# TFHAZ

### Transcription Factor High Accumulation Zones

Alberto Marchesi and Marco Masseroli

#### 27 October 2021

#### Package

TFHAZ 1.16.0

# 1 Introduction

Transcription factors (TFs) are proteins that bind the DNA in specific regions and regulate gene expression. The regolation of the gene expression is often controlled by many TFs interacting with each other. Recent high throughput methods like chromatin immunoprecipitation followed by sequencing (ChIP-seq)1 provide a large number of data regarding TF binding regions, which are available in public repositories such as ENCODE2 or Roadmap Epigenomics.3
Starting from a dataset containing the genomic positions of TF binding regions, the TFHAZ package allows finding trascription factor high accumulation DNA zones, i.e., regions along the genome where there is a high presence of different transcription factors. In addition, some functions are provided in order to analyze and compare results obtained with different input parameters.

# 2 Dataset

Transcription factor dense DNA zones are found from a GRanges object that contains genomic regions of transcription factors at the ranges side and the name of the transcription factors at the metadata side. As in every object of GRanges class, the genomic coordinates are located on the left-hand side. The first column of the ranges side contains the chromosome of each region; the second column contains the genomic coordinates of each region (starting and ending position of the transcription factor binding region, considering a 1-based inclusive coordinate system); the third column contains the strand of each region (“+”, “-”, or “*” if unknown).
The dataset we consider (called Ishikawa) is obtained from computation of ENCODE ChIP-Seq data of the localization of transcription factor binding regions for the Ishikawa cell line. The data have been processed and extracted with GMQL (GenoMetric Query Language http://www.bioinformatics.deib.polimi.it/GMQL/)4 5 6. The Ishikawa dataset contains 283,009 ranges of 16 different transcription factors.

    # load and visualize the dataset:
    data("Ishikawa")
    dim(as.data.frame(Ishikawa))

    ## [1] 283009      6

    head(Ishikawa)

    ## GRanges object with 6 ranges and 1 metadata column:
    ##       seqnames        ranges strand |         TF
    ##          <Rle>     <IRanges>  <Rle> |   <factor>
    ##   [1]     chr1 840014-840266      * | NFIC-human
    ##   [2]     chr1 841252-841697      * | NFIC-human
    ##   [3]     chr1 856253-856932      * | NFIC-human
    ##   [4]     chr1 858967-859537      * | NFIC-human
    ##   [5]     chr1 859558-860319      * | NFIC-human
    ##   [6]     chr1 867077-867783      * | NFIC-human
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome; no seqlengths

# 3 Transcription factor accumulation

The first step in finding transcription factor dense DNA zones is to count the accumulation of TFs for each chromosome base. The function accumulation in the TFHAZ package creates a vector in which, for each chromosome base, the accumulation of the TFs present in the input dataset is calculated. We considered three types of accumulation: TF accumulation, region accumulation and base accumulation.

TF accumulation: for each base, it is the number of different TFs present in the neighborhood of the considered base. The neighborhood is defined by a window with half-width w centered on the considered base.

Region accumulation: for each base, it is the number of regions containing TFs in the neighborhood of the considered base. If in the neighborhood of a base there are two input binding regions of the same TF, the accumulation value in that base is equal to 2 (differently from the TF accumulation, whose value in the same case is equal to 1).

Base accumulation: for each base, it is the total number of bases belonging to input regions containing TFs in the neighborhood of the considered base.

With w = 0, a single base approach is applied (no base neighborhood is considered). In this case, if in the input dataset overlapping regions for the same TF and chromosome do not exist, the results of TF, region and base accumulation are equal.

The function accumulation takes in input:

- a GRanges object containing coordinates of TF binding regions and their TF name;
- a string with the name of the accumulation type: “TF”, “region”, “base”;
- a string with the name of the chromosome (e.g., “chr1”) With chr = “all”, all the chromosomes in the input GRanges object are considered;
- an integer, half-width of the window that defines the neighborhood of each base.

The result of the accumulation function is a list containing:

- accvector: a Rle (or SimpleRleList if chr = “all”) object containing the accumulation for each base of the selected chromosome;
- acctype: a string with the accumulation type used;
- chr: a string with the chromosome name associated with the accumulation vector;
- w: an integer with the half-width of the window used to calculate the accumulation vector.

The accumulation vector obtained can be plotted using the function plot_accumulation.
This function takes in input the output of the accumulation function and saves the plot in a .png file. If the accumulation input is found with chr = “all”, the chromosomes (one or more) to be considered can be chosen by the “chr” argument.

    # calculate TF accumulation for the chromosome 21 for w=0
    TF_acc_21_w_0 <- accumulation(Ishikawa, "TF", "chr21", 0)

    # plot the accumulation vector
    plot_accumulation(TF_acc_21_w_0)

Figure 1: Plot of the TF accumulation vector for the chromosome 21, obtained for w=0.

As we can see in Figure 1, in this example considering no base neighborhood (w=0), the maximum value of accumulation found is 14. It means that in the bases with that accumulation value there are overlapping binding regions of 14 out of the 16 transcription factors present in the dataset.

# 4 Transcription factor dense DNA zones

Once the accumulation for each chromosome base is calculated, we can find transcription factor dense zones with the dense_zones function. For each accumulation threshold value defined, the function finds transcription factor dense DNA zones (regions). Starting from the accumulation vector calculated with the accumulation function, each dense zone is formed by contiguous bases with accumulation equal or higher than the threshold. Threshold values are selected by setting the threshold_step parameter.
For each accumulation threshold value, a “.bed” file with the chromosome and genomic coordinates of the dense zones found can be created (Figure 2). The function finds also the number of dense zones, the number of total bases belonging to the dense zones, the minimum, maximum, mean, median and standard deviation of the dense zone lengths and of the distances between adjacent dense zones.

The function dense_zones takes in input:

- a list of four elements containing: a Rle (or SimpleRleList) with accumulation values (e.g., obtained with the accumulation function), the accumulation type, a chromosome name, and the half-width of the window used for the accumulation count;
- an integer, the step used to calculate the threshold values. These values vary from 1 to the maximum accumulation value in the considered accumulation vector (e.g., found with the accumulation function);
- a string with a cromosome name (chr, optional argument). It is needed to apply the function only to a single cromosome present in the accumulation input found. If chr = “all” (default value) the function operates on all the chromosomes present in the input;
- a logical argument, writeBed. When set to TRUE, for each threshold value (and for each chromosome) a “.bed” file with the chromosome and genomic coordinates of the dense zones found is created.

The result of the dense_zones function is a list containing:

- zones: a list with “GRanges” objects with the dense zones found for each chromosome and threshold value considered.
- zones_count: a list with a data frame for each chromosome considered, containing the considered threshold values and the number of dense zones obtained with each of the threshold values;
- bases_count: a list with a data frame for each chromosome considered, containing the considered threshold values and the total number of bases belonging to the dense zones obtained with each of the threshold values;
- lengths: a list with a data frame for each chromosome considered, containing the considered threshold values and min, max, mean, median and standard deviation of the dense zone lengths obtained with each of the considered threshold values;
- distances: a list with a data frame for each chromosome considered, containing the considered threshold values and min, max, mean, median and standard deviation of the distances between adjacent dense zones obtained with each of the threshold values;
- acctype: a string with the accumulation type used;
- chr: a string with the chromosome name associated with the output zones;
- w: an integer with half-width of the window used to calculate the accumulation vector.

    # find dense DNA zones, with threshold step equal to 1
    TF_dense_21_w_0 <- dense_zones(TF_acc_w_0, 1, chr = "chr21")
    TF_dense_21_w_0

    ## $zones
    ## $zones$chr21
    ## $zones$chr21$th_1
    ## GRanges object with 1265 ranges and 0 metadata columns:
    ##          seqnames            ranges strand
    ##             <Rle>         <IRanges>  <Rle>
    ##      [1]    chr21   9647703-9648184      *
    ##      [2]    chr21   9696048-9696229      *
    ##      [3]    chr21   9878315-9878892      *
    ##      [4]    chr21   9881528-9882531      *
    ##      [5]    chr21   9908929-9910245      *
    ##      ...      ...               ...    ...
    ##   [1261]    chr21 48017979-48018220      *
    ##   [1262]    chr21 48023037-48023509      *
    ##   [1263]    chr21 48024867-48025287      *
    ##   [1264]    chr21 48054801-48056406      *
    ##   [1265]    chr21 48086981-48088470      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_2
    ## GRanges object with 558 ranges and 0 metadata columns:
    ##         seqnames            ranges strand
    ##            <Rle>         <IRanges>  <Rle>
    ##     [1]    chr21   9878496-9878825      *
    ##     [2]    chr21   9881537-9882417      *
    ##     [3]    chr21   9909101-9910088      *
    ##     [4]    chr21 10597536-10597745      *
    ##     [5]    chr21 11098303-11099464      *
    ##     ...      ...               ...    ...
    ##   [554]    chr21 47877766-47879257      *
    ##   [555]    chr21 47974706-47975150      *
    ##   [556]    chr21 47982985-47983832      *
    ##   [557]    chr21 48054865-48056329      *
    ##   [558]    chr21 48087039-48088442      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_3
    ## GRanges object with 424 ranges and 0 metadata columns:
    ##         seqnames            ranges strand
    ##            <Rle>         <IRanges>  <Rle>
    ##     [1]    chr21   9881552-9882414      *
    ##     [2]    chr21   9909189-9910019      *
    ##     [3]    chr21 11098310-11099444      *
    ##     [4]    chr21 11144304-11144918      *
    ##     [5]    chr21 15645943-15646549      *
    ##     ...      ...               ...    ...
    ##   [420]    chr21 47877787-47879256      *
    ##   [421]    chr21 47974750-47975126      *
    ##   [422]    chr21 47983035-47983824      *
    ##   [423]    chr21 48054865-48056292      *
    ##   [424]    chr21 48087094-48088369      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_4
    ## GRanges object with 343 ranges and 0 metadata columns:
    ##         seqnames            ranges strand
    ##            <Rle>         <IRanges>  <Rle>
    ##     [1]    chr21   9881686-9882348      *
    ##     [2]    chr21   9909399-9909966      *
    ##     [3]    chr21 11098350-11099365      *
    ##     [4]    chr21 15645945-15646537      *
    ##     [5]    chr21 15755207-15755932      *
    ##     ...      ...               ...    ...
    ##   [339]    chr21 47744464-47744564      *
    ##   [340]    chr21 47877938-47879206      *
    ##   [341]    chr21 47983079-47983639      *
    ##   [342]    chr21 48054878-48056209      *
    ##   [343]    chr21 48087549-48088359      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_5
    ## GRanges object with 283 ranges and 0 metadata columns:
    ##         seqnames            ranges strand
    ##            <Rle>         <IRanges>  <Rle>
    ##     [1]    chr21   9881864-9882344      *
    ##     [2]    chr21 11098361-11099296      *
    ##     [3]    chr21 15646005-15646499      *
    ##     [4]    chr21 15755224-15755898      *
    ##     [5]    chr21 16247979-16248666      *
    ##     ...      ...               ...    ...
    ##   [279]    chr21 47877954-47879170      *
    ##   [280]    chr21 47983164-47983617      *
    ##   [281]    chr21 48054915-48055327      *
    ##   [282]    chr21 48055643-48056179      *
    ##   [283]    chr21 48087643-48088251      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_6
    ## GRanges object with 196 ranges and 0 metadata columns:
    ##         seqnames            ranges strand
    ##            <Rle>         <IRanges>  <Rle>
    ##     [1]    chr21   9881972-9882267      *
    ##     [2]    chr21 11098374-11099096      *
    ##     [3]    chr21 15646071-15646480      *
    ##     [4]    chr21 15755231-15755829      *
    ##     [5]    chr21 16248048-16248630      *
    ##     ...      ...               ...    ...
    ##   [192]    chr21 47705611-47706730      *
    ##   [193]    chr21 47743778-47744198      *
    ##   [194]    chr21 47744412-47744444      *
    ##   [195]    chr21 47877966-47879071      *
    ##   [196]    chr21 48087776-48088105      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_7
    ## GRanges object with 134 ranges and 0 metadata columns:
    ##         seqnames            ranges strand
    ##            <Rle>         <IRanges>  <Rle>
    ##     [1]    chr21 11098474-11099081      *
    ##     [2]    chr21 15646181-15646398      *
    ##     [3]    chr21 15755291-15755618      *
    ##     [4]    chr21 16437133-16437148      *
    ##     [5]    chr21 16437156-16437702      *
    ##     ...      ...               ...    ...
    ##   [130]    chr21 46823750-46824553      *
    ##   [131]    chr21 46847273-46848145      *
    ##   [132]    chr21 46961476-46961952      *
    ##   [133]    chr21 47705641-47706648      *
    ##   [134]    chr21 47878255-47878872      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_8
    ## GRanges object with 93 ranges and 0 metadata columns:
    ##        seqnames            ranges strand
    ##           <Rle>         <IRanges>  <Rle>
    ##    [1]    chr21 16437167-16437660      *
    ##    [2]    chr21 16976653-16977176      *
    ##    [3]    chr21 17079029-17079434      *
    ##    [4]    chr21 17094988-17095357      *
    ##    [5]    chr21 17102094-17102125      *
    ##    ...      ...               ...    ...
    ##   [89]    chr21 46847506-46848135      *
    ##   [90]    chr21 46961496-46961941      *
    ##   [91]    chr21 47705885-47706620      *
    ##   [92]    chr21 47878395-47878750      *
    ##   [93]    chr21 47878815-47878836      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_9
    ## GRanges object with 56 ranges and 0 metadata columns:
    ##        seqnames            ranges strand
    ##           <Rle>         <IRanges>  <Rle>
    ##    [1]    chr21 16437178-16437644      *
    ##    [2]    chr21 16976710-16977097      *
    ##    [3]    chr21 17079059-17079381      *
    ##    [4]    chr21 17792433-17792742      *
    ##    [5]    chr21 17906640-17907222      *
    ##    ...      ...               ...    ...
    ##   [52]    chr21 46749546-46750481      *
    ##   [53]    chr21 46783762-46784481      *
    ##   [54]    chr21 46847519-46848135      *
    ##   [55]    chr21 46961503-46961928      *
    ##   [56]    chr21 47705894-47706507      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_10
    ## GRanges object with 32 ranges and 0 metadata columns:
    ##        seqnames            ranges strand
    ##           <Rle>         <IRanges>  <Rle>
    ##    [1]    chr21 16437246-16437603      *
    ##    [2]    chr21 17906738-17907135      *
    ##    [3]    chr21 17936017-17936530      *
    ##    [4]    chr21 18884908-18885519      *
    ##    [5]    chr21 26979590-26980079      *
    ##    ...      ...               ...    ...
    ##   [28]    chr21 46359623-46360089      *
    ##   [29]    chr21 46749631-46750470      *
    ##   [30]    chr21 46783769-46784454      *
    ##   [31]    chr21 46847582-46847985      *
    ##   [32]    chr21 47705905-47706333      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_11
    ## GRanges object with 15 ranges and 0 metadata columns:
    ##        seqnames            ranges strand
    ##           <Rle>         <IRanges>  <Rle>
    ##    [1]    chr21 17936079-17936490      *
    ##    [2]    chr21 18885005-18885518      *
    ##    [3]    chr21 26979675-26980039      *
    ##    [4]    chr21 29765568-29766071      *
    ##    [5]    chr21 33984736-33985219      *
    ##    ...      ...               ...    ...
    ##   [11]    chr21 45209153-45209668      *
    ##   [12]    chr21 46359626-46360076      *
    ##   [13]    chr21 46749679-46750446      *
    ##   [14]    chr21 46783821-46784394      *
    ##   [15]    chr21 47705958-47706318      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_12
    ## GRanges object with 7 ranges and 0 metadata columns:
    ##       seqnames            ranges strand
    ##          <Rle>         <IRanges>  <Rle>
    ##   [1]    chr21 17936082-17936489      *
    ##   [2]    chr21 18885028-18885512      *
    ##   [3]    chr21 40284873-40285700      *
    ##   [4]    chr21 40685540-40686019      *
    ##   [5]    chr21 43054505-43054878      *
    ##   [6]    chr21 45209176-45209657      *
    ##   [7]    chr21 46359647-46360047      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_13
    ## GRanges object with 2 ranges and 0 metadata columns:
    ##       seqnames            ranges strand
    ##          <Rle>         <IRanges>  <Rle>
    ##   [1]    chr21 18885132-18885398      *
    ##   [2]    chr21 40685550-40685969      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ## $zones$chr21$th_14
    ## GRanges object with 1 range and 0 metadata columns:
    ##       seqnames            ranges strand
    ##          <Rle>         <IRanges>  <Rle>
    ##   [1]    chr21 40685632-40685961      *
    ##   -------
    ##   seqinfo: 24 sequences from an unspecified genome
    ##
    ##
    ##
    ## $zones_count
    ## $zones_count$chr21
    ##    threshold n_zones
    ## 1          1    1265
    ## 2          2     558
    ## 3          3     424
    ## 4          4     343
    ## 5          5     283
    ## 6          6     196
    ## 7          7     134
    ## 8          8      93
    ## 9          9      56
    ## 10        10      32
    ## 11        11      15
    ## 12        12       7
    ## 13        13       2
    ## 14        14       1
    ##
    ##
    ## $bases_count
    ## $bases_count$chr21
    ##    threshold n_bases
    ## 1          1  884594
    ## 2          2  429675
    ## 3          3  315332
    ## 4          4  235669
    ## 5          5  173254
    ## 6          6  111781
    ## 7          7   72784
    ## 8          8   45232
    ## 9          9   27580
    ## 10        10   16873
    ## 11        11    7802
    ## 12        12    3458
    ## 13        13     687
    ## 14        14     330
    ##
    ##
    ## $lengths
    ## $lengths$chr21
    ##    threshold n_zones length_zone_min length_zone_max length_zone_mean
    ## 1          1    1265             168            4164         699.2838
    ## 2          2     558               2            3179         770.0269
    ## 3          3     424               2            2244         743.7075
    ## 4          4     343               2            2039         687.0816
    ## 5          5     283               3            1545         612.2049
    ## 6          6     196              12            1225         570.3112
    ## 7          7     134               1            1212         543.1642
    ## 8          8      93               9            1077         486.3656
    ## 9          9      56               7             971         492.5000
    ## 10        10      32             264             960         527.2812
    ## 11        11      15             328             920         520.1333
    ## 12        12       7             374             828         494.0000
    ## 13        13       2             267             420         343.5000
    ## 14        14       1             330             330         330.0000
    ##    length_zone_median length_zone_sd
    ## 1               566.0       415.2782
    ## 2               706.0       383.8741
    ## 3               687.0       344.1256
    ## 4               660.0       306.2085
    ## 5               609.0       287.4903
    ## 6               576.0       268.5662
    ## 7               532.0       257.2716
    ## 8               459.0       252.1179
    ## 9               519.0       228.1558
    ## 10              478.5       162.7088
    ## 11              504.0       161.1095
    ## 12              480.0       154.0682
    ## 13              343.5       108.1873
    ## 14              330.0             NA
    ##
    ##
    ## $distances
    ## $distances$chr21
    ##    threshold n_zones dist_zone_min dist_zone_max dist_zone_mean
    ## 1          1    1265             4       3967595       29713.16
    ## 2          2     558             6       4500973       67829.14
    ## 3          3     424             2       4501025       89578.98
    ## 4          4     343             6       4546580      111027.33
    ## 5          5     283             2       4546709      134870.27
    ## 6          6     196             8       6065108      195356.66
    ## 7          7     134             3       6065276      275998.11
    ## 8          8      93             4       7787560      341266.63
    ## 9          9      56            25       7787773      568032.82
    ## 10        10      32          6669       8094071     1008136.97
    ## 11        11      15         33375       8094157     2125889.43
    ## 12        12       7        399840      21399361     4736752.33
    ## 13        13       2      21800152      21800152    21800152.00
    ## 14        14       1            NA            NA             NA
    ##    dist_zone_median dist_zone_sd
    ## 1             11388     122569.1
    ## 2             18144     260613.7
    ## 3             23311     320704.8
    ## 4             31221     358342.4
    ## 5             33190     439562.7
    ## 6             50995     608044.2
    ## 7             87341     727219.5
    ## 8            113364     904014.4
    ## 9            114684    1209207.0
    ## 10           389542    1662356.6
    ## 11          1652100    2175152.0
    ## 12          1652144    8196883.8
    ## 13         21800152           NA
    ## 14               NA           NA
    ##
    ##
    ## $chr
    ## [1] "chr21"
    ##
    ## $w
    ## [1] 0
    ##
    ## $acctype
    ## [1] "TF"

Figure 2: Content of the ‘bed’ file with the coordinates of the seven dense DNA zones found for the chromosome 21 with transcription factor accumulation threshold value equal to 12.

We can plot the results present in the zones_count data frame with the function plot_n_zones (Figure 3) and we can see how the number of dense DNA zones decreases as the accumulation threshold value increases. The function also plots the point of the graph with maximum slope change, corresponding to the maximum second derivative of the curve, circulating it with a red full line.

    plot_n_zones(TF_dense_w_0, chr = "chr21")

Figure 3: Plot of the number of dense DNA zones found varying the TF accumulation threshold value for the chromosome 21; the point with maximum slope change is plotted circulated with a red full line.

# 5 Transcription factor dense DNA zones analysis

After finding transcription factor dense DNA zones, we can use two functions of the TFHAZ package to compare the results obtained with different values of w half-width of the base neighborhood window and different accumulation types.

With the function w_analysis we can plot the number of dense zones and the total number of bases belonging to these dense zones present in a set of inputs, obtained (all with accumulation threshold=1) using the dense_zones function, for the same accumulation type, same chromosome, and different values of w half-width of the window defining the neighborhood of each base. The function takes in input a list of multiple outputs of the dense_zones function and returns a plot (with x axis logarithmic-scale).

    # l is a list with four objects obtained with the dense_zones function with
    # w = 10, 100, 1000, 10000.
    l <- list(TF_dense_w_10, TF_dense_w_100, TF_dense_w_1000, TF_dense_w_10000)
    # plot
    w_analysis(l, chr = "chr21")

Figure 4: Plot of the number of dense DNA zones (red full line) and of the total number of bases belonging to dense DNA zones (blue dashed line) obtained with different values of neighborhood window half-width w for the chromosome 21.

If we consider the four different values of w half-width of the base neighborhood window in the example, we can notice in Figure 4 that the two measures (i.e., the number of dense zones and the total number of bases belonging to these dense zones) are inversely correlated; the number of bases increases with the size of the neighborhood, while the number of dense zones decreases. Furthermore, observing the plot, we can notice that the highest increase or decrease of the two measures occurs when the half-width of the neighborhood assumes values higher than 1000 bases. So, w=1000 can be considered a good value in finding dense zones when using an accumulation approach with neighborhood (w different from 0). It is worth noting that the calculation time of the accumulation vector increases considerably with higher values of w.

In order to understand how to integrate the results obtained with the three different accumulation types, using the function n_zones_PCA we can perform the Principal Component Analysis (PCA)7 8 of the number of dense zones obtained by varying the threshold on accumulation values obtained with the three methods of accumulation (TF, region, base).

The Principal Component Analysis produces a low dimensional representation of a dataset, finding a linear sequence of linear combinations of the variables that have maximal variance. With PCA we want to find if there is a possible way to combine the three measures (TF, region, base accumulation), or if the information obtained is the same, and we can use only one of these measures for our study. For this purpose it is useful to observe the variance associated with the first principal component and the loadings, the coefficients of the linear combination of each principal component, that explain the proportion of each variable along each principal component.

This function takes in input:

- a list with the results of the dense_zones function using the TF accumulation method and varying the thresholds on the considered accumulation values;
- a list with the results of the dense_zones function using the region accumulation method and varying the thresholds on the considered accumulation values;
- a list with the results of the dense_zones function using the base accumulation method and varying the thresholds on the considered accumulation values.
- an optional argument, chr, needed if the input was found with chr = “all”; a string or a vector containing strings with the name of the chromosome (e.g., “chr1”)

The outputs of the function are:

- a list with a summary containing the standard deviation on each principal component, the proportion of variance explained by each principal component, the cumulative proportion of variance described by each principal component, and the loadings of each principal component;
- a plot with the variances of the principal components;
- a plot with the cumulate variances of the principal components;
- a plot with the loadings of the three principal components.

Note that the function n_zones_PCA works only if the number of different threshold values used to find the dense zones with the dense_zones function is the same for all the three accumulation types, while the threshold values can be different.

    # TF_dense_21_w_10 is the output of dense_zones function applied to the
    # accumulation vector found with w=10, chr="chr21", acctype="TF".
    # reg_dense_21_w_10 is the output of dense_zones function applied to the
    # accumulation vector found with w=10, chr="chr21", acctype="reg".
    # base_dense_21_w_10 is the output of dense_zones function (with
    # threshold_step=21 in order to have 14 threshold values as in the other two
    # inputs) applied to the accumulation vector found with w=10, chr="chr21",
    # acctype="base".
    # PCA
    n_zones_PCA(TF_dense_w_10, reg_dense_w_10, base_dense_w_10, chr = "chr21")

    ## $summary
    ## Importance of components:
    ##                          PC1      PC2      PC3
    ## Standard deviation     1.732 0.006086 0.001916
    ## Proportion of Variance 1.000 0.000010 0.000000
    ## Cumulative Proportion  1.000 1.000000 1.000000
    ##
    ## $loadings
    ##                     PC1        PC2        PC3
    ## TF_zones     -0.5773531 -0.1901966  0.7940331
    ## region_zones -0.5773501 -0.5925539 -0.5617355
    ## base_zones   -0.5773476  0.7827549 -0.2323028

Figure 5: Plot of the variances of the principal components.

Figure 6: Plot of the cumulate variances of the principal components.

Figure 7: Plot of the loadings of the three principle components.

From this example we can see how the first principal component explains most of the variation (Figure 5 and Figure 6), so it accounts for maximum information. Furthermore, we can see how the values of loadings of the first principal component are very similar (Figure 7). Therefore, we can say that the information obtained with the three methods of accumulation is the same and for our study regarding transcription factor dense DNA zones we can use only one method of the three; we suggest using the TF or region accumulation because the running time of the accumulation function with acctype=base is higher, especially in chromosomes with an elevated number of input regions.

# 6 Transcription factor high accumulation DNA zones

In the previous part we found transcription factor dense DNA zones with different thresholds of transcription factor accumulation, and we compared the results using different input parameters in order to identify the best way to find regions of the genome where there is a high presence of different trascription factors. Now, with the function high_accumulation_zones, setting only one threshold value, we can find these regions; we call them transcription factor high accumulation DNA zones (TFHAZ). Starting from the accumulation vector calculated with the accumulation function, two different methods for the search of TF high accumulation DNA zones are available. The binding regions method is based on the identification of DNA regions with presence of TF binding (at least one TF) from which those with a high number of different TFs (above the threshold) are selected. This method works only if the accumulation vector is found with w=0. The overlaps method is the method used also in dense_zones function. It uses a single base local approach, identifying DNA bases, that form the dense zones, in which there is high overlap of TFs. For the binding regions method the high accumulation zones are the accumulation regions with values higher or equal to the threshold, while in the overlaps these zones are defined as sets of contiguous bases with accumulation value higher or equal to the considered threshold. The threshold value is found considering two methods. The std method considers all and only the bases of the accumulation vector (accvector) with values higher than zero, and the threshold is found with the following formula: TH = mean(accvector) + 2 std(accvector). The top_perc method considers the accumulation regions and selects those in the top x percentage, with x chosen by the user through the perc argument. The function finds also the number of high accumulation zones, the number of total bases belonging to these zones, the minimum, maximum, mean, median and standard deviation of these zone lengths and of the distances between adjacent high accumulation zones. In the case of binding regions method, it is needed to include the data input argument, that is the GRanges object used in the accumulation function. Furhermore, in the case of single chromosome accumulation vector, the function can plot, for each chromosome base (x axis), the value of accumulation (y axis) calculated with the accumulation function. On this graph there are also shown the threshold (with a red line) and, on the x axis, the bases belonging to the high accumulation zones (with red boxes). The plot can be saved in a “.png” file. The function also can generate a “.bed” file with the chromosome and genomic coordinates of the high accumulation zones found.

The function high_accumulation_zones takes in input:

- a list of four elements containing: a sparse vector with accumulation values (e.g., obtained with the function), the accumulation type, a chromosome name, and the half-width of the window used for the accumulation count;
- a string with the name of the method used to find high accumulation zones: “binding_regions” or “overlaps”;
- a GRanges object containing coordinates of TF binding regions and their TF name. It is needed in the case of binding regions method;
- a string with the name of the method used to find the threshold value: “std” or “top_perc”;
- an integer with the percentage value to be used in order to find the threshold with the top_perc method;
- a logical argument, writeBed. When set to TRUE, for each threshold value a “.bed” file with the chromosome and genomic coordinates of the dense zones found is created.
- a logical argument, plotZones. When set to TRUE, and the accumulation in input is calculated for a single chromosome, a “.png” file with the plot of the high accumulation zones on the accumulation vector is created.

The result of the high_accumulation_zones function is a list containing:

- zones: a GRanges object containing the coordinates of the high accumulation zones.
- n_zones: an integer containing the number of high accumulation zones obtained;
- n_bases: an integer containing the total number of bases belonging to the high accumulation zones obtained;
- lengths: a vector containing the considered threshold value and min, max, mean, median and standard deviation of the high accumulation zone lengths obtained;
- distances: a vector containing the considered threshold value and min, max, mean, median and standard deviation of the distances between adjacent high accumulation zones obtained;
- TH: a number with the threshold value found;
- acctype: a string with the accumulation type used;
- chr: a string with the chromosome name associated with the accumulation vector used;
- w: an integer with half-width of the window used to calculate the accumulation vector.

    # find high accumulation DNA zones
    TF_acc_21_w_0 <- accumulation(Ishikawa, "TF", "chr21", 0)
    TFHAZ_21_w_0 <- high_accumulation_zones(TF_acc_21_w_0, method = "overlaps",
    threshold = "std")
    TFHAZ_21_w_0

    ## $zones
    ## GRanges object with 93 ranges and 0 metadata columns:
    ##        seqnames            ranges strand
    ##           <Rle>         <IRanges>  <Rle>
    ##    [1]    chr21 16437167-16437660      *
    ##    [2]    chr21 16976653-16977176      *
    ##    [3]    chr21 17079029-17079434      *
    ##    [4]    chr21 17094988-17095357      *
    ##    [5]    chr21 17102094-17102125      *
    ##    ...      ...               ...    ...
    ##   [89]    chr21 46847506-46848135      *
    ##   [90]    chr21 46961496-46961941      *
    ##   [91]    chr21 47705885-47706620      *
    ##   [92]    chr21 47878395-47878750      *
    ##   [93]    chr21 47878815-47878836      *
    ##   -------
    ##   seqinfo: 1 sequence from an unspecified genome; no seqlengths
    ##
    ## $n_zones
    ## [1] 93
    ##
    ## $n_bases
    ## [1] 45232
    ##
    ## $lengths
    ##                 TH            n_zones    length_zone_min    length_zone_max
    ##           7.268413          93.000000           9.000000        1077.000000
    ##   length_zone_mean length_zone_median     length_zone_sd
    ##         486.365591         459.000000         252.117932
    ##
    ## $distances
    ##               TH          n_zones    dist_zone_min    dist_zone_max
    ##     7.268413e+00     9.300000e+01     4.000000e+00     7.787560e+06
    ##   dist_zone_mean dist_zone_median     dist_zone_sd
    ##     3.412666e+05     1.133640e+05     9.040144e+05
    ##
    ## $TH
    ## [1] 7.268413
    ##
    ## $chr
    ## [1] "chr21"
    ##
    ## $w
    ## [1] 0
    ##
    ## $acctype
    ## [1] "TF"

From the results of this example we can see that for the overlaps method with a threshold equal to 7.3 (obtained with the std method) we find 93 high accumulation zones. We can see the distribution of these zones along the chromosome (in this case the chromosome 21) in Figure 8, while in Figure 9 it is shown a part (31 out of 93 zones) of the “.bed” file with the coordinates of the zones.

Figure 8: Plot of the TF accumulation vector (for the chromosome 21, obtained for w=0) and of the high accumulation DNA zones (red boxes on the x axis) found; the threshold used to find these zones (7,268413) is shown with a red horizontal line.

Figure 9: Content of the ‘bed’ file with the coordinates of 31 out of the 93 high accumulation DNA zones found.

# 7 Acknowledgement

We really appreciate the generous support and suggestions by Stefano Campaner and Stefano Perna.

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