In DEIB-GECO/TFHAZ: Transcription Factor High Accumulation Zones
knitr::opts_chunk$set(echo = TRUE)
library(TFHAZ)
library(GenomicRanges)
library(IRanges)
library(S4Vectors)
data("data_man")
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)
[@park2009chip] provide a large number of data regarding TF binding regions,
which are available in public repositories such as ENCODE [@encode2004encode]
or Roadmap Epigenomics [@bernstein2010nih].
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.
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/)
[@masseroli2015genometric] [@ceri2016data] [@masseroli2016modeling].
The Ishikawa dataset contains 283,009 ranges of 16 different transcription
factors.
# load and visualize the dataset:
data("Ishikawa")
dim(as.data.frame(Ishikawa))
head(Ishikawa)
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)
knitr::include_graphics('./TF_w_0_chr21.png')
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.
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
knitr::include_graphics('./dense_zones_12.PNG')
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")
\newpage
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")
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) [@johnson2014applied] [@bro2014principal]
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")
knitr::include_graphics('./PCA_1.png')
knitr::include_graphics('./PCA_2.png')
knitr::include_graphics('./PCA_3.png')
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.
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 \emph{accumulation} 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 k (by defeault equals to 2) with the percentage (with the
top_perc method) or the number of std deviations (with the std method) to
be used in order to find the threshold.
- 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
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.
knitr::include_graphics('./high_accumulation_zones_TH_7.3_TF_acc_w_0_chr21.png')
knitr::include_graphics('./HAZ_bed.PNG')
Acknowledgement
We really appreciate the generous support and suggestions by Stefano Campaner
and Stefano Perna.
References
DEIB-GECO/TFHAZ documentation built on July 29, 2023, 5:45 p.m.
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knitr::opts_chunk$set(echo = TRUE)
library(TFHAZ) library(GenomicRanges) library(IRanges) library(S4Vectors) data("data_man")
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)
[@park2009chip] provide a large number of data regarding TF binding regions,
which are available in public repositories such as ENCODE [@encode2004encode]
or Roadmap Epigenomics [@bernstein2010nih].
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.
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/)
[@masseroli2015genometric] [@ceri2016data] [@masseroli2016modeling].
The Ishikawa dataset contains 283,009 ranges of 16 different transcription
factors.
# load and visualize the dataset: data("Ishikawa") dim(as.data.frame(Ishikawa)) head(Ishikawa)
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)
knitr::include_graphics('./TF_w_0_chr21.png')
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.
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
knitr::include_graphics('./dense_zones_12.PNG')
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")
\newpage
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")
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) [@johnson2014applied] [@bro2014principal] 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")
knitr::include_graphics('./PCA_1.png')
knitr::include_graphics('./PCA_2.png')
knitr::include_graphics('./PCA_3.png')
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.
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 \emph{accumulation} 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 k (by defeault equals to 2) with the percentage (with the top_perc method) or the number of std deviations (with the std method) to be used in order to find the threshold.
- 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
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.
knitr::include_graphics('./high_accumulation_zones_TH_7.3_TF_acc_w_0_chr21.png')
knitr::include_graphics('./HAZ_bed.PNG')
Acknowledgement
We really appreciate the generous support and suggestions by Stefano Campaner and Stefano Perna.
References
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