Control experiment to assess robustness of protein detection via flycodes

Pascal Egloff1, Christian Panse2* and Markus Seeger,1

1Institute of Medical Microbiology, University of Zurich
2Functional Genomics Center Zurich, UZH|ETHZ

*cp@fgcz.ethz.ch

2018-09-18, 2018-09-22, 2018-09-27, 2018-09-28, 2018-10-02, 2018-10-03

Abstract

The following content was used to compile the Supplementary Note 1 in Egloff et al. (2018) (under review NMETH-A35040) to demonstrate the robustness of protein detection via flycodes.

1 Getting started

library(lattice)
library(knitr)
library(parallel)
library(NestLink)

cv <- 1 - 1:7 / 10
t <- trellis.par.get("strip.background")
t$col <- (rgb(cv,cv,cv))
trellis.par.set("strip.background", t)
n.simulation <- 10

2 Load data

# filename <- system.file("extdata/PGexport2_normalizedAgainstSBstandards_Peptides.csv",
#                        package = "NestLink")
# library(ExperimentHub)
# eh <- ExperimentHub()
# filename <- query(eh, c("NestLink", "PGexport2_normalizedAgainstSBstandards_Peptides.csv"))[[1]]

filename <- getExperimentHubFilename("PGexport2_normalizedAgainstSBstandards_Peptides.csv")
P <- read.csv(filename,
              header = TRUE, sep=';')
dim(P)

## [1] 721  27

2.1 Clean

remove modifications

P <- P[P$Modifications == '', ]
dim(P)

## [1] 697  27

select rows

P <- P[,c('Accession', 'Sequence', "X20170919_05_62465_nl5idx1.3_6titratecoli",
          "X20170919_16_62465_nl5idx1.3_6titratecoli", 
          "X20170919_09_62466_nl5idx1.3_7titratesmeg",
          "X20170919_14_62466_nl5idx1.3_7titratesmeg")]
dim(P)

## [1] 697   6

rename column names

names(P)<-c('Accession','Sequence','coli1', 'coli2', 'smeg1', 'smeg2')
dim(P)

## [1] 697   6

remove all rows with invalid identidfier

P<- P[grep("^P[0-9][A-Z][0-9]", P$Accession), ] 

P<-droplevels(P)

add flycode set annotation

P$ConcGr <- NA

P$ConcGr[P$Accession %in% c('P1A4', 'P1B4', 'P1C4', 'P1D4', 'P1E4', 'P1F4')] <- 92

P$ConcGr[P$Accession %in% c('P1A5', 'P1B5', 'P1C5', 'P1D5', 'P1G4', 'P1H4')] <- 295

P$ConcGr[P$Accession %in% c('P1A6', 'P1B6', 'P1E5', 'P1F5', 'P1G5', 'P1H5')] <- 943

P$ConcGr[P$Accession %in% c('P1C6', 'P1D6', 'P1E6', 'P1F6', 'P1G6', 'P1H6')] <- 3017

2.2 Sanity check

table(P$ConcGr)

## 
##   92  295  943 3017 
##   82  122  135  165

Pabs <- P

table(P$Accession)

## 
## P1A4 P1A5 P1A6 P1B4 P1B5 P1B6 P1C4 P1C5 P1C6 P1D4 P1D5 P1D6 P1E4 P1E5 P1E6 P1F4 
##   11   22   24   15   22   23   16   19   26   15   16   29   13   23   30   12 
## P1F5 P1F6 P1G4 P1G5 P1G6 P1H4 P1H5 P1H6 
##   19   28   22   24   24   21   22   28

2.3 Camera ready summary table

P.summary <- aggregate(. ~ ConcGr * Accession, data=P[,c('Accession', 'coli1',
    'coli2', 'smeg1', 'smeg2', 'ConcGr')], FUN=sum)
P.summary$nDetectedFlycodes <- aggregate(Sequence ~ ConcGr * Accession,
    data=na.omit(P), FUN=length)[,3]
P.summary$nTotalFlycodes <- 30
P.summary$coverage <- round(100 * P.summary$nDetectedFlycodes  / P.summary$nTotalFlycodes)
kable(P.summary[order(P.summary$ConcGr),], row.names = FALSE)

ConcGr	Accession	coli1	coli2	smeg1	smeg2	nDetectedFlycodes	nTotalFlycodes	coverage
92	P1A4	3473996	3670152	3524234	3629077	11	30	37
92	P1B4	3972002	3951215	3685668	3632472	15	30	50
92	P1C4	5582053	5716917	5700899	5623891	16	30	53
92	P1D4	5188468	5642192	5245252	5281381	15	30	50
92	P1E4	4697745	4824760	5051017	5146804	13	30	43
92	P1F4	3968239	4026336	4246879	4251951	12	30	40
295	P1A5	23970332	24546550	26479936	25950084	22	30	73
295	P1B5	16033017	16352277	17209165	17490691	22	30	73
295	P1C5	24016078	24734329	22810916	22589773	19	30	63
295	P1D5	17658145	17864382	17760463	17773297	16	30	53
295	P1G4	16016015	16618336	18270569	19036154	22	30	73
295	P1H4	19519544	20301903	20111340	20174474	21	30	70
943	P1A6	65538576	67507722	66123186	66400185	24	30	80
943	P1B6	55078431	58048226	50652047	50278919	23	30	77
943	P1E5	60305499	62836186	62173846	61952054	23	30	77
943	P1F5	46800670	49088967	47748401	47930977	19	30	63
943	P1G5	54312219	55033298	51968903	51106582	24	30	80
943	P1H5	59931716	61370897	55971370	56588298	22	30	73
3017	P1C6	168463728	180586807	158342929	158748952	26	30	87
3017	P1D6	159828074	163103139	140519542	138765621	29	30	97
3017	P1E6	166626467	176697478	159850632	161744675	30	30	100
3017	P1F6	191955804	203793127	181359940	182939796	28	30	93
3017	P1G6	183248427	189386707	177588746	178178834	24	30	80
3017	P1H6	181057205	185326019	161715001	152753819	28	30	93

# write.csv(P.summary, file='Figs/FigureS6b.csv')

The following function defines the computation and rendering of the by the paris function called panels.

panel.cor <- function(x, y, digits = 2, prefix = "", cex.cor, ...)
{
    usr <- par("usr"); on.exit(par(usr))
    par(usr = c(0, 1, 0, 1))
    r <- abs(cor(x, y))
    txt <- format(c(r, 0.123456789), digits = digits)[1]
    txt <- paste0(prefix, txt)
    if(missing(cex.cor)) cex.cor <- 0.8/strwidth(txt)
    text(0.5, 0.5, txt, cex = cex.cor * r)
}

rv <-lapply(unique(P$ConcGr), function(q){
pairs((P[P$ConcGr == q ,c('coli1', 'coli2', 'smeg1', 'smeg2')]),
      pch=16, col=rgb(0.5,0.5,0.5,alpha = 0.3),
      lower.panel = panel.cor,
      asp=1,
      main=q)
})

2.4 Define `FCfill2max`

to conduct a fair random experiment we add dummy flycodes to the input data.frame.

FCfill2max <- function(P, n = max(table(P$Accession))){
   for (i in unique(P$Accession)){
     idx <- which(P$Accession == i)
     # determine the number of missing rows for Accession i
     ndiff <- n - length(idx)
     
     if(length(idx) < n){
       cand <- P[idx[1], ]  
       cand[,2 ] <- "xxx"
       cand[,3:6 ] <- NA
       
       for (j in 1:ndiff){
         P <- rbind(P, cand)
       }
     }
   }
  P
}

2.5 Plot compute CVs for each row

P.mean <- apply(P[, c('coli1', 'coli2', 'smeg1', 'smeg2')],1, FUN=mean)
P.sd <- apply(P[, c('coli1', 'coli2', 'smeg1', 'smeg2')],1, FUN=sd)

boxplot(100*P.sd/P.mean ~ P$ConcGr,log='y', ylab='CV%')

P <- FCfill2max(P)

3 Absolute Quantification

3.1 Define function `FlycodeAbsoluteStatistics` using `coli1` column

FlycodeAbsoluteStatistics <- function(P){
  
  PP <- aggregate(P$coli1 ~ P$Accession + P$ConcGr, FUN=sum)
  
  names(PP) <- c('Accession', 'ConcGr', 'coli1_sum')
  PPP <- aggregate(PP$coli1_sum ~ PP$ConcGr, FUN=mean)

  P.mean <- aggregate(PP$coli1_sum ~ PP$ConcGr, FUN=mean)
  P.sd <- aggregate(PP$coli1_sum ~ PP$ConcGr, FUN=sd)
  P.cv <- aggregate(PP$coli1_sum ~ PP$ConcGr,
      FUN = function(x){ 100 * sd(x) / mean(x) })
  P.length <- max(aggregate(P$coli1 ~ P$Accession, FUN=length)[,2])
 
 rv <- data.frame(ConcGr=P.sd[,1],
                  mean=P.mean[,2],
                  sd=P.sd[,2],
                  cv=round(P.cv[,2],2))
 rv$nFCAccession <-  P.length
 rv
}

3.2 Camera ready absolute table

kable(FlycodeAbsoluteStatistics(P))

ConcGr	mean	sd	cv	nFCAccession
92	4480417	811894.8	18.12	30
295	19535522	3685706.9	18.87	30
943	56994519	6440051.4	11.30	30
3017	175196618	12124519.7	6.92	30

3.3 Define `FCrandom`

# TODO(cp); make it work for n = 0
FCrandom <- function(P, n = 1){
  if(n == 0){
    return (P)
  }
  for (i in unique(P$Accession)){
    idx <- which(P$Accession == i)
    stopifnot(length(idx) >= n)
    smp <- sample(length(idx), n)
    P <- P[-idx[smp],]
  }
  P$n <- n
  P
}

3.4 Conduct the random experiment

set.seed(8)
S <- do.call('rbind', lapply(1:29, function(i){
  FlycodeAbsoluteStatistics(FCrandom(P, i))
  }))

xyplot(cv ~ nFCAccession | ConcGr, 
       data = S, 
       layout = c(4, 1),
       strip = strip.custom(strip.names = TRUE, strip.levels = TRUE)
       )

set.seed(1)

S.rep <- do.call('rbind', 
    lapply(1:n.simulation, function(s){
       S <- do.call('rbind', 
           lapply(1:29, function(i){
                FlycodeAbsoluteStatistics(FCrandom(P, i))
             }))
       }))

3.5 Camera ready plot of absolute flycode simulation

NestLink_absolute_flycode_simulation <- xyplot(cv ~ nFCAccession |  ConcGr,
       data = S.rep,
       panel = function(x,y,...){
         panel.abline(h=c(10, 50), col='red')
         panel.xyplot(x, y, ...)
         xy.median <- (aggregate(y, by=list(x), FUN=median, na.rm = TRUE))
         xy.quantile <- aggregate(y, by=list(x), FUN=function(d){quantile(d, c(0.05, 0.5, 0.95), na.rm = TRUE)})
         panel.points( xy.median[,1], xy.median[,2], pch=16, cex=0.5)
         # print((xy.quantile[,2])[,3])
         panel.points( xy.quantile[,1],(xy.quantile[,2])[,1], pch='-')
         panel.points( xy.quantile[,1],(xy.quantile[,2])[,3], pch='-')
       },
       xlab= 'Number of flycodes',
       ylab ='CV [%]',
       strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       scales=list(x=list(at=c(1,5,10,15,20,25,30)),
                   y=list(at=c(0,10,50,100,150,200))),
       ylim=c(0,175),
       
       pch=16,
       col=rgb(0.5, 0.5, 0.5, alpha = 0.01),
       layout = c(4,1))

print(NestLink_absolute_flycode_simulation)

# png("NestLink_absolute_flycode_simulation.png", 1200,800)
# print(NestLink_absolute_flycode_simulation)
# dev.off()

4 Relative Quantification

4.1 Normalization

P <- na.omit(P)
P <- P[P$coli1 >0,]


P$coli1 <- P$coli1 / sum(P$coli1)
P$coli2 <- P$coli2 / sum(P$coli2)
P$smeg1 <- P$smeg1 / sum(P$smeg1)
P$smeg2 <- P$smeg2 / sum(P$smeg2)

sanity check

sum(P$coli1)

## [1] 1

sum(P$coli2)

## [1] 1

sum(P$smeg1)

## [1] 1

sum(P$smeg2)

## [1] 1

4.2 Define ratios

P$ratios <- (0.5* (P$coli1 + P$coli2)) / (0.5 * (P$smeg1 + P$smeg2))

b <- boxplot(P$coli1 / P$coli2, P$coli1 / P$smeg1, P$coli1 / P$smeg2,P$coli2 / P$smeg1, P$coli2 / P$smeg2 , P$smeg1 / P$smeg2, P$ratios, 
        ylab='ratios', ylim = c(0,2 ))
axis(1, 1:6, c('coli[12]', 'coli1-smeg1', 'coli1-smeg2', 'coli2-smeg1', 'coli2- smeg2','smeg[12]'))

op <- par(mfrow = c(1, 4))
boxplot(P$coli1 ~ P$ConcGr)
boxplot(P$coli2 ~ P$ConcGr)
boxplot(P$smeg1 ~ P$ConcGr)
boxplot(P$smeg2 ~ P$ConcGr)

4.3 Determine outliers (removal)

op <- par(mfrow=c(1,1), mar=c(5,5,5,2) )

b <- boxplot(df<-cbind(P$coli1/P$coli2, P$coli1/P$smeg1, P$coli1/P$smeg2, P$coli2/P$smeg1, P$coli2/P$smeg2, P$smeg1/P$smeg2, P$ratios),
             log='y',
        ylab='normalized ratios',
        #ylim = c(0, 2),
        axes=FALSE,
        main=paste("ConcGr = all"))
axis(1, 1:7, c('coli[12]', 'coli1-smeg1', 'coli1-smeg2', 'coli2-smeg1', 'coli2- smeg2','smeg[12]', 'ratio'))
abline(h=1, col='red')
box()
axis(2)
#axis(3, 1:7, b$n)
outliers.idx <- sapply(1:length(b$group),
    function(i){
      q <- df[, b$group[i]] == b$out[i];
      text(b$group[i], b$out[i], P[q, 2], pos=4, cex=0.4);
      text(b$group[i], b$out[i], P[q, 1], pos=2, cex=0.4);
      which(q)})

b <- boxplot(df<-cbind(P$coli1/P$coli2, P$coli1/P$smeg1, P$coli1/P$smeg2, P$coli2/P$smeg1, P$coli2/P$smeg2, P$smeg1/P$smeg2, P$ratio),
             log='',
        ylab='normalized ratios',
        ylim = c(0, 2),
        axes=FALSE,
        main=paste("ConcGr = all"))
axis(1, 1:7, c('coli[12]', 'coli1-smeg1', 'coli1-smeg2', 'coli2-smeg1', 'coli2- smeg2','smeg[12]', 'ratio'))
abline(h=1, col='red')
box()
axis(2)
axis(3, 1:length(b$n), b$n)
outliers.idx <- sapply(1:length(b$group),
    function(i){
      q <- df[, b$group[i]] == b$out[i];
      text(b$group[i], b$out[i], P[q, 2], pos=4, cex=0.4);
      text(b$group[i], b$out[i], P[q, 1], pos=2, cex=0.4);
      which(q)})

kable(P[unique(outliers.idx),])

	Accession	Sequence	coli1	coli2	smeg1	smeg2	ConcGr	ratios
38	P1H6	GSSEDDAEGWLR	0.0000121	0.0000003	0.0000001	0.0000003	3017	31.1061717
61	P1F6	GSPAADDVSWQSR	0.0000135	0.0000090	0.0000103	0.0000099	3017	1.1148184
69	P1F6	GSGTAEESYWQEGGR	0.0000287	0.0000086	0.0000209	0.0000089	3017	1.2538971
105	P1C6	GSNDPEVDGWLTVR	0.0000133	0.0000093	0.0000168	0.0000153	3017	0.7040914
115	P1D6	GSELAPSVGWQEGGR	0.0000604	0.0000103	0.0000095	0.0000101	3017	3.6002928
117	P1D6	GSAAVAPNVWR	0.0000051	0.0000007	0.0000020	0.0000013	3017	1.7807121
119	P1D6	GSDTTSVDTWQEGGR	0.0000311	0.0000110	0.0000386	0.0000396	3017	0.5385343
126	P1D6	GSVSTYDPVWR	0.0062807	0.0049329	0.0053530	0.0057151	3017	1.0131416
169	P1G6	GSEPVADADWQSR	0.0000282	0.0000066	0.0000275	0.0000121	3017	0.8813330
216	P1A6	GSANTVEPGWQSR	0.0000027	0.0000019	0.0000096	0.0000103	943	0.2370577
270	P1G5	GSPPDVFSTWQEGGR	0.0000212	0.0000015	0.0000046	0.0000041	943	2.6019477
303	P1H4	GSDGAVADSWLTVR	0.0003608	0.0002935	0.0003736	0.0003876	295	0.8596582
307	P1H4	GSEAVVTVDWLR	0.0000450	0.0000649	0.0000700	0.0000755	295	0.7553914
347	P1G4	GSETTYYVDWQSR	0.0002854	0.0002333	0.0002281	0.0002364	295	1.1168094
348	P1G4	GSAVWEPDYWLR	0.0000360	0.0000473	0.0002191	0.0002166	295	0.1911726
349	P1G4	GSPDLADDVWLTVR	0.0002689	0.0001850	0.0002258	0.0001999	295	1.0662495
352	P1G4	GSQENGGADWQSR	0.0000062	0.0000156	0.0000256	0.0000313	295	0.3831785
355	P1H5	GSSVGQAVEWQEGGR	0.0000634	0.0000139	0.0000543	0.0000162	943	1.0965878
452	P1D5	GSDEPAYAVWLR	0.0000139	0.0000110	0.0000139	0.0000136	295	0.9059102
468	P1C4	GSADVTVGLWR	0.0000098	0.0000079	0.0000099	0.0000097	92	0.9012831
508	P1B4	GSVVTVGETWQSR	0.0001717	0.0001229	0.0001143	0.0001188	92	1.2636110
511	P1B4	GSVAAVVPDWR	0.0000332	0.0000252	0.0000361	0.0000342	92	0.8299291
527	P1E4	GSDTEADPEWLTVR	0.0001087	0.0000872	0.0001407	0.0001372	92	0.7051292
551	P1F4	GSVEGDVETWLTVR	0.0000389	0.0000587	0.0000522	0.0000428	92	1.0273511
23	P1E6	GSEVVPDTVWR	0.0011784	0.0010995	0.0005598	0.0005781	3017	2.0017582
28	P1E6	GSTEVAEVAWLR	0.0002027	0.0001978	0.0001375	0.0001396	3017	1.4453411
29	P1E6	GSTDEAAFAWQSR	0.0000664	0.0000622	0.0000367	0.0000401	3017	1.6748641
30	P1E6	GSWYEVDGTWLTVR	0.0000208	0.0000258	0.0001270	0.0001108	3017	0.1960714
56	P1H6	GSVEYTTAAWR	0.0000943	0.0000880	0.0000622	0.0000537	3017	1.5729054
83	P1F6	GSPWEGEAAWQSR	0.0002075	0.0001782	0.0001289	0.0001387	3017	1.4418672
111	P1C6	GSGEPSAYSWR	0.0001660	0.0001797	0.0000974	0.0000950	3017	1.7973706
112	P1C6	GSEVTEEVVWQSR	0.0004082	0.0003699	0.0002116	0.0001778	3017	1.9980931
163	P1E5	GSVWDGSVDWLR	0.0003851	0.0003446	0.0008695	0.0007912	943	0.4394173
166	P1E5	GSTAATEAAWLR	0.0000796	0.0000764	0.0000434	0.0000487	943	1.6937723
236	P1A6	GSDPPAVVGWR	0.0000216	0.0000268	0.0000141	0.0000164	943	1.5894671
255	P1B6	GSTDDTVTVWR	0.0001116	0.0001050	0.0000642	0.0000718	943	1.5927951
256	P1B6	GSTTPPLLVWQEGGR	0.0002999	0.0002926	0.0001905	0.0001922	943	1.5481110
259	P1B6	GSVAATEELWLTVR	0.0000609	0.0000537	0.0000328	0.0000276	943	1.8979393
285	P1G5	GSFFSYQGDWLR	0.0000119	0.0000127	0.0000717	0.0000768	943	0.1652766
371	P1H5	GSYTDALEVWLR	0.0000306	0.0000357	0.0002221	0.0002426	943	0.1427107
374	P1H5	GSFVGGGGWWR	0.0000264	0.0000315	0.0000589	0.0000574	943	0.4976272
397	P1B5	GSEDDGDVGWQEGGR	0.0000121	0.0000131	0.0000343	0.0000351	295	0.3621272
451	P1D5	GSVTETASTWQEGGR	0.0000333	0.0000292	0.0000219	0.0000234	295	1.3821678
530	P1E4	GSWLATPDVWLR	0.0000068	0.0000085	0.0000325	0.0000314	92	0.2390561
571	P1A4	GSPGTVWYDWR	0.0000187	0.0000163	0.0000423	0.0000412	92	0.4179539
21	P1E6	GSSPVEDTSWLR	0.0008161	0.0007886	0.0006707	0.0005384	3017	1.3272331
54	P1H6	GSAAPVSAVWQSR	0.0002341	0.0002321	0.0001699	0.0001553	3017	1.4331093
95	P1C6	GSVDVGSAVWQSR	0.0040710	0.0038983	0.0029346	0.0027473	3017	1.4025928
104	P1C6	GSVVASVEAWQSR	0.0010448	0.0009853	0.0008741	0.0006633	3017	1.3204326
184	P1G6	GSSAEDYAVWQEGGR	0.0024441	0.0023660	0.0018494	0.0016301	3017	1.3823930
467	P1C4	GSQSVDTTVWR	0.0000086	0.0000094	0.0000082	0.0000058	92	1.2894310
572	P1A4	GSSTGTVTPWQSR	0.0001916	0.0002032	0.0001307	0.0001230	92	1.5565379
213	P1F5	GSVETETAYWQEGGR	0.0000315	0.0000338	0.0000247	0.0000222	943	1.3915324
8	P1E6	GSVSEGEDTWQEGGR	0.0000133	0.0000128	0.0000119	0.0000152	3017	0.9595206
31	P1H6	GSVATDVPDWQEGGR	0.0233676	0.0221316	0.0198411	0.0166058	3017	1.2483702
35	P1H6	GSPDTVEYDWQSR	0.0129522	0.0136876	0.0123987	0.0101462	3017	1.1816328
39	P1H6	GSGTYVSDDWR	0.0046986	0.0040630	0.0038690	0.0047031	3017	1.0221084
62	P1F6	GSPTGTDPVWLR	0.0084956	0.0081820	0.0081703	0.0067783	3017	1.1156570
64	P1F6	GSVDAEPTVWQSR	0.0070020	0.0071016	0.0060481	0.0052024	3017	1.2535815
113	P1D6	GSTAATELEWQEGGR	0.0178374	0.0173241	0.0158409	0.0133260	3017	1.2055235
121	P1D6	GSYATGAEPWR	0.0031632	0.0030784	0.0028792	0.0035680	3017	0.9681174
122	P1D6	GSPQLAPDGWR	0.0000541	0.0000579	0.0000554	0.0000462	3017	1.1025485
208	P1F5	GSEVATTAVWQEGGR	0.0005998	0.0005649	0.0005134	0.0004285	943	1.2364966
250	P1B6	GSAADDGYSWLR	0.0007042	0.0006728	0.0006125	0.0004923	943	1.2463635
268	P1G5	GSASENDEDWLTVR	0.0032788	0.0030958	0.0028999	0.0024500	943	1.1915266
292	P1H4	GSVVDGNVTWR	0.0003710	0.0003775	0.0003789	0.0003051	295	1.0943579
329	P1A5	GSVATAYESWQSR	0.0000360	0.0000295	0.0000406	0.0000304	295	0.9217020
342	P1G4	GSPDVVGTAWQEGGR	0.0003646	0.0003627	0.0004204	0.0003465	295	0.9483575
382	P1B5	GSVEPEADVWR	0.0004167	0.0004184	0.0004865	0.0004043	295	0.9374374
406	P1C5	GSAAVPGGVWQEGGR	0.0012621	0.0012378	0.0012112	0.0010131	295	1.1239207
442	P1D5	GSETSGYDVWQSR	0.0007695	0.0007892	0.0007024	0.0006113	295	1.1864482
453	P1C4	GSAVVPDADWQSR	0.0005392	0.0005215	0.0004984	0.0003983	92	1.1829564

rv <-lapply(unique(P$ConcGr), function(q){
pairs((P[P$ConcGr == q ,c('coli1', 'coli2', 'smeg1', 'smeg2')]),
      pch=16, col=rgb(0.5,0.5,0.5,alpha = 0.3),
      lower.panel = panel.cor,
      asp=1,
      main=q)
})

bwplot(ratios ~ Accession | ConcGr,
       data = P,
         strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       panel = function(...){
         
         panel.abline(h=1, col='red')
         panel.bwplot(...)
       },
        ylim=c(-0,2),
       scales = list(x = list(relation = "free", rot=45)),
       layout = c(4,1))

bwplot(ratios ~ ConcGr,
       data = P,
       horizontal = FALSE,
       panel = function(...){
         
         panel.abline(h=1, col='red')
         panel.bwplot(...)
       },
       ylim=c(0,2),
       scales = list(x = list(relation = "free", rot=45)),
       layout = c(1,1))

boxplot(ratios ~ ConcGr,data=P,ylim=c(0,2))
abline(h=1, col=rgb(1,0,0,alpha=0.4))

P<-na.omit(P)
xyplot(ratios ~ Accession |  ConcGr,
       data = P,
         strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       panel =function(x,y, ...){
         panel.abline(h=mean(y), col='red')
          panel.xyplot(x,y, pch=16, col=rgb(0.5,0.5,0.5,alpha = 0.5))
          xy.mean <- (aggregate(y, by=list(x), FUN=mean, na.rm = TRUE))
           xy.sd <- (aggregate(y, by=list(x), FUN=sd, na.rm = TRUE))
          panel.points( xy.mean[,1], xy.mean[,2])
          panel.points( xy.mean[,1], xy.mean[,2] + xy.sd[,2] , pch='-', col='red', cex=4)
           panel.points( xy.mean[,1], xy.mean[,2] - xy.sd[,2] , pch='-', col='red', cex=4)},
        ylim=c(0,2),
       scales = list(x = list(relation = "free", rot=45)),
       layout = c(4,1))

## Warning in order(as.numeric(x)): NAs introduced by coercion

## Warning in diff(as.numeric(x[ord])): NAs introduced by coercion

## Warning in order(as.numeric(x)): NAs introduced by coercion

## Warning in diff(as.numeric(x[ord])): NAs introduced by coercion

## Warning in order(as.numeric(x)): NAs introduced by coercion

## Warning in diff(as.numeric(x[ord])): NAs introduced by coercion

## Warning in order(as.numeric(x)): NAs introduced by coercion

## Warning in diff(as.numeric(x[ord])): NAs introduced by coercion

## Warning in panel.xyplot(x, y, pch = 16, col = rgb(0.5, 0.5, 0.5, alpha = 0.5)):
## NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in panel.xyplot(x, y, pch = 16, col = rgb(0.5, 0.5, 0.5, alpha = 0.5)):
## NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in panel.xyplot(x, y, pch = 16, col = rgb(0.5, 0.5, 0.5, alpha = 0.5)):
## NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in panel.xyplot(x, y, pch = 16, col = rgb(0.5, 0.5, 0.5, alpha = 0.5)):
## NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

P <- na.omit(P)
xyplot(ratios ~ Accession |  ConcGr,
       data = P,
       strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       panel = function(x,y, ...){
         panel.abline(h=mean(y), col='red')
          panel.xyplot(x,y, pch=16, col=rgb(0.5,0.5,0.5,alpha = 0.5))
          xy.mean <- (aggregate(y, by=list(x), FUN=mean, na.rm = TRUE))
           xy.sd <- (aggregate(y, by=list(x), FUN=sd, na.rm = TRUE))
          panel.points( xy.mean[,1], xy.mean[,2])
          panel.points( xy.mean[,1], xy.mean[,2] + xy.sd[,2] , pch='-', col='red', cex=4)
           panel.points( xy.mean[,1], xy.mean[,2] - xy.sd[,2] , pch='-', col='red', cex=4)
           ltext(xy.mean[,1], (xy.mean[,2] + xy.sd[,2]) , round(xy.sd[,2],2), pos=3, cex=0.5)
           },
        
       layout = c(4,1),
       scales = list(y=list(log=TRUE),
                     x = list(relation = "free", rot=45)),
       )

## Warning in order(as.numeric(x)): NAs introduced by coercion

## Warning in diff(as.numeric(x[ord])): NAs introduced by coercion

## Warning in order(as.numeric(x)): NAs introduced by coercion

## Warning in diff(as.numeric(x[ord])): NAs introduced by coercion

## Warning in order(as.numeric(x)): NAs introduced by coercion

## Warning in diff(as.numeric(x[ord])): NAs introduced by coercion

## Warning in order(as.numeric(x)): NAs introduced by coercion

## Warning in diff(as.numeric(x[ord])): NAs introduced by coercion

## Warning in panel.xyplot(x, y, pch = 16, col = rgb(0.5, 0.5, 0.5, alpha = 0.5)):
## NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in panel.xyplot(x, y, pch = 16, col = rgb(0.5, 0.5, 0.5, alpha = 0.5)):
## NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in panel.xyplot(x, y, pch = 16, col = rgb(0.5, 0.5, 0.5, alpha = 0.5)):
## NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in panel.xyplot(x, y, pch = 16, col = rgb(0.5, 0.5, 0.5, alpha = 0.5)):
## NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Warning in xy.coords(x, y, recycle = TRUE): NAs introduced by coercion

## Detect outlier

# P.cv <- aggregate(P$ratios ~ P$Accession, FUN=function(x){100*sd(x)/mean(x)})

P<-na.omit(P)
trellis.par.set("strip.background",t)

xyplot(ratios ~ ConcGr | ConcGr,
       data = P,
         strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       panel = function(x,y){
         panel.abline(h=1, col='red')
          panel.xyplot(x,y, pch=16, col=rgb(0.5,0.5,0.5,alpha = 0.5))
          panel.points(x, mean(y))
         #   panel.points(x, median(y),col='green')
          panel.points(x, mean(y) + sd(y), pch='-', col='red',cex=5)
          ltext(x, mean(y) + sd(y), round(sd(y),3), pos=4)
         
           panel.points(x, mean(y) - sd(y), pch='-', col='red',cex=5)
         },
        #ylim=c(-1,3),
       scales = list(x = list(relation = "free", rot=45)),
       layout = c(4,1))

Figure 1: measured ratios were plotted; red represents the sd and blue points the mean

outlier.idx <- which(P$ratios > 2)
P[outlier.idx, ]

##     Accession        Sequence        coli1        coli2        smeg1
## 23       P1E6     GSEVVPDTVWR 1.178365e-03 1.099467e-03 5.598233e-04
## 38       P1H6    GSSEDDAEGWLR 1.210304e-05 3.215364e-07 1.065422e-07
## 115      P1D6 GSELAPSVGWQEGGR 6.038516e-05 1.025768e-05 9.528549e-06
## 270      P1G5 GSPPDVFSTWQEGGR 2.117599e-05 1.510987e-06 4.601046e-06
##            smeg2 ConcGr    ratios
## 23  5.780923e-04   3017  2.001758
## 38  2.928825e-07   3017 31.106172
## 115 1.009287e-05   3017  3.600293
## 270 4.118184e-06    943  2.601948

# We do not remove outliers.
# P <- P[-outlier.idx,]

P<-na.omit(P)
trellis.par.set("strip.background",t)

xyplot(ratios ~ ConcGr | ConcGr,
       data = P,
         strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       panel = function(x,y){
         panel.abline(h=1, col='red')
          panel.xyplot(x,y, pch=16, col=rgb(0.5,0.5,0.5,alpha = 0.5))
          panel.points(x, mean(y))
         #   panel.points(x, median(y),col='green')
          panel.points(x, mean(y) + sd(y), pch='-', col='red',cex=5)
          ltext(x, mean(y) + sd(y), round(sd(y),3), pos=4)
         
           panel.points(x, mean(y) - sd(y), pch='-', col='red',cex=5)
         },
        #ylim=c(-1,3),
       scales = list(x = list(relation = "free", rot=45)),
       layout = c(4,1))

Figure 2: measured ratios were plotted; red represents the sd and blue points the mean

4.4 Define function `FlycodeRelativeStatistics`

to make the random experiment fair!

P <- FCfill2max(P)

FlycodeRelativeStatistics <- function(X, mode='bio'){
   nFlycodesConcGr <- aggregate(X$Sequence ~ X$ConcGr, FUN=length)
  names(nFlycodesConcGr) <- c('ConcGr', 'nFlycodesConcGr')
  nFlycodesAccession.max <- max(aggregate(X$Sequence ~ X$Accession, FUN=length)[,2])
 
  
  P.sum.coli1 <- aggregate(X$coli1 ~ X$Accession + X$ConcGr, FUN=sum)
  P.sum.coli2 <- aggregate(X$coli2 ~ X$Accession + X$ConcGr, FUN=sum)[,3]
  P.sum.smeg1 <- aggregate(X$smeg1 ~ X$Accession + X$ConcGr, FUN=sum)[,3]
  P.sum.smeg2 <- aggregate(X$smeg2 ~ X$Accession + X$ConcGr, FUN=sum)[,3]
  
  X <- P.sum.coli1
  names(X) <- c('Accession', 'ConcGr', 'coli1')
  
  X$coli2 <- P.sum.coli2
  X$smeg1 <- P.sum.smeg1
  X$smeg2 <- P.sum.smeg2
  
  
  if(!"ratios" %in% names(X)){
    if (mode == 'tech_smeg'){
      X$ratios <- X$smeg1 / X$smeg2
    }
    else if(mode == 'tech_coli'){
      X$ratios <- X$coli1 / X$coli2
    }else{
      # bio
      X$ratios <- ((0.5 * (X$coli1 + X$coli2)) / (0.5 * (X$smeg1 + X$smeg2)))
    }
    #warning("define ratios.")
  }
  
  #nFlycodesConcGr <- aggregate(X$Sequence ~ X$ConcGr, FUN=length)
  #names(nFlycodesConcGr) <- c('ConcGr', 'nFlycodesConcGr')
  X <- na.omit(X)
  
  
  P.mean <- aggregate(X$ratios ~ X$ConcGr, FUN=mean)
  names(P.mean) <- c('ConcGr', 'mean')
  
  P.median <- aggregate(X$ratios ~ X$ConcGr, FUN=median)
  names(P.median) <- c('ConcGr', 'median')
  
  P.sd <- aggregate(X$ratios ~ X$ConcGr, FUN=sd)
  names(P.sd) <- c('ConcGr', 'sd')
  
 rv <- data.frame(ConcGr=P.mean$ConcGr,
                  median=P.median$median,
                  mean=P.mean$mean,
                  sd=P.sd$sd)
         #         nFlycodesConcGr=nFlycodesConcGr[,2])
 
 rv$cv <- 100 * rv$sd / rv$mean 
 rv$length <- nFlycodesAccession.max
 rv
}

4.5 Conduct the random experiment

message(paste("Number of simulations =", n.simulation))

## Number of simulations = 10

set.seed(1)

P.replicate <- do.call('rbind',
  lapply(1:n.simulation, 
    function(run){
      do.call('rbind', lapply(1:29,
        function(i) {
          rv <- FlycodeRelativeStatistics(FCrandom(P, i))
                                                   rv$run = run
                                                   rv
                                                 }))
                       }))

set.seed(1)

P.replicate.smeg <- do.call('rbind',
                       lapply(1:n.simulation/2, function(run){
                         do.call('rbind', lapply(1:29,
                                                 function(i) {
                                                   rv <- FlycodeRelativeStatistics(FCrandom(P, i), mode='tech_smeg')
                                                   rv$run = run
                                                   rv
                                                 }))
                       }))

set.seed(1)

P.replicate.coli <- do.call('rbind',
                       lapply(1:n.simulation/2, function(run){
                         do.call('rbind', lapply(1:29,
                                                 function(i) {
                                                   rv <- FlycodeRelativeStatistics(FCrandom(P, i), mode='tech_coli')
                                                   rv$run = run
                                                   rv
                                                 }))
                       }))

xyplot(mean ~  length | ConcGr, 
       data=P.replicate,
       panel = function(...){
         panel.abline(h=1, col='red')
         panel.xyplot(...)
       },
         strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       ylim=c(0,2),
       pch=16, col=rgb(0.5, 0.5, 0.5, alpha = 0.1),
       layout = c(4,1),
       xlab= 'number of FlyCodes',
       )

the grey point cloud represents the means, sd, and cv of `n.simulation` conducted random experiments (removals) with a different number of FlyCodes.

Figure 3: the grey point cloud represents the means, sd, and cv of n.simulation conducted random experiments (removals) with a different number of FlyCodes

xyplot(sd ~  length | ConcGr, 
       data=P.replicate,
       panel = function(...){
         panel.xyplot(...)
       },
         strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       pch=16, col=rgb(0.5, 0.5, 0.5, alpha = 0.1),
       layout = c(4,1),
       xlab= 'number of FlyCodes',
       )

Figure 4: the grey point cloud represents the means, sd, and cv of n.simulation conducted random experiments (removals) with a different number of FlyCodes

xyplot(cv ~  length | ConcGr, 
       data=P.replicate,
       panel = function(...){
         panel.xyplot(...)
       },
       strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       pch=16, col=rgb(0.5, 0.5, 0.5, alpha = 0.01),
       layout = c(4,1),
       xlab= 'number of FlyCodes',
       ylab ='cv [in %]'
       )

Figure 5: the grey point cloud represents the means, sd, and cv of n.simulation conducted random experiments (removals) with a different number of FlyCodes

4.6 Camera ready plot of relative flycode simulation

SIM <- P.replicate
SIM$Type <- "Biological replicates"
P.replicate.coli$Type <- "Technical replicates"
P.replicate.smeg$Type <- "Technical replicates"

NestLink_relative_flycode_simulation <- xyplot(cv ~ length | ConcGr, 
       index.cond=list(c(1,2,3,4)),
       data=do.call('rbind', list(SIM, P.replicate.coli, P.replicate.smeg)),
       subset = Type == "Biological replicates",
       panel = function(x,y,...){
         panel.abline(h=10, col='red')
         panel.xyplot(x, y, ...)
         xy.median <- (aggregate(y, by=list(x), FUN=median, na.rm = TRUE))
         xy.quantile <- aggregate(y, by=list(x), FUN=function(d){quantile(d, c(0.05, 0.5, 0.95), na.rm = TRUE)})
         panel.points( xy.median[,1], xy.median[,2], pch=16, cex=0.5)
         # print((xy.quantile[,2])[,3])
         panel.points( xy.quantile[,1],(xy.quantile[,2])[,1], pch='-')
         panel.points( xy.quantile[,1],(xy.quantile[,2])[,3], pch='-')
       },
       strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       scales=list(x=list(at=c(1,5,10,15,20,25,30)),
                   y=list(at=c(0, 10,20,30,40,50))),
       pch=16,
       col=rgb(0.5, 0.5, 0.5, alpha = 0.01),
       layout = c(4, 1),
       ylim = c(0, 50),
       xlab= 'Number of flycodes',
       ylab ='CV [%]'
       )

print(NestLink_relative_flycode_simulation)

NestLink_relative_flycode_simulation <- xyplot(cv ~ length | ConcGr, 
       index.cond=list(c(1,2,3,4)),
       data=do.call('rbind', list(SIM, P.replicate.coli, P.replicate.smeg)),
       subset = Type == "Technical replicates",
       panel = function(x,y,...){
         panel.abline(h=10, col='red')
         panel.xyplot(x, y, ...)
         xy.median <- (aggregate(y, by=list(x), FUN=median, na.rm = TRUE))
         xy.quantile <- aggregate(y, by=list(x), FUN=function(d){quantile(d, c(0.05, 0.5, 0.95), na.rm = TRUE)})
         panel.points( xy.median[,1], xy.median[,2], pch=16, cex=0.5)
         # print((xy.quantile[,2])[,3])
         panel.points( xy.quantile[,1],(xy.quantile[,2])[,1], pch='-')
         panel.points( xy.quantile[,1],(xy.quantile[,2])[,3], pch='-')
       },
       strip = strip.custom(strip.names = TRUE, strip.levels = TRUE),
       scales=list(x=list(at=c(1,5,10,15,20,25,30)),
                   y=list(at=c(0, 10,20,30,40,50))),
       pch=16,
       col=rgb(0.5, 0.5, 0.5, alpha = 0.01),
       layout = c(4, 1),
       ylim = c(0, 50),
       xlab= 'Number of flycodes',
       ylab ='CV [%]'
       )

print(NestLink_relative_flycode_simulation)

4.7 Camera ready relative table

length corresponds to the number accessions. i indicates the number of removed Flycodes in each accession group and can be ignored.

kable(FlycodeRelativeStatistics(P, mode = 'bio'))

ConcGr	median	mean	sd	cv	length
92	0.9294538	0.9284512	0.0519245	5.592595	30
295	0.8947774	0.8994735	0.0649453	7.220370	30
943	0.9614609	0.9711361	0.0481363	4.956702	30
3017	1.0179646	1.0278351	0.0444473	4.324363	30

kable(FlycodeRelativeStatistics(P, mode = 'tech_coli'))

ConcGr	median	mean	sd	cv	length
92	1.015500	1.0080013	0.0316037	3.135279	30
295	1.014147	1.0140046	0.0106994	1.055162	30
943	1.005331	1.0061221	0.0151953	1.510284	30
3017	0.994935	0.9967548	0.0210467	2.111524	30

kable(FlycodeRelativeStatistics(P, mode = 'tech_smeg'))

ConcGr	median	mean	sd	cv	length
92	0.9918049	0.9912911	0.0172931	1.7445066	30
295	0.9938872	0.9908330	0.0211242	2.1319627	30
943	0.9956908	0.9972972	0.0098568	0.9883481	30
3017	0.9928825	1.0032881	0.0263150	2.6228775	30

5 Session info

Here is the output of the sessionInfo() command.

## R version 4.1.0 (2021-05-18)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.2 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.13-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.13-bioc/R/lib/libRlapack.so
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        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       
## 
## attached base packages:
## [1] stats4    parallel  stats     graphics  grDevices utils     datasets 
## [8] methods   base     
## 
## other attached packages:
##  [1] lattice_0.20-44             specL_1.26.0               
##  [3] seqinr_4.2-5                RSQLite_2.2.7              
##  [5] DBI_1.1.1                   knitr_1.33                 
##  [7] scales_1.1.1                ggplot2_3.3.3              
##  [9] NestLink_1.8.0              ShortRead_1.50.0           
## [11] GenomicAlignments_1.28.0    SummarizedExperiment_1.22.0
## [13] Biobase_2.52.0              MatrixGenerics_1.4.0       
## [15] matrixStats_0.58.0          Rsamtools_2.8.0            
## [17] GenomicRanges_1.44.0        BiocParallel_1.26.0        
## [19] protViz_0.6.8               gplots_3.1.1               
## [21] Biostrings_2.60.0           GenomeInfoDb_1.28.0        
## [23] XVector_0.32.0              IRanges_2.26.0             
## [25] S4Vectors_0.30.0            ExperimentHub_2.0.0        
## [27] AnnotationHub_3.0.0         BiocFileCache_2.0.0        
## [29] dbplyr_2.1.1                BiocGenerics_0.38.0        
## [31] BiocStyle_2.20.0           
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_2.0-1              hwriter_1.3.2                
##  [3] ellipsis_0.3.2                farver_2.1.0                 
##  [5] bit64_4.0.5                   interactiveDisplayBase_1.30.0
##  [7] AnnotationDbi_1.54.0          fansi_0.4.2                  
##  [9] codetools_0.2-18              splines_4.1.0                
## [11] cachem_1.0.5                  ade4_1.7-16                  
## [13] jsonlite_1.7.2                png_0.1-7                    
## [15] shiny_1.6.0                   BiocManager_1.30.15          
## [17] compiler_4.1.0                httr_1.4.2                   
## [19] assertthat_0.2.1              Matrix_1.3-3                 
## [21] fastmap_1.1.0                 later_1.2.0                  
## [23] prettyunits_1.1.1             htmltools_0.5.1.1            
## [25] tools_4.1.0                   gtable_0.3.0                 
## [27] glue_1.4.2                    GenomeInfoDbData_1.2.6       
## [29] dplyr_1.0.6                   rappdirs_0.3.3               
## [31] Rcpp_1.0.6                    jquerylib_0.1.4              
## [33] vctrs_0.3.8                   nlme_3.1-152                 
## [35] xfun_0.23                     stringr_1.4.0                
## [37] mime_0.10                     lifecycle_1.0.0              
## [39] gtools_3.8.2                  zlibbioc_1.38.0              
## [41] MASS_7.3-54                   hms_1.1.0                    
## [43] promises_1.2.0.1              RColorBrewer_1.1-2           
## [45] yaml_2.2.1                    curl_4.3.1                   
## [47] memoise_2.0.0                 sass_0.4.0                   
## [49] latticeExtra_0.6-29           stringi_1.6.2                
## [51] BiocVersion_3.13.1            highr_0.9                    
## [53] caTools_1.18.2                filelock_1.0.2               
## [55] rlang_0.4.11                  pkgconfig_2.0.3              
## [57] bitops_1.0-7                  evaluate_0.14                
## [59] purrr_0.3.4                   labeling_0.4.2               
## [61] bit_4.0.4                     tidyselect_1.1.1             
## [63] magrittr_2.0.1                bookdown_0.22                
## [65] R6_2.5.0                      magick_2.7.2                 
## [67] generics_0.1.0                DelayedArray_0.18.0          
## [69] pillar_1.6.1                  withr_2.4.2                  
## [71] mgcv_1.8-35                   KEGGREST_1.32.0              
## [73] RCurl_1.98-1.3                tibble_3.1.2                 
## [75] crayon_1.4.1                  KernSmooth_2.23-20           
## [77] utf8_1.2.1                    rmarkdown_2.8                
## [79] progress_1.2.2                jpeg_0.1-8.1                 
## [81] grid_4.1.0                    blob_1.2.1                   
## [83] digest_0.6.27                 xtable_1.8-4                 
## [85] httpuv_1.6.1                  munsell_0.5.0                
## [87] bslib_0.2.5.1

References

Egloff, Pascal, Iwan Zimmermann, Fabian M. Arnold, Cedric A.J. Hutter, Damien Damien Morger, Lennart Opitz, Lucy Poveda, et al. 2018. “Engineered Peptide Barcodes for In-Depth Analyses of Binding Protein Ensembles.” bioRxiv. https://doi.org/10.1101/287813.