```
source("https://bioconductor.org/biocLite.R")
biocLite("ctsGE")
```

Build the expression matrix from expression data

Define an expression index (i.e., a sequence of 1,-1, and 0) for each gene

Cluster the gene set with the same index, applying

**K-means**: \[kmeans(genesInIndex,k)\]Graphic visualization of expression patterns

Interactive visualization and exploration of gene-expression data

As input, the **ctsGE** package expects a normalized expression table, where
rows are genes and columns are samples. This can consist of count data as
obtained, e. g., from RNA-Seq or other high-throughput sequencing experiment or
microarray experiment. Example data from the [Gene Expression Omnibus (GEO)]
(http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE2077) are used here
illustrate ctsGE’s potential. The data are the expression profile of
*Cryptosporidium parvum*-infected human ileocecal adenocarcinoma cells
(HCT-8),^{3}) comprised of 12,625 genes over 18 samples
(three replicates of six developmental stages in human cancer). For tutorial
purposes and for simplification, only one replicate out of three is used,
for six overall time points.

Load the files and make a list of the `matrix`

:

When reading the normalized expression values the function check whether there are rows that their median absolute deviation (MAD) value equal to zero and remove these rows. This step is important in order to continue to the next step of indexing the data.

```
library(GEOquery)
gse2077 <- getGEO('GSE2077')
gseAssays <- Biobase::assayData(gse2077)
gseExprs <- Biobase::assayDataElement(gseAssays[[1]][,c(1:6)],'exprs')
# list of the time series tables use only 6 samples
gseList <- lapply(1:6,function(x){data.frame(Genes = rownames(gseExprs),Value = gseExprs[,x])})
names(gseList) <- colnames(gseExprs)
```

Build the expression matrix from the list of matrices:

`rts <- readTSGE(gseList,labels = c("0h","6h","12h","24h","48h","72h")) `

Here is an example of how to load the time-series files from your directory;
data were imported from the **ctsGE** package:

```
data_dir <- system.file("extdata", package = "ctsGE")
files <- dir(path=data_dir,pattern = "\\.xls$")
```

**Building from a directory:**

`rts <- readTSGE(files, path = data_dir, labels = c("0h","6h","12h","24h","48h","72h") )`

**ctsGE Object summary:**

`names(rts)`

`## [1] "tsTable" "samples" "tags" "timePoints"`

`rts$timePoints`

`## [1] 6`

`head(rts$samples)`

`## [1] "0h" "6h" "12h" "24h" "48h" "72h"`

`head(rts$tags)`

`## [1] "1000_at" "1001_at" "1002_f_at" "1003_s_at" "1004_at" "1005_at"`

`head(rts$tsTable)`

0h | 6h | 12h | 24h | 48h | 72h | |
---|---|---|---|---|---|---|

1000_at |
3741 | 3134 | 2724 | 2182 | 2730 | 3379 |

1001_at |
53.3 | 44.1 | 43.8 | 113.9 | 43.9 | 68.5 |

1002_f_at |
158.7 | 130.8 | 110.5 | 39.4 | 48.7 | 126 |

1003_s_at |
517 | 81.6 | 168.6 | 352.5 | 186 | 127.5 |

1004_at |
346.5 | 338.3 | 399.5 | 391.2 | 502.6 | 366 |

1005_at |
85 | 439.9 | 941.7 | 449.6 | 616 | 553.2 |

Please use the `desc`

option in the function: `readTSGE`

in order to add genes
annotation to the time series table.

First, the expression matrix is standardized. The function default standardizing method is a median-based scaling; alternatively, a mean-based scaling can be used. The new scaled values represent the distance of each gene at a certain time point from its center, median or mean, in median absolute deviation (MAD) units or standard deviation (SD) units, respectively.

Next, the standardized values are converted to index values that indicate whether gene expression is above, below or within the limits around the center of the time series, i.e.,

**1 / -1 / 0**, respectively. The function defines a parameter cutoff (see Section 4.1) that determines the limits around the gene-expression center.Then the function calculates the index value at each time point according to:**0:**standardized value is within the limits (+/- cutoff)**1:**standardized value exceeds the upper limit (+ cutoff)**-1:**standardized value exceeds the lower limit (- cutoff)

The

`+/- cutoff`

parameter defines a reference range to which the data are compared. When the range is too big, more time-series points will fall into it and will get an index value of 0, and this may be misleading. Too small range can result in too many index groups that will be too sensitive to small fluctuations in the time-series index. The function chooses the optimal cutoff (see Section 4.1) after testing different cutoff values from 0.5 to 0.7 in increments of 0.05.

##Checking the optimal cutoff
The function `PreparingTheIndexes`

generates an expression index
(i.e., a sequence of 1,-1, and 0) that represents the expression pattern along
time points for each gene. Setting different limits for the center era
(with the parameter cutoff) will change the index for each gene-expression
profile and consequently, the number of genes in each index group. Following the
idea that instead of filtering “irrelevant” genes to reduce the noise, the
clustering will be performed on small gene groups, one would like to choose a
cutoff value, that will minimize the number of genes in each group, i.e.,
generate index groups of equal size. The test for equality is performed by
calculating the chi-squared value from a comparison between the number of genes
in the index groups and the null hypothesis that all index groups are equal.
The test is performed for all the cutoffs in the range and the cutoff that gives
the minimal chi-squared value is the most likely to generate equal index groups.
The range of the cutoff values is given by `min_cutoff`

and `max_cutoff`

arguments. However, by setting the same value to min and max parameters one can
define a cutoff regardless of what was suggested by the function.

`prts <- PreparingTheIndexes(x = rts, min_cutoff=0.5, max_cutoff=0.7, mad.scale = TRUE)`

`cutoff = 0.55`

is the optimal cutoff with the lowest chi-squared value

`prts$cutoff`

`## [1] 0.55`

To get an idea of how the data look, and to determine the nature of the indexes formed from certain cutoff value, the number of zero values for each index is counted. In this tutorial example, the index can have no zeros, one zero or up to six zeros; overall, the indexes and genes are divided into seven groups. Indexes for which most of the time points present a zero value (in this example, three or more time points) are expected to show a pattern in which gene-expression does not change much along the time points. Indexes with less zeros to no zeros (two or less in the example) will show genes with up- or downregulated expression at each time point.

```
With cutoff =
0.55, most of the genes were assigned to indexes with three or two zeros,
indicating a variety of expression patterns.
```

##Preparing the indexes for the data

A ** cutoff = 0.55** was chosen

```
prts <- PreparingTheIndexes(x = rts, mad.scale = TRUE)
names(prts)
```

```
## [1] "tsTable" "samples" "tags" "timePoints" "scaled"
## [6] "index" "cutoff"
```

**Gene expression after standardization: **
`head(prts$scaled)`

0h | 6h | 12h | 24h | 48h | 72h | |
---|---|---|---|---|---|---|

1000_at |
1.665 | 0.4156 | -0.4283 | -1.544 | -0.4156 | 0.9207 |

1001_at |
0.6397 | -0.6397 | -0.6814 | 9.067 | -0.6675 | 2.754 |

1002_f_at |
1.03 | 0.3194 | -0.1973 | -2.007 | -1.77 | 0.1973 |

1003_s_at |
3.149 | -0.8873 | -0.08066 | 1.624 | 0.08066 | -0.4617 |

1004_at |
-0.817 | -1.026 | 0.532 | 0.3207 | 3.156 | -0.3207 |

1005_at |
-3.19 | -0.4711 | 3.373 | -0.3968 | 0.8779 | 0.3968 |

**Gene expression indexing with cutoff = 0.55:**

`head(prts$index)`

0h | 6h | 12h | 24h | 48h | 72h | index | |
---|---|---|---|---|---|---|---|

1000_at |
1 | 0 | 0 | -1 | 0 | 1 | 100-101 |

1001_at |
1 | -1 | -1 | 1 | -1 | 1 | 1-1-11-11 |

1002_f_at |
1 | 0 | 0 | -1 | -1 | 0 | 100-1-10 |

1003_s_at |
1 | -1 | 0 | 1 | 0 | 0 | 1-10100 |

1004_at |
-1 | -1 | 0 | 0 | 1 | 0 | -1-10010 |

1005_at |
-1 | 0 | 1 | 0 | 1 | 0 | -101010 |

The clustering is done with K-means. To choose an optimal k for K-means
clustering, the Elbow method was applied^{4}, this method looks at the percentage
of variance explained as a function of the number of clusters: the chosen number
of clusters should be such that adding another cluster does not give much better
modeling of the data. First, the ratio of the within-cluster sum of squares
(WSS) to the total sum of squares (TSS) is computed for different values of
k (i.e., 1, 2, 3 …). The WSS, also known as sum of squared error (SSE),
decreases as k gets larger. The Elbow method chooses the k at which the SSE
decreases abruptly. This happens when the computed value of the WSS-to-TSS ratio
first drops from 0.2.

\(\frac{WSS}{TSS} < 0.2\)

```
ClustIndexes <- ClustIndexes(prts, scaling = TRUE)
names(ClustIndexes)
# table of the index and the recommended k that were found by the function
head(ClustIndexes$optimalK)
# Table of clusters index for each gene
head(ClustIndexes$ClusteredIdxTable)
```

Running `kmeans`

and calculating the optimal k for each one of the indexes in
the data could take a long time. To shorten the procedure the user can skip this
step altogether and directly view a specific index and its clusters by running either
the `PlotIndexesClust()`

or the `ctsGEShinyApp()`

function

The `PlotIndexesClust()`

function generates graphs and tables of a specific
index and its clusters. The user decides whether to supply the k or let the
function calculate the k for the selected index.

```
indexPlot <- PlotIndexesClust(prts,idx = "1100-1-1",scaling = TRUE)
names(indexPlot)
```

`## [1] "Clust_4_1100-1-1" "graphs"`

**Genes in ‘1100-1-1’ index and their clusters **
**(k was chosen by the function):**

Number of clusters (k) for ‘1100-1-1’ is: `length(indexPlot$graphs)`

`## [1] 4`

**Table of genes in ‘1100-1-1’ index, seperated to clusters:**
`head(indexPlot[[1]])`

0h | 6h | 12h | 24h | 48h | |
---|---|---|---|---|---|

1048_at |
0.6255 | 0.9085 | 0.1815 | -0.1815 | -1.143 |

104_at |
0.8152 | 0.7462 | -0.09904 | 0.09904 | -1.028 |

1870_at |
0.7476 | 0.6014 | 0.1628 | -0.1628 | -2.814 |

1872_at |
0.5597 | 1.259 | 0.3135 | -0.3135 | -2.256 |

31423_at |
0.954 | 0.6654 | 0.1701 | -0.1701 | -0.7231 |

31474_r_at |
0.7112 | 1.276 | -0.3497 | 0.3497 | -0.6378 |

72h | clusters | |
---|---|---|

1048_at |
-0.7235 | 4 |

104_at |
-0.6028 | 4 |

1870_at |
-2.136 | 4 |

1872_at |
-0.7892 | 4 |

31423_at |
-0.6836 | 4 |

31474_r_at |
-1.523 | 4 |

For this example, the index `1100-1-1`

is used. by Looking at this index, it can
be assumed that the expression of the genes belonging to it was downregulated
along the time points. Since the index only states whether gene expression
is upregulated (1), downregulated (-1) or stays the same (0), gene subsets
of the same profile will usually show more than one expression pattern.
K-means helps distinguish these patterns from one another.

**Line graphs of the genes’ expression patterns in index ‘1100-1-1’ separated**
**into clusters:**

`indexPlot$graphs`

`## $`Clust_1_1100-1-1``

```
##
## $`Clust_2_1100-1-1`
```

```
##
## $`Clust_3_1100-1-1`
```

```
##
## $`Clust_4_1100-1-1`
```