DATAN GenEx 20060212 - MultiD GenEx.pdf · GenEx Page 3 MultiD 1. Introduction Optimal use of real-time PCR measurements requires proper analysis of real-time PCR data. DATAN framework

MultiD Analyses AB GenEx Users Manual February 2006

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Table of Contents 1.0 Introduction 3

1.1 Installation 4

2.0 GenEx Interface 5

2.1 Getting Started 6

2.2 Data Preprocessing 7

3.0 Control Panel 17

3.1 Data Manager 22

3.2 Plotting Data 27

4.0 Data Analysis 28

4.1 GeNorm 29

4.2 Scatter Plot 31

4.3 Principal Component Analysis 34

4.4 Potential Curves 43

4.5 Hierarchical Clustering 45

4.6 Self Organizing Map 52

4.7 3-Way Analysis 57

5 Upgrades and support 60

6 Acknowledgement 61

7 References 62

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1. Introduction

Optimal use of real-time PCR measurements requires proper analysis of real-

time PCR data. DATAN framework GenEx package provides the appropriate

tools to analyze real-time PCR gene expression data and to extract valuable

information from the measurements. Behind a user friendly interface DATAN

makes available:

• Handling missing data

• Scaling and normalization options for gene expression data

• Advance plot functions including 3D plots and scatter plots

• Pearson to calculate correlations between genes

• Grouping of data

• GeNorm to find most stably expressed house keeping genes

• Hierarchical Clustering to find associations between data

• Kohonen Neural Networks to classify data

• Principal Component Analysis to find hidden structures in data

• Potential curves to classify test samples based on training set

• Trilinear decomposition to analyze series of expression profiles

For more information about these methods and references visit the MultiD

website: www.multid.se.

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1.1. Installation

Genex should be run on a PC computer with a Pentium processor of at least

200 MHz (500 MHz or better recommended) and 64 MB (128 MB

recommended) RAM. Recommended screen resolution is 1024 x 768 or

higher.

Install GenEx by running GenEx.exe. This starts an installation program that

takes you through the installation process and installs all files, examples, and

documentation required to run GenEx. If you have an unregistered copy a

register screen appears that indicates how much is left of your evaluation

period.

When you have registered your copy the register screen will no longer appear.

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2.0. GenEx Interface

GenEx user interface is divided into sections.

Top left are menus and buttons to read data. Next is a curtain window to

select data for plotting. It is followed by buttons to transpose, manage and

view data. Then there is a tick box to activate advanced plotting, followed by

three plot buttons. Bellow the buttons is a menu for the different analyses that

are available. In the main window is the control panel. Here data files and

analyses results are managed.

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2.1. Getting started

GenEx is really easy to use. All you need to get started is to arrange your CT

values in a spreadsheet such as Microsoft Excel with the genes as rows and

samples as columns, using first column and first row to label and index the

data. Additional columns can be added for classification of the data or

normalization. These columns are distinguished by having # preceding the

label. In the example file Xenopus.xls the column #Stage indexes early

stages, mid blastula transition, and late stages. The column #RNA stores the

total amount of RNA used in the different samples for normalization purpose.

The A1 element is used to label the experiment.

Data can be stored either as excel sheet, comma or tab separated text files,

or as MultiD mdf files. The latter file format is preferred for larger data files,

because its read and stored faster than e.g., excel files.

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2.2. Data Preprocessing

GenEx has a powerful data editor for data preprocessing that is fully Excel

compatible. The GenEx data editor is used to handle missing data, convert CT

to copy numbers, normalize data and optionally rescale data. A data file is

opened for editing with the button.

The editor is compatible can read several file types including the MultiD mdf

format and Microsoft Excel. Open the file yeast_wt.xls.

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On the left of the data sheet are buttons to insert , delete , add ,

and duplicate rows, and insert , delete , add , and duplicate

rows, shift cells left , right , down , and up , and merge

file to the top , to the bottom , to the left , and to the right .

To move a row or column within the sheet, hold the mouse on the row/column

index and drag it to the new position. The data sheet can be sorted by the

elements in a column, by clicking the column label.

transposes the data sheet. opens a menu to edit row labels:

“Suffix” adds a common suffix such as “sample” to all rows. “1st index” is the

value of the 1st index. “Start row”, “Step” and “End row” selects the rows to be

indexed. Ticking “Ignore Index” makes it possible to label with only the suffix.

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validates the sheet by looking for missing data, alpha numeric entries, and

other non-allowed characters. It also removes any empty rows and columns.

Pressing with the file yeast_wt.xls open will generate this error report:

In the sheet cells with erroneous content are identified by color.

activates a menu to handle missing data.

Here all cells with missing data can be given the same value. Missing data in

a column can also be given a certain value. Finally, all missing data can be

replaced with columns’ means. To replace with rows’ means instead the data

sheet must first be transposed.

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Chose to replace the missing data with columns’ means.

This editor has advanced copy & paste function. For example, select data

between 1 and 30 seconds for every second gene plus data between 20 and

60 seconds for SUC2:

Copy the selection using . Now open a new data sheet and select, for

example, cell (B,3) and press paste . The content is copied with the

selected cell as reference.


This advanced copy and paste option makes it very convenient to assemble

data in new sets.

cuts a selection. By default data sheets are not editable. Pressing

activates editing. is “undo” and is “select all”. The button loads

the data as a new project in the control panel for analysis. If any cell contains

not-allowed entries when the data are loaded, those entries are replaced by

zeros.

To the right are function buttons for data handling. Open the file

yeast_wt_nmd.mdf and press the button . It activates a menu to set CT’s

above a certain value above which samples are negative, to the same CT:

opens menu to convert CT values to copy numbers:


Enter the estimated PCR efficiency and the Ct of a single copy sample. This

can be done for one gene at a time, using gene specific parameters, or to all

genes (columns). For the yeast_wt.xls data set efficiency to 0.8 and Ct of

single copy to 40. This gives:

Now expression of all genes is in copy number.

Usually data are collected from the same amount of material, such as the

number of cell, volume of blood or total RNA amount. If that is not the case,

the information can be added as an extra column that in the heading shall be

identified with a #. Such as in the case below:

Pressing the button opens the “normalization” menu, where the user can

select among the columns identified by # for the appropriate one for

normalization.


Pressing “Apply” divides the copy numbers along rows (=samples) with the

total amount of RNA as specified in the column labeled #Total RNA.

opens menu for normalization with reference or house-keeping genes.1

The menu lists all genes (columns). Select ACT, IPPI, and PDA, which are the

presumed house-keeping genes in this study

.

Press “Apply” and all expression values are divided with the geometric mean 1

1

−

⎟⎟⎠

⎞⎜⎜⎝

⎛

=

nn

iiXC of the reference genes, and the reference genes are removed from

the sheet.


All data are now expressed relative to the average of the expression of the

reference genes. Note that geometric normalization shall be performed on

copy numbers and not on CT values.

Many aspects of nature are logarithmic and usually we prefer to compare

expression in logarithmic scale.2 In logarithmic scale 0.1 and 10, which is 10

fold decrease and 10 fold increase, respectively, obtain the same numerical

values but of opposite signs. calculates the logarithm with base 10 of all

values in the sheet, calculates the logarithm with base 2, calculates

the logarithm with base 10 of the values +1, which is convenient if some

values are zero, and calculates the logarithm with base e.

The yeast wt gene expression data expressed in logarithmic scale with base 2

relative to the house keeping genes is:


Most analyses are simplified by subtracting the mean from all values, which is

called mean centering. Depending on the problem studied it can be the

sample or gene mean. Pressing subtracts the column mean, which

typically is the gene expression mean. To mean center samples the data shall

first be transposed.

When either the variation of all the genes or variation of all the samples is

considered equally important one can autoscale the data. Pressing mean

centers first the data and then divides by the columns’ (genes') standard

deviations. The autoscaled data have mean = 0 and standard deviation = 1.

Third scaling option is 0 – 1 scaling. Pressing divides all values with

column maximum.

The yeast wt expression data expressed relative to house-keeping genes in

logarithmic scale (base 2) and autoscaled to give all genes same significance

are shown below:

calculates the Pearson correlation matrix. The Pearson coefficient is -1 ≤ r

≤ 1 and reflects how similar the expressions of the different genes are. 1

indicates maximum correlation (identical expression), 0 indicates no

correlation, and -1 indicates maximum anticorrelation (high expression of one

gene correlates with low expression of the other). The Pearson correlation


matrix for the yeast wt expression data expressed relative to house-keeping

genes in logarithmic scale (base 2) and autoscaled is shown below:

Above we have shadowed entries reflecting the correlation between the

expressions of the glycolysis genes PGK, PDC, ADH1, and TPI. All have r >

0.95 suggesting these genes behave similarly.

The “File Editor” is very powerful and supports most operations needed in

advanced pre-processing of real-time PCR data. But in most cases advanced

pre-processing is not necessary. In fact, often no pre-processing at all is

needed! If

1. Data are collected from the same total amount material

2. Primer-dimers are negligible (CT cutoff is not needed)

3. PCR efficiency and sensitivity is the same for all PCR assays and in all

samples.

4. All genes are equally important (normalization with reference genes is not

needed)

The measured CT values can be Autoscaled directly. Going via CT -> copy

number followed by taking the log of the data does not have any effect (try it!).

Autoscaling is available also in the Data Manager (see section 3.1). Hence, in

these cases the raw CT values can be loaded directly to the control panel,

autoscaled using the Data Manager, for immediate analysis.


3.0. Control Panel

The control panel is used to handle data. Data are handled in three levels:

projects, data sets, and data files. A data file is a set of data that can be edited

by the data editor. A data set is a collection of data files including settings

such as labels, colors, groups, classification etc. A project is a collection of

data sets.

Use to open the files wt.mdf, hxt.mdf, Null.mdf, and Tm6.mdf, containing

expression data for four yeast strains.

A project can be exported or saved , which also gives option to name

it. A saved project (*.dpr) stores all settings and the path to the data files,

while an exported project (*.dpx) also stores the data. Pressing opens an

editor to write comments to the project. The editor has cut (Ctrl x), copy (Ctrl

c), and paste (Ctrl v) functions compatible with Windows. deletes a

project from the Control Panel (but not from disc, if it has been stored)..

Below we commented the project and named it “yeast” by saving it on file.


Initially a single data set called Set1 is created. It can be named/renamed by

ticking the “Rename” box. creates a new data set within the same project

that initially has no files. copies the selected data set into a new one

with the same files and settings as the original. This is a convenient way to

compare analyses of data sets normalized differently, or two subsets of data.

Below we cloned the initial dataset and in the new set we will inactivate the

genes MIG, HSP, and CYC for analysis.


Each data set may contain several data files. Although most methods analyze

only one data file at a time, GenEx offers trilinear decomposition to compare

also sets of gene expression profiles (see below).


Files with the same number of genes and samples as those already present in

a data set can be added with the button, and data files are removed with

. opens the selected file in the Data Editor.

The files in the selected set that are available for analysis appear in the top

curtain window, where the file to analyze and to plot is selected.


3.1 Data Manager

Data can be sorted, grouped and colored in the “Data Manager”. The “Data

Manager” operates either on genes are samples. To switch between the data

are transposed. Transposition is indicated in bottom panel:

Import the project Yeast and open the “Data Manager” by pressing .


Select the rows panel, which in transposed form are the genes. Recall, a data

set could be cloned to convert all information and settings. In the cloned set,

some genes or samples can be inactivated for analysis for simple comparison.

Samples can also be classified as test and training samples. This is of interest

when analyzing the data with predictive methods such as self organizing

maps (SOM), potential curves and partial least squares (PLS). There is also

option to scale data. Note, this option to scale data is reversible and does not

affect the data stored on disk. In contrast, scaling using the Data Editor in pre-

processing of data is irreversible once the data are stored to disc.

In the column form columns, this time samples, are handled:

Also columns can be inactivated. They can also be classified as predictors

and responses. The response columns are used by predictive modeling,

where the content in the response columns is predicted by the content in the


predictor columns. By default expression data are predictors and classification

columns (identified by #) are responses.

Plot colors are chosen in the color form. Colors can be based on intensity

value, or set for each sample or group of samples. Plot symbols are also

selected in the colors folder.

Alternatively the rows are color coded. Color code the genes as: reference

genes (ACT, IPPI, PDA) in lime, glycolysis genes (TPI, PGK, PDC, ADH1) in

navy blue, glycogenesis genes (FBP, MDH2, SUC2, ADH2) in red, other

genes (HSP, CYC, MIG) in yellow, and unknown genes (ADH3, ADH4, ADH5,

ADH6) in fuchsia.


Data are grouped in the groups form. Groups are created by typing a group

name and adding it to the group list by pressing . A group is then selected

and members added.


Data can also be grouped using classification variables.


A classification variable is selected and the samples are grouped using logical

operator and variable index.

Selections are finally applied by pressing .

Having color coded and grouped data, it is advisable to save the settings as a

project.


3.2 Plotting Data

GenEx offers very powerful plotting options. Data file for plotting is selected

from the active data set in the top curtain window.

Data are plotted with the ”2D line plot” , ”3D line plot” , and ”3D surface

plot” buttons. More advanced plots are available by ticking the “Adv plot”

button. This activates ”2D/3D scatter plot” , ”2D/3D line plot” , and

”2D/3D surface plot” . Almost anything can be set and adjusted in the

advanced plots allowing the user to present data in most attractive ways.

Different data sets are readily plotted in separate windows for direct

comparison.


4.0 Data Analysis

The analytical modules available in your version of GenEx are found in the top

menu.

Select the analysis you wish to perform by clicking its icon. This opens the

appropriate dialog box in the Control panel Analysis sheet. Here the

parameters for the analysis are set. The sheet also shows analyses that

already have been performed, which makes it convenient to retrieve

calculated data for comparisons.


4.1 GeNorm

GeNorm was developed by Jo Vandesompelle to determine the most stable

housekeeping genes from a set of tested genes on a sample panel.1 It starts

by comparing the relative expression of all genes, by calculating the gene

expression stability measure M for each gene as the average pairwise

variation with all the other genes, and stepwise excluding the gene with

highest M. This produces ranking of the tested genes according to their

expression stability.

Select the file wt.mdf in the top curtain window. Make sure that the data are

not transposed and remove any normalization by selecting scaling “None” in

the Data Manager. Then activate GeNorm.

This opens the GeNorm control panel:


Press “Run” to analyze the data. GeNorm eliminates genes successively in

the order of expression instability and presents a plot of the geometric

average of the M value after each removal. The most stably expressed genes

are those to the right.


4.2 Scatter Plot

The traditional scatter plot is powerful to classify samples

characterized by the expression of only two or three genes. The

scatter plot control menu is activated by pressing the scatter plot

button:

This opens the Scatter Plot control menu in the Control panel (data

from the project kappa_lambda.dpx):


Radio buttons in the Control Menu let the user select to plot either

columns or rows (in original data columns are genes and rows

samples; if you have transposed the data it is the opposite). The

there are two curtain windows to select the genes to plot. Finally,

there is a curtain window to select the data file to plot, in case the

data set contains multiple files. In this particular case the plot

shows the expression of immunoglobulin kappa light chain versus

the immunoglobulin lambda light chain. Each symbol is one sample.

Using the Data Manager (see below) we have colored the negative

samples green and the positive samples red. As predicted, the

negative samples fall on a straight line representing 60:40

expression ratio expected for non-clonal samples.3

The correlation in expression of up to three genes can be visualized

in the scatter plot. Ticking the 3D box adds a third curtain window,

which allows three genes to be selected. Below three genes were

selected from the project Xenopus.dpx:


The three genes are expressed in different developmental stages of

Xenopus, which is evident from the scatter plot:


4.3 Principal Component Analysis

We cannot plot more than three genes in a tradition scatter plot,

because we have no way to visualize four dimensions. For studies

based on more than three genes, we must, if we want to account

for all of them in the analysis, use methods to collect the

multidimensional information in a lower dimensional space, such as

two and 3 dimensions. The most powerful way to do this is by

means of principal components (PC).

Think of the genes as axes making up a multidimensional space.

Each sample can now be represented in this space by the

coordinates (g1, g2, g3….), where g1, g2, g3 etc., is the expression

of gene 1, gene 2, gene 3 etc., in the sample. Samples that are

close in the space will be similar, while samples far apart will be

different. The disadvantage with this representation is that it’s hard

to visualize when the number of genes exceeds three. For this

purpose principal components are useful. The principal components

are axes in the multidimensional space such that maximum

variation is explained on the first axis; second most variation is

represented on the second axis and so on. This way most of the

information in the multidimensional space can be represented in a

graph of few dimensions.

In PCA the measured data are decomposed into a product of a

target matrix and a projection matrix with orthogonal columns and

orthonormal rows:


''q

1iTPptA ii =≈ ∑

=

(Eq. 1)

A is the data matrix. ti and pi’ are the scores and loadings, which

jointly are referred to as the principal components. q is the number

of projection vectors used to reproduce data. Typically 2-3 are used

because such space can be visualized in conventional plots.

Open the project yeast.dpr. Select “Full data set” and select PCA.

This opens the PCA dialogue screen in the “Analysis” frame in the “Control

Panel”.

Here the number of principle components used to represent data can be set.

Selecting Auto Genex uses statistical test to select the optimum number of

principal components. Pressing run calculates the principal components. If the


data set has more than one file, the principal components are calculated for all

files simultaneously, such that a common loading is obtained.

If the data set has more than one file, the principal components are calculated

for all files simultaneously, such that common loadings are obtained. These

are plotted together with the scores for the data file shown in the curtain

window.


Selecting a different file in the curtain window and pressing run we calculate a

different set of scores together with the common loadings:

Here the scores represent genes and the loadings samples. Hence, the

sample response is common to all files. If we instead want the genes’

response to be common we transpose the data first.

“View Eigenvalues” shows the eigenvalues that reflect the importance of the

principle components.


The accounted variation shows how much of the total variation in the data is

accounted for by different numbers of principal components. Two principal

components account for 70 % of the variation in the original data. This rather

low number is because four strains were analyzed simultaneously and

common principal components were calculated. If only calculating principal

components for the wt strain the first two pairs of principal components

account for 91.5 % (such comparison is easily done using the GenEx clone

function on data sets).

The calculated scores can be viewed in a spreadsheet.

“Reconstruction” plots the measured data and overlays the data reconstructed

from the selected number of components. Below is reconstruction with two

principal components.


The most informative plots for classification are the scatter plots. Below is the

PC1 vs. PC2 loading plot, reflecting the samples. Pressing opens an

extra window, where the samples are identified when pointing on a data point

with the mouse (a small red triangle appears next to the identified data point).


The scattered points follow a curved path, which is expected for a continuous

process such as a time study. In such plot the time point when a test sample

was taken could readily be determined by interpolation.

For these data the PC1 vs. PC2 scores plot is even more interesting. Here

genes with similar expression patterns form groups.

The three reference genes in green form a cluster revealing they are

expressed similarly among the samples in the wild-type strain. In this cluster

we find also HSP, suggesting that HSP in this system is not regulated or more

correctly is regulated as the reference genes. Also the glycolysis (blue) and

the glycogenesis (red) genes from clusters. The two unknown genes, ADH3

and ADH5, are found in the glycogenesis cluster indicating they are involved

in a process related to glycogenesis.

Changing the curtain window to three and pressing run the data are

reproduced with three principle components.


This gives option to view the data in 3D scatter plots that account for more of

the variation in the original data (in this example, 80% compared to 70 % in

the 2D scatter plots). Below is the PC1 vs. PC2 vs. PC3 scatter plot for the

loadings (genes).



4.4 Potential Curves

Potential curves is a predictive application of PCA.4,5 To use potential curves

the data must have a training set divided into groups and then there must be

test samples. Import the project yeast.dpx and activate Potential Curves:

sd

This opens the P-curves control box:

Here one can adjust the no. of levels and the fitness of the potential curves,

as well as the color coding. Potential curves performs PCA but only on the

training data. Furthermore, iso-probability so called potential curves are


calculated for each group of data. In the example below three groups were

defined:

For the test data probabilities are calculated that it belongs to the different

groups. The results are shown in a table.


4.5 Hierarchical Clustering

GenEx offers module for hierarchical agglomerate clustering, which is the

most common method for grouping data. The construction of a hierarchical

agglomerative classification can be achieved by the following general

algorithm.

1. Find the two closest objects and merge them into a cluster

2. Find and merge the next two closest points, where a point is either an

individual object or a cluster of objects.

3. If more than one cluster remains, return to step 2

In GenEx hierarchical clustering is performed by pressing the icon on:

This opens the dialogue form:


“Run” clusters the data using default settings, which is unweighted pairs and

Euclidian distance. The “advanced” button opens menu to change settings.


Here user can select among different clustering methods and distance

measures.6

The single linkage, also called, nearest neighbor method can be used both

with similarity measures and with distance measures. Groups are fused

according to the distance between their nearest members.

The complete linkage, also called the furthest neighbor method is the opposite

of the single linkage method. The distance between groups is now defined as

the distance between their most remote pair of individuals

Ward’s method groups to minimize the increase in the variance in distances in

the new group. Internal variance is computed as the sum of distances

between each sample in the group and the group’s centroid. Ward’s method

tends to produce compact clusters.7


The Unweighted pairs linkage defines distance between groups as the

average of the distances between all pairs of individuals in the two groups. It

is sometimes also referred to as UPGMA (Unweighted Pair-Group Method

using Arithmetic averages), and is a compromise between the single and

complete linkage methods.

The distances between objects can also be measured differently. Most

common for continuous data, where we measure gene expression in copy

number or CT, are:

Manhattan distance = ( ) ( ) )()( ybyaxbxa −+−∑

Euclidian distance = ( ) ( )( )[ ] 5.02∑ − rbra

Euclidian squared distance = ( ) ( )( )∑ − 2rbra

For discrete data, where we for each sample either have expression (1) or no

expression (0), we generate a contingency table:

For example, the observations:

Sample X = ( 1 , 1 , 0 , 1 , 0 , 0 , 1 )

Sample Y = ( 0 , 1 , 1 , 0 , 0 , 1 , 1 )

Give:

Y

1 0

1 a b a + b

X 0 c d c + d

a + c b + d a+b+c+d


Dice coefficient = (b + c) / (a + b + c + d)

Jaccard coefficient = (b + c) / (a + b + c)

When performing hierarchical agglomerate clustering it is good practice to

analyze the data set using a few different methods and distance measures to

verify that the main clusters predicted are independent of these choices.

Note that data can be clustered as groups of genes or groups of samples.

Genes that form a cluster have similar expression, while samples that are, for

example, negative and positive for a disease should fall in different groups if

proper expression markers are measured. To switch between classification of

genes and classification of samples the data are transposed.

In the top curtain window select the file wt.mdf

and analyze it with default settings (single linkage & Euclidian distance).

Y

1 0

1 2 2 4

X 0 2 1 3

4 3 7


The dendrogram reveals four clusters. From the bottom we find cluster with

the glycolysis genes PGK, ADH1, PDC, and TPI. Then follows cluster with the

reference genes IPPI, PDA, and ACT together with HSP. Third cluster is the

glycogenesis genes SUC2, MDH2, ADH2, and FBP together with the

unknown genes ADH3 and ADH5. Notably, these clusters are the same as

found by PCA. Finally, ADH4, AHD6, and MIG form a last cluster, which,

however, is less well defined as judged from the larger distances between its

elements as indicated on the y-axis. CYC appears to behave unique.

Analyzing the same data with Ward’s algorithm, we obtain:


The same clusters are found. Only difference is that here CYC is suggested to

be a remote member of the glycogenesis genes’ cluster.


4.6 Self Organizing Map

The self-organizing map (SOM) was developed by Teuvo Kohonen.8 The

basic idea behind SOM is to setup a structure of interconnected processing

units ("neurons") that compete for the signal.

The input is either genes or samples. If genes are classified the input vectors

are the expressions of the genes in the samples. If there are n samples, each

vector has elements:

Xgene = (x1, x2, x3...xn)

In the network each node has a specific position (i, j)-coordinate and contains

a vector of weights of the same dimension as the input vectors:

Wij = (w1, w2, w3...wn)

A SOM does not need a target output to be specified unlike many other types

of network. Instead, where the node weights match the input vector, that area

of the lattice is selectively optimized to more closely resemble the data for the

class the input vector is a member of. From an initial distribution of random

weights, and over many iterations the SOM eventually settles into a map of


stable zones. The zones are effectively feature classifiers. Any new,

previously unseen input vectors presented to the network will stimulate nodes

in the zone with similar weight vectors.

Training occurs in several steps and over many iterations:

1. Each node's weights are initialized.

2. A vector is chosen at random from the set of training data and

presented to the lattice.

3. Every node is examined to calculate which one's weights are most like

the input vector. The winning node is commonly known as the Best

Matching Unit (BMU).

4. The neighbors to BMU are now identified. This is a value that starts

large, typically set to the 'radius' of the lattice, but diminishes each

time-step.

5. Each neighboring node's weights are adjusted to make them more like

the input vector. The closer a node is to the BMU the more its weights

get altered.

6. Repeat from step 2 a fixed number of iterations.

The range of the neighborhood (step 4) as well as the amount of adjustment

(step 5) decreases during the training from initial values set by the user. This

ensures that there are coarse adjustments in the first phase of the training,

while fine tuning occurs during the end of the training.

A special feature of this particular implementation of SOM is the availability of

cyclic maps. This means that the neighborhood is extended beyond the map

borders and wrapped to the opposite boundary. In this case a rectangular

map becomes a torus and a linear map will be a circle.

Select the file wt.mdf in the top curtain window and activate Kohonen neural

network by pressing the Kohonen icon.


This opens the SOM control windows:

Select a 10 × 10 non-cyclic map with ten initial neighbors (for a square non-

cyclic map setting the initial no. of neighbors to the size of the square’s side

assures the entire map is trained from start. For a cyclic map half of the

square’s side is sufficient). Set alpha to 0.4, the number of iterations to 150

and train the network. Due to stochastic elements in the training process, the

SOM will look different in different trainings based on the same input vectors,

but, typically, it will have the same regions. Below are three maps generated

from the yeast wt expression data in file wt.mdf with the settings above.


Clearly, the SOMs display a region with the glycolysis genes (UPGK, ADH1,

PDC, and TPIR), a region with the glycogenesis genes (SUC2, MDH2, ADH2,

and FBP) with the unknown genes ADH3 and ADH5, a region with the

reference genes (IPPI, PDA, and ACT) and HSP, and a region with ADH4,

ADH6, and MIG. CYC is a wild card. These regions agree with the clusters

found both by PCA and hierarchical clustering.

In GenEx it is possible to classify data as training and test data.


Only the training data are used to train the SOM. This is very useful when

there is a subset of highly reliable and extensively tested data, based on

which a SOM shall be created, for classification of more uncertain data. If we

activate all data in the wt.mdf the SOM may then look something like:

Once trained a SOM can be saved on disk and later loaded to classify new

data. Load the network yeast.xml, activate file wt.mdf, and press run. This will

classify the yeast wild-type data using the loaded network, which shall give:

The same clusters appear as before.


4.7 3-Way Analysis

Recently very powerful methods have been developed to compare sets of

data.9,10 This can be, for example, comparing the time dependent expression

of different strains. The project yeast.dpx contains four data files, where each

file is an expression profiling study of one yeast strain, measuring the

response of metabolic switch. The study compares wild-type yeast with three

mutants. Activate 3-way analysis:

To open the 3-way control panel. Here one can set the number underlying

components and also choose to normalize the data.

Pressing run perform trilinear decomposition of the data based on the

selected number of underlying components. If Auto is selected statistical tests


are used to determine the optimum number of underlying components. This

number is later shown in the control box:

Also a button appears to reconstruct the original data to test the goodness of

the trilinear fit. Next to the button appears a curtain menu to select which of

the data files to reconstruct. The result of the trilinear decomposition are three

plots: one showing the underlying components along the time points, one

showing them along the genes and one showing them along the strains.

The first graph shows that two time dependences dominate; one with

maximum around 10 minutes and one with maximum around 20 minutes.

Second graph shows which genes correspond to the different time behaviors.


The responses are color coded such that each underlying component is

shown with the same color in all three graphs. Hence, a gene that has a large

signal in one underlying component has important contribution to the time

behavior of this component. The third graph compares the strains. Also here

the color codes show which underlying component is important in which

strain. Furthermore, the different strains are compared. Here, for example, we

see that both underlying components show the trend: strain 1, strain 2, strain

4 and strain 3, suggesting that Hxt7 (= strain 2) is most similar to wt, than

comes Tm6 (= strain 4), and the most deviant strain is null (= strain 3).


5. Upgrades and support

Upgrades and corrections of GenEx are available on the Internet on

http://www.multid.se. On the MultiD website you also find additional

information about GenEx, Procrustes rotation, trilinear decomposition and

other methods to analyze multidimensional data. Registered customers can

obtain support at their local MultiD representative or at the MultiD Analyses

AB main office.

MultiD Analyses AB

Lotsgatan 5A

414 58 Gothenburg

SWEDEN

E-mail: [email protected]


6. Acknowledgements

Example real-time PCR data were kindly provided by Anders Stålberg, Karin

Elbing, Radek Sindelka, Jiri Jonák and Mikael Kubista from the TATAA

Biocenter. Dr José Manuel Andrade Garda from University A Coruña has

provided most valuable feedback on early versions and beta releases.


7. References

1 J. Vandesompele, K. De Preter, F. Pattyn, B. Poppe, N. Van Roy, A.

De Paepe and F. Speleman. Accurate normalization of real-time quantitative RT-PCR data by geometric averaging of multiple internal control genes. Genome Biology, 3:research0034.1-0034.11 (2002)

2 M. Bengtsson, A. Ståhlberg, P. Rorsman, and M. Kubista, Gene

expression profiling in single cells from the pancreatic islets of Langerhans reveals lognormal distribution of mRNA levels. Genome Research 15, 1388-1392 (2005).

Research Highlights in Nature Review Genetics 6, 1758 (2005).

3 A. Ståhlberg, P. Åman, B. Ridell, P. Mostad & M. Kubista. Quantitative Real-Time PCR Method for Detection of B-Lymphocyte Monoclonality by Comparison of k and l Immunoglobulin Light Chain Expression. Clin. Chem. 49, 51-59 (2003).

4 M. Forina, C. Armanino, R. Leardi and G. Drava, J. Chemom., 1991, 5,

435–453. 5 X. Tomas and J. M. Andrade, Quim. Anal., 1999, 18, 225–231. 6 G.H. Lance, W.T. Williams A general theory of classificatory sorting

strategies. I. Hierarchical Systems. Comp. J. 9 (1966) 373-380. 7 J. H. Ward. Hierarchical grouping to optimize an objective function,

Journal of Amer. Statist. Assoc. 58: 236-244 (1963). 8 T. Kohonen: Self-Organizing Maps. Springer-Verlag, Heidelberg 1995. 9 A. Smilde, R. Bro & P. Geladi. MultiWay Analysis. John Wiley & Sons

Ltd. ISBN: 0-471-98691-7 (2004). 10 J. M. Andrade, M, P. Gómez-Carracedo, W. Krzanowski & M. Kubista.

Procrustes rotation in analytical chemistry, a tutorial. Chemometrics and Intelligent Laboratory Systems 72 123 (2004).

Documents

DATAN GenEx 20060212 - MultiD GenEx.pdf · GenEx Page 3 MultiD 1. Introduction Optimal use of real-time PCR measurements requires proper analysis of real-time PCR data. DATAN framework