensities.

## Write data to an XDS file

The necessity to modify existing XDS ascii files or to simulate new ones (by developers to test software, for example) can be satisfied with the use of the `writeXDS_ASCII` function. The nature and quality of the file produced will depend on the feasibility and accuracy of the information provided. For this reason, it is more difficult to write an XDS ascii file for unmerged data because a lot of information of an experimental nature has to be provided so to produce a sensible header.

In this section the original data from the “6vww_xds_ascii_merged.hkl” file will be truncated to 2 angstroms and written to a new XDS ascii file with a different date.

    # Date
    ddd <- as.character(Sys.Date())
    stmp <- strsplit(ddd,"-")[[1]]
    allMonths <- c("Jan","Feb","Mar","Apr","May","Jun",
                   "Jul","Aug","Sep","Oct","Nov","Dec")
    objXDS2$header$DATE <- paste0(stmp[3],"-",
                allMonths[as.integer(stmp[2])],"-",stmp[1])

    # Generated by
    objXDS2$header$GENERATED_BY <- "CRY"

    # Data to 2 angstroms resolution
    idx <- which(resos >= 2)
    objXDS2$reflections <- objXDS2$reflections[idx,]

    # Temporary directory for output
    tdir <- tempdir()
    fname <- file.path(tdir,"new.hkl")

    # Write changed data to the new XDS ascii file
    writeXDS_ASCII(objXDS2$processing_info,objXDS2$header,
                   objXDS2$reflections,fname)

Data from the new XDS ascii file can either be explored using XDS software, or read back into R using again `readXDS_ASCII`.

    # Read data from "new.hkl"
    newXDS <- readXDS_ASCII(fname,message=TRUE)
    #>
    #>  File read successfully.
    #>  There are 24689 reflections in this file.
    #>  Here is a summary of the observations:
    #>
    #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
    #>  -1.085   2.383   3.091   3.062   3.782   5.888