The goal of HERON (Hierarchical Epitope pROtein biNding) is to analyze peptide binding array data measured from nimblegen or any high density peptide binding array data.
You can install the released version of HERON from bioconductor with:
if (!require("BiocManager", quietly = TRUE))
install.packages("BiocManager")
# The following initializes usage of Bioc devel
BiocManager::install(version='devel')
BiocManager::install("HERON")And the development version from GitHub with:
options(warn=2)
library(HERON)
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#> anyMissing, rowMediansThese are examples which shows you how to interact with the code. We will be using a subset of the COVID-19 peptide binding array dataset from the https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8245122/ publication.
First, we start with a sequence data.frame where rows are amino acid sequences of the peptide binding probe and the columns are samples.
| Sample_9 | Sample_1 | Sample_39 | Sample_23 | Sample_56 | |
|---|---|---|---|---|---|
| AAAYYVGYLQPRTFLL | 0.3746667 | 0.5423724 | 0.7329991 | 0.1225761 | 0.9727648 |
| AADLDDFSKQLQQSMS | 2.8056786 | 3.1205293 | 9.2330091 | 4.2324981 | 9.8410852 |
| AAEASKKPRQKRTATK | 0.2704410 | 0.7198765 | 2.6648164 | 1.7079940 | 4.5664978 |
| AAEIRASANLAATKMS | 0.7120529 | 1.3820778 | 1.5463912 | 3.2038894 | 7.3400386 |
| AAIVLQLPQGTTLPKG | 2.9876932 | 0.1259101 | 4.6971758 | 5.6496847 | 2.2246734 |
The data is pre-processed by first quantile normalizing on sequence-level data.
| Sample_9 | Sample_1 | Sample_39 | Sample_23 | Sample_56 | |
|---|---|---|---|---|---|
| AAAYYVGYLQPRTFLL | 0.3569421 | 0.8802587 | 0.5174103 | 0.1539593 | 0.8632584 |
| AADLDDFSKQLQQSMS | 2.4975483 | 4.4552679 | 6.6610043 | 4.8175685 | 7.2030291 |
| AAEASKKPRQKRTATK | 0.2706685 | 1.1883782 | 2.0845928 | 1.6878615 | 3.4542907 |
| AAEIRASANLAATKMS | 0.6506443 | 2.1632309 | 1.1600102 | 3.6584394 | 5.0898633 |
| AAIVLQLPQGTTLPKG | 2.8027363 | 0.2307280 | 3.2037424 | 6.1906585 | 1.8298191 |
| AALALLLLDRLNQLES | 0.5432972 | 0.4990815 | 2.2830699 | 0.0681958 | 2.9236376 |
The quantile normalized data is then used with the colData and probe_meta data frames to calculate probe-level p-values. The colData data frame describes the experimental setup of the samples. for the colData data frame, the important columns are ptid, visit, and SampleName. The SampleName is the column name of the sequence table, ptid is the name of the sample, and visit is either pre or post. The ptid can the same value for one pre and post sample, which would indicate a paired design. A condition column can also be provided which can indicate multiple conditions for the post samples.
| SampleName | ptid | visit | condition | |
|---|---|---|---|---|
| Sample_9 | Sample_9 | Sample_9 | pre | Control |
| Sample_1 | Sample_1 | Sample_1 | pre | Control |
| Sample_39 | Sample_39 | Sample_39 | post | COVID |
| Sample_23 | Sample_23 | Sample_23 | post | COVID |
| Sample_56 | Sample_56 | Sample_56 | post | COVID |
| Sample_53 | Sample_53 | Sample_53 | post | COVID |
The probe_meta data frame describes the mapping the amino acid sequence (PROBE_SEQUENCE) of the probes to the probe identifier (PROBE_ID). The PROBE_ID contains the name of the protein and the position within the protein of the first acid of the probe sequence separated by a semicolon.
probe_meta <- metadata(heffron2021_wuhan)$probe_meta
knitr::kable(head(probe_meta[,c("PROBE_SEQUENCE", "PROBE_ID")]))| PROBE_SEQUENCE | PROBE_ID | |
|---|---|---|
| 76322 | MYSFVSEETGTLIVNS | NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;1 |
| 76323 | YSFVSEETGTLIVNSV | NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;2 |
| 76324 | SFVSEETGTLIVNSVL | NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;3 |
| 76325 | FVSEETGTLIVNSVLL | NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;4 |
| 76326 | VSEETGTLIVNSVLLF | NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;5 |
| 76327 | SEETGTLIVNSVLLFL | NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;6 |
The calcCombPValues call will first calculate the probe level p-values using the colData, adjust the probe p-values on a column-by-column basis frame.
The combined p-values can be calculated on the sequence data set, then converted to a probe data set through convertSequenceDSToProbeDS, or calculated on the probe data set. If the data was smoothed prior using consecutive probes, then the p-values should calculated on the smoothed probe data set.
seq_pval_res <- calcCombPValues(seq_ds_qn)
probe_pval_res <- convertSequenceDSToProbeDS(seq_pval_res)
knitr::kable(head(assays(probe_pval_res)$padj))| Sample_39 | Sample_23 | Sample_56 | Sample_53 | Sample_43 | Sample_22 | Sample_51 | Sample_49 | Sample_25 | Sample_33 | Sample_30 | Sample_55 | Sample_59 | Sample_27 | Sample_36 | Sample_54 | Sample_31 | Sample_45 | Sample_26 | Sample_58 | Sample_60 | Sample_32 | Sample_24 | Sample_42 | Sample_29 | Sample_34 | Sample_35 | Sample_44 | Sample_38 | Sample_21 | Sample_40 | Sample_57 | Sample_47 | Sample_46 | Sample_41 | Sample_28 | Sample_48 | Sample_52 | Sample_50 | Sample_37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;1 | 1 | 1.0000000 | 1.0000000 | 0.7009991 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.9804672 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1 | 0.0109035 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;2 | 1 | 1.0000000 | 1.0000000 | 1.0000000 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1 | 0.0444799 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;3 | 1 | 0.1693163 | 0.7731021 | 1.0000000 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 0.9938559 | 1 | 1 | 1 | 1 | 0.1018061 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;4 | 1 | 1.0000000 | 1.0000000 | 1.0000000 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1 | 0.6824978 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;5 | 1 | 1.0000000 | 1.0000000 | 1.0000000 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;6 | 1 | 1.0000000 | 1.0000000 | 1.0000000 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1 | 1.0000000 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Once the p-values have been calculated, the makeProbeCalls will make the calls using the adjusted p-values calculated. makeProbeCalls also includes a filter to remove one-hit probes, which are probes that were called only in one sample and do not have a consecutive probe called in a single sample. The return value is HERONProbeDataSet with the calls included as an additional assay.
probe_calls_res <- makeProbeCalls(probe_pval_res)
knitr::kable(head(assay(probe_calls_res, "calls")[,1:5]))| Sample_39 | Sample_23 | Sample_56 | Sample_53 | Sample_43 | |
|---|---|---|---|---|---|
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;1 | FALSE | FALSE | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;2 | FALSE | FALSE | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;3 | FALSE | FALSE | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;4 | FALSE | FALSE | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;5 | FALSE | FALSE | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;6 | FALSE | FALSE | FALSE | FALSE | FALSE |
K of N, Fraction, and Percent of calls made per sequence, probe, epitope, or protein can be determined using the getKofN function.
After calculating probe p-values and calls, the HERON can find epitope segments, i.e. blocks of consecutive probes that have been called within a sample or cluster of samples. The unique method finds all consecutive probes for each sample, then returns the unique set of all epitopic regions.
epi_segments_uniq_res <- findEpitopeSegments(
probe_calls_res,
segment_method = "unique"
)
knitr::kable(head(epi_segments_uniq_res))| x |
|---|
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_140_141 |
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_172_173 |
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_247_247 |
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_542_546 |
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_553_560 |
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_568_577 |
The format of the epitope segments are SEQID_Begin_End, where the SEQID is the protein name, Begin is the starting position of the first probe within the consecutive block, and the End is the starting position of the last probe within the consecutive block.
With the epitope segments and the probe p-values, HERON can calculate a significance value for the segments using a meta p-value method. Here, we are calculating epitope p-values using Wilkinson’s max meta p-value method.
epi_padj_uniq <- calcEpitopePValues(
probe_calls_res,
epitope_ids = epi_segments_uniq_res,
metap_method = "wmax1"
)You can add sequence annotations to the row data of the HERONEpitopeDataSet object.
The makeEpitopeCalls method will work on the epitope adjusted p-values to make epitope-level sample. getKofN can also get the K of N results.
epi_calls_uniq <- makeEpitopeCalls(epi_padj_uniq, one_hit_filter = TRUE)
epi_calls_k_of_n_uniq <- getKofN(epi_calls_uniq)
knitr::kable(head(epi_calls_k_of_n_uniq))| K | F | P | |
|---|---|---|---|
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_140_141 | 4 | 0.100 | 10.0 |
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_172_173 | 9 | 0.225 | 22.5 |
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_247_247 | 11 | 0.275 | 27.5 |
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_542_546 | 12 | 0.300 | 30.0 |
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_553_560 | 34 | 0.850 | 85.0 |
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface_568_577 | 37 | 0.925 | 92.5 |
Calculate protein p-values using Tippet’s (Wilkinson’s Min) meta p-value method.
prot_calls_uniq <- makeProteinCalls(prot_padj_uniq)
prot_calls_k_of_n_uniq <- getKofN(prot_calls_uniq)
knitr::kable(head(prot_calls_k_of_n_uniq))| K | F | P | |
|---|---|---|---|
| NC_045512.2;YP_009724390.1;Wu1-SARS2_surface | 40 | 1.0 | 100 |
| NC_045512.2;YP_009724393.1;Wu1-SARS2_membrane | 40 | 1.0 | 100 |
| NC_045512.2;YP_009724397.2;Wu1-SARS2_nucleoca | 40 | 1.0 | 100 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope | 12 | 0.3 | 30 |
The are other functions to utilize depending upon what you would like to do. For example, there are different methods for finding the epitope segments that involve clustering across samples. There are two main methods, one using hierarchical clustering and another using the skater method from the spdep package. In addition to the two methods, how the distance matrix is calculated can be modified. The following subsections demonstrate how to find epitope segment blocks using hclust or skater and using a binary hamming distance or a numeric euclidean distance for making calls. After the segments are found, you can then use the calcEpitopePValuesMat and makeEpitopeCalls functions as before to find the epitope p-values, protein p-values, and the respective calls.
HERON also allows a choice for a number of meta p-value methods for combining p-values for epitopes (calcEpitopePValuesPDS) and proteins (calcProteinPValuesEDS). The methods supported by HERON are : min_bonf, min, max, fischer/sumlog, hmp/harmonicmeanp, wilkinsons_min1/tippets, wilkinsons_min2/wmin2, wilkinsons_min3, wilkinsons_min4, wilkinsons_min5, wilkinsons_max1/wmax1, wilkinsons_max2/wmax2, and cct.
When choosing a p-value method, keep in mind that the epitope p-value should be one that requires most of the probe p-values to be small (e.g. wmax1) and the protein should be one that requires at least one of the epitope p-values to be small (e.g. wmax1). Other p-value methods such as the cct and the hmp have been shown to be more accurate with p-value that have dependencies.
Some investigators would like to make z-score global level calls rather than using adjusted p-values. HERON is flexible to allow for such a setup. For example, the user wanted to make probe-level calls using a z-score cutoff > 2.
seq_pval_res_z <- calcCombPValues(
obj = seq_ds_qn,
use = "z",
p_adjust_method = "none"
)
p_cutoff <- pnorm(2, lower.tail = FALSE)
probe_pval_res_z <- convertSequenceDSToProbeDS(seq_pval_res_z, probe_meta)
probe_calls_z2 <- makeProbeCalls(probe_pval_res_z, padj_cutoff = p_cutoff)
probe_k_of_n_z2 <- getKofN(probe_calls_z2)
knitr::kable(head(assay(probe_calls_z2,"calls")[,1:5]))| Sample_39 | Sample_23 | Sample_56 | Sample_53 | Sample_43 | |
|---|---|---|---|---|---|
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;1 | FALSE | FALSE | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;2 | FALSE | FALSE | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;3 | FALSE | FALSE | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;4 | FALSE | FALSE | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;5 | FALSE | FALSE | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;6 | FALSE | FALSE | FALSE | FALSE | FALSE |
| K | F | P | |
|---|---|---|---|
| NC_045512.2;YP_009724393.1;Wu1-SARS2_membrane;4 | 1 | 0.025 | 2.5 |
| NC_045512.2;YP_009724393.1;Wu1-SARS2_membrane;5 | 3 | 0.075 | 7.5 |
| NC_045512.2;YP_009724393.1;Wu1-SARS2_membrane;6 | 1 | 0.025 | 2.5 |
| NC_045512.2;YP_009724393.1;Wu1-SARS2_membrane;7 | 4 | 0.100 | 10.0 |
| NC_045512.2;YP_009724393.1;Wu1-SARS2_membrane;8 | 10 | 0.250 | 25.0 |
| NC_045512.2;YP_009724393.1;Wu1-SARS2_membrane;156 | 2 | 0.050 | 5.0 |
The calls can also be used to find epitopes segments, p-values, and calls. Also, can be used to make protein level calls.
If we want to find regions where the z > 2 for all of the consecutive probes, using the max meta p-value method will ensure that.
epi_pval_uniq_z2 <- calcEpitopePValues(
probe_pds = probe_pval_res_z,
epitope_ids = epi_segments_uniq_z2_res,
metap_method = "max",
p_adjust_method = "none"
)Again, makeEpitopeCalls will be used in order to find significant regions.
Other segmentation methods can be used with the called regions through the binary score clustering methods.
The pepStat paper (https://pubmed.ncbi.nlm.nih.gov/23770318/) mentions that smoothing can sometimes help reduce the high-variability of the peptide array data. HERON has implemented a running average smoothing algorithm across protein probes that can handle missing values. The function smoothProbeMat will take as input a probe matrix and will return a matrix that has been smoothed. The smoothed matrix can then be processed through the workflow using the calcProbePValuesProbeMat call instead of the calcProbePValuesSeqMat call since now the probe signal is no longer a direct copy from the sequence.
probe_ds_qn <- convertSequenceDSToProbeDS(seq_ds_qn, probe_meta )
smooth_ds <- smoothProbeDS(probe_ds_qn)After you smoothed the data using the probes, the probe p-value will be calculated on the probe-level rather than the sequence-level.
The probe calls can then be made as before.
probe_sm_calls <- makeProbeCalls(probe_sm_pval)
probe_sm_k_of_n <- getKofN(probe_sm_calls)
knitr::kable(assay(probe_sm_calls,"calls")[1:3,1:3])| Sample_39 | Sample_23 | Sample_56 | |
|---|---|---|---|
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;1 | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;2 | FALSE | FALSE | FALSE |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;3 | FALSE | FALSE | FALSE |
| K | F | P | |
|---|---|---|---|
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;1 | 1 | 0.025 | 2.5 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;2 | 1 | 0.025 | 2.5 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;57 | 1 | 0.025 | 2.5 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;58 | 1 | 0.025 | 2.5 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;59 | 1 | 0.025 | 2.5 |
| NC_045512.2;YP_009724392.1;Wu1-SARS2_envelope;60 | 2 | 0.050 | 5.0 |
Paired t-tests can be utilized and combined with the z-tests as well. Here is an example where we pair the five COVID- samples to the COVID+ samples and run calcProbePValuesSeqMat with the t_paired parameter set.
data(heffron2021_wuhan)
probe_meta <- attr(heffron2021_wuhan, "probe_meta")
colData_paired <- colData(heffron2021_wuhan)
## Make some samples paired by setting the sample ids
pre_idx <- which(colData_paired$visit == "pre")
colData_post <- colData_paired[colData_paired$visit == "post",]
new_ids <- colData_post$SampleName[seq_len(5)]
colData_paired$ptid[pre_idx[seq_len(5)]] = new_ids
paired_ds <- heffron2021_wuhan
colData(paired_ds) <- colData_paired
## calculate p-values
pval_res <- calcCombPValues(
obj = paired_ds,
t_paired = TRUE
)
knitr::kable(assay(pval_res[1:3,],"pvalue"))| Sample_39 | Sample_23 | Sample_56 | Sample_53 | Sample_43 | |
|---|---|---|---|---|---|
| AAAYYVGYLQPRTFLL | 0.4192558 | 0.8596157 | 0.3643977 | 0.5703188 | 0.5695711 |
| AADLDDFSKQLQQSMS | 0.0001467 | 0.0913935 | 0.0000501 | 0.7835355 | 0.0000709 |
| AAEASKKPRQKRTATK | 0.0839504 | 0.2146309 | 0.0049659 | 0.2129732 | 0.1286111 |
col_data <- colData(heffron2021_wuhan)
covid <- which(col_data$visit == "post")
col_data$condition[covid[1:10]] <- "COVID2"
seq_ds <- heffron2021_wuhan
colData(seq_ds) <- col_data
seq_ds_qn <- quantileNormalize(seq_ds)
seq_pval_res <- calcCombPValues(seq_ds_qn)
probe_pval_res <- convertSequenceDSToProbeDS(seq_pval_res)
probe_calls_res <- makeProbeCalls(probe_pval_res)
probe_calls_k_of_n <- getKofN(probe_calls_res)HERON and its developers have been partially supported by funding from the Clinical and Translational Science Award (CTSA) program (ncats.nih.gov/ctsa), through the National Institutes of Health National Center for Advancing Translational Sciences (NCATS), grants UL1TR002373 and KL2TR002374, NIH National Institute of Allergy and Infectious Diseases, 2U19AI104317-06, NIH National Cancer Institute (P30CA14520, P50CA278595, and P01CA250972), startup funds through the University of Wisconsin Department of Obstetrics and Gynecology and the University of Wisconsin-Madison Office of the Chancellor and the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation through the Data Science Initiative award.
We have benefited in the development of HERON from the help and feedback of many individuals, including but not limited to:
The Bioconductor Core Team, Paul Sondel, Anna Hoefges, Amy Erbe Gurel, Jessica Vera, Rene Welch, Ken Lo (Nimble Therapeutics), Brad Garcia (Nimble Therapeutics), Jigar Patel (Nimble Therapeutics), John Tan, Nicholas Mathers, Richard Pinapatti.
sessionInfo()
#> R version 4.3.1 (2023-06-16)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 22.04.3 LTS
#>
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.18-bioc/R/lib/libRblas.so
#> LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_GB LC_COLLATE=C
#> [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
#> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
#> [9] LC_ADDRESS=C LC_TELEPHONE=C
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
#>
#> 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] HERON_1.0.0 SummarizedExperiment_1.32.0
#> [3] Biobase_2.62.0 GenomicRanges_1.54.0
#> [5] GenomeInfoDb_1.38.0 IRanges_2.36.0
#> [7] S4Vectors_0.40.0 BiocGenerics_0.48.0
#> [9] MatrixGenerics_1.14.0 matrixStats_1.0.0
#>
#> loaded via a namespace (and not attached):
#> [1] tidyselect_1.2.0 dplyr_1.1.3 bitops_1.0-7
#> [4] fastmap_1.1.1 RCurl_1.98-1.12 TH.data_1.1-2
#> [7] mathjaxr_1.6-0 digest_0.6.33 lifecycle_1.0.3
#> [10] sf_1.0-14 cluster_2.1.4 survival_3.5-7
#> [13] statmod_1.5.0 magrittr_2.0.3 compiler_4.3.1
#> [16] rlang_1.1.1 sass_0.4.7 tools_4.3.1
#> [19] utf8_1.2.4 plotrix_3.8-2 yaml_2.3.7
#> [22] data.table_1.14.8 knitr_1.44 sn_2.1.1
#> [25] S4Arrays_1.2.0 sp_2.1-1 classInt_0.4-10
#> [28] mnormt_2.1.1 DelayedArray_0.28.0 multcomp_1.4-25
#> [31] abind_1.4-5 KernSmooth_2.23-22 numDeriv_2016.8-1.1
#> [34] grid_4.3.1 fansi_1.0.5 multtest_2.58.0
#> [37] e1071_1.7-13 MASS_7.3-60 cli_3.6.1
#> [40] mvtnorm_1.2-3 rmarkdown_2.25 crayon_1.5.2
#> [43] generics_0.1.3 metap_1.9 spdep_1.2-8
#> [46] DBI_1.1.3 cachem_1.0.8 proxy_0.4-27
#> [49] zlibbioc_1.48.0 splines_4.3.1 s2_1.1.4
#> [52] XVector_0.42.0 vctrs_0.6.4 boot_1.3-28.1
#> [55] Matrix_1.6-1.1 sandwich_3.0-2 jsonlite_1.8.7
#> [58] spData_2.3.0 limma_3.58.0 jquerylib_0.1.4
#> [61] units_0.8-4 glue_1.6.2 codetools_0.2-19
#> [64] deldir_1.0-9 tibble_3.2.1 pillar_1.9.0
#> [67] htmltools_0.5.6.1 GenomeInfoDbData_1.2.11 R6_2.5.1
#> [70] wk_0.9.0 Rdpack_2.5 evaluate_0.22
#> [73] lattice_0.22-5 rbibutils_2.2.15 qqconf_1.3.2
#> [76] TFisher_0.2.0 bslib_0.5.1 class_7.3-22
#> [79] mutoss_0.1-13 Rcpp_1.0.11 SparseArray_1.2.0
#> [82] xfun_0.40 pkgconfig_2.0.3 zoo_1.8-12