1. Bioinformatics: gene expression basics
Ollie Rando, LRB 903

2. Experimental Cycle
Biological question (hypothesis-driven or explorative)
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
Experimental design
Failed
Microarray experiment
Quality
Measurement
Image analysis
Pre-processing
Normalization
Pass
Analysis
Estimation
Testing
Clustering
Discrimination
Biological verification
and interpretation

3. DNA Microarray
Lecture 1.1

4. From experiment to data

5. Microarrays & Spot Colour
Lecture 1.1

6. Microarray Analysis Examples
Brain
67,679
Heart
9,400
Liver
37,807
Colon
4,832
Prostate
7,971
Skin
3,043
Bone
Lung
20,224
Brain
Lung
Liver
Liver Tumor
Lecture 1.1

7. 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

8. Scatterplot Data Data (log scale)
Message: look at your data on log-scale!

9. MA Plot
A = 1/2 log2(RG)
M = log2(R/G)

10. Median centering
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.
Log Signal, centered at 0

11. Problem of median-centering
Median-Centering is a global Method. It does not adjust for local effects, intensity dependent effects, print-tip effects, etc.
Log Green
Log Red
Scatterplot of log-Signals after Median-centering
A = (Log Green + Log Red) / 2
M = Log Red - Log Green
M-A Plot of the same data

12. Lowess normalization Local estimate Use the estimate to bend
A = (Log Green + Log Red) / 2
M = Log Red - Log Green
Local estimate
Use the estimate to bend
the banana straight

13. 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

14. OK, so I’ve got a gene list with expression changes: now what?
YPL171C
YBR008C
YFL056C
YKL086W
YOL150C
YOL151W
YFL057C
YKL071W
YLR327C
YLL060C
YLR460C
YML131W
YDL243C
YKR076W
YOR374W
“Huh. Turns out the standard names for the
most upregulated genes all start with ‘HSP’,
or ‘GAL’ … I wonder if that’s real …”

15. Gene Ontology Organization of curated biological knowledge
3 branches: biological process, molecular function, cellular component

16. 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

17. 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:

18. GO term Enrichment Tools
SGD’s & Princeton’s GoTermFinder
GOLEM (
HIDRA
Sealfon et al., 2006

19. 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.

20. 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.

21. Supervised analysis
Calvin, 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

22. Un-supervised analysis
Calvin, 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 …

23. 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.

24. One microarray, one dot
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.
Expression of gene 2
Expression of gene 1

25. Which line separates best?D

26. No sharp knive, but a …
FAT PLANE

27. Support Vector Machines
Maximal margin
separating hyperplane
Datapoints closest
to separating
hyperplane
= support vectors

28. How well did we do?
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?
Same classifier (= line)
New data from same classes
The classifier will usually perform worse than before:
Test error > training error

29. Train classifier and test it
Cross-validation
Training error
Train classifier and test it
Test error
Train
Test
K-fold Cross-validation
Step 1.
Train
Train
Test
Here for
K=3
Step 2.
Train
Test
Train
Step 3.
Test
Train
Train

30. Additional supervised approaches might depend on your goal: cell cycle analysis

31. 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

32. Quick Example
Conditions
Genes

33. 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

34. 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 t .

35. 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

36. Distance Metrics Spearman Correlation Euclidean Distance
Pearson Correlation

37. Hierarchical clustering
Imposes (pair-wise) hierarchical structure on all of the data
Often good for visualization
Basic Method (agglomerative):
Calculate all pair-wise distances
Join the closest pair
Calculate pair’s distance to all others
Repeat from 2 until all joined

38. Hierarchical clustering

39. Hierarchical clustering

40. Hierarchical clustering

41. Hierarchical clustering

42. Hierarchical clustering

43. Hierarchical clustering

44. 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

45. 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

46. Cluster analysis of combined yeast data sets
Eisen M B et al. PNAS 1998;95:
Cluster analysis of combined yeast data sets. Data from separate time courses of gene expression in the yeast S. cerevisiae were combined and clustered. Data were drawn from time courses during the following processes: the cell division cycle (9) after synchronization by alpha factor arrest (ALPH; 18 time points); centrifugal elutriation (ELU; 14 time points), and with a temperature-sensitive cdc15 mutant (CDC15; 15 time points); sporulation (10) (SPO, 7 time points plus four additional samples); shock by high temperature (HT, 6 time points); reducing agents (D, 4 time points) and low temperature (C; 4 time points) (P. T. S., J. Cuoczo, C. Kaiser, P.O. B., and D. B., unpublished work); and the diauxic shift (8) (DX, 7 time points). All data were collected by using DNA microarrays with elements representing nearly all of the ORFs from the fully sequenced S. cerevisiae genome (8); all measurements were made against a time 0 reference sample except for the cell-cycle experiments, where an unsynchronized sample was used. All genes (2,467) for which functional annotation was available in the Saccharomyces Genome Database were included (12). The contribution to the gene similarity score of each sample from a given process was weighted by the inverse of the square root of the number of samples analyzed from that process. The entire clustered image is shown in A; a larger version of this image, along with dendrogram and gene names, is available at Full gene names are shown for representative clusters containing functionally related genes involved in (B) spindle pole body assembly and function, (C) the proteasome, (D) mRNA splicing, (E) glycolysis, (F) the mitochondrial ribosome, (G) ATP synthesis, (H) chromatin structure, (I) the ribosome and translation, (J) DNA replication, and (K) the tricarboxylic acid cycle and respiration. The full-color range represents log ratios of −1.2 to 1.2 for the cell-cycle experiments, −1.5 to 1.5 for the shock experiments, −2.0 to 2.0 for the diauxic shift, and −3.0 to 3.0 for sporulation. Gene name, functional category, and specific function are from the Saccharomyces Genome Database (13). Cluster I contains 112 ribosomal protein genes, seven translation initiation or elongation factors, three tRNA synthetases, and three genes of apparently unrelated function.
©1998 by The National Academy of Sciences

47. To demonstrate the biological origins of patterns seen in Figs
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).
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:
©1998 by The National Academy of Sciences

48. Hierarchical Clustering: Another Example
Expression of tumors hierarchically clustered
Expression groups by clinical class
Garber et al.

49. K-means Clustering
Groups genes into a pre-defined number of independent clusters
Basic algorithm:
Define k = number of clusters
Randomly initialize each cluster with a seed (often with a random gene)
Assign each gene to the cluster with the most similar seed
Recalculate all cluster seeds as means (or medians) of genes assigned to the cluster
Repeat 3 & 4 until convergence
(e.g. No genes move, means don’t change much, etc.)

50. K-means example

51. K-means example

52. K-means example

53. K-means example

54. 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

55. 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

56. 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

57. 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

58. SVD (& PCA) 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 =
Singular values
“Eigen-genes”
Original
Data matrix
“Eigen-conditions”

59. SVD
SVD

60. 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

61. Where do we go for relevant datasets?
GO: see previous
Yeast genomic annotations: Saccharomyces Genome Database
Potential regulatory sites – MEME:
TATA box data for yeast: Basehoar … Pugh, Cell, 2004
Stress response: Gasch et al