Please note that ârifiâ is only available for Unix based systems. To install this package, start R (>= version â4.2â) and enter:
if (!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install("rifi")The stability or halflife of bacterial transcripts is often estimated using Rifampicin timeseries data. Rifampicin has the special feature that it prevents the initiation of transcprition, but RNA polymerases which are already elongating are unaffected (Campbell et al. 2001). This has the implication that the RNA concentrations of positions downstream of the transcriptional start site appear unchanged until the last polymerase has passed this point. The result is a delayed exponential decay (Chen et al. 2015), which can be fitted by the following model:
\(c(t,n) = \begin{cases} \frac{\alpha}{\lambda} & \quad \text{if } t < \frac{n}{v}\\ \frac{\alpha}{\lambda} \times e^{-\lambda t} & \quad \text{if } t \geq \frac{n}{v} \end{cases}\)
The model (Chen et al. 2015) consists of two phases; the firts phase describes the delay where the transcript concentration is in its steady state defined by the ratio of the synthesis rate \(\alpha\) and the decay constant \(\lambda\) (\(steadystate = \frac{\alpha}{\lambda}\)). The delay is dependent on the distance from the transcriptional start site \(n\) and the transcription velocity \(v\). If the time after the Rifampicin additon is greater than the delay (\(delay = \frac{n}{v}\)) the exponential decay phase starts.
In addition to the standard model, we are using a second model which describes the behaviour at positions were the concentration increases after Rifampicin addition (Figure 1, right panel). This phenomenon can be explained by Rifampicin relievable transcription termination, e.g. through the transcriptional interference (TI) collision mechanism (Shearwin, Callen, and Egan 2005) or termination by short-lived factors such as sRNAs (Wang et al. 2015). In the following we will call this model the âTI modelâ which consists of three phases:
\(c(t,n) = \begin{cases} \frac{\alpha - \alpha \times \beta}{\lambda} & \quad \text{if } t < \frac{n - n_{term}}{v}\\ \frac{\alpha}{\lambda} - \frac{\alpha \times \beta}{\lambda} \times e ^{-\lambda (t -\frac{n - n_{term}}{v})} & \quad \text{if } \frac{n - n_{term}}{v} < t < \frac{n}{v}\\ (\frac{\alpha}{\lambda} - \frac{\alpha \times \beta}{\lambda} \times e ^{-\lambda (t -\frac{n_{term}}{v})}) \times e^{-\lambda (t-\frac{n}{v})} & \quad \text{if } \frac{n}{v} \leq t \end{cases}\)
The first phase describes again the steady state concentration at a given transcript position, but here the synthesis rate \(\alpha\) is reduced by the TI-termination-factor \(\beta\). We assume a short lived factor responsible for the termination whose synthesis is stopped after rifampicin addition. Thus after the relieve of termination all polymerases that start at the transcriptional start site can reach positions downstream of the former termination site (\(n_{term}\)), the time polymerases need from the position of termination to the position \(n\) is delay for the increase (\(delay_{increase}= \frac{n - n_{term}}{v}\)). After the last polymerase has passed the respective position, the exponential decay phase starts.
ârifiâ is a tool to do a stability analysis on high-throughput rifampicin data. RNA sequencing and microarray data derived from rifampicin treated bacteria with sufficiently high time resolution can reveal many insights into the mechanics of transcription, RNAP velocity and RNA stability. ârifiâ is a tool for the holistic identification of these transcription processes. The core part of the data analysis by rifi is the utilization of one of the two non linear regression models applied on the time series data of each probe (or bin), giving the probe/bin specific delay, decay constant \(\lambda\) and half-life (\(t_\frac{1}{2} = \frac{\ln(2)}{\lambda}\)) (Figure 1, left panel).
Figure 1: Fit models
Fits from both models. Left: the two-phase standard fit. Right the TI model fits the increase in intensity. Black dotes represent the average intensity for each timepoint, colored circles indicate the respective replicate.
After the fit of the individual probes/bins, common worklfows usually combine the individual half-life values based on the given genome annotation to get an average for the gene based stability. This procedure can not deal with differences within a given gene, e.g. due to processing sites. ârifiâ uses an annotation agnostic approach to get an unbiased estimate of individual transcripts as they actually appear in vivo. probes/bins with equal properties in the extracted values delay, half-life, TI_termination_factor and the given intensity values are combined into segments by dynamic programming (called fragmentation in ârifiâ), independent of an existing genome annotation (Figure 2). The fragmentation is performed hierarchically.
Initially segments of bins are grouped by regions without significant sequencing depth into position_segments. Those are grouped into delay_fragments by common velocity. Subsequently, each delay-fragment is grouped by similar half-life into half_life_fragments, on which the bins finally are grouped into intensity_fragments by similar intensity. From the fragmentation, many events can be extracted; iTSS (internal transcription start sites), transcription pausing_sites, velocity_changes,processing_sites, partial terminations, as well as instances of Rifampicin relievable transcription termination, e.g. by TI (transcription interference). All data are integrated to give an estimate of continuous transcriptional units, i.e. operons. Comprehensive output tables and visualizations of the full genome result and the individual fits for all probes/bins are produced.
Figure 2: Fragmentation hirarchy
The hierarchy of the workflow is separated into five steps. At first segments are formed based on the distance to the next data point. The threshold is 200 nucleotides. Next, segments are parted into delay fragments. The delay fragments are parted by the half-life and likewise the half-life fragments are parted by intensity. Groups of TUs are formed based on the distance between the starts and ends of the delay fragments. Finally, within TUs, TI fragments are formed.
If you have your data prepared as described in [The Input Data Frame] (#the-input-data-frame) you can use the rifi_wrapper to run ârifi" with default options. rifi_wrapper conveniently wraps all functions included in rifi. That allows the user to run the whole workflow with one function. If the data contain a background component, e.g. in case of microarray data, take to define a meaningful background intensity.
The functions used are:
check_inputrifi_preprocessrifi_fitrifi_penaltiesrifi_fragmentationrifi_statsrifi_summaryrifi_visualization
For rifi_wrapper you only need to provide the path to a .gff file of the respective genome and the input SummarizedExperiment object. The genome annotation is needed for the visualization and to map fragmented segments to annotated genes for an easier interpretation.
library(rifi)
data(example_input_e_coli)
Path = gzfile(system.file("extdata", "gff_e_coli.gff3.gz", package = "rifi"))
wrapper_minimal <-
rifi_wrapper(
inp = example_input_e_coli,
cores = 2,
path = Path,
bg = 0,
restr = 0.01
)
}
The wrapper saves the output of each sub-function in a list. Thus each intermediate result can be re-run with custom settings. the object âwrapper_minimalâ contains only minimal artificial data to reduce the runtime of the test run.
data(wrapper_minimal)
# list of 6 SummarizedExperiment objects
length(wrapper_minimal)## [1] 6#the first intermediate result
wrapper_minimal[[1]]## class: RangedSummarizedExperiment
## dim: 4 33
## metadata(2): replicates timepoints
## assays(1): ''
## rownames: NULL
## rowData names(7): position ID ... flag position_segment
## colnames: NULL
## colData names(2): timepoint replicateA small example output can be loaded with data(summary_minimal). The final output is a SummarizedExperiment object.
All main results are stored as metadata in the SummarizedExperiment object. The first five entries are not of immediate importance.
data(summary_minimal)
# the main results
names(metadata(summary_minimal)) ## [1] "timepoints" "replicates"
## [3] "logbook" "logbook_details"
## [5] "annot" "dataframe_summary_1"
## [7] "dataframe_summary_2" "dataframe_summary_events"
## [9] "dataframe_summary_events_HL_int" "dataframe_summary_events_ps_itss"
## [11] "dataframe_summary_events_velocity" "dataframe_summary_TI"Entry 6, dataframe_summary_1, contains all fit results for each individual bin/probe and a mapping to the genome annotation. They can be exported to an .csv file using write.csv().
# bin/probe probe based results
head(metadata(summary_minimal)$dataframe_summary_1)## ID feature_type gene locus_tag position strand segment TU
## 1 1 <NA> <NA> <NA> 50 + S_1 TU_1
## 2 2 <NA> <NA> <NA> 100 + S_1 TU_1
## 3 3 <NA> <NA> <NA> 150 + S_1 TU_1
## 4 4 CDS thrL BW25113_RS00005 200 + S_1 TU_1
## 5 5 CDS thrL BW25113_RS00005 250 + S_1 TU_1
## 6 6 <NA> <NA> <NA> 300 + S_1 TU_1
## delay_fragment delay HL_fragment half_life intensity_fragment intensity flag
## 1 D_1 0.08 Dc_1 1.57 I_1 138.55 _ABG_
## 2 D_1 0.17 Dc_1 1.54 I_1 146.89 _ABG_
## 3 D_1 0.50 Dc_1 1.52 I_1 152.35 _ABG_
## 4 D_1 0.76 Dc_1 1.54 I_1 163.39 _ABG_
## 5 D_1 1.00 Dc_1 1.50 I_1 149.01 _ABG_
## 6 D_1 1.21 Dc_1 1.58 I_1 160.37 _ABG_
## TI_termination_factor
## 1 NA
## 2 NA
## 3 NA
## 4 NA
## 5 NA
## 6 NA#export to csv
write.csv(metadata(summary_minimal)$dataframe_summary_1, file="filename.csv")Entry 7, dataframe_summary_2, contains all fit results for each intensity_fragment. Due to the hierachic fragmentation strategy [Figure 2] several intensity_fragment (I_x) can belong to one decay_fragment (Dc_x), one delay_fragment (D_x) and one transcriptional unit (TU_x). The fragment IDs can be used to locate the fragment in the output PDF file. The fragments are mapped to the genome annotation and the mean halflife given in minutes and the mean intensity is given with their standard deviations. Also the estimated velocity in nt/min is given. The table can be exported as an .csv file using write.csv().
# all estimated fragments
metadata(summary_minimal)$dataframe_summary_2## feature_type gene locus_tag first_position_frg last_position_frg
## 1 NA|CDS NA|thrL NA|BW25113_RS00005 50 300
## 2 CDS thrA BW25113_RS00010 350 600
## 3 CDS thrA BW25113_RS00010 650 900
## 4 NA NA NA 1151 1051
## 5 NA NA NA 1001 901
## strand TU segment delay_fragment HL_fragment half_life HL_SD HL_SE
## 1 + TU_1 S_1 D_1 Dc_1 1.54 0.03 0.01
## 2 + TU_1 S_1 D_1 Dc_2 3.04 0.04 0.02
## 3 + TU_1 S_1 D_2 Dc_3 3.00 0.05 0.02
## 4 - TU_2 S_2 D_3 Dc_4 2.00 0.02 0.01
## 5 - TU_2 S_2 D_3 Dc_4 2.00 0.02 0.01
## intensity_fragment intensity intensity_SD intensity_SE velocity
## 1 I_1 151.53 9.12 3.72 143.86
## 2 I_2 300.24 5.75 2.35 143.86
## 3 I_3 446.67 7.36 3.00 417.25
## 4 I_4 205.03 1.78 1.03 201.10
## 5 I_5 102.47 3.88 2.24 201.10#export to csv
write.csv(metadata(summary_minimal)$dataframe_summary_2, file="filename.csv")Entry 8, dataframe_summary_events, contains all estimated transcriptional events. Events always appear between two transcript fragments.
# all estimated events
metadata(summary_minimal)$dataframe_summary_events## event p_value p_adjusted FC_HL FC_intensity FC_HL_adapted
## 1 iTSS_I NA NA NA NA NA
## 2 Termination NA NA NA NA 0.99
## 3 iTSS_II NA NA NA NA 1.97
## 4 iTSS_II NA NA NA NA 0.99
## 5 Int_event NA NA NA 0.98 1.97
## 6 Int_event NA NA NA 0.57 0.99
## 7 Int_event NA NA NA -1.00 0.99
## 8 HL_event 2.68e-10 4.02e-10 0.98 NA NA
## 9 HL_event 1.07e-11 3.21e-11 -0.02 NA NA
## 10 velocity 1.91e-04 1.91e-04 NA NA NA
## FC_HL_FC_intensity event_position velocity_ratio feature_type gene
## 1 NA 625 NA CDS thrA
## 2 0.50 1026 NA
## 3 1.00 325 NA
## 4 1.51 625 NA CDS thrA
## 5 NA 325 NA
## 6 NA 625 NA CDS thrA
## 7 NA 1026 NA
## 8 NA 325 NA
## 9 NA 625 NA CDS thrA
## 10 NA 625 2.9 CDS thrA
## locus_tag strand TU segment_1 segment_2
## 1 BW25113_RS00010 + TU_1 S_1|TU_1|D_1 S_1|TU_1|D_2
## 2 - TU_2 S_2|TU_2|D_3|Dc_4|I_4 S_2|TU_2|D_3|Dc_4|I_5
## 3 + TU_1 S_1|TU_1|D_1|Dc_1|I_1 S_1|TU_1|D_1|Dc_2|I_2
## 4 BW25113_RS00010 + TU_1 S_1|TU_1|D_1|Dc_2|I_2 S_1|TU_1|D_1|Dc_3|I_3
## 5 + TU_1 S_1|TU_1|D_1|Dc_1|I_1 S_1|TU_1|D_1|Dc_1|I_2
## 6 BW25113_RS00010 + TU_1 S_1|TU_1|D_1|Dc_2|I_2 S_1|TU_1|D_1|Dc_2|I_3
## 7 - TU_2 S_2|TU_2|D_3|Dc_4|I_4 S_2|TU_2|D_3|Dc_4|I_5
## 8 + TU_1 S_1|TU_1|D_1|Dc_1 S_1|TU_1|D_1|Dc_2
## 9 BW25113_RS00010 + TU_1 S_1|TU_1|D_1|Dc_2 S_1|TU_1|D_1|Dc_3
## 10 BW25113_RS00010 + TU_1 S_1|TU_1|D_1 S_1|TU_1|D_2
## event_duration gap_fragments features
## 1 -1.27 50 2
## 2 NA 50 3
## 3 NA 50 4
## 4 NA 50 4
## 5 NA 50 2
## 6 NA 50 2
## 7 NA 50 2
## 8 NA 50 2
## 9 NA 50 2
## 10 NA 50 2#export to csv
write.csv(metadata(summary_minimal)$dataframe_summary_events, file="filename.csv")
Changes in the linear increase of the delay indicate a potential pausing site if there is a sudden delay increase (Figure 3A), a potential internal starting site iTSS_I if there is a sudden decrease in the delay (Figure 3B) and a velocity change of the RNA polymerase if there is a slope change (Figure 3C). The events are statistically evaluated by Ancova (apply_ancova) or a t-test (apply_Ttest_delay).
A fragment border between halflife segments (HL_event) which belong to the same transcriptional unit might indicate a processing site (Figure 3D) and a fragment border between intensity fragments (Int_event) (Figure 3E) can indicate a processing site (Figure 3F), a new transcriptional start site (iTSS_II) (Figure 3G) or an partial termination (Figure 3H), depending on the respective intensity foldchanges and the halflife foldchanges.
Each event is described by is type, its p-Value and adjusted p-Value, the foldchange or event duration, the estimated event position, a mapping to existing annotations and the IDs of the two bordering fragments.
Figure 3: Transcriptional events
The entries 9 to 11 contain specific subsets of events, i.e they are subsets of dataframe_summary_events.
4. Rifampicin relievable termination - TI instancesEntry 12, dataframe_summary_TI, contains the identified instances of Rifampicin relievable termination, with termination factor, position and mapped annotation. TI_fragments are investigated independent of the delay/decay/intensity fragment hierarchy. A clear TI event should consist of two segments; a pre termination segment with a termination factor of ~0 and a post termination segment with a termination factor of >0.
#
metadata(summary_minimal)$dataframe_summary_TI## event TI_fragment TI_termination_factor p_value p_adjusted feature_type
## 1 TI TI_1:TI_2 0|0.51 2.05e-05 2.05e-05 NA|NA
## gene locus_tag strand TU features event_position position_1 position_2
## 1 NA|NA NA|NA - TU_2 2 1026 1151 901#export to csv
write.csv(metadata(summary_minimal)$dataframe_summary_TI, file="filename.csv")All fits and results for the individual probes or bins are also added as additional columns to the rowRanges of the object. The data can be exported to an .csv file.
#the first 5 rows and 10/45 colums of the final rowRanges
rowRanges(summary_minimal)[1:5,1:10]## GRanges object with 5 ranges and 10 metadata columns:
## seqnames ranges strand | position ID FLT intensity
## <Rle> <IRanges> <Rle> | <numeric> <integer> <numeric> <numeric>
## [1] chr 1-50 + | 50 1 0 138.552
## [2] chr 51-100 + | 100 2 0 146.886
## [3] chr 101-150 + | 150 3 0 152.349
## [4] chr 151-200 + | 200 4 0 163.387
## [5] chr 201-250 + | 250 5 0 149.006
## probe_TI flag position_segment delay half_life
## <numeric> <character> <character> <numeric> <numeric>
## [1] -1 _ABG_ S_1 0.0833902 1.56869
## [2] -1 _ABG_ S_1 0.1737020 1.54311
## [3] -1 _ABG_ S_1 0.5035339 1.52367
## [4] -1 _ABG_ S_1 0.7566749 1.53506
## [5] -1 _ABG_ S_1 0.9972509 1.49575
## TI_termination_factor
## <numeric>
## [1] NA
## [2] NA
## [3] NA
## [4] NA
## [5] NA
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genome#export to csv
write.csv(rowRanges(summary_minimal), file="filename.csv")Figure 4: Whole genome visualization
Example visualization of an Rifampicin microarray experiment from Synechocystis PCC6803. A segment of the forward strand with its GenBank annotation is shown. The first track shows the delay of the onset of the decay for the individual probes. The delay should be linearly increasing for continuous transcripts, which are clustered by dynamic programming and indicated by matching colors and a trendline. A sudden delay increase between two segments indicates a transcription polymerase pausing site (PS), while a sudden decrease indicates a new (internal) transcriptional start site (iTSS). The slope of the delay segment allows to estimate the speed of the RNA Polymerase. Changes in the velocity are indicated by a âVâ. The second track shows the fitted half-life of the probes and the clustered half-life segments. If two segments within the same transcriptional unit have different half-life (HL) a processing/stabilization site for one or the other segment can be assumed. The third track shows the intensity and the intensity segments at timepoint 0 (before Rifampicin addition). If two segments within the same transcriptional unit have different intensities this (FC) this could be either due to a partial termination (Ter) or a new transcriptional start site (NS). Significant events are assigned with an â*â
It is recommended to check the fit after running rifi_fit. If more than 30 % of the fits show a misfit, you may consider to check:
Raw data
Background
You may need to check your penalties if the last visualization shows:
1. A high frequency of considerable long segmentsFigure 5: Long segments
In this case you may need to double check your data either the mini-segments are artifact of rifi or the data. The example below shows rather an artifact of the data since the segmentation is hierarchical. The half-life and intensity segments are rather short because of the delay segmentation.
Figure 6: Mini segments
Figure 7: High values
Absence of events in case you run big data.
Absence of outliers.
rifi
We hope you enjoy using rifi. Please cite the package in case of usage.
## To cite package 'rifi' in publications use:
##
## Youssar L, Wanney W, Georg J (2025). _rifi: 'rifi' analyses data from
## rifampicin time series created by microarray or RNAseq_.
## doi:10.18129/B9.bioc.rifi <https://doi.org/10.18129/B9.bioc.rifi>, R
## package version 1.13.1, <https://bioconductor.org/packages/rifi>.
##
## A BibTeX entry for LaTeX users is
##
## @Manual{,
## title = {rifi: 'rifi' analyses data from rifampicin time series created by microarray or RNAseq},
## author = {Loubna Youssar and Walja Wanney and Jens Georg},
## year = {2025},
## note = {R package version 1.13.1},
## url = {https://bioconductor.org/packages/rifi},
## doi = {10.18129/B9.bioc.rifi},
## }The first step in the analysis of rifampicin time series data with rifi is preprocessing. The three major steps are filtration (to get rid of artifacts or background datapoints), fitting the data to the correct model (standard model or TI model) and merge the coefficients and the input data frame into one structure for the downstream process. The steps can be performed with five low level functions or the wrapper function rifi_preprocess (see section [rifi_preprocess] (#rifi_preprocess)). The following paragraphs describe the sub-steps of rifi_preprocess. To directly read about the application or rifi_preprocess jump to section [rifi_preprocess] (#rifi_preprocess).
The Input Data Frame is a SummarizedExperiment (SE) input format. SE structure as known includes the colData (description of each sample), assays (probes/bins intensity measurements), rowRanges(coordinates of probes/bin including probe identifier and positions). Rifi package includes two example SE: E.coli data from RNAseq (data with replicates, input_df) (Dar and Sorek 2018) and Synechocystis PCC 6803 data from microarrays (data with averaged replicates, see. âinput_dfâ). E.coli is the input for this tutorial. In case of the E.coli RNAseq dataset the intensities are binned for every 50 nt. We recommend to use a similar strategy if working with RNAseq data. The binning is not performed by ârifiâ and needs to be done beforehand. Data from microarrays need to be checked carefully for background. We recommend to run the workflow with low background e.g ~ 30 till rifi_fit and check the probes fit to get an idea about the background level. The value estimated is used to rerun rifi workflow.
## [1] "<font color='red'>example of E.coli data from RNA-seq</font>"## [1] "assay e.coli"## 0 1 10 15 2 20 3 4 5 6 8 0 1 10 15 2 20 3 4 5 6 8 0 1 10 15 2 20 3 4 5 6
## 17920 0 0 0 0 0 NA 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 17921 0 0 0 0 0 NA 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 17922 0 0 0 0 0 NA 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 17923 0 0 0 0 0 NA 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 17924 0 0 0 0 0 NA 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 17925 0 0 0 0 0 NA 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 8
## 17920 0
## 17921 0
## 17922 0
## 17923 0
## 17924 0
## 17925 0## [1] "rowRanges e.coli"## GRanges object with 6 ranges and 0 metadata columns:
## seqnames ranges strand
## <Rle> <IRanges> <Rle>
## 17920 chr 895951-896000 +
## 17921 chr 896001-896050 +
## 17922 chr 896051-896100 +
## 17923 chr 896101-896150 +
## 17924 chr 896151-896200 +
## 17925 chr 896201-896250 +
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genome## [1] "colData e.coli"## DataFrame with 33 rows and 2 columns
## timepoint replicate
## <numeric> <numeric>
## 0 0 1
## 1 1 1
## 10 10 1
## 15 15 1
## 2 2 1
## ... ... ...
## 3 3 3
## 4 4 3
## 5 5 3
## 6 6 3
## 8 8 3## [1] "example of Synechocystis data from microarrays"## [1] "assay synechocystis"## 0 2 4 8 16 32 64
## [1,] 1367.080 1116.401 864.0274 843.1331 829.7530 845.8492 811.0059
## [2,] 3316.336 2868.275 2324.4041 2524.7296 2273.0208 2346.8724 2411.1342
## [3,] 1112.101 939.558 834.7110 799.2554 800.8527 768.8366 788.5206
## [4,] 2012.294 1643.996 1023.7357 922.3281 1086.0212 1790.5634 3612.8782
## [5,] 1627.467 1392.391 997.9808 1007.3211 1071.9016 1016.9927 997.1751
## [6,] 1890.722 1830.202 902.2958 868.9673 840.6043 849.9464 887.8550## [1] "rowRanges synechocystis"## GRanges object with 6 ranges and 0 metadata columns:
## seqnames ranges strand
## <Rle> <IRanges> <Rle>
## [1] chr 22-67 +
## [2] chr 107-153 +
## [3] chr 145-199 +
## [4] chr 207-259 +
## [5] chr 260-320 +
## [6] chr 353-400 +
## -------
## seqinfo: 1 sequence from an unspecified genome; no seqlengths## [1] "colData synechocystis"## DataFrame with 7 rows and 2 columns
## timepoint replicate
## <numeric> <numeric>
## 0 0 1
## 2 2 1
## 4 4 1
## 8 8 1
## 16 16 1
## 32 32 1
## 64 64 1The SE needs to comply to the following rules:
check_input
Not complying to any of the rules will result in errors and/or warnings by running âcheck_inputâ:
As our standard input contains probes that are not expressed and thus have a relative intensity of 0 at time point 0, in our example check_input gives a warning on which IDs have been removed, but the output can be safely used.
The result contains the processed input data frame.
## Number of replicates: 3## Timepoints: 0 1 2 3 4 5 6 8 10 15 20## No IDs were given in the input. Default IDs were assigned.Filtration_Below_Background
At this point, a custom filtration function can be applied to remove replicates that are below the background.
This is especially useful for microarrays data. We supply a function filtration_below_backg that filters for background but retains replicates that show a promising pattern even when they are below background. When a different custom function is applied within rifi_preprocess the input variable x must refer to the intensity vector over all timepoints. The output must be a character string containing FLT for all replicates that should be filtered. Additional arguments must be hard coded or given as default value, as additional arguments can not be passed into rifi_preprocess.
Application outside of rifi_preprocess can modify the âfiltrationâ column in the input dataframe in any way, as that rows with replicates that should be filtered contain the character string FLT. The filtrated column would contain either(âFLTâ, âFLTâ, âFLT_your_text", NA, "â, âpassedâ)
make_df
make_df calculates the means of all replicates, excluding the filtered replicates. Optionally, probes or bins, where all replicates are filtered can be removed, when rm_FLT is set to TRUE (default is FALSE). The column probe_TI is added to rowRanges for a later step, in which it is decided which probes are fitted with the TI model (see finding_TI).
For microarray data, the probes with intensity of the latest time point does not fall below the background are considered stables mRNA. Those probes are marked in the flag column with the tag âABGâ(âabove backgroundâ). âbgâ is the relative intensity threshold of the background. For RNAseq data the âABGâ sub-model is used and bg is set to 0, so that all probes are flagged as âABGâ. The flag column is used to distribute different probes to the different fitting models (see 7. finding_TI) The output of âmake_dfâ is the probe based SE probe_df. At this stage, The rowRanges contain the columns ID, position, and intensity (of time point 0) as mean of all replicates from assay and the columns probe_TI and flag. For our tutorial bg is set to 0, because its RNAseq data, and rm_FLT is TRUE to remove ID 18558 that we tagged with âFLTâ,"_" and "_FLT_your_text".
probe <-
make_df(
inp = probe,
cores = 2,
bg = 0,
rm_FLT = TRUE
)
head(rowRanges(probe))## GRanges object with 4 ranges and 6 metadata columns:
## seqnames ranges strand | position ID FLT intensity
## <Rle> <IRanges> <Rle> | <integer> <character> <numeric> <numeric>
## [1] chr 951-1000 + | 1000 1 0 296.671
## [2] chr 1951-2000 + | 2000 2 0 297.339
## [3] chr 2951-3000 + | 3000 3 0 308.067
## [4] chr 3951-4000 + | 4000 4 0 303.609
## probe_TI flag
## <numeric> <character>
## [1] 1 _ABG_
## [2] -1 _ABG_
## [3] 1 _ABG_
## [4] -1 _ABG_
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genomesegment_pos
For the segmentation into position-segments by regions without significant sequencing depth, segment_pos is called. This step is needed to enhance performance of the program, since large position segments increase the runtime.
The size of the regions without significant sequencing depth (aka positions not present in the rowRanges) or absence of probes is determined by the argument dist (default is 300). Lower numbers create more, but smaller position segments. Position segments are strand specific.
probe <- segment_pos(inp = probe, dista = 300)
head(rowRanges(probe))## GRanges object with 4 ranges and 7 metadata columns:
## seqnames ranges strand | position ID FLT intensity
## <Rle> <IRanges> <Rle> | <integer> <character> <numeric> <numeric>
## [1] chr 951-1000 + | 1000 1 0 296.671
## [2] chr 1951-2000 + | 2000 2 0 297.339
## [3] chr 2951-3000 + | 3000 3 0 308.067
## [4] chr 3951-4000 + | 4000 4 0 303.609
## probe_TI flag position_segment
## <numeric> <character> <character>
## [1] 1 _ABG_ S_1
## [2] -1 _ABG_ S_2
## [3] 1 _ABG_ S_3
## [4] -1 _ABG_ S_4
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genomefinding_PDD
Under the assumption of the standard model the RNA concentration should be the same over the whole length of the transcript, if the decay constant is unchanged and no partial premature termination appears. A linear or exponential intensity decline indicates regions were something interesting happens. This could be in theory a decay by the post transcription decay model (PDD) (Chen et al. 2015), which is characterized by a linear decrease of intensity by position. More likely is a fixed termination probability after each elongation step (exponential decrease), e.g. resulting from the collision mode of transcriptional interference. finding_PDD flags potential candidates for post transcription decay with âPDDâ. finding_PDD uses âscore_fun_linearâ function to make groups by the difference to the slope. The rowRanges contains ID, intensity, position and position_segment columns. finding_PDD needs additional parameters as pen, pen_out and thrsh
#Due to increased run time, this example is not evaluated in the vignette
probe <-
finding_PDD(
inp = probe,
cores = 2,
pen = 2,
pen_out = 2,
thrsh = 0.001
)
head(rowRanges(probe))## GRanges object with 4 ranges and 7 metadata columns:
## seqnames ranges strand | position ID FLT intensity
## <Rle> <IRanges> <Rle> | <integer> <character> <numeric> <numeric>
## [1] chr 951-1000 + | 1000 1 0 296.671
## [2] chr 1951-2000 + | 2000 2 0 297.339
## [3] chr 2951-3000 + | 3000 3 0 308.067
## [4] chr 3951-4000 + | 4000 4 0 303.609
## probe_TI flag position_segment
## <numeric> <character> <character>
## [1] 1 _ABG_ S_1
## [2] -1 _ABG_ S_2
## [3] 1 _ABG_ S_3
## [4] -1 _ABG_ S_4
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genomefinding_TI
As described in the introduction we want to indentify regions with a rifampicin relieved termination. Transcription interference (TI) is one explanation of the rifampicin relieved termination. Here TI is used as a synonym for rifampicin relieved termination. finding_TI identifies regions of potential transcription interference (TI). finding_TI uses score_fun_ave to make groups by the mean of âprobe_TIâ. The identified regions and a defined number of probes before the potential TI event are flagged with âTIâ. The identification is based on the probe_TI column, which is a report for each probe, whether a later time point is higher in relative intensity than the first time point. The rowRanges needs the columns ID, intensity, position and position_segment. finding_TI needs additional parameters as pen, thrsh and add.
#Due to increased run time, this example is not evaluated in the vignette
probe <-
finding_TI(
inp = probe,
cores = 2,
pen = 10,
thrsh = 0.001
)
head(rowRanges(probe))## GRanges object with 4 ranges and 7 metadata columns:
## seqnames ranges strand | position ID FLT intensity
## <Rle> <IRanges> <Rle> | <integer> <character> <numeric> <numeric>
## [1] chr 951-1000 + | 1000 1 0 296.671
## [2] chr 1951-2000 + | 2000 2 0 297.339
## [3] chr 2951-3000 + | 3000 3 0 308.067
## [4] chr 3951-4000 + | 4000 4 0 303.609
## probe_TI flag position_segment
## <numeric> <character> <character>
## [1] 1 _ABG_TI_ S_1
## [2] -1 _ABG_ S_2
## [3] 1 _ABG_TI_ S_3
## [4] -1 _ABG_ S_4
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genomerifi_preprocess
All preprocessing steps can be run with rifi_preprocess at once. This section will focus on all possible arguments that can be passed to the function.
#From here on the examples are shown on minimal examples.
#Two bigger data sets can be used to run the example as well.
preprocess_minimal <-
rifi_preprocess(
inp = probe,
cores = 2,
bg = 0,
rm_FLT = TRUE,
thrsh_check = 10,
dista = 300,
run_PDD = TRUE
)## running check_input...## Number of replicates: 3## Timepoints: 0 1 2 3 4 5 6 8 10 15 20## running make_df...## running segment_pos...## running finding_PDD...## running finding_TI...head(rowRanges(preprocess_minimal))## GRanges object with 4 ranges and 7 metadata columns:
## seqnames ranges strand | position ID FLT intensity
## <Rle> <IRanges> <Rle> | <integer> <character> <numeric> <numeric>
## [1] chr 951-1000 + | 1000 1 0 296.671
## [2] chr 1951-2000 + | 2000 2 0 297.339
## [3] chr 2951-3000 + | 3000 3 0 308.067
## [4] chr 3951-4000 + | 4000 4 0 303.609
## probe_TI flag position_segment
## <numeric> <character> <character>
## [1] 1 _ABG_TI_ S_1
## [2] -1 _ABG_ S_2
## [3] 1 _ABG_TI_ S_3
## [4] -1 _ABG_ S_4
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genomerifi_fit wraps all fitting steps. The fitting functions fit the intensities against the time series data. The first uses nls2_fit function to estimate delay, half-life, first time point intensity and background intensity. The second uses TI_fit function to estimate delay and half-life additionally to the TI-termination-factor.
The function used are:
nls2_fitTI_fitplot_nls2plot_singleProbe_function## running nls2_fit...## running TI_fit...#Output
data(fit_e_coli)
head(rowRanges(fit_e_coli))## GRanges object with 6 ranges and 10 metadata columns:
## seqnames ranges strand | position ID FLT
## <Rle> <IRanges> <Rle> | <integer> <character> <numeric>
## 18558 chr 927851-927900 + | 927900 82 0
## 18559 chr 927901-927950 + | 927950 83 0
## 18560 chr 927951-928000 + | 928000 84 0
## 18561 chr 928001-928050 + | 928050 85 0
## 18562 chr 928051-928100 + | 928100 86 0
## 18563 chr 928101-928150 + | 928150 87 0
## intensity probe_TI flag position_segment delay half_life
## <numeric> <numeric> <character> <character> <numeric> <numeric>
## 18558 42.4409 -1 _ABG_ S_1 0.001 2.25009
## 18559 140.3354 -1 _ABG_ S_1 0.001 2.06593
## 18560 103.5798 -1 _ABG_ S_1 0.001 2.11729
## 18561 175.4605 -1 _ABG_ S_1 0.001 2.32701
## 18562 143.4705 -1 _ABG_ S_1 0.001 2.93859
## 18563 109.2939 -1 _ABG_ S_1 0.001 3.16701
## TI_termination_factor
## <numeric>
## 18558 NA
## 18559 NA
## 18560 NA
## 18561 NA
## 18562 NA
## 18563 NA
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genomenls2_fit
nls2_fit function uses nls2 function to fit a probe or bin using intensities from different time point. nls2 is able to use different starting values using expand grid and select the best fit. The SE assays containing intensity of all timeserie and ID intensity, position, probe_TI, flag and position_segment columns from rowRanges are used as inputs (see below Table_2). nls2_fit function has two different models, one includes the background as parameter and estimates decay subtracting it. The other excludes the background coefficient and is applied for probes flagged with ABG. All probes flagged with FLT are not fitted as they are below background. Finally probes flagged with TI are fitted with TI model. The output data is an extension of SE metaData, delay and half-life coefficients are added (see below âhead(probe)â).
nls2_fit(inp = preprocess_minimal,
cores = 1,
decay = seq(.08, 0.11, by = .02),
delay = seq(0, 10, by = .1),
k = seq(0.1, 1, 0.2),
bg = 0.2
)Table_2 <- rowRanges(preprocess_minimal)
head(Table_2)## GRanges object with 4 ranges and 7 metadata columns:
## seqnames ranges strand | position ID FLT intensity
## <Rle> <IRanges> <Rle> | <integer> <character> <numeric> <numeric>
## [1] chr 951-1000 + | 1000 1 0 296.671
## [2] chr 1951-2000 + | 2000 2 0 297.339
## [3] chr 2951-3000 + | 3000 3 0 308.067
## [4] chr 3951-4000 + | 4000 4 0 303.609
## probe_TI flag position_segment
## <numeric> <character> <character>
## [1] 1 _TI_ S_1
## [2] -1 _ S_2
## [3] 1 _ABG_TI_ S_3
## [4] -1 _ABG_ S_4
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genomeprobe <- metadata(fit_minimal)[[3]]
head(probe)## ID position delay decay k bg
## delay 2 2000 3.982766 0.65368274 0.42096687 0.3241019
## delay1 4 4000 2.628328 0.04253037 0.04041971 0.0000000TI_fit
TI_fit estimates transcription interference and termination factor using nls function for probe or bin flagged as TI. It estimates the transcription interference level (referred later to TI) as well as the transcription factor fitting the probes/bins with nls function looping into several starting values. To determine TI and termination factor, TI_fit function is applied to the flagged probes and to the probes localized 200 nucleotides upstream. Before applying TI_fit function, some probes/bins are filtered out if they are below the background using generic_filter_BG. The model loops into a dataframe containing sequences of starting values and the coefficients are extracted from the fit with the lowest residuals. When many residuals are equal to 0, the lowest residual can not be determined and the coefficients extracted could be wrong. Therefore, a second filter was developed. First a loop is applied into all starting values, nls objects are collected in tmp_v vector and the corresponding residuals in tmp_r vector. The residuals are sorted and those non equal to 0 are collected into a vector. If the first values are not equal to 0, the best 20% of the list are collected in tmp_r_min vector and the minimum termination factor is selected. On the other hand residuals between 0 to 20% of the values collected in tmp_r_min vector are gathered. The minimum termination factor coefficient is determined and stored. The coefficients are gathered in res vector and saved as an object. The output data are additional columns in SE rowRanges named delay, half-life and TI_termination_factor (see. âhead(probe)â).
TI_fit(inp = preprocess_minimal,
cores = 1,
restr = 0.2,
k = seq(0, 1, by = 0.5),
decay = c(0.05, 0.1, 0.2, 0.5, 0.6),
ti = seq(0, 1, by = 0.5),
ti_delay = seq(0, 2, by = 0.5),
rest_delay = seq(0, 2, by = 0.5),
bg = 0
)probe <- metadata(fit_minimal)[[4]]
head(probe)## ID position ti_delay rest_delay decay k ti
## ti_delay 1 1000 0.9257506 2.465721 0.71438975 0.5894164 0.24540387
## ti_delay1 3 3000 0.6660732 1.432176 0.05845456 0.1271130 0.08344505
## bg
## ti_delay 0.2370688
## ti_delay1 0.0000000plot_nls2
plot_nls2 plots the fit from nls2 with the corresponding coefficients, delay and decay. delay is indicated on the x-axis and half_life is calculated from ln2/decay. The output is shown on nls2Plot figure.
plot_nls2_function(inp = probe_df)Figure 8: Standard fit with nls2
plot_nls2 also plots the fit from TI with the corresponding coefficients, delay, ti_delay, half_life, TI_termination_factor and TI. Additional parameters are included on the legend a, the output is shown on TIPlot figure.
plot_nls2_function(inp = probe_df)Figure 9: TI model fit
ârifiâ uses dynamic programming to combine probes/bins with equal properties in the extracted values into segments (called fragmentation in ârifiâ). The penalties define the specificity and sensitivity of the fragmentation. Higher penalties will result in less segments, i.e. a lower sensitivity but a higher specificity and vice versa. For convenience ârifiâ provides an automatic method which tries to maximize the correct segment splits and to minimize the wrong splits using statistics. The result can be best investigated in the final visualization. If needed the penalties can be manually adapted.
rifi_penalties wraps all penalty steps, wraps the functions: make_pen and viz_pen_obj. For use of this wrapper jump to rifi_penalties
make_pen
make_pen calls one of four available penalty functions to automatically assign penalties for the dynamic programming. Four functions are called:
fragment_delay_pen
fragment_HL_pen
fragment_inty_pen
fragment_TI_pen
These functions return the amount of statistically correct and statistically wrong splits at a specific pair of penalties. âmake_penâ iterates over many penalty pairs and picks the most suitable pair based on the difference between wrong and correct splits. The sample size, penalty range and resolution as well as the number of cycles can be customized. The primary start parameters create a matrix with n = rez_pen rows and n = rez_pen_out columns with values between sta_pen/sta_pen_out and end_pen/end_pen_out. The best penalty pair is picked. If dept is bigger than 1 the same process is repeated with a new matrix of the same size based on the result of the previous cycle. Only position segments with length within the sample size range are considered for the penalties to increase run time. ALso, outlier penalties cannot be smaller than 40% of the respective penalty. make_pen returns a penalty object (list of 4 objects) the first being the logbook.
data(fit_minimal)
pen_delay <-
make_pen(
probe = fit_minimal,
FUN = rifi:::fragment_delay_pen,
cores = 2,
logs = logbook,
dpt = 1,
smpl_min = 0,
smpl_max = 18,
sta_pen = 0.5,
end_pen = 4.5,
rez_pen = 9,
sta_pen_out = 0.5,
end_pen_out = 3.5,
rez_pen_out = 7
)
pen_HL <- make_pen(
probe = fit_minimal,
FUN = rifi:::fragment_HL_pen,
cores = 2,
logs = logbook,
dpt = 1,
smpl_min = 0,
smpl_max = 18,
sta_pen = 0.5,
end_pen = 4.5,
rez_pen = 9,
sta_pen_out = 0.5,
end_pen_out = 3.5,
rez_pen_out = 7
)
pen_inty <-
make_pen(
probe = fit_minimal,
FUN = rifi:::fragment_inty_pen,
cores = 2,
logs = logbook,
dpt = 1,
smpl_min = 0,
smpl_max = 18,
sta_pen = 0.5,
end_pen = 4.5,
rez_pen = 9,
sta_pen_out = 0.5,
end_pen_out = 3.5,
rez_pen_out = 7
)
pen_TI <- make_pen(
probe = fit_minimal,
FUN = rifi:::fragment_TI_pen,
cores = 2,
logs = logbook,
dpt = 1,
smpl_min = 0,
smpl_max = 18,
sta_pen = 0.5,
end_pen = 4.5,
rez_pen = 9,
sta_pen_out = 0.5,
end_pen_out = 3.5,
rez_pen_out = 7
)fragment_delay_pen
fragment_delay_pen is called by make_pen function to automatically assign penalties for the dynamic programming of delay fragment. The function used for fragment_delay_pen is score_fun_linear. score_fun_linear scores the values of y on how close they are to a linear fit, for more details check functions_scoring.r.
fragment_HL_pen
fragment_HL_pen is called by make_pen function to automatically assign penalties for the dynamic programming of half-life fragments. The function used for fragment_HL_pen is score_fun_ave. score_fun_ave scores the values of y on how close they are to the mean, for more details check âfunctions_scoring.râ.
fragment_inty_pen
fragment_inty_pen is called by make_pen function to automatically assign penalties for the dynamic programming of intensity fragments. The function used for fragment_inty_pen is score_fun_ave. score_fun_ave scores the values of y on how close they are to the mean, for more details check âfunctions_scoring.râ.
fragment_TI_pen
fragment_TI_pen is called by make_pen function to automatically assign penalties for the dynamic programming of TI fragments. The function used for fragment_TI_pen is score_fun_ave. score_fun_ave scores the values of y on how close they are to the mean, for more details check âfunctions_scoring.râ.
viz_pen_obj
viz_pen_obj an optional visualization of any penalty object created by make_pen and can be customized to show only the n = top_i top results. Results are ranked from worst to best for correct-wrong ratio, and color coded by penalty, while the outlier-penalty is given as a number for each point. Red and green dots represent the wrong and correct splits respectively.
viz_pen_obj(obj = pen_delay, top_i = 10)Figure 10: penalty plot: The graphic shows penalties ranked by the correct fits subtracted by the wrong fits
Each penalty corresponds to a color given in the legend. Red dots represent wrong splits, green dots represent correct splits. In the zoomed window (bottom) numbers above the dots represent the outlier-penalty.
rifi_fragmentation conveniently wraps all fragmentation steps, wraps the functions: fragment_delay, fragment_HL, fragment_inty, TUgether and fragment_TI.
The functions called are:
fragment_delayfragment_HLfragment_intyfragment_TITUgether## running fragment_delay...## running fragment_HL...## running fragment_inty...## running TUgether...## running fragment_TI...data(fragmentation_e_coli)
head(rowRanges(fragmentation_e_coli))## GRanges object with 6 ranges and 22 metadata columns:
## seqnames ranges strand | position ID FLT
## <Rle> <IRanges> <Rle> | <integer> <character> <numeric>
## 18558 chr 927851-927900 + | 927900 82 0
## 18559 chr 927901-927950 + | 927950 83 0
## 18560 chr 927951-928000 + | 928000 84 0
## 18561 chr 928001-928050 + | 928050 85 0
## 18562 chr 928051-928100 + | 928100 86 0
## 18563 chr 928101-928150 + | 928150 87 0
## intensity probe_TI flag position_segment delay half_life
## <numeric> <numeric> <character> <character> <numeric> <numeric>
## 18558 42.4409 -1 _ABG_ S_1 0.001 2.25009
## 18559 140.3354 -1 _ABG_ S_1 0.001 2.06593
## 18560 103.5798 -1 _ABG_ S_1 0.001 2.11729
## 18561 175.4605 -1 _ABG_ S_1 0.001 2.32701
## 18562 143.4705 -1 _ABG_ S_1 0.001 2.93859
## 18563 109.2939 -1 _ABG_ S_1 0.001 3.16701
## TI_termination_factor delay_fragment velocity_fragment intercept
## <numeric> <character> <numeric> <numeric>
## 18558 NA D_1 20699.5 -44.8333
## 18559 NA D_1 20699.5 -44.8333
## 18560 NA D_1 20699.5 -44.8333
## 18561 NA D_1 20699.5 -44.8333
## 18562 NA D_1 20699.5 -44.8333
## 18563 NA D_1 20699.5 -44.8333
## slope HL_fragment HL_mean_fragment intensity_fragment
## <numeric> <character> <numeric> <character>
## 18558 4.83103e-05 Dc_1 2.19008 I_1
## 18559 4.83103e-05 Dc_1 2.19008 I_1
## 18560 4.83103e-05 Dc_1 2.19008 I_1
## 18561 4.83103e-05 Dc_1 2.19008 I_1
## 18562 4.83103e-05 Dc_2 3.01682 I_2
## 18563 4.83103e-05 Dc_2 3.01682 I_2
## intensity_mean_fragment TU TI_termination_fragment
## <numeric> <character> <character>
## 18558 102.000 TU_1 <NA>
## 18559 102.000 TU_1 <NA>
## 18560 102.000 TU_1 <NA>
## 18561 102.000 TU_1 <NA>
## 18562 77.528 TU_1 <NA>
## 18563 77.528 TU_1 <NA>
## TI_mean_termination_factor seg_ID
## <numeric> <character>
## 18558 NA S_1|TU_1|D_1|Dc_1|I_1
## 18559 NA S_1|TU_1|D_1|Dc_1|I_1
## 18560 NA S_1|TU_1|D_1|Dc_1|I_1
## 18561 NA S_1|TU_1|D_1|Dc_1|I_1
## 18562 NA S_1|TU_1|D_1|Dc_2|I_2
## 18563 NA S_1|TU_1|D_1|Dc_2|I_2
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genomefragment_delay
fragment_delay makes delay_fragments based on position_segments and assigns all gathered information to the probe based data frame. The columns âdelay_fragmentâ, âvelocity_fragmentâ, âinterceptâ and âslopeâ are added. fragment_delay makes delay_fragments, assigns slopes, velocity (1/slope) and intercepts for the TU calculation.
The function used are:
score_fun_linear
score_fun_linear is the score function used by dynamic programming for delay fragmentation, for more details, see below.
data(fragmentation_minimal)
data(penalties_minimal)
probe_df <- fragment_delay(
inp = fragmentation_minimal,
cores = 2,
pen = penalties_minimal["delay_penalty"],
pen_out = penalties_minimal["delay_outlier_penalty"]
)
head(rowRanges(probe_df))fragment_HL
fragment_HL performs the half_life fragmentation based on delay_fragments and assigns all gathered information to the probe based data frame. The columns âHL_fragmentâ and âHL_mean_fragmentâ are added to rowRanges(SE). fragment_HL makes half-life_fragments and assigns the mean of each fragment.
The function used is:
score_fun_ave
score_fun_ave is the score function used by dynamic programming for half-life fragmentation, for more details, see below.
data(fragmentation_minimal)
data(penalties_minimal)
probe_df <- fragment_HL(
probe = fragmentation_minimal,
cores = 2,
pen = penalties_minimal["half_life_penalty"],
pen_out = penalties_minimal["half_life_outlier_penalty"]
)
head(rowRanges(probe_df))fragment_inty
fragment_inty performs the intensity fragmentation based on HL_fragments and assigns all gathered information to the probe based data frame. The columns âintensity_fragmentâ and âintensity_mean_fragmentâ are added rowRanges(SE). fragment_inty makes intensity_fragments and assigns the mean of each fragment.
The function used is:
score_fun_ave
score_fun_ave is the score function used by dynamic programming for intensity fragmentation, for more details, see below.
data(fragmentation_minimal)
data(penalties_minimal)
probe_df <- fragment_inty(
inp = fragmentation_minimal,
cores = 2,
pen = penalties_minimal["intensity_penalty"],
pen_out = penalties_minimal["intensity_outlier_penalty"]
)
head(rowRanges(probe_df))TUgether
TUgether combines delay fragments into TUs and adds a new column âTUâ to rowRanges(SE).
The function used is:
score_fun_increasing
score_fun_increasing is the score function used by dynamic programming for TUgether, for more details, see below.
data(fragmentation_minimal)
probe_df <- TUgether(inp = fragmentation_minimal, cores = 2, pen = -0.75)
head(rowRanges(probe_df))fragment_TI
fragment_TI performs the TI fragmentation based on TUs and assigns all gathered information to the probe based SE. The columns âTI_termination_fragmentâ and âTI_mean_termination_factorâ are added to rowRanges(SE). fragment_TI makes TI_fragments and assigns the mean of each fragment.
The function used are:
score_fun_ave
score_fun_ave is the score function used by dynamic programming for TI fragmentation, for more details, see below.
data(fragmentation_minimal)
data(penalties_minimal)
probe_df <- fragment_TI(
inp = fragmentation_minimal,
cores = 2,
pen = penalties_minimal["TI_penalty"],
pen_out = penalties_minimal["TI_outlier_penalty"]
)
head(rowRanges(probe_df))rifi_stats wraps all statistical prediction steps.
The function wrapped are:
predict_ps_itssapply_Ttest_delayapply_ancovaapply_event_positionapply_t_testfold_changeapply_manovaapply_t_test_tigff3_preprocessdata(fragmentation_minimal)
Path = gzfile(system.file("extdata", "gff_e_coli.gff3.gz", package = "rifi"))
stats_minimal <- rifi_stats(inp = fragmentation_minimal, dista = 300,
path = Path)## running predict_ps_itss...## running apply_Ttest_delay...## running apply_ancova...## running apply_event_position...## running apply_t_test...## running fold_change...## running apply_manova...## running apply_t_test_ti...## Warning in `[<-.factor`(structure(c(3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, :
## invalid factor level, NA generatedhead(rowRanges(stats_minimal))## GRanges object with 6 ranges and 45 metadata columns:
## seqnames ranges strand | position ID FLT intensity
## <Rle> <IRanges> <Rle> | <numeric> <integer> <numeric> <numeric>
## [1] chr 1-50 + | 50 1 0 138.552
## [2] chr 51-100 + | 100 2 0 146.886
## [3] chr 101-150 + | 150 3 0 152.349
## [4] chr 151-200 + | 200 4 0 163.387
## [5] chr 201-250 + | 250 5 0 149.006
## [6] chr 251-300 + | 300 6 0 160.369
## probe_TI flag position_segment delay half_life
## <numeric> <character> <character> <numeric> <numeric>
## [1] -1 _ABG_ S_1 0.0833902 1.56869
## [2] -1 _ABG_ S_1 0.1737020 1.54311
## [3] -1 _ABG_ S_1 0.5035339 1.52367
## [4] -1 _ABG_ S_1 0.7566749 1.53506
## [5] -1 _ABG_ S_1 0.9972509 1.49575
## [6] -1 _ABG_ S_1 1.2143562 1.57844
## TI_termination_factor delay_fragment velocity_fragment intercept
## <numeric> <character> <numeric> <numeric>
## [1] NA D_1 143.864 -0.504141
## [2] NA D_1 143.864 -0.504141
## [3] NA D_1 143.864 -0.504141
## [4] NA D_1 143.864 -0.504141
## [5] NA D_1 143.864 -0.504141
## [6] NA D_1 143.864 -0.504141
## slope HL_fragment HL_mean_fragment intensity_fragment
## <numeric> <character> <numeric> <character>
## [1] 0.006951 Dc_1 1.54079 I_1
## [2] 0.006951 Dc_1 1.54079 I_1
## [3] 0.006951 Dc_1 1.54079 I_1
## [4] 0.006951 Dc_1 1.54079 I_1
## [5] 0.006951 Dc_1 1.54079 I_1
## [6] 0.006951 Dc_1 1.54079 I_1
## intensity_mean_fragment TU TI_termination_fragment
## <numeric> <character> <character>
## [1] 151.529 TU_1 <NA>
## [2] 151.529 TU_1 <NA>
## [3] 151.529 TU_1 <NA>
## [4] 151.529 TU_1 <NA>
## [5] 151.529 TU_1 <NA>
## [6] 151.529 TU_1 <NA>
## TI_mean_termination_factor seg_ID pausing_site iTSS_I
## <numeric> <character> <character> <character>
## [1] NA S_1|TU_1|D_1|Dc_1|I_1 - -
## [2] NA S_1|TU_1|D_1|Dc_1|I_1 - -
## [3] NA S_1|TU_1|D_1|Dc_1|I_1 - -
## [4] NA S_1|TU_1|D_1|Dc_1|I_1 - -
## [5] NA S_1|TU_1|D_1|Dc_1|I_1 - -
## [6] NA S_1|TU_1|D_1|Dc_1|I_1 - -
## ps_ts_fragment event_duration event_ps_itss_p_value_Ttest p_value_slope
## <character> <numeric> <numeric> <numeric>
## [1] <NA> NA NA 0.000191393
## [2] <NA> NA NA 0.000191393
## [3] <NA> NA NA 0.000191393
## [4] <NA> NA NA 0.000191393
## [5] <NA> NA NA 0.000191393
## [6] <NA> NA NA 0.000191393
## delay_frg_slope velocity_ratio event_position FC_fragment_HL FC_HL
## <character> <numeric> <numeric> <character> <numeric>
## [1] D_1:D_2 2.90033 NA <NA> 0.980823
## [2] D_1:D_2 2.90033 NA <NA> 0.980823
## [3] D_1:D_2 2.90033 NA <NA> 0.980823
## [4] D_1:D_2 2.90033 NA <NA> 0.980823
## [5] D_1:D_2 2.90033 NA <NA> 0.980823
## [6] D_1:D_2 2.90033 NA <NA> 0.980823
## p_value_HL FC_fragment_intensity FC_intensity p_value_intensity
## <numeric> <character> <numeric> <numeric>
## [1] 5.19732e-14 <NA> 0.984576 2.68496e-10
## [2] 5.19732e-14 <NA> 0.984576 2.68496e-10
## [3] 5.19732e-14 <NA> 0.984576 2.68496e-10
## [4] 5.19732e-14 <NA> 0.984576 2.68496e-10
## [5] 5.19732e-14 <NA> 0.984576 2.68496e-10
## [6] 5.19732e-14 <NA> 0.984576 2.68496e-10
## FC_HL_intensity FC_HL_intensity_fragment FC_HL_adapted synthesis_ratio
## <numeric> <logical> <logical> <logical>
## [1] 0.00375293 <NA> <NA> <NA>
## [2] 0.00375293 <NA> <NA> <NA>
## [3] 0.00375293 <NA> <NA> <NA>
## [4] 0.00375293 <NA> <NA> <NA>
## [5] 0.00375293 <NA> <NA> <NA>
## [6] 0.00375293 <NA> <NA> <NA>
## synthesis_ratio_event p_value_Manova p_value_TI TI_fragments_p_value
## <logical> <logical> <numeric> <character>
## [1] <NA> <NA> NA <NA>
## [2] <NA> <NA> NA <NA>
## [3] <NA> <NA> NA <NA>
## [4] <NA> <NA> NA <NA>
## [5] <NA> <NA> NA <NA>
## [6] <NA> <NA> NA <NA>
## -------
## seqinfo: 1 sequence (1 circular) from BW25113 genomepredict_ps_itss
predict_ps_itss predicts pausing sites ps and internal starting sites iTSS_I between delay fragments within the same TU. predict_ps_itss compares the neighboring delay segments to each other by positioning the intercept of the second segment into the first segment using slope and intercept coefficients. predict_ps_itss selects unique TUs, delay fragments, slope, velocity fragment and intercept. It loops into all delay segments and estimate the coordinates of the last point of the first segment using the coefficients of the second segment and vice versa. The difference between the predicted positions is compared to the threshold. In case the strand is â-â, the positions of both segments are ordered from the last position to the first one. All positions are merged into one column and subtracted from the maximum position. The column is split in 2, the first and second correspond to the positions of the first and second segments respectively. Both segments are subsequently subjected to lm fit and the positions predicted are used on the same way as on the opposite strand. The difference between the predicted positions is compared to the negative threshold, ps is assigned otherwise, and if the difference is higher than the positive threshold, iTSS_I is assigned. The event duration is additionally added.
data(fragmentation_minimal)
probe <- predict_ps_itss(inp = fragmentation_minimal, maxDis = 300)
head(rowRanges(probe))apply_Ttest_delay
apply_Ttest_delay uses t-test to check the significance of the points between 2 segments showing pausing site ps and internal starting site iTSS_I independently. apply_Ttest_delay selects the last point from the first segment and the first point from the second segment and added them to the residuals of each model, the sum is subjected to t-test.
probe <- apply_Ttest_delay(inp = probe)
head(rowRanges(probe))apply_ancova
apply_ancova uses ancova to check the slope significance between two delay fragments showing either pausing site (ps) or internal starting site (ITSS_I). apply_ancova brings both fragments to the same position and apply ancova test.
probe <- apply_ancova(inp = probe)
head(rowRanges(probe))apply_event_position
apply_event_position extract the position between 2 segments with pausing site or iTSS_I event.
probe <- apply_event_position(inp = probe)
head(rowRanges(probe))apply_t_test
apply_t_test uses the statistical t_test to check if the fold-change of half-life (HL) fragments and the fold-change intensity fragments respectively is significant. apply_t_test compares the mean of two neighboring fragments within the same TU to check if the fold-change is significant. Fragments with distance above threshold are not subjected to t-test.
The functions used are:
fragment_functiont_test_functionfragment_function
fragment_function checks number of fragments inside TU, only fragments above 2 are gathered for analysis.
t_test_function
t_test_function makes fold-change and apply t-test, assign fragments names and ratio, add columns with the corresponding p_values.
probe <- apply_t_test(inp = probe, threshold = 300)
head(rowRanges(probe))fold_change
fold_change sets a fold-change ratio between the neighboring fragments of Half_life (HL) and intensity of two successive fragments. Two intensity fragments could belong to one HL fragment therefore the function sets first the borders using the position and applies the fold-change ratio between the neighboring fragments of HL and those from intensity ((half-life frgB / half-life frgA) / (intensity frgB/intensity frgA)). All grepped fragments are from the same TU excluding outliers.
The function used is:
synthesis_r_Function
synthesis_r_Function assigns events depending on the ratio between HL and intensity of two consecutive fragments. Intensity (int) in steady state is equivalent to synthesis rate(k)/decay(deg).
int = k/deg
int1/int2 = k1/deg1 * deg2/k2
The synthesis ratio is equivalent to: int1 * (deg1/int2) * deg2 = k1/k2
Comparing the synthesis ratio to threshold, an event is assigned:
probe <- fold_change(inp = probe)
head(rowRanges(probe))apply_manova
apply_manova checks if the ratio of HL ratio and intensity ratio is statistically significant. apply_manova compares the variance between two fold-changes, Half-life and intensity within the same TU ((half-life frgB / half-life frgA) / (intensity frgB/intensity frgA)). One half-life fragment could cover two intensity fragments therefore the fragments borders should be set first.
the function used is:
manova_function
manova_function checks the variance between 2 segments (independent variables) and two dependents variables (HL and intensity). The dataframe template is depicted below. The lm fit is applied and p_value is extracted.
apply_manova(inp = probe)
head(rowRanges(probe))apply_t_test_ti
apply_t_test_ti compares the mean of two neighboring TI fragments within the same TU using the statistical t_test to check if two neighboring TI fragments are significant. apply_t_test_ti selects TI fragments within the same TU excluding the outliers. Two new columns are added, âti_fragmentsâ and âp_value_tiTestâ referring to TI fragments subjected to t-test and their p_value.
gff3_preprocess
gff3_preprocess processes gff3 file from database, extracting gene names and locus_tag from all coding regions (CDS). Other features like UTRs, ncRNA, asRNA ect.. are extracted if available on one hand and the genome length on other hand. The output is a list of 2 elements and added to the input as metadata.
The output data frame from gff3_preprocess function contains the following columns:
Path = gzfile(system.file("extdata", "gff_e_coli.gff3.gz", package = "rifi"))
metadata(stats_minimal)$annot <- gff3_preprocess(path = Path)path path: path to the directory containing the gff3 file
probe <- apply_t_test_ti(inp = probe)
head(rowRanges(probe))rifi_summary wraps and summarizes all rifi outputs into different tables in a compact form. The tables connect rifi output and genes annotation. Four tables are generated and gathered as metadata into SE.
The functions used are:
event_dataframedataframe_summarydataframe_summary_eventsdataframe_summary_events_HL_intdataframe_summary_events_ps_itssdataframe_summary_events_velocitydataframe_summary_TIdata(stats_minimal)
summary_minimal <- rifi_summary(stats_minimal)data(summary_minimal)
head(metadata(summary_minimal))event_dataframe
event_dataframe creates a data frame only with events for segments and genes. event_dataframe selects columns with statistical features in addition to âIDâ, âpositionâ and âTUâ columns. The data frame combines fragments, events and statistical test and the corresponding genes. The column are:
region: feature of the genome e.g. CD, ncRNA, 5âUTR ectâ¦.
gene: gene annotation
locus_tag: locus tag annotation
strand: strand if data is stranded
TU: TU annotation
position: position on the genome
FC_fragment_intensity: The intensity fragments subjected to fold change
FC_intensity: fold change of two intensity fragments
p_value_intensity: p_value of the fold change of two intensity fragments
FC_fragment_HL: The halflife fragments subjected to fold change
FC_HL: fold change of two HL fragments
p_value_HL: p_value of the fold change of two HL fragments
FC_HL_intensity_fragment: The fragments subjected to ratio of fold-change of two intensity fragments and the two half-life fragments
FC_HL_intensity: ratio of fold-change of two intensity fragments and the two half-life fragments
FC_int_adapted: fold change of two intensity fragments
FC_HL_adapted: fold change of two HL fragments adapted to the intensity fragments
p_value_Manova: p_value of the statistical test Manova applied to FC_HL_intensity
synthesis_ratio: ratio of FC_HL_intensity
synthesis_ratio_event: event related to ratio
pausing_site: presence or absence of ps is indicated by +/-
ITSS_I: presence or absence of ITSS_I is indicated by +/-
event_ps_itss_p_value_Ttest: p_value of the t-test applied to ps and iTSS_I.
ps_ts_fragment: The fragments subjected to ps and iTSS_I
event_position: event position
delay: delay coefficient extracted from the fit
half_life: half-life coefficient extracted from the fit
intensity: intensity coefficient extracted from the fit
data(stats_minimal)
event_dataframe(data = stats_minimal, data_annotation = metadata(stats_minimal)$annot[[1]])probe data frame: the probe based data frame
data_annotation data frame: the coordinates extracted from gff3 file
The function used are:
position_function
annotation_function_event
strand_function
position_function
position_function adds the specific position of pausing sites and iTSS_I events.
annotation_function_event
annotation_function_event adds the events to the annotated genes.
strand_function
strand_function used by annotation_function_event function in case of stranded data.
dataframe_summary
dataframe_summary creates two tables summary of segments relating gene annotation to fragments. dataframe_summary creates two tables summary of segments and their half-lives. The first output is bin/probe features and the second one is intensity fragment based. Both tables are added as metaData.
dataframe_summary_events
dataframe_summary_events creates one table relating gene annotation to all events. The events are assigned on the first column. The table is added as metaData.
dataframe_summary_events_HL_int
dataframe_summary_events_HL_int creates one table relating gene annotation to all termination and new starting sites detected from half_life and intensity ratios. The events are assigned on the first column. The table is added as metaData.
dataframe_summary_events_ps_itss
dataframe_summary_events_ps_itss creates one table relating gene annotation with pausing sites and internal starting sites events detected from delay fragments. The events are assigned on the first column. The table is added as metaData.
dataframe_summary_events_velocity
dataframe_summary_events_velocity creates one table relating gene annotation with velocity ration detected from delay fragments. The events are assigned on the first column. The table is added as metaData.
dataframe_summary_TI
dataframe_summary_TI creates one table relating gene annotation to transcription interference. The table is added as metaData.
rifi_visualization plots the whole genome with genes, transcription units (TUs), delay, half-life (HL), intensity fragments features, events, velocity, annotation, coverage if available. The function plots all annotation features including genes, as-RNA, ncRNA, 5/3âUTR if available and TUs as segments. rifi_visualization plots delay, HL and intensity fragments with statistical t-test between the neighboring fragment, significant t-tests are assigned with â*â. The events are also indicated with asterisks if p_value is significant.
The functions used are:
gff3_preprocess: see rifi_stats section
strand_selection: check if data is stranded and arrange by position
splitGenome_function: splits the genome into fragments
indice_function: assign a new column to the data to distinguish between fragments, outliers and terminals from delay, HL and intensity
TU_annotation: designs the segments border for the genes and TUs annotation
gene_annot_function: requires gff3 file, returns a dataframe adjusting each fragment according to the annotation. It allows the plot of genes and TUs shared in two pages
label_log2_function: adds log scale to intensity values
label_square_function: adds square scale to coverage values
coverage_function: the function is used only in case of coverage is available
secondaryAxis: adjusts the halflife or delay to 20 in case of the dataframe row numbers is equal to 1 and the halflife or delay exceed the limit, they are plotted with different shape and color
outlier_plot: plot the outliers with half-life between 10 and 30 on the maximum of the yaxis
add_genomeBorders: resolves the issue when the annotated genes are on the borders and can not be plotted. The function splits the region in 2 adding the row corresponding to the split part to the next page except for the first page
my_arrow: creates an arrow for the annotation
arrange_byGroup: selects the last row for each segment and add 40 nucleotides in case of negative strand for a nice plot
regr: plots the predicted delay from linear regression. If data is stranded (strand==1) and if the data is on negative strand
meanPosition: assign a mean position for the plot
delay_mean: adds a column in case of velocity is NA or equal to 60. The mean of the delay is calculated excluding terminals and outliers
my_segment_T: plots terminals and pausing sites labels
my_segment_NS: plots internal starting sites âiTSSâ
min_value: returns minimum value for event plots in intensity plot
velocity_fun: function to plot velocity
limit_function: for values above 10 or 20 in delay and hl, Limit of the axis is set differently. yaxis limit is applied only if 3 values above 10 and lower or equal to 20 are present. An exception is added in case a dataframe has less than 3 rows and 1 or more values are above 10, the rest of the values above 20 are adjusted to 20 on secondaryAxis function
empty_boxes: used only in case the dataframe from the positive strand is not empty, the TU are annotated
function_TU_arrow: avoids plotting arrows when a TU is split into two pages
terminal_plot_lm: draws a linear regression line when terminal outliers have an intensity above a certain threshold and are consecutive. Usually are smallRNA (ncRNA, asRNA)
slope_function: replaces slope lower than 0.0009 to 0
velo_function: replaces infinite velocity with NA
TI_frag_threshold: splits the TI fragments on the same TI event
stats_minimal
rifi_visualization(
data = stats_minimal
)Figure 11: Fragments Plot Forward Strand
Figure 12: Fragments Plot Reverse Strand
The plot is located on vignette âgenome_fragments.pdfâ and shows 4 sections: annotation, delay, half-life and intensity.
TU: Transcription unit annotation from Rifi workflow
Locus tag: Locus_tag annotation from genome annotation
gene: gene annotation from genome annotation. If gene annotation is not available, locus_tag is given instead
2. DelayDelay: Delay fragments, fragments annotation, â+/++/+++â indicates velocity degree, events are indicated by âPSâ or âiTSSâ, "*" indicates significant statistical test
3. Half-lifeHalf-life: HL fragments, fragments annotation, events like termination and iTTS_II are indicated by âTerâ or âNSâ; "*" indicates significant statistical test for HL fold change
4. Intensity/coverageIntensity: Intensity fragments, fragments annotation, â" indicates significant statistical test for intensity fold change. An additional black line above the fragments indicate the mean of TI factor for each fragment and dots indicate TI factor for each bin. Dot vertical green lines shows TI fragments, "Tinterf()â indicate significant statistical test between fragments
Coverage: In case of available coverage, it could be plotted on the same section as intensity
5. Additional featuresoutliers: are indicated by square shape an grey color
high values: are indicated by square shape an cyan color
IX. Additional functionsscore_fun_linear
score_fun_ave
score_fun_increasing
All these 3 functions are using the dynamic programming approach to part a sequence of continuous points into fragments. It uses three principles steps:
score_fun_linear
score_fun_linear scores the residuals from a linear fit. score_fun_linear fits a regression line from a vector of minimum 3 values y, a vector of positions x. The IDs z and the sum of residuals are stored. A new value y and x is added, the fit is performed and the new IDs and sum of residuals are stored. After several fits, the minimum score and the corresponding IDs is selected and stored as the best fragment. In case of the slope is bigger as 1/60, the residuals are calculated as if the slope was 1/60. In case of the stranded option is inactive and the slope is smaller as -1/60 the residuals are calculated as if the slope was -1/60. In both cases, the velocity is limited to 1 nucleotide per second. score_fun_linear selects simultaneously for outliers, the maximum number is fixed previously. Outliers are those values with high residuals, they are stored but excluded from the next fit. The output of the function is a vector of IDs separated by â,â, a vector of velocity (1/slope) separated by â", a vector of intercept separated by "â and a vector of outliers.
score_fun_linear(y, x, z = x, pen, stran, n_out = min(10,
max(1, 0.4 * length(x))))score_fun_ave
score_fun_ave scores the difference of the values from their mean. score_fun_ave calculates the mean of a minimum 2 values y and substrates the difference from their mean. The IDs z and the sum of differences from the mean are stored. A new value y is added, the mean is calculated and the new IDs and sum of differences are stored. After several rounds, the minimum score and the corresponding IDs is selected and stored as the best fragment. score_fun_ave selects simultaneously for outliers, the maximum number is fixed previously. Outliers are those values with high difference from the mean, they are stored but excluded from the next calculation. The output of the function is a vector of IDs separated by â,â, a vector of mean separated by "_" and a vector of outliers separated by â,â.
score_fun_ave(y, z, pen, n_out = min(10, max(1, 0.4*length(z))))score_fun_increasing
score_fun_increasing scores the difference between 2 values. score_fun_increasing calculates the difference between 2 values y comparing to their position, x. The sum of differences is stored and a new value y is added. The difference is newly calculated and the sum is stored. After several rounds, the maximum score is selected and TU is assigned.
score_fun_increasing(x, y)Campbell, E. A., N. Korzheva, A. Mustaev, K. Murakami, S. Nair, A. Goldfarb, and S. A. Darst. 2001. âStructural Mechanism for Rifampicin Inhibition of Bacterial Rna Polymerase.â Cell 104 (6): 901â12. https://doi.org/10.1016/s0092-8674(01)00286-0.
Chen, Huiyi, Katsuyuki Shiroguchi, Hao Ge, and Xiaoliang Sunney Xie. 2015. âGenome-Wide Study of mRNA Degradation and Transcript Elongation in Escherichia Coli.â Molecular Systems Biology 11 (1): 781. https://doi.org/10.15252/msb.20145794.
Dar, Daniel, and Rotem Sorek. 2018. âExtensive Reshaping of Bacterial Operons by Programmed mRNA Decay.â PLOS Genetics 14 (4): e1007354. https://doi.org/10.1371/journal.pgen.1007354.
Shearwin, Keith E., Benjamin P. Callen, and J. Barry Egan. 2005. âTranscriptional Interference â a Crash Course.â Trends in Genetics 21 (6): 339â45. https://doi.org/10.1016/j.tig.2005.04.009.
Wang, Xun, Sang Chun Ji, Heung Jin Jeon, Yonho Lee, and Heon M. Lim. 2015. âTwo-Level Inhibition of galK Expression by Spot 42: Degradation of mRNA mK2 and Enhanced Transcription Termination Before the galK Gene.â Proceedings of the National Academy of Sciences 112 (24): 7581â6. https://doi.org/10.1073/pnas.1424683112.
sessionInfo()## R version 4.5.1 (2025-06-13)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.2 LTS
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## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.22-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0 LAPACK version 3.12.0
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## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
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## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
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## time zone: America/New_York
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats4 stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] SummarizedExperiment_1.39.1 Biobase_2.69.0
## [3] GenomicRanges_1.61.1 Seqinfo_0.99.1
## [5] IRanges_2.43.0 S4Vectors_0.47.0
## [7] BiocGenerics_0.55.0 generics_0.1.4
## [9] MatrixGenerics_1.21.0 matrixStats_1.5.0
## [11] rifi_1.13.1 BiocStyle_2.37.0
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## loaded via a namespace (and not attached):
## [1] bitops_1.0-9 gridExtra_2.3 remotes_2.5.0
## [4] rlang_1.1.6 magrittr_2.0.3 compiler_4.5.1
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## [13] fastmap_1.2.0 XVector_0.49.0 ellipsis_0.3.2
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## [100] mime_0.13RetroSearch is an open source project built by @garambo | Open a GitHub Issue
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