Version 1.0 – 19 Jan 2009

4. Functional Genomics and Microarray Analysis (1)

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BackgroundFunctional Genomics

Functional Genomics: – Systematic analysis of gene activity in healthy and diseased tissues.– Obtaining an overall picture of genome functions, including the expression

profiles at the mRNA level and the protein level.

Functional Genome Analysis: – used to understand the functions of genes and proteins in an organism. This is

typically known as genome annotation.– used in integrative biology and systems biology studies aiming to understand

health and disease states (e.g. cancer, obesity, …etc)– Used as an important step in the search for new target molecules in the drug

discovery process. (which genes, proteins to target and how)

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What is…?

Gene Expression:– The process by which the information encoded in a gene is converted into an

observable phenotype (most commonly production of a protein).– The degree to which a gene is active in a certain tissue of the body, measured

by the amount of mRNA in the tissue.

Microarrays:– Tools used to measure the presence and abundance of gene expression

(measure as mRNA) in tissue.– microarray technologies provide a powerful tool by which the expression

patterns of thousands of genes can be monitored simultaneously and measured quantitatively

determines

DNA sequence(split into genes)

Amino Acid Sequence

Protein

3DStructure

ProteinFunction

Cell Activity

codes for

folds into

dictates

has

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Applications of Microarray Technology

Applications covered only as example contexts, emphasis is on analysis methods

– Identify Genes expressed in different cell types (e.g. Liver vs Kidney)

– Learn how expression levels change in different developmental stages (embryo vs. adult)

– Learn how expression levels change in disease development (cancerous vs non-cancerous)

– Learn how groups of genes inter-relate (gene-gene interactions)

– Identify cellular processes that genes participate in (structure, repair, metabolism, replication, … etc)

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MicroarraysBasic Idea

A Microarray is a device that detects the presence and abundance of labelled nucleic acids in a biological sample.

In the majority of experiments, the labelled nucleic acids are derived from the mRNA of a sample or tissue.

The Microarray consists of a solid surface onto which known DNA molecules have been chemically bonded at special locations.

– Each array location is typically known as a probe and contains many replicates of the same molecule.

– The molecules in each array location are carefully chosen so as to hybridise only with mRNA molecules corresponding to a single gene.

Affymetrix Inc. is the leading provider of Microarray

technology (GeneChip® )http://www.affymetrix.com/

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Basic Idea

A Microarray works by exploiting the ability of a given mRNA molecule to bind specifically to, or hybridize to, the DNA template from which it originated.

By using an array containing many DNA samples, scientists can determine, in a single experiment, the expression levels of hundreds or thousands of genes within a cell by measuring the amount of mRNA bound to each site on the array.

With the aid of a computer, the amount of mRNA bound to the spots on the Microarray is precisely measured, generating a profile of gene expression in the cell.

Several companies sell equipment to make DNA chips, including spotters to deposit the DNA on the surface and scanners to detect the fluorescent or radioactive signals.

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Microarray Process

The molecules in the target biological sample are labelled using a fluorescent dye before sample is applied to array

– If a gene is expressed in the sample, the corresponding mRNA hybridises with the molecules on a given probe (array location).

– If a gene is not expressed, no hybridisation occurs on the corresponding probe.

Reading the array output– After the sample is applied, a laser light source is applied to the array.– The fluorescent label enables the detection of which probes have

hybridised (presence) via the light emitted from the probe.– If gene is highly expressed, more mRNA exists and thus more mRNA

hybridises to the probe molecules (abundance) via the intensity of the light emitted.

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The array

Chemistry Basics:

Surface Chemistry is used to attach the probe molecules to the glass substrate.

Chemical reactions are used to attach the florescent dyes to the target molecules

Probe and Target hybridise to form a double helix

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Affymetrix GeneChipExample of Single Label Chips

Hundreds of thousands of oligonucleotide probes packed at extremely high densities. The probes designed to maximize sensitivity, specificity, and reproducibility, allowing consistent discrimination between specific and background signals, and between closely related target sequences.

RNA labeled and scanned in a single “color” one sample per chip

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From Microarray images to Gene Expression Matrices

Images

Spo

ts

Spot/Image quantiations

Intermediate data

Samples

Gen

es

Gene expression levels

Final data Gene Expression MatrixRaw data

Array scans

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Steps of a Microarray Experiment

Biological question

Biological verification and interpretation

Microarray experiment

Experimental designPlatform Choice

Image analysis

Normalization

Clustering

Pattern Discovery

Sample Attributes

16-bit TIFF Files

Quantify the Dots

Data MiningClassification

Statistical Analysis

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Qualitative Interpretation of Reads

GREEN represents High Control hybridization 

RED represents High Sample hybridization 

YELLOW represents a combination of Control and Sample where both hybridized equally. BLACK represents areas where neither the Control nor Sample hybridized.

Main issue is to quantify the results: – How green is green?– What is the ratio of the signal to background noise?– How to compare multiple experiments using different chips?– How to quantify cross hybridization (if any)?

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Normalization

Normalisation is a general term for a collection of methods that are directed at reasoning about and resolving the systematic errors and bias introduced by microarray experimental platforms

Normalisation methods stand in contrast with the data analysis methods described in other lectures (e.g. differential gene expression analysis, classification and clustering).

Our overall aim is to be able to quantify measured/calculated variability, differentials and similarity:

– Are they biologically significant or just side effects of the experimental platforms and conditions?

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Why NormalizationSources of Microarray Data Variability

There are several levels of variability in measured gene expression of a feature.

At the highest level, there is biological variability in the population from which the sample derives.

At an experimental level, there is – variability between preparations and

labelling of the sample, – variability between hybridisations of the

same sample to different arrays, and – variability between the signal on replicate

features on the same array.

Variability between IndividualsTrue gene expression of individual

Variability between sample preparations

Variability between arrays and hybridisations

Variability between replicate features

Measured gene expression

The measured gene expression in any experiment includes true gene expression,together with contributions from many sources of variability

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Normalisation Examples Probe Intensity Value

The raw intensities of signal from each spot on the array are not directly comparable. Depending on the types of experiments done, a number of different approaches to normalization may be needed. Not all types of normalization are appropriate in all experiments. Some experiments may use more than one type of normalization.

Reasonable Assumption: intensities of fluorescent molecules reflect the abundance of the mRNA molecules – generally true but could be problematic

Example:– intensity of gene A spot is 100 units in normal-tissue array– intensity of gene A spot is 50 units in cancer-tissue array – Conclusion: gene A’s expression level in normal issue is significantly

higher than in cancer tissue

Typical Problem: Usually more variability at low intensity

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Normalisation Examples Probe Intensity Value

Problem? What if the overall background intensity of the normal-tissue array is 95 units while the background intensity of cancer-tissue array is 10 units?

Solutions: – Subtract background intensity value– Take ratio of spot intensity to background intensity (preferable)– In both cases have to decide where to measure background intensity (e.g.

local to spot or globally per chip)

In general, There could be many factors contributing to the background intensity of a microarray chip

– To compare microarray data across different chips, data (intensity levels) need to be normalized to the “same” level

Images showing examples of how background intensity can be calculated

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Differential Gene Expression Analysis

Consider a microarray experiment– that measures gene expression in two groups of rat tissue (>5000

genes in each experiment).

– The rat tissues come from two groups: WT: Wild-Type rat tissue, KO: Knock Out Treatment rat tissue

– Gene expression for each group measured under similar conditions

– Question: Which genes are affected by the treatment? How significant is the effect? How big is the effect?

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Calculating Expression Ratios

In Differential Gene Expression Analysis, we are interested in identifying genes with different expression across two states, e.g.:

– Tumour cell lines vs. Normal cell lines– Treated tissue vs. diseased tissue– Different tissues, same organism– Same tissue, different organisms– Same tissue, same organism– Time course experiments

We can quantify the difference (effect) by taking a ratio

i.e. for gene k, this is the ratio between expression in state a compared to expression in state b

– This provides a relative value of change (e.g. expression has doubled)– If expression level has not changed ratio is 1

kb

kakE

ER

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Fold change(Fold ratio)

Ratios are troublesome since – Up-regulated & Down-regulated genes treated differently

Genes up-regulated by a factor of 2 have a ratio of 2 Genes down-regulated by same factor (2) have a ratio of 0.5

– As a result down regulated genes are compressed between 1 and 0 up-regulated genes expand between 1 and infinity

Using a logarithmic transform to the base 2 rectifies problem, this is typically known as the fold change

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)(log)(log

22

22

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ERF

A gene is up-regulated in state 2 compared to state 1 if it has a higher value in state 2

A gene is down-regulated in state 2 compared to state 1 if it has a lower value in state 2

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Examples of fold change

Gene ID Expression in state 1

Expression in state 2

Ratio Fold Change

A 100 50 2 1

B 10 5 2 1

C 5 10 0.5 -1

D 200 1 200 7.65

E 10 10 1 0

You can calculate Fold change between pairs of expression values:

e.g. Between State 1 vs State 2 for gene A

Or Between mean values of all measurements for a gene in the WT/KO experiments

•mean(WT1..WT4) vs mean (KO1..KO4)

A, B and D are down regulated

C is up-regulated

E has no change

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StatisticsSignificance of Fold Change

For our problem we can calculate an average fold ratio for each gene (each row)

This will give us an average effect value for each gene– 2, 1.7, 10, 100, etc

Question which of these values are significant?– Can use a threshold, but what threshold value should we set?– Use statistical techniques based on number of members in each

group, type of measurements, etc -> significance testing.

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StatisticsUnpaired statistical experiments

Overall setting: 2 groups of 4 individuals each– Group1: Imperial students– Group2: UCL students

Experiment 1:– We measure the height of all students – We want to establish if members of one group are consistently (or on

average) taller than members of the other, and if the measured difference is significant

Experiment 2:– We measure the weight of all students – We want to establish if members of one group are consistently (or on

average) heavier than the other, and if the measured difference is significant

Experiment 3:– ………

Condition

Group 1 members

Condition

Group 2 members

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StatisticsUnpaired statistical experiments

In unpaired experiments, you typically have two groups of people that are not related to one another, and measure some property for each member of each group

e.g. you want to test whether a new drug is effective or not, you divide similar patients in two groups:

– One groups takes the drug– Another groups takes a placebo– You measure (quantify) effect of both groups some time later

You want to establish whether there is a significant difference between both groups at that later point

The WT/KO example is an unpaired experiment if the rats in the experiments are different !

Condition

Group 1 members

Condition

Group 2 members

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StatisticsUnpaired statistical experiments

The WT/KO example is an unpaired experiment if the rats in the experiments are different!

Experiment for WT Rats for Gene 96608_at

Rat # WT gene expression

WT1 100

WT2 100

WT3 200

WT4 300

Experiment for KO Rats for Gene 96608_at

Rat # KO gene expression

KO1 150

KO2 300

KO3 100

KO4 300

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StatisticsUnpaired statistical experiments

How do we address the problem? Compare two sets of results

(alternatively calculate mean for each group and compare means)

Graphically:

– Scatter Plots– Box plots, etc

Compare Statistically– Use unpaired t-test

0

20

40

60

80

100

120

140

Are these two series significantly different?

0

20

40

60

80

100

120

140

Are these two series significantly different?

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StatisticsPaired statistical experiments

In paired experiments, you typically have one group of people, you typically measure some property for each member before and after a particular event (so measurement come in pairs of before and after)

e.g. you want to test the effectiveness of a new cream for tanning– You measure the tan in each individual before the cream is applied– You measure the tan in each individual after the cream is applied

You want to establish whether the there is a significant difference between measurements before and after applying the cream for the group as a whole

Group members

Condition 1

Condition 2

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StatisticsPaired statistical experiments

The WT/KO example is a paired experiment if the rats in the experiments are the same!

Experiments for Gene 96608_at

Rat # WT gene expression

KO gene expression

Rat1 100 200

Rat2 100 300

Rat3 200 400

Rat4 300 500

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StatisticsPaired statistical experiments

How do we address the problem? Calculate difference for each pair Compare differences to zero Alternatively (compare average

difference to zero)

Graphically:– Scatter Plot of difference– Box plots, etc

Statistically– Use unpaired t-test

Are differences close to Zero?

-15

-10

-5

0

5

10

15

-15

-10

-5

0

5

10

15

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StatisticsSignificance testing

In both cases (paired and unpaired) you want to establish whether the difference is significant

Significance testing is a statistical term and refers to estimating (numerically) the probability of a measurement occurring by chance.

To do this, you need to review some basic statistics– Normal distributions: mean, standard deviations, etc– Hypothesis Testing– t-distributions– t-tests and p-values

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Mean and standard deviation

Mean and standard deviation tell you the basic features of a distribution

mean = average value of all members of the groupu = (x1+x2+x3 ….+xN)/N

standard deviation = a measure of how much the values of individual members vary in relation to the mean

The normal distribution is symmetrical about the mean 68% of the normal distribution lies within 1 s.d. of the mean

68% of dist.

1 s.d. 1 s.d.

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Note on s.d. calculation

Through the following slides and in the tutorials, I use the following formula for calculating standard deviation

Some people use the unbiased form below (for good reasons)

Please use the simple form if you want the answers to add up at the end

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The Normal Distribution

Many continuous variables follow a normal distribution, and it plays a special role in the statistical tests we are interested in;

•The x-axis represents the values of a particular variable

•The y-axis represents the proportion of members of the population that have each value of the variable

•The area under the curve represents probability – i.e. area under the curve between two values on the x-axis represents the probability of an individual having a value in that range

68% of dist.

1 s.d. 1 s.d.

X

x

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Hypothesis Testing: Are two data sets different

HHo

HHa

Population 1

Population 2

Population 1 Population 2

If standard deviation known use z test, else use t-test

We use z-test (normal distribution) if the standard deviations of two populations from which the data sets came are known (and are the same)

We pose a null hypothesis that the means are equal

We try to refute the hypothesis using the curves to calculate the probability that the null hypothesis is true (both means are equal)

– if probability is low (low p) reject the null hypothesis and accept the alternative hypothesis (both means are different)

– If probability is high (high p) accept null hypothesis (both means are equal)

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Comparing Two SamplesGraphical interpretation

To compare two groups you can compare the mean of one group graphically.

The graphical comparison allows you to visually see the distribution of the two groups.

If the p-value is low, chances are there will be little overlap between the two distributions. If the p-value is not low, there will be a fair amount of overlap between the two groups.

We can set a critical value for the x-axis based on the threshold of p-value

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t-test terminology

t-test: Used to compare the mean of a sample to a known number Assumptions: Subjects are randomly drawn from a population and the

distribution of the mean being tested is normal.

Test: The hypotheses for a single sample t-test are: – Ho: u = u0 – Ha: u < > u0

p-value: probability of error in rejecting the hypothesis of no difference between the two groups.

(where u0 denotes the hypothesized value to which you are comparing a population mean)

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t-Tests Intuitively

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t-test terminologyUnpaired vs. paired t-test

Same as before !! Depends on your experiment

Unpaired t-Test: The hypotheses for the comparison of two independent groups are:

– Ho: u1 = u2 (means of the two groups are equal) – Ha: u1 <> u2 (means of the two group are not equal)

Paired t-test: The hypothesis of paired measurements in same individuals

– Ho: D = 0 (the difference between the two observations is 0) – Ha: D <> 0 (the difference is not 0)

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Calculating t-test (t statistic)

First calculate t statistic value and then calculate p value

For the paired t-test, t is calculated using the following formula:

And n is the number of pairs being tested.

For an unpaired (independent group) t-test, the following formula is used:

Where σ (x) is the standard deviation of x and n (x) is the number of elements in x.

nddmean

t)(

)( Where d is calculated by

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)()(

)()(

)()(22

yny

xnx

ymeanxmeant

Remember these formulae !!

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Calculating p-value for t-test

When carrying out a test, a P-value can be calculated based on the t-value and the ‘Degrees of freedom’.

There are three methods for calculating P:– One Tailed >: – One Tailed <: – Two Tailed:

Where p(t,v) is looked up from the t-distribution table

The number of degrees (v) of freedom is calculated as:– UnPaired: n (x) +n (y) -2 – Paired: n- 1 (where n is the number of pairs.)

2/),( tpP 2/),(1 tpP

),( tpP

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p-values

Results of the t-test: If the p-value associated with the t-test is small (usually set at p < 0.05), there is evidence to reject the null hypothesis in favour of the alternative.

In other words, there is evidence that the mean is significantly different than the hypothesized value. If the p-value associated with the t-test is not small (p > 0.05), there is not enough evidence to reject the null hypothesis, and you conclude that there is evidence that the mean is not different from the hypothesized value.

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t-value and p-value

Given a t-value, and degrees of freedom, you can look-up a p-value

Alternatively, if you know what p-value you need (e.g. 0.05) and degrees of freedom you can set the threshold for critical t

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Degrees of Freedom1 3.078 6.314 12.706 31.821 63.6572 1.886 2.92 4.303 6.965 9.925. . . . . .. . . . . .

10 1.372 1.812 2.228 2.764 3.169. . . . . .. . . . . .

200 1.286 1.653 1.972 2.345 2.6011.282 1.645 1.96 2.326 2.576

tc

t.100 t.05 t.025 t.01 t.005

A = .05A = .05

-tc =1.812=-1.812

The table provides the t values (tc) for which P(tx > tc) = AFinding a critical t

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Meaning of t-valueHigh t-value

Take Gene A, assuming paired test:

For Either type of test Average Difference is = 100, SD. = 0 t value is near infinity, p is extremely low

Gene R1a R2a R3a R4a R1b R2b R3b R4bA 10 20 30 40 110 120 130 140

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Consider Gene M for a paired experiment

Gene R1a R2a R3a R4a R1b R2b R3b R4bT 10 20 30 40 10 20 30 40

0 Change Average

nddmean

t)(

)( Where d is calculated

byiii yxd

Average Difference is = 0 t value is zero, what does this mean?

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Consider Gene T for a paired experiment

Gene R1a R2a R3a R4a R1b R2b R3b R4bT 11 19 32 39 110 120 130 140

75.994

1019810199 Change Avergae

4

)75.99101()75.9998()75.99101()75.9999(SD

2222 29.1

1554/29.1

75.99t

nddmean

t)(

)( Where d is calculated

byiii yxd

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Hypothesis Testing

Uses hypothesis testing methodology.

For each Gene (>5,000)– Pose Null Hypothesis (Ho) that gene is not affected– Pose Alternative Hypothesis (Ha) that gene is affected– Use statistical techniques to calculate the probability of rejecting the hypothesis (p-value)– If p-value < some critical value reject Ho and Accept Ha

The issues:– Large number of genes (or experiments)– Need quick way to filter out significant genes that have high fold change – Need also to sort genes by fold change and significance

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Volcano PlotsA visual approach

For each gene calculate the significance of the change

(t-test, p-value)

For each gene compare the value of the effect between population WT vs. KO

(fold change)

Identify Genes with high effect and high significance

Volcano Plot

Volcano plots are a graphical means for visualising results of large numbers of t-tests allowing us to plot both the Effect and significance of each test in an easy to interpret way

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Volcano plots

In a volcano plot: X-axis represents effect measured as fold

change:

y-axis represents the number of zeroes in the p-value

Effect = log(WT) – log(KO)

2 2 = log(WT / KO)

2

If WT = WO, Effect Fold Change = 0 , If WT = 2 WO, Effect Fold Change = 1

...

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Numerical Interpretation (Significance)

Using log10 for Y axis:

p< 0.1

(1 decimal place)

p< 0.01

(2 decimal places)