1. Sporulation in Bacillus
Dormant spore
Growth
Stage VI,VII.
Maturation, Cell lysis
Germination
Stage V. Spore Coat
Polar division
Medial division
Stage IV.
Cortex
Vegetative cycle
Stage II. Asymmetric cell division
Stage III. Engulfment
After Errington, 2004

2. There is a hierarchy of gene expression during sporulation
Sporulation gene expression is temporally regulated by a transcription factor cascade sF sG sK sE
Spo0A sA
There is a hierarchy of gene expression during sporulation

3. Which genes are controlled by which transcription factor??sE sG sK sF
Spo0A sA
What if we knock-out a transcription factor gene?!

4. Which genes are controlled by which transcription factor??sE sF sG sK
Spo0A sA
What if we knock-out a transcription factor gene?!

5. B. Subtilis spotted dsDNA microarray
Contains ~4100 B. subtilis genes as PCR products

6. High speed spotting robot

7. Microarray hybridization

8. Raw microarray data is hard to interpret!

9. Image Analysis & Data Visualization
Cy5
Cy3
Cy5
Cy3
log2
Cy3
Cy5
Underexpressed
Overexpressed 8 4 2
fold

10. Experimental Design
Spo0A
Spo0A sA sA

11. Introduction to Clustering
“An intelligent being cannot treat every object it sees as a unique entity unlike anything else in the universe. It has to put objects in categories so that it may apply its hard-won knowledge about similar objects encountered in the past, to the object at hand.”
Steven Pinker, from
How the Mind Works, 1997

12. Class prediction using supervised learning
Classification by gene expression required a training set
i.e. we had a priori knowledge of the system.

13. Clustering is an unsupervised method for data exploration
microarrays
Genes
No training set or preconceived notions about the data labels are required. The data will reveal its natural structure to us

14. We start with many nodes, and end up with only one!
Agglomerative Hierarchical Clustering
We start with many nodes, and end up with only one!

15. Hierarchies are ubiquitous in biology
N. Pace, SCIENCE, 1997

16. Clustering Terminology
Clustering Dendrogram
Genes
Gene names
“pseudogenes”
Edge length is proportional to “distance”
between connected genes or nodes

20. Clustering Reveals the "Molecular Logic" of Gene Expression
Genes
Experiments

21. Similarity Metrics
In order to implement a clustering algorithm, we require some quantitative concept comparing the behaviour of two genes across some set of conditions
Are they behaving similarly, or differently?

22. between two coordinates
Euclidian Distance 2 3 Y
(1,4)
What is the distance
between two coordinates
In 2D space?
(3,1) X
From Pythagoras, distance = sqrt( )

23. d = Dx2 + Dy2+Dz2 Euclidian Distance How about objects in 3D space?
(2,4,1) X
(0,0,0)
d =
Dx2 + Dy2+Dz2 Z

25. d = |X Y| = S (xi - yi)2 Euclidian Distance X = (xi, xi+1, xi+2,…,xn)
It turns out that the Euclidian distance generalizes to N-dimensional space..
d = |X Y| = S N
(xi - yi)2
i = 1
X = (xi, xi+1, xi+2,…,xn)
Y = (yi, yi+1, yi+2,…,yn)
These look an awful lot like a list in Perl,
or a line of gene expression data, yes?
One way to conceptualize an individual gene expression vector
as therefore as a coordinate in some high-dimensional space.
If we have two such vectors, then we can use
the Euclidian distance to ask “How far apart are they?”

26. S r = (xi - ux ) (yi - uy ) Nsysx Pearson Correlation Coefficient
Kellie introduced the Pearson as a true correlation
Measure that varies in the range -1 to 1

27. S S S S S S S r = xi yi N (xi yi ) - ( ) ( ) N (xi )2 -( xi )2 N
Pearson Correlation Coefficient
computational form N S
i = 1 N S
i = 1 N S
i = 1 xi yi N
(xi yi ) - ( ) ( )
r = N S
i = 1 N S
i = 1 N S
i = 1 N S
i = 1 N
(xi )2 -( xi )2 N
(yi )2 -( yi )2
Incredibly, this form makes our lives
easier if we want to implement a Pearson() subroutine in Perl!

28. Strategies for clustering
Single linkage clustering
Similarity between the clusters is defined as the
similarity of the closest pair of observations between the two groups

29. Strategies for clustering
Complete linkage clustering
Similarity between the clusters is defined as the
similarity of the farthest pair of observations between the two groups

30. Strategies for clustering
Average linkage clustering
Nodes are represented by the average of vectors from the
two component nodes, and the average pairwise distance
within the newly formed cluster is thus minimized

31. S Average Linkage Clustering X = (1, 4, 2,-1) Y = (3, 2,-2,-3)
Once we have decided that two genes (or nodes)
should join to make a new node, how do we define
the contents of the new node?
X = (1, 4, 2,-1)
Y = (3, 2,-2,-3)
Avg(X,Y) = (2, 3, 0,-2)
This makes life easy:
avg( avg(I,J), avg(K,L) ) = avg(I,J,K,L)

32. Cluster implements various flavours of clustering algorithms,
Cluster and TreeView by Mike Eisen
Cluster implements various flavours of clustering algorithms,
While TreeView provides a graphical output of the files produced by Cluster