TFHAZ
Transcription Factor High Accumulation Zones
30 October 2017
Package
TFHAZ 1.0.0
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 Epigenomics3.
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/)456. 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 6head(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 seqlengths3 Trascription 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”);
- 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 sparse vector 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.
# 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: 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 is 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 sparse vector 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).
The result of the dense_zones function is a list containing:
- zones_count: a data frame containing the considered threshold values and the number of dense zones obtained with each threshold value;
- bases_count: a data frame containing the considered threshold values and the total number of bases belonging to the dense zones obtained with each threshold value;
- lengths: a data frame containing the considered threshold values and min, max, mean, median and standard deviation of the dense zone lengths obtained with each threshold value;
- distances: data frame containing the considered threshold values and min, max, mean, median and standard deviation of the distances between adjacent dense zones obtained with each threshold value;
- 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 dense DNA zones, with threshold step equal to 1
TF_dense_21_w_0 <- dense_zones(TF_acc_21_w_0, 1)
TF_dense_21_w_0## $zones_count
## 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
## 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
## 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
## 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: Figure2: Content of the ‘bed’ file with the coordinates of the seven dense DNA zones found 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_21_w_0)
Figure 3: Figure 3: Plot of the number of dense DNA zones found varying the TF accumulation threshold value; 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_21_w_10, TF_dense_21_w_100, TF_dense_21_w_1000, TF_dense_21_w_10000)
# plot
w_analysis(l)
Figure 4: 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
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)78 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.
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_21_w_10, reg_dense_21_w_10, base_dense_21_w_10)## $summary
## Importance of components:
## PC1 PC2 PC3
## Standard deviation 1.6242 0.6016 0.002013
## Proportion of Variance 0.8793 0.1207 0.000000
## Cumulative Proportion 0.8793 1.0000 1.000000
##
## $loadings
## PC1 PC2 PC3
## TF_zones.zones_count.n_zones -0.5997158 -0.3761260 -0.706307402
## region_zones.zones_count.n_zones -0.6000147 -0.3726357 0.707901821
## base_zones.zones_count.n_zones 0.5294556 -0.8483348 0.002205636
Figure 5: Figure 5: Plot of the variances of the principal components
Figure 6: Figure 6: Plot of the cumulate variances of the principal components
Figure 7: 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 Trancription 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 function, each TFHAZ is formed by contiguous bases with accumulation higher than the threshold (TH). The threshold is found, considering all the accumulation values of the vector higher than zero, with the following formula: , where and are respectively the mean and standard deviation of the accumulation values higher than zero in the .
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 the zone lengths and of the distances between adjacent zones. Furhermore, the function plots, for each chromosome base (x axis), the value of accumulation (y axis) calculated with the function. On this graph there are also shown the threshold (with a red horizontal line) and, on the x axis, the bases belonging to the high accumulation zones (with red boxes). The plot is saved in a “.png” file.
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.
The result of the high_accumulation_zones function is a list containing:
- 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.
Furthermore, a “.bed” file with the chromosome and genomic coordinates of the high accumulation zones found is created.
# find high accumulation DNA zones
TFHAZ_21_w_0 <- high_accumulation_zones(TF_acc_21_w_0)
TFHAZ_21_w_0## $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 with a threshold equal to 7.3 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: 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: 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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