Bioinformatics: gene expression basics

Ollie Rando, LRB 903

Biological verification and interpretation

Microarray experiment

Experimental design

Image analysis

Normalization

Biological question (hypothesis-driven or explorative)

TestingEstimation DiscriminationAnalysis

Clustering

Experimental Cycle

Quality Measurement

Failed

Pass

Pre-processing

To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination:

He may be able to say what the experiment died of.

Ronald Fisher

Lecture 1.1 3

DNA Microarray

From experiment to data

Lecture 1.1 5

Microarrays & Spot Colour

Lecture 1.1 6

Microarray Analysis Examples

Brain Brain 67,67967,679

Heart Heart 9,4009,400

Liver Liver 37,80737,807 Colon Colon

4,8324,832Prostate Prostate 7,9717,971

Skin Skin 3,0433,043

Bone Bone 4,8324,832

Lung Lung 20,22420,224

BrainBrain LungLung

LiverLiver Liver TumorLiver Tumor

Raw data are not mRNA concentrations

• tissue contamination• RNA degradation• amplification efficiency• reverse transcription efficiency• Hybridization efficiency and

specificity• clone identification and

mapping• PCR yield, contamination

• spotting efficiency

• DNA support binding

• other array manufacturing related issues

• image segmentation

• signal quantification

• “background” correction

Data Data (log scale)

Scatterplot

Message: look at your data on log-scale!

MA Plot

A = 1/2 log2(RG)

M =

log 2(R

/G)

Median centering

Log S

ignal, c

ente

red

at

0

One of the simplest strategies is to bring all „centers“ of the array data to the same level.

Assumption: the majority of genes are un-changed between conditions.

Median is more robust to outliers than the mean.

Divide all expression measurements of each array by the Median.

Problem of median-centering

Log Green

Log

Red

Scatterplot of log-Signals after Median-centering

A = (Log Green + Log Red) / 2

M =

Log

Red

- Lo

g G

reen

M-A Plot of the same data

Median-Centering is a global Method. It does not adjust for local effects, intensity dependent effects, print-tip effects, etc.

Lowess normalization

A = (Log Green + Log Red) / 2

M =

Log

Red

- Lo

g G

reen

Local

estimateUse the estimate to bend

the banana straight

Summary I

• Raw data are not mRNA concentrations• We need to check data quality on different

levels– Probe level– Array level (all probes on one array)– Gene level (one gene on many arrays)

• Always log your data• Normalize your data to avoid systematic (non-

biological) effects• Lowess normalization straightens banana

OK, so I’ve got a gene list with expression changes: now what?

YPL171C 7.743877387

YBR008C 6.390877387

YFL056C 5.740877387

YKL086W 5.408877387

YOL150C 4.831877387

YOL151W 4.760877387

YFL057C 4.725877387

YKL071W 4.172877387

YLR327C 4.167877387

YLL060C 4.130877387

YLR460C 4.063877387

YML131W 4.047877387

YDL243C 4.031877387

YKR076W 3.942877387

YOR374W 3.937877387

“Huh. Turns out the standard names for themost upregulated genes all start with ‘HSP’,or ‘GAL’ … I wonder if that’s real …”

Gene Ontology• Organization of curated biological knowledge

– 3 branches: biological process, molecular function, cellular component

Hypergeometric Distribution• Probability of observing x or more genes in a cluster of n

genes with a common annotation

– N = total number of genes in genome– M = number of genes with annotation– n = number of genes in cluster– x = number of genes in cluster with annotation

• Multiple hypothesis correction required if testing multiple functions (Bonferroni, FDR, etc.)

• Additional genes in clusters with strong enrichment may be related

Kolmogorov-Smirnov test• Hypergeometric test requires “hard calls” – this list of

278 genes is my upregulated set• But say all 250 genes involved in oxygen consumption go

up ~10-20% each – this would not likely show up• KS test asks whether *distribution* for a given geneset

(GO category, etc.) deviates from your dataset’s background, and is nonparametric

• Cumulative Distribution Function (CDF) plot:

• Gene Set Enrichment Analysis:• http://www.broadinstitute.org/gsea/

GO term Enrichment Tools• SGD’s & Princeton’s GoTermFinder

– http://go.princeton.edu• GOLEM (http://function.princeton.edu/GOLEM)

• HIDRA

Sealfon et al., 2006

Supervised analysis= learning from examples, classification

– We have already seen groups of healthy and sick people. Now let’s diagnose the next person walking into the hospital.

– We know that these genes have function X (and these others don’t). Let’s find more genes with function X.

– We know many gene-pairs that are functionally related (and many more that are not). Let’s extend the number of known related gene pairs.

Known structure in the data needs to be generalized to new data.

Un-supervised analysis

= clustering– Are there groups of genes that behave similarly in

all conditions?– Disease X is very heterogeneous. Can we identify

more specific sub-classes for more targeted treatment?

No structure is known. We first need to find it. Exploratory analysis.

Supervised analysisCalvin, I still don’t know the difference between cats and dogs …Oh, now I get it!!

Don’t worry!I’ll show you once more:

Class 1: cats Class 2: dogs

Un-supervised analysisCalvin, I still don’t know the difference between cats and dogs …

I don’t know it either.

Let’s try to figure it out together …

Supervised analysis: setup• Training set

– Data: microarrays– Labels: for each one we know if it falls into our class

of interest or not (binary classification)

• New data (test data)– Data for which we don’t have labels. – Eg. Genes without known function

• Goal: Generalization ability– Build a classifier from the training data that is good

at predicting the right class for the new data.

One microarray, one dotExpre

ssio

n o

f g

en

e 2

Expression of gene 1

Think of a space with #genes dimensions (yes, it’s hard for more than 3).

Each microarray corresponds to a point in this space.

If gene expression is similar under some conditions, the points will be close to each other.

If gene expression overall is very different, the points will be far away.

Which line separates best?A B

C D

No sharp knive, but a …

FAT P

LANE

Support Vector Machines

Maximal margin separating hyperplane

Datapoints closest to separating hyperplane= support vectors

How well did we do?

The classifier will usually perform worse than before:

Test error > training error

Same classifier (= line)

New data from same classes

Training error: how well do we do on the data we trained the classifier on?

But how well will we do in the future, on new data?

Test error: How well does the classifier generalize?

Cross-validation

Train classifier and test itTraining error

Train TestTest error

K-fold Cross-validation

Train TestTrainStep 1.

Test TrainTrainStep 2.

Train TrainTestStep 3.

Here for K=3

Additional supervised approaches might

depend on your goal: cell cycle analysis

Clustering

• Let the data organize itself

• Reordering of genes (or conditions) in the dataset so that similar patterns are next to each other (or in separate groups)

• Identify subsets of genes (or experiments) that are related by some measure

Quick ExampleG

enes

Conditions

Why cluster?

• “Guilt by association” – if unknown gene X is similar in expression to known genes A and B, maybe they are involved in the same/related pathway

• Visualization: datasets are too large to be able to get information out without reorganizing the data

Clustering Techniques

• Algorithm (Method)– Hierarchical– K-means– Self Organizing Maps– QT-Clustering– NNN– .– .– .

• Distance Metric– Euclidean (L2)

– Pearson Correlation– Spearman Correlation– Manhattan (L1)

– Kendall’s – .– .– .

Distance Metrics

• Choice of distance measure is important for most clustering techniques

• Pair-wise metrics – compare vectors of numbers– e.g. genes x & y, ea. with n measurements

Euclidean Distance

Pearson Correlation

Spearman Correlation

Distance MetricsEuclidean Distance

Pearson Correlation

Spearman Correlation

Hierarchical clustering

• Imposes (pair-wise) hierarchical structure on all of the data

• Often good for visualization• Basic Method (agglomerative):

1. Calculate all pair-wise distances2. Join the closest pair3. Calculate pair’s distance to all others4. Repeat from 2 until all joined

Hierarchical clustering

Hierarchical clustering

Hierarchical clustering

Hierarchical clustering

Hierarchical clustering

Hierarchical clustering

HC – Interior Distances

• Three typical variants to calculate interior distances within the tree– Average linkage: mean/median over all possible

pair-wise values

– Single linkage: minimum pair-wise distance

– Complete linkage: maximum pair-wise distance

Hierarchical clustering: problems

• Hard to define distinct clusters• Genes assigned to clusters on the basis of all

experiments• Optimizing node ordering hard (finding the optimal

solution is NP-hard)• Can be driven by one strong cluster – a problem for

gene expression b/c data in row space is often highly correlated

Cluster analysis of combined yeast data sets

Eisen M B et al. PNAS 1998;95:14863-14868

©1998 by The National Academy of Sciences

To demonstrate the biological origins of patterns seen in Figs. 1 and 2, data from Fig. 1 were clustered by using methods described here before and after random permutation within rows

(random 1), within columns (random 2), and both (random 3).

Eisen M B et al. PNAS 1998;95:14863-14868

©1998 by The National Academy of Sciences

Hierarchical Clustering: Another Example

• Expression of tumors hierarchically clustered• Expression groups by clinical class

Garber et al.

K-means Clustering• Groups genes into a pre-defined number of

independent clusters• Basic algorithm:

1. Define k = number of clusters2. Randomly initialize each cluster with a seed (often with

a random gene)3. Assign each gene to the cluster with the most similar

seed4. Recalculate all cluster seeds as means (or medians) of

genes assigned to the cluster5. Repeat 3 & 4 until convergence

(e.g. No genes move, means don’t change much, etc.)

K-means example

K-means example

K-means example

K-means example

K-means: problems

• Have to set k ahead of time– Ways to choose “optimal” k: minimize within-

cluster variation compared to random data or held out data

• Each gene only belongs to exactly 1 cluster• One cluster has no influence on the others

(one dimensional clustering) • Genes assigned to clusters on the basis of all

experiments

Clustering “Tweaks”

• Fuzzy clustering – allows genes to be “partially” in different clusters

• Dependent clusters – consider between-cluster distances as well as within-cluster

• Bi-clustering – look for patterns across subsets of conditions– Very hard problem (NP-complete)– Practical solutions use heuristics/simplifications that

may affect biological interpretation

Cluster Evaluation

• Mathematical consistency– Compare coherency of clusters to background

• Look for functional consistency in clusters– Requires a gold standard, often based on GO,

MIPS, etc.

• Evaluate likelihood of enrichment in clusters– Hypergeometric distribution, etc.– Several tools available

More Unsupervised Methods

• Search-based approaches– Starting with a query gene/condition, find most

related group• Singular Value Decomposition (SVD) & Principal

Component Analysis (PCA)– Decomposition of data matrix into “patterns”

“weights” and “contributions”– Real names are “principal components”

“singular values” and “left/right eigenvectors”– Used to remove noise, reduce dimensionality, identify

common/dominant signals

• SVD is the method, PCA is performing SVD on centered data

• Projects data into another orthonormal basis• New basis ordered by variance explained

X U

Vt

=

SVD (& PCA)

OriginalData matrix

“Eigen-conditions”

Singular values

“Eigen-genes”

SVD

SVD

OK, so all that’s fine. Let’s give it a shot

• Say we’ve run a gene expression array for changes in gene expression when chromatin protein X is deleted

• What GO categories show differential expression?• What TF binding sites regulate these genes?• I think this protein will affect genes near the ends of

the chromosomes – how do I check?• I bet TATA-containing genes are disproportionately

affected, so let’s check.• I think this protein is involved in stress response – let’s

compare it to a stress response dataset

Where do we go for relevant datasets?

• GO: see previous• Yeast genomic annotations: Saccharomyces

Genome Database• Potential regulatory sites – MEME:

http://meme.sdsc.edu/meme4_3_0/cgi-bin/meme.cgi

• TATA box data for yeast: Basehoar … Pugh, Cell, 2004

• Stress response: Gasch et al