R/BioC序列处理之五：Rle和Ranges

（本文已于2015.09.08更新）

生物序列信息不仅仅指序列本身，它们还包括其他类型的信息，如基因都定位在哪些序列（染色体）上，正链还是负链，什么位置，其他数据库对应的编号是什么，有什么功能等等。下面介绍BioC中用于这些数据存储和处理的Rle和Ranges类。

1 Rle（Run Length Encoding，行程编码）

1.1 Rle类和Rle对象

序列或基因最终要定位到染色体上。序列往往数量非常巨大，但染色体数量很少，如果每条序列的染色体定位都显式标注，将会产生大量的重复信息，更糟糕的是它们要占用大量的内存。BioC的IRanges包为这些数据提供了一种简便可行的信息压缩方式，即Rle。如果染色体1-3分别有3000,5000和2000个基因，基因的染色体注释可以用字符向量表示，也可以用Rle对象表示：

library(IRanges)  ##可以不执行，载入Biostrings包将自动载入依赖包IRanges
library(Biostrings)
chr.str <- c(rep("ChrI", 3000), rep("ChrII", 5000), rep("ChrIII", 2000))
chr.rle <- Rle(chr.str)

两种方式的效果是完全一样的，但是Rle对象占用空间还不到字符向量的2%：

## Rle对象向量化后和原向量是完全相同的：
identical(as.vector(chr.rle), chr.str)

## [1] TRUE

## 对象大小（内存占用）比：
as.vector(object.size(chr.rle)/object.size(chr.str))

## [1] 0.01616283

使用Rle并不总是可以“压缩”数据。如果信息没有重复或重复量很少，Rle会占用更多的内存：

strx <- sample(DNA_BASES, 10000, replace = TRUE)
strx.rle <- Rle(strx)
as.vector(object.size(strx.rle)/object.size(strx))

## [1] 1.130721

Rle对象用两个属性来表示原向量，一个是值（values），可以是向量或因子；另一个是长度（lengths），为整型数据，表示对应位置的value的重复次数。

chr.rle

## character-Rle of length 10000 with 3 runs
##   Lengths:     3000     5000     2000
##   Values :   "ChrI"  "ChrII" "ChrIII"

getClass(class(chr.rle))

## Class "Rle" [package "S4Vectors"]
## 
## Slots:
##                                                                       
## Name:           values         lengths elementMetadata        metadata
## Class:  vectorORfactor         integer DataTableORNULL            list
## 
## Extends: 
## Class "Vector", directly
## Class "Annotated", by class "Vector", distance 2

1.2 Rle对象的处理方法

1.2.1 Rle对象构建/获取：

Rle对象可以用构造函数Rle来产生，它有两种用法：

Rle(values)
Rle(values, lengths)

values和lengths均为（原子）向量。第一种用法前面已经出现过了，我们看看第二种用法：

chr.rle <- Rle(values = c("Chr1", "Chr2", "Chr3", "Chr1", "Chr3"), lengths = c(3,
    2, 5, 4, 5))
chr.rle

## character-Rle of length 19 with 5 runs
##   Lengths:      3      2      5      4      5
##   Values : "Chr1" "Chr2" "Chr3" "Chr1" "Chr3"

原子向量也可以通过类型转换函数as由原子向量产生，它等价于上面的第一种方式：

as(chr.str, "Rle")

## character-Rle of length 10000 with 3 runs
##   Lengths:     3000     5000     2000
##   Values :   "ChrI"  "ChrII" "ChrIII"

1.2.2 获取属性：

Rle是S4类，Rle对象的属性如值、长度等可以使用属性读取函数获取：

runLength(chr.rle)

## [1] 3 2 5 4 5

runValue(chr.rle)

## [1] "Chr1" "Chr2" "Chr3" "Chr1" "Chr3"

nrun(chr.rle)

## [1] 5

start(chr.rle)

## [1]  1  4  6 11 15

end(chr.rle)

## [1]  3  5 10 14 19

width(chr.rle)

## [1] 3 2 5 4 5

1.2.3 属性替换：

Rle对象的长度和值还可以使用属性替换函数进行修改：

runLength(chr.rle) <- rep(3, nrun(chr.rle))
chr.rle

## character-Rle of length 15 with 5 runs
##   Lengths:      3      3      3      3      3
##   Values : "Chr1" "Chr2" "Chr3" "Chr1" "Chr3"

runValue(chr.rle)[3:4] <- c("III", "IV")
chr.rle

## character-Rle of length 15 with 5 runs
##   Lengths:      3      3      3      3      3
##   Values : "Chr1" "Chr2"  "III"   "IV" "Chr3"

## 替换向量和被替换向量的长度必需相同，否则出错。下面两个语句都不正确：
runValue(chr.rle) <- c("ChrI", "ChrV")

## Error in .Call2("Rle_constructor", values, lengths, check, 0L, PACKAGE = "S4Vectors"): 'length(lengths)' != 'length(values)'

runLength(chr.rle) <- 3

## Error in .Call2("Rle_constructor", values, lengths, check, 0L, PACKAGE = "S4Vectors"): 'length(lengths)' != 'length(values)'

1.2.4 类型转换：

除使用as.vector函数外，Rle对象还可以使用很多函数进行类型转换，如：

as.factor(chr.rle)

##  [1] Chr1 Chr1 Chr1 Chr2 Chr2 Chr2 III  III  III  IV   IV   IV   Chr3 Chr3
## [15] Chr3
## Levels: Chr1 Chr2 Chr3 III IV

as.character(chr.rle)

##  [1] "Chr1" "Chr1" "Chr1" "Chr2" "Chr2" "Chr2" "III"  "III"  "III"  "IV"  
## [11] "IV"   "IV"   "Chr3" "Chr3" "Chr3"

1.2.5 Rle的S4类集团泛函数运算

Rle是BioC定义的基础数据类型。既然“基础”，那么它应当能进行R语言中数据的一般性运算，比如加减乘除、求模、求余等数学运算。事实也是如此，Rle支持R语言S4类集团泛函数（group generic functions，“集团通用函数”？）运算，包括算术、复数、比较、逻辑、数学函数和R语言的汇总（"max", "min", "range", "prod", "sum", "any", "all"等）运算（没有去验证是否所有运算都已实现）。下面仅简单具几个例子，具体情况请参考Rle-class的相关说明：

set.seed(0)
rle1 <- Rle(sample(4, 6, replace = TRUE))
rle2 <- Rle(sample(5, 12, replace = TRUE))
rle3 <- Rle(sample(4, 8, replace = TRUE))
rle1 + rle2

## integer-Rle of length 12 with 11 runs
##   Lengths: 1 1 1 1 1 1 1 1 1 2 1
##   Values : 9 7 6 7 5 3 5 6 4 7 5

rle1 + rle3

## integer-Rle of length 8 with 8 runs
##   Lengths: 1 1 1 1 1 1 1 1
##   Values : 8 4 6 7 5 4 5 4

rle1 * rle2

## integer-Rle of length 12 with 11 runs
##   Lengths:  1  1  1  1  1  1  1  1  1  2  1
##   Values : 20 10  8 12  4  2  4  8  4 12  4

sqrt(rle1)

## numeric-Rle of length 6 with 5 runs
##   Lengths:                1                2 ...                1
##   Values :                2  1.4142135623731 ...                1

range(rle1)

## [1] 1 4

cumsum(rle1)

## integer-Rle of length 6 with 6 runs
##   Lengths:  1  1  1  1  1  1
##   Values :  4  6  8 11 15 16

(rle1 <- Rle(sample(DNA_BASES, 10, replace = TRUE)))

## character-Rle of length 10 with 9 runs
##   Lengths:   1   1   1   1   2   1   1   1   1
##   Values : "C" "A" "C" "T" "C" "G" "C" "A" "T"

(rle2 <- Rle(sample(DNA_BASES, 8, replace = TRUE)))

## character-Rle of length 8 with 8 runs
##   Lengths:   1   1   1   1   1   1   1   1
##   Values : "G" "T" "A" "G" "C" "T" "G" "T"

paste(rle1, rle2, sep = "")

## character-Rle of length 10 with 10 runs
##   Lengths:    1    1    1    1    1    1    1    1    1    1
##   Values : "CG" "AT" "CA" "TG" "CC" "CT" "GG" "CT" "AG" "TT"

2 Ranges（序列区间/范围）

2.1 BioC中的Ranges

Ranges是一类特殊但又常用的数据类型，它们可以表示小段序列在大段序列中的位置、名称和组织结构等信息。BioC中与Ranges定义有关的软件包主要有IRanges, GenomicRanges和GenomicFeatures。
IRanges包定义了Ranges的一般数据结构和处理方法，但不直接面向序列处理；GenomicRanges包定义的GRanges和GRangesList类除了储存Ranges信息外还包含了序列的名称和DNA链等信息；而GenomicFeatures（包）则处理以数据库形式提供的GRanges信息，如基因、外显子、内含子、启动子、UTR等。
先看看BioC中Ranges最基本的类定义：

getClass("Ranges")

## Virtual Class "Ranges" [package "IRanges"]
## 
## Slots:
##                                                       
## Name:      elementType elementMetadata        metadata
## Class:       character DataTableORNULL            list
## 
## Extends: 
## Class "IntegerList", directly
## Class "RangesORmissing", directly
## Class "AtomicList", by class "IntegerList", distance 2
## Class "List", by class "IntegerList", distance 3
## Class "Vector", by class "IntegerList", distance 4
## Class "Annotated", by class "IntegerList", distance 5
## 
## Known Subclasses: 
## Class "IRanges", directly
## Class "Partitioning", directly
## Class "GappedRanges", directly
## Class "NCList", directly
## Class "IntervalTree", directly
## Class "NormalIRanges", by class "IRanges", distance 2
## Class "PartitioningByEnd", by class "Partitioning", distance 2
## Class "PartitioningByWidth", by class "Partitioning", distance 2
## Class "PartitioningMap", by class "Partitioning", distance 3

Ranges是虚拟类，实际应用中最常用的IRanges子类，它继承了Ranges的数据结构，另外多设置了3个slots（存储槽），分别用于存贮Ranges的起点、宽度和名称信息。由于Ranges由整数确定，所以称为IRanges（Integer Ranges，整数区间），但也有人理解成间隔区间（Interval Ranges）：

getSlots("Ranges")

##       elementType   elementMetadata          metadata 
##       "character" "DataTableORNULL"            "list"

getSlots("IRanges")

##             start             width             NAMES       elementType 
##         "integer"         "integer" "characterORNULL"       "character" 
##   elementMetadata          metadata 
## "DataTableORNULL"            "list"

GRanges是Ranges概念在序列处理上的具体应用，但它和IRanges没有继承关系：

library(GenomicRanges)
getSlots("GRanges")

##        seqnames          ranges          strand elementMetadata 
##           "Rle"       "IRanges"           "Rle"     "DataFrame" 
##         seqinfo        metadata 
##       "Seqinfo"          "list"

Ranges对于序列处理非常重要，除GenomicRanges外，Biostrings一些类的定义也应用了Ranges：

getSlots("XStringViews")

##           subject            ranges       elementType   elementMetadata 
##         "XString"         "IRanges"       "character" "DataTableORNULL" 
##          metadata 
##            "list"

2.2 对象构建和属性获取

IRanges对象可以使用对象构造函数IRanges产生，需提供起点（start）、终点（end）和宽度（width）三个参数中的任意两个：

ir1 <- IRanges(start = 1:10, width = 10:1)
ir2 <- IRanges(start = 1:10, end = 11)
ir3 <- IRanges(end = 11, width = 10:1)
ir1

## IRanges of length 10
##      start end width
## [1]      1  10    10
## [2]      2  10     9
## [3]      3  10     8
## [4]      4  10     7
## [5]      5  10     6
## [6]      6  10     5
## [7]      7  10     4
## [8]      8  10     3
## [9]      9  10     2
## [10]    10  10     1

GRanges对象也可以使用构造函数生成，其方式与数据框对象生成有些类似：

genes <- GRanges(seqnames = c("Chr1", "Chr3", "Chr3"), ranges = IRanges(start = c(1300,
    1050, 2000), end = c(2500, 1870, 3200)), strand = c("+", "+", "-"), seqlengths = c(Chr1 = 1e+05,
    Chr3 = 2e+05))
genes

## GRanges object with 3 ranges and 0 metadata columns:
##       seqnames       ranges strand
##                
##   [1]     Chr1 [1300, 2500]      +
##   [2]     Chr3 [1050, 1870]      +
##   [3]     Chr3 [2000, 3200]      -
##   -------
##   seqinfo: 2 sequences from an unspecified genome

IRanges和GRanges都是S4类，其属性获取有相应的函数：

start(ir1)

##  [1]  1  2  3  4  5  6  7  8  9 10

end(ir1)

##  [1] 10 10 10 10 10 10 10 10 10 10

width(ir1)

##  [1] 10  9  8  7  6  5  4  3  2  1

ranges(genes)

## IRanges of length 3
##     start  end width
## [1]  1300 2500  1201
## [2]  1050 1870   821
## [3]  2000 3200  1201

start(ranges(genes))

## [1] 1300 1050 2000

Views对象也包含有IRanges属性：

## 按长度设置产生随机序列的函数
rndSeq <- function(dict, n) {
    paste(sample(dict, n, replace = T), collapse = "")
}
set.seed(0)
dna <- DNAString(rndSeq(DNA_BASES, 1000))
vws <- as(maskMotif(dna, "TGA"), "Views")
(ir <- ranges(vws))

## IRanges of length 18
##      start  end width
## [1]      1  104   104
## [2]    108  264   157
## [3]    268  268     1
## [4]    272  300    29
## [5]    304  393    90
## ...    ...  ...   ...
## [14]   586  752   167
## [15]   756  851    96
## [16]   855  912    58
## [17]   916  989    74
## [18]   993 1000     8

模式匹配的match类函数返回IRanges对象，而vmatch类函数返回GRanges类对象：

2.3 IRanges对象的运算和处理方法

2.3.1 Ranges内变换（Intra-range transformations）

这种类型的处理函数包括shift，flank，narrow，reflect，resize，restrict和promoters等，它们对每个Ranges进行独立处理。为了方便理解，我们使用IRanges包的Vignette提供的一个很有用的IRanges作图函数（稍做修改）：

plotRanges <- function(x, xlim = x, main = deparse(substitute(x)), col = "black",
    add = FALSE, ybottom = NULL, ...) {
    require(scales)
    col <- alpha(col, 0.5)
    height <- 1
    sep <- 0.5
    if (is(xlim, "Ranges")) {
        xlim <- c(min(start(xlim)), max(end(xlim)) * 1.2)
    }
    if (!add) {
        bins <- disjointBins(IRanges(start(x), end(x) + 1))
        ybottom <- bins * (sep + height) - height
        par(mar = c(3, 0.5, 2.5, 0.5), mgp = c(1.5, 0.5, 0))
        plot.new()
        plot.window(xlim, c(0, max(bins) * (height + sep)))
    }
    rect(start(x) - 0.5, ybottom, end(x) + 0.5, ybottom + height, col = col,
        ...)
    text((start(x) + end(x))/2, ybottom + height/2, 1:length(x), col = "white",
        xpd = TRUE)
    title(main)
    axis(1)
    invisible(ybottom)
}

shift函数对Ranges进行平移（下面图形中蓝色为原始Ranges，红色为变换后的Ranges，黑色/灰色则为参考Ranges，其他颜色为重叠区域）：

ir <- IRanges(c(3000, 2500), width = c(300, 850))
ir.trans <- shift(ir, 500)
xlim <- c(0, max(end(ir, ir.trans)) * 1.3)
ybottom <- plotRanges(ir, xlim = xlim, main = "shift", col = "blue")
plotRanges(ir.trans, add = TRUE, ybottom = ybottom, main = "", col = "red")

flank函数获取Ranges的相邻区域，width参数为整数表示左侧，负数表示右侧：

ir.trans <- flank(ir, width = 200)
xlim <- c(0, max(end(ir, ir.trans)) * 1.3)
ybottom <- plotRanges(ir, xlim = xlim, main = "flank", col = "blue")
plotRanges(ir.trans, add = TRUE, ybottom = ybottom, main = "", col = "red")

reflect函数获取Ranges的镜面对称区域，bounds为用于设置镜面位置的Ranges对象：

bounds <- IRanges(c(2000, 3000), width = 500)
ir.trans <- reflect(ir, bounds = bounds)
xlim <- c(0, max(end(ir, ir.trans, bounds)) * 1.3)
ybottom <- plotRanges(ir, xlim = xlim, main = "reflect", col = "blue")
plotRanges(bounds, add = TRUE, ybottom = ybottom, main = "")
plotRanges(ir.trans, add = TRUE, ybottom = ybottom, main = "", col = "red")

promoters函数获取promoter区域，upstream和downstream分别设置上游和下游截取的序列长度：

ir.trans <- promoters(ir, upstream = 1000, downstream = 100)
xlim <- c(0, max(end(ir, ir.trans)) * 1.3)
ybottom <- plotRanges(ir, xlim = xlim, main = "promoters", col = "blue")
plotRanges(ir.trans, add = TRUE, ybottom = ybottom, main = "", col = "red")

resize函数改变Ranges的大小，width设置宽度，fix设置固定位置（start/end/center）：

ir.trans <- resize(ir, width = c(100, 1300), fix = "start")
xlim <- c(0, max(end(ir, ir.trans)) * 1.3)
ybottom <- plotRanges(ir, xlim = xlim, main = "resize, fix=\"start\"", col = "blue")
plotRanges(ir.trans, add = TRUE, ybottom = ybottom, main = "", col = "red")
ir.trans <- resize(ir, width = c(100, 1300), fix = "center")
xlim <- c(0, max(end(ir, ir.trans)) * 1.3)
ybottom <- plotRanges(ir, xlim = xlim, main = "resize, fix=\"center\"", col = "blue")
plotRanges(ir.trans, add = TRUE, ybottom = ybottom, main = "", col = "red")

其他函数的使用请自行尝试使用。

2.3.2 Ranges间转换（Inter-range transformations）

range函数用于获取Ranges所包括的整个区域（包括间隔区）；reduce将重叠区域合并；gaps用于获取间隔区域：

ir <- IRanges(c(200, 1000, 3000, 2500), width = c(600, 1000, 300, 850))
ir.trans <- range(ir)
xlim <- c(0, max(end(ir, ir.trans)) * 1.3)
ybottom <- plotRanges(ir, xlim = xlim, col = "blue")
plotRanges(ir.trans, xlim = xlim, col = "red", main = "range")
ir.trans <- reduce(ir)
plotRanges(ir.trans, xlim = xlim, col = "red", main = "reduce")
ir.trans <- gaps(ir)
plotRanges(ir.trans, xlim = xlim, col = "red", main = "gaps")

2.3.3 Ranges对象间的集合运算

intersect求交集区域；setdiff求差异区域；union求并集：

ir1 <- IRanges(c(200, 1000, 3000, 2500), width = c(600, 1000, 300, 850))
ir2 <- IRanges(c(100, 1500, 2000, 3500), width = c(600, 800, 1000, 550))
xlim <- c(0, max(end(ir1, ir2)) * 1.3)
ybottom <- plotRanges(reduce(ir1), xlim = xlim, col = "blue", main = "original")
plotRanges(reduce(ir2), xlim = xlim, col = "blue", main = "", add = TRUE, ybottom = ybottom)
plotRanges(intersect(ir1, ir2), xlim = xlim, col = "red")
plotRanges(setdiff(ir1, ir2), xlim = xlim, col = "red")
plotRanges(union(ir1, ir2), xlim = xlim, col = "red")

此外还有punion，pintersect，psetdiff和pgap函数，进行element-wise的运算。

3 SessionInfo()

sessionInfo()

## R version 3.2.2 (2015-08-14)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Debian GNU/Linux 8 (jessie)
## 
## locale:
##  [1] LC_CTYPE=zh_CN.utf8       LC_NUMERIC=C             
##  [3] LC_TIME=zh_CN.utf8        LC_COLLATE=zh_CN.utf8    
##  [5] LC_MONETARY=zh_CN.utf8    LC_MESSAGES=zh_CN.utf8   
##  [7] LC_PAPER=zh_CN.utf8       LC_NAME=C                
##  [9] LC_ADDRESS=C              LC_TELEPHONE=C           
## [11] LC_MEASUREMENT=zh_CN.utf8 LC_IDENTIFICATION=C      
## 
## attached base packages:
## [1] stats4    parallel  stats     graphics  grDevices utils     datasets 
## [8] methods   base     
## 
## other attached packages:
##  [1] scales_0.3.0         GenomicRanges_1.18.4 GenomeInfoDb_1.2.5  
##  [4] Biostrings_2.34.1    XVector_0.6.0        IRanges_2.0.1       
##  [7] S4Vectors_0.4.0      BiocGenerics_0.12.1  zblog_0.1.0         
## [10] knitr_1.11          
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_0.12.0      plyr_1.8.3       formatR_1.2      magrittr_1.5    
##  [5] evaluate_0.7.2   highr_0.5        stringi_0.5-5    zlibbioc_1.12.0 
##  [9] tools_3.2.2      stringr_1.0.0    munsell_0.4.2    colorspace_1.2-6

---

作者: ZGUANG@LZU

Created: 2015-09-08 二 10:46

Emacs 24.4.1 (Org mode 8.2.10)