Class 9
Structural Bioinformatics (Pt. 1)
Barry Grant < http://thegrantlab.org/teaching/ >
2022-10-25 (17:20:23 on Tue, Oct 25)
1: Introduction to the RCSB Protein Data Bank (PDB)
The PDB archive is the major repository of information about the 3D structures of large biological molecules, including proteins and nucleic acids. Understanding the shape of these molecules helps to understand how they work. This knowledge can be used to help deduce a structure’s role in human health and disease, and in drug development. The structures in the PDB range from tiny proteins and bits of DNA or RNA to complex molecular machines like the ribosome composed of many chains of protein and RNA.
In the first section of this lab we will interact with the main US based PDB website (note there are also sites in Europe and Japan).
Visit: http://www.rcsb.org/ and answer the following questions
NOTE: The “Analyze” > “PDB Statistics” > “by Experimental Method and Molecular Type” on the PDB home page should allow you to determine most of these answers.
PDB statistics
Open RStudio and begin a new class09 project. If we have covered GitHub in a previous class then you should create this within your GitHub tacked directory/folder from that class. Make sure “Create a git repository” option is NOT ticked. This is because we want to use the same git repository as we used last day and not start a new one - if you are not sure what this means ask Barry now!
Next, open a new Quarto document (File > New File > Quarto Document…). As always, we will aim to have a rendered PDF report with working code by the end of this class!
Download a CSV file from the PDB site (accessible from “Analyze” > “PDB Statistics” > “by Experimental Method and Molecular Type”. Move this CSV file into your RStudio project and use it to answer the following questions:
Q1: What percentage of structures in the PDB are solved by X-Ray and Electron Microscopy.
Q2: What proportion of structures in the PDB are protein?
Q3: Type HIV in the PDB website search box on the home page and determine how many HIV-1 protease structures are in the current PDB?
The PDB format
Now download the “PDB File” for the HIV-1 protease structure with the PDB identifier 1HSG. On the website you can “Display” the contents of this “PDB format” file.
Alternatively, you can examine the contents of your downloaded file in a suitable text editor or use the Terminal tab from within RStudio (or your favorite Terminal/Shell) and try the following command:
less ~/Downloads/1hsg.pdb ## (use ‘q’ to quit)NOTE: When viewing the file stop when you come the lines beginning with the word “ATOM”. We will discuss this ubiquitous PDB file format when you have got this far.
Protein Data Bank files (or PDB files) are the most common format for the distribution and storage of high-resolution biomolecular coordinate data. At their most basic, PDB coordinate files contain a list of all the atoms of one or more molecular structures. Each atom position is defined by its x, y, z coordinates in a conventional orthogonal coordinate system. Additional data, including listings of observed secondary structure elements, are also commonly (but not always) detailed in PDB files.
Molecular graphics programs such as Mol*, VMD, PyMol and Chimera take these files and plot them in 3D with the ability to make simplified and stylized representations such as the one shown below:
Figure 1. HIV-1 protease structure (PDB code: 1HSG) in complex with the small molecule indinavir.
2. Visualizing the HIV-1 protease structure
The HIV-1 protease is an enzyme that is vital for the replication of HIV. It cleaves newly formed polypeptide chains at appropriate locations so that they form functional proteins. Hence, drugs that target this protein could be vital for suppressing viral replication. A handful of drugs - called HIV-1 protease inhibitors (saquinavir, ritonavir, indinavir, nelfinavir, etc.) - are currently commercially available that inhibit the function of this protein, by binding in the catalytic site that typically binds the polypeptide.
In this section we will use the 2Å resolution X-ray crystal structure of HIV-1 protease with a bound drug molecule indinavir (PDB ID: 1HSG). We will use the Mol* molecular viewer to visually inspect the protein, the binding site and the drug molecule. After exploring features of the complex we will move on to perform bioinformatics analysis of single and multiple crystallographic stuctures to explore the conformational dynamics and flexibility of the protein - important for it’s function and for considering during drug design.
Using Mol*
Mol* (pronounced “molstar”) is a new web-based molecular viewer that is rapidly gaining in popularity and utility. At the time of writing it is still a long way from having the full feature set of stand-alone molecular viewer programs like VMD, PyMol or Chimera. However, it is gaining new features all the time and does not require any download or complicated installation.
You can use Mol* directly at the PDB website (as well as UniProt and elsewhere). However, for the latest and greatest version we will visit the Mol* homepage at: https://molstar.org/viewer/.
To load a structure from the PDB we can enter the PDB code and click “Apply” in the “Download Structure” menu (see figure below)
Once loaded the sidebar should change to the so-called hierarchical “State Tree” menu. Of particular note there are entries for Polymer, Ligand and Water. You can turn the display of any of these entries OFF/ON by clicking on the eye icon or delete them by clicking the “trash” bin icon (but we will not do that just yet). We can turn this left-side control panel off to save screen space. Especially as we will not need it again until we come to close the molecule or read a new molecule later.
Key-point: You can access and change all visual representations on the opposite right side control panel under the “Components” drop-down menu (see figure below). Try togling ON/OFF the display of Ligand and Water with the “eye” icon.
Getting to know HIV-Pr
Let’s temporally toggle OFF/ON the display of water molecules and change the display representation of the Ligand to Spacefill (a.k.a VdW spheres). To do this:
- Click on three dots for the “Ligand” components entry in the right side control panel (blue box in above image),
- Then from the drop-down select Add Representation > Spacefill.
- Note that there are now two “reps” listed for the ligand component that you can control independently in the expandable menu accessible from clicking the three dots (see red box below).
Let’s also change the protein “Polymer” > “Set Coloring” > “Residue Property” > “Secondary Structure”.
Key-point: All these expanding drop-down menus can quickly become overwhelming. I find that closing them by clicking the 3 dots again can help keep things tidy and avoid menu items disappearing off small screens.
Saving an image
Once you are happy with your display you can save a high-resolution image to your computer for including in your Quarto document. To do this find the “iris-like” screenshot icon on the right side of the display region and select your resolution and click download (see figure below)
Delving deeper
To help highlight important amino acid residues that interact with the ligand you can click on the ligand itself. This will lead to a new “Focus Surroundings (5A)” display component to appear. Mousing over this will highlight the corresponding amino acids in the Sequence display panel.
Note: Zoom in and rotate to examine these ligand interactions. Of these positions Asp 25 (D25) in both chains is critical for protease activity. Can you find this amino acid in both chains? Note the residue information displayed in the bottom right of the viewing window as you mouse over different amino acids.
Cleaning up the display
Most viewers will find that displaying all ligand surrounding amino acids is too busy for a single display. Turn off the display of these positions by clicking the eye” icon for the “Focus Surroundings (5A)” Components entry in the right side control panel.
Now we can highlight a subset of the most important positions:
- Using the top Sequence display select position Asp
25 (D25) in one of the chains.
- Now activate so-called “Selection Mode” by clicking
the Arrow icon (red box to the right side of the 3D viewer
panel in the figure below).
- Then select the two Asp 25 positions in the 3D structure.
- Finally click the cube icon (blue box in below figure) and from the drop-down menu that appears select Representation Spacefill or Ball & Stick (whatever you prefer), then click +Create Component.
Note that a new “Custom Selection” component has appeared in the right side control panel. This will contain your two D25 positions. You can again delete the “Focus Surroundings (5A)” and Focus Target Components to clean up the display.
At this point you should consider saving an image as discussed above.
The important role of water
Toggle on the display of all water molecules again.
Q4: Water molecules normally have 3 atoms. Why do we see just one atom per water molecule in this structure?
Q5: There is a critical “conserved” water molecule in the binding site. Can you identify this water molecule? What residue number does this water molecule have
Now you should be able to produce an image similar or even superior to Figure 2 and save it to an image file.
Q6: Generate and save a figure clearly showing the two distinct chains of HIV-protease along with the ligand. You might also consider showing the catalytic residues ASP 25 in each chain and the critical water (we recommend “Ball & Stick” for these side-chains). Add this figure to your Quarto document.
Discussion Topic: Can you think of a way in which indinavir, or even larger ligands and substrates, could enter the binding site?
Q7: [Optional] As you have hopefully observed HIV protease is a homodimer (i.e. it is composed of two identical chains). With the aid of the graphic display can you identify secondary structure elements that are likely to only form in the dimer rather than the monomer?
3. Introduction to Bio3D in R
Bio3D is an R package for structural bioinformatics. Features include the ability to read, write and analyze biomolecular structure, sequence and dynamic trajectory data.
In your existing Rmarkdown document load the Bio3D package by typing in a new code chunk:
library(bio3d)Side-Note: If you see an error message reported then you will first need to install the package with the command:
install.packages("bio3d")in your R Console (i.e. don’t put this in your Rmarkdown document or it will be re-installed every time you knit/render your document). This is only required once whereas thelibrary(bio3d)command is required at the start of every new R session where you want to use Bio3D.
Reading PDB file data into R
To read a single PDB file with Bio3D we can use the
read.pdb() function. The minimal input required for this
function is a specification of the file to be read. This can be either
the file name of a local file on disc, or the RCSB PDB identifier of a
file to read directly from the on-line PDB repository. For example to
read and inspect the on-line file with PDB ID 1HSG:
pdb <- read.pdb("1hsg")## Note: Accessing on-line PDB fileTo get a quick summary of the contents of the pdb object you just
created you can issue the command print(pdb) or simply type
pdb (which is equivalent in this case):
pdb##
## Call: read.pdb(file = "1hsg")
##
## Total Models#: 1
## Total Atoms#: 1686, XYZs#: 5058 Chains#: 2 (values: A B)
##
## Protein Atoms#: 1514 (residues/Calpha atoms#: 198)
## Nucleic acid Atoms#: 0 (residues/phosphate atoms#: 0)
##
## Non-protein/nucleic Atoms#: 172 (residues: 128)
## Non-protein/nucleic resid values: [ HOH (127), MK1 (1) ]
##
## Protein sequence:
## PQITLWQRPLVTIKIGGQLKEALLDTGADDTVLEEMSLPGRWKPKMIGGIGGFIKVRQYD
## QILIEICGHKAIGTVLVGPTPVNIIGRNLLTQIGCTLNFPQITLWQRPLVTIKIGGQLKE
## ALLDTGADDTVLEEMSLPGRWKPKMIGGIGGFIKVRQYDQILIEICGHKAIGTVLVGPTP
## VNIIGRNLLTQIGCTLNF
##
## + attr: atom, xyz, seqres, helix, sheet,
## calpha, remark, callQ7: How many amino acid residues are there in this pdb object?
Q8: Name one of the two non-protein residues?
Q9: How many protein chains are in this structure?
Note that the attributes (+ attr:) of this object are
listed on the last couple of lines. To find the attributes of any such
object you can use:
attributes(pdb)## $names
## [1] "atom" "xyz" "seqres" "helix" "sheet" "calpha" "remark" "call"
##
## $class
## [1] "pdb" "sse"To access these individual attributes we use the
dollar-attribute name convention that is common with R list
objects. For example, to access the atom attribute or
component use pdb$atom:
head(pdb$atom)Predicting functional motions of a single structure
Let’s read a new PDB structure of Adenylate Kinase and perform Normal mode analysis.
adk <- read.pdb("6s36")## Note: Accessing on-line PDB file
## PDB has ALT records, taking A only, rm.alt=TRUEadk##
## Call: read.pdb(file = "6s36")
##
## Total Models#: 1
## Total Atoms#: 1898, XYZs#: 5694 Chains#: 1 (values: A)
##
## Protein Atoms#: 1654 (residues/Calpha atoms#: 214)
## Nucleic acid Atoms#: 0 (residues/phosphate atoms#: 0)
##
## Non-protein/nucleic Atoms#: 244 (residues: 244)
## Non-protein/nucleic resid values: [ CL (3), HOH (238), MG (2), NA (1) ]
##
## Protein sequence:
## MRIILLGAPGAGKGTQAQFIMEKYGIPQISTGDMLRAAVKSGSELGKQAKDIMDAGKLVT
## DELVIALVKERIAQEDCRNGFLLDGFPRTIPQADAMKEAGINVDYVLEFDVPDELIVDKI
## VGRRVHAPSGRVYHVKFNPPKVEGKDDVTGEELTTRKDDQEETVRKRLVEYHQMTAPLIG
## YYSKEAEAGNTKYAKVDGTKPVAEVRADLEKILG
##
## + attr: atom, xyz, seqres, helix, sheet,
## calpha, remark, callNormal mode analysis (NMA) is a structural bioinformatics method to predict protein flexibility and potential functional motions (a.k.a. conformational changes).
# Perform flexiblity prediction
m <- nma(adk)## Building Hessian... Done in 0.088 seconds.
## Diagonalizing Hessian... Done in 0.269 seconds.plot(m)
To view a “movie” of these predicted motions we can generate a
molecular “trajectory” with the mktrj() function.
mktrj(m, file="adk_m7.pdb")Now we can load the resulting “adk_m7.pdb” PDB into Mol* with the “Open Files” option on the right side control panel. Once loaded click the “play” button to see a movie (see image below). We will discuss how this method works at the end of this lab when we apply it across a large set of homologous structures.
Here is what the output movie looks like:
4. Comparative structure analysis of Adenylate Kinase
The goal of this section is to perform principal component analysis (PCA) on the complete collection of Adenylate kinase structures in the protein data-bank (PDB).
Adenylate kinase (often called simply Adk) is a ubiquitous enzyme that functions to maintain the equilibrium between cytoplasmic nucleotides essential for many cellular processes. Adk operates by catalyzing the reversible transfer of a phosphoryl group from ATP to AMP. This reaction requires a rate limiting conformational transition (i.e. change in shape). Here we analyze all currently available Adk structures in the PDB to reveal detailed features and mechanistic principles of these essential shape changing transitions.
Figure 5. Adenylate kinase structure (PDB code: 1AKE) with a bound inhibitor molecule.
The bio3d package pca() function
provides a convenient interface for performing PCA of biomolecular
structure data. As we have discussed in previous classes, PCA is a
statistical approach used to transform large data-sets down to a few
important components that usefully describe the directions where there
is most variance. In terms of protein structures PCA can be used to
capture major structural variations within a set of structures (a.k.a.
structure ensemble). This can make interpreting major conformational
states (such as ‘active’ and ‘inactive’ or ‘ligand bound’ and ‘un-bound’
states) and structural mechanisms for activation or regulation more
clear.
Overview
Starting from only one Adk PDB identifier (PDB ID: 1AKE) we will search the entire PDB for related structures using BLAST, fetch, align and superpose the identified structures, perform PCA and finally calculate the normal modes of each individual structure in order to probe for potential differences in structural flexibility.
Setup
We will begin by first installing the packages we need for today’s session.
# Install packages in the R console NOT your Rmd/Quarto file
install.packages("bio3d")
install.packages("devtools")
install.packages("BiocManager")
BiocManager::install("msa")
devtools::install_bitbucket("Grantlab/bio3d-view")Q10. Which of the packages above is found only on BioConductor and not CRAN?
Q11. Which of the above packages is not found on BioConductor or CRAN?:
Q12. True or False? Functions from the devtools package can be used to install packages from GitHub and BitBucket?
The install.packages() function is used to install
packages from the main CRAN repository for R packages.
BioConductor is a separate repository of R packages
focused on high-throughput biomolecular assays and biomolecular data.
Packages from BioConductor can be installed using the
BiocManager::install() function. Finally, R packages found
on GitHub or BitBucket can be installed using
devtools::install_github() and
devtools::install_bitbucket() functions.
Search and retrieve ADK structures
Below we perform a blast search of the PDB database to identify
related structures to our query Adenylate kinase (ADK) sequence. In this
particular example we use function get.seq() to fetch the
query sequence for chain A of the PDB ID 1AKE and use this as input to
blast.pdb(). Note that get.seq() would also
allow the corresponding UniProt identifier.
library(bio3d)
aa <- get.seq("1ake_A")## Fetching... Please wait. Done.aa## 1 . . . . . 60
## pdb|1AKE|A MRIILLGAPGAGKGTQAQFIMEKYGIPQISTGDMLRAAVKSGSELGKQAKDIMDAGKLVT
## 1 . . . . . 60
##
## 61 . . . . . 120
## pdb|1AKE|A DELVIALVKERIAQEDCRNGFLLDGFPRTIPQADAMKEAGINVDYVLEFDVPDELIVDRI
## 61 . . . . . 120
##
## 121 . . . . . 180
## pdb|1AKE|A VGRRVHAPSGRVYHVKFNPPKVEGKDDVTGEELTTRKDDQEETVRKRLVEYHQMTAPLIG
## 121 . . . . . 180
##
## 181 . . . 214
## pdb|1AKE|A YYSKEAEAGNTKYAKVDGTKPVAEVRADLEKILG
## 181 . . . 214
##
## Call:
## read.fasta(file = outfile)
##
## Class:
## fasta
##
## Alignment dimensions:
## 1 sequence rows; 214 position columns (214 non-gap, 0 gap)
##
## + attr: id, ali, call- Q13. How many amino acids are in this sequence, i.e. how long is this sequence?
Now we can use this sequence as a query to BLAST search the PDB to find similar sequences and structures.
# Blast or hmmer search
#b <- blast.pdb(aa)Side-note: Due to the number of students in this class session this command, which uses online NCBI blast service, may time-out. If this happens please jump ahead to the next Side-note below to skip running the actual blast search.
The function plot.blast() facilitates the visualization
and filtering of the Blast results. It will attempt to set a seed
position to the point of largest drop-off in normalized scores (i.e. the
biggest jump in E-values). In this particular case we specify a cutoff
(after initial plotting) of to include only the relevant E.coli
structures:
# Plot a summary of search results
#hits <- plot(b)Figure 6: Blast results. Visualize and filter blast results through
function plot.blast(). Here we proceed with only the top
scoring hits (black).
# List out some 'top hits'
#head(hits$pdb.id)Side-note: If blast did not return results (likely due to the large number of simultaneous requests from the class) you can use the following vector of PDB IDs
hits <- NULL
hits$pdb.id <- c('1AKE_A','6S36_A','6RZE_A','3HPR_A','1E4V_A','5EJE_A','1E4Y_A','3X2S_A','6HAP_A','6HAM_A','4K46_A','3GMT_A','4PZL_A')The Blast search and subsequent filtering identified a total of 13
related PDB structures to our query sequence. The PDB identifiers of
this collection are accessible through the $pdb.id
attribute to the hits object (i.e. hits$pdb.id). Note that
adjusting the cutoff argument (to plot.blast()) will result
in a decrease or increase of hits.
We can now use function get.pdb() and
pdbslit() to fetch and parse the identified structures.
# Download releated PDB files
files <- get.pdb(hits$pdb.id, path="pdbs", split=TRUE, gzip=TRUE)Align and superpose structures
Next we will use the pdbaln() function to align and also
optionally fit (i.e. superpose) the identified PDB structures.
# Align releated PDBs
pdbs <- pdbaln(files, fit = TRUE, exefile="msa")Note that if you get an error msg above include the optional
exefile="msa" input argument to pdbaln().
# Vector containing PDB codes for figure axis
ids <- basename.pdb(pdbs$id)
# Draw schematic alignment
plot(pdbs, labels=ids)
Figure 7: Schematic representation of alignment. Grey regions depict aligned residues, while white depict gap regions. The red bar at the top depict sequence conservation.
Optional: Viewing our superposed structures
We can view our superposed results with the new
bio3d.view view() function:
library(bio3d.view)
library(rgl)
view.pdbs(pdbs)Figure 8: 3D view of superposed ADK structures available in the PDB.
Annotate collected PDB structures
The function pdb.annotate() provides a convenient way of
annotating the PDB files we have collected. Below we use the function to
annotate each structure to its source species. This will come in handy
when annotating plots later on:
anno <- pdb.annotate(ids)
unique(anno$source)## [1] "Escherichia coli"
## [2] "Escherichia coli K-12"
## [3] "Escherichia coli O139:H28 str. E24377A"
## [4] "Escherichia coli str. K-12 substr. MDS42"
## [5] "Photobacterium profundum"
## [6] "Vibrio cholerae O1 biovar El Tor str. N16961"
## [7] "Burkholderia pseudomallei 1710b"
## [8] "Francisella tularensis subsp. tularensis SCHU S4"We can view all available annotation data:
annoPrincipal component analysis
Function pca() provides principal component analysis
(PCA) of the structure data. PCA is a statistical approach used to
transform a data set down to a few important components that describe
the directions where there is most variance. In terms of protein
structures PCA is used to capture major structural variations within an
ensemble of structures.
PCA can be performed on the structural ensemble (stored in the pdbs
object) with the function pca.xyz(), or more simply
pca().
# Perform PCA
pc.xray <- pca(pdbs)
plot(pc.xray)
Figure 9: Results of PCA on Adenylate kinase X-ray structures. Each dot represents one PDB structure.
Function rmsd() will calculate all pairwise RMSD values
of the structural ensemble. This facilitates clustering analysis based
on the pairwise structural deviation:
# Calculate RMSD
rd <- rmsd(pdbs)
# Structure-based clustering
hc.rd <- hclust(dist(rd))
grps.rd <- cutree(hc.rd, k=3)
plot(pc.xray, 1:2, col="grey50", bg=grps.rd, pch=21, cex=1)
Figure 10: Projection of Adenylate kinase X-ray structures. Each dot represents one PDB structure.
The plot shows a conformer plot – a low-dimensional representation of the conformational variability within the ensemble of PDB structures. The plot is obtained by projecting the individual structures onto two selected PCs (e.g. PC-1 and PC-2). These projections display the inter-conformer relationship in terms of the conformational differences described by the selected PCs.
5. Optional further visualization
To visualize the major structural variations in the ensemble the
function mktrj() can be used to generate a trajectory PDB
file by interpolating along a give PC (eigenvector):
# Visualize first principal component
pc1 <- mktrj(pc.xray, pc=1, file="pc_1.pdb")You can open this file, pc_1.pdb, in Mol*. In a in web
browser page visit https://molstar.org/viewer/ and “Open
Files” from the left control panel selecting .
Once loaded you can animate the structure and visualize the major structural variations along PC1 by clicking the “Play” icon and Start button (see below).
You can also save a movie of this motion via the “Export Animation” menu option on the right control panel:
Figure 11: Visualization of PC-1 in VMD. Trajectory PDB file is
generated using mktrj().
We can also view our results with the new bio3d.view
view() function:
view.xyz(pc1)## Potential all C-alpha atom structure(s) detected: Using calpha.connectivity()Figure 12: Visualization of PC-1 trajectory generated using
mktrj().
We could set the color to highlight the most variable regions like so:
view.xyz(pc1, col=vec2color( rmsf(pc1) ))## Potential all C-alpha atom structure(s) detected: Using calpha.connectivity()We can also plot our main PCA results with ggplot:
#Plotting results with ggplot2
library(ggplot2)
library(ggrepel)
df <- data.frame(PC1=pc.xray$z[,1],
PC2=pc.xray$z[,2],
col=as.factor(grps.rd),
ids=ids)
p <- ggplot(df) +
aes(PC1, PC2, col=col, label=ids) +
geom_point(size=2) +
geom_text_repel(max.overlaps = 20) +
theme(legend.position = "none")
p
6. Normal mode analysis [optional]
Function nma() provides normal mode analysis (NMA) on
both single structures (if given a singe PDB input object) or the
complete structure ensemble (if provided with a PDBS input object). This
facilitates characterizing and comparing flexibility profiles of related
protein structures.
# NMA of all structures
modes <- nma(pdbs)plot(modes, pdbs, col=grps.rd)
Q14. What do you note about this plot? Are the black and colored lines similar or different? Where do you think they differ most and why?
Collectively these results indicate the existence of two major distinct conformational states for Adk. These differ by a collective low frequency displacement of two nucleotide-binding site regions that display distinct flexibilities upon nucleotide binding.
Important-Note: Remember to save your Quarto document and Render to generate a HTML and PDF report for GradeScope.
Here we use the sessionInfo() function to report on our
R systems setup at the time of document execution.
sessionInfo()## R version 4.1.2 (2021-11-01)
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## LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib
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## [1] stats graphics grDevices utils datasets methods base
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## [1] ggrepel_0.9.1 ggplot2_3.3.6 rgl_0.110.2
## [4] bio3d.view_0.1.0.9000 bio3d_2.4-3 NGLVieweR_1.3.1
## [7] labsheet_0.1.2
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## [1] httr_1.4.4 sass_0.4.2 jsonlite_1.8.3
## [4] bslib_0.4.0 shiny_1.7.2 assertthat_0.2.1
## [7] highr_0.9 stats4_4.1.2 GenomeInfoDbData_1.2.7
## [10] yaml_2.3.6 Rttf2pt1_1.3.11 pillar_1.8.1
## [13] glue_1.6.2 extrafontdb_1.0 digest_0.6.30
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## [34] BiocGenerics_0.40.0 cli_3.4.1 magrittr_2.0.3
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## [43] stringr_1.4.1 S4Vectors_0.32.4 munsell_0.5.0
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## [49] GenomeInfoDb_1.30.1 rlang_1.0.6 grid_4.1.2
## [52] RCurl_1.98-1.9 rstudioapi_0.14 htmlwidgets_1.5.4
## [55] bitops_1.0-7 base64enc_0.1-3 labeling_0.4.2
## [58] rmarkdown_2.17 gtable_0.3.1 DBI_1.1.3
## [61] curl_4.3.3 R6_2.5.1 knitr_1.40
## [64] dplyr_1.0.10 fastmap_1.1.0 extrafont_0.18
## [67] utf8_1.2.2 stringi_1.7.8 parallel_4.1.2
## [70] Rcpp_1.0.9 vctrs_0.5.0 tidyselect_1.2.0
## [73] xfun_0.34Powered by labsheet
