1. Lecture 21 Gene expression and the transcriptome II

2. Content SAGE mRNA abundance and function Comparing expression profiles
Eisen dataset
Array CGH

3. SAGE SAGE = Serial Analysis of Gene Expression
Based on serial sequencing of 10 to 14-bp tags that are unique to each and every gene
SAGE is a method to determine absolute abundance of every transcript expressed in a population of cells
Because SAGE does not require a preexisting clone (such as on a normal microarray), it can be used to identify and quantitate new genes as well as known genes.

4. SAGE
A short sequence tag (10-14bp) contains sufficient information to uniquely identify a transcript provided that that the tag is obtained from a unique position within each transcript;
Sequence tags can be linked together to form long serial molecules (strings) that can be cloned and sequenced; and
Counting the number of times a particular tag is observed in the string provides the expression level of the corresponding transcript.
A list of each unique tag and its abundance in the population is assembled
An elegant series of molecular biology manipulations is developed for this

5. Some of the steps of SAGE
Trap RNAs with beads
Convert the RNA into cDNA
Make a cut in each cDNA so that there is a broken end sticking out
Attach a "docking module" to this end; here a new enzyme can dock, reach down the molecule, and cut off a short tag
Combine two tags into a unit, a di-tag
Make billions of copies of the di-tags (using a method called PCR)
Remove the modules and glue the di-tags together into long concatamers
Put the concatamers into bacteria and copy them millions of times
Pick the best concatamers and sequence them
Use software to identify how many different cDNAs there are, and count them;
Match the sequence of each tag to the gene that produced the RNA.

6. Trap RNA with beads
Unlike other molecules, most messenger RNAs end with a long string of "As" (A stands for the nucleotide adenine.)
This allows researchers to trap them. Adenine forms very strong chemical bonds with another nucleotide, thymine (T). A molecule that consists of 20 or so Ts acts like a chemical bait to capture RNAs.
Researchers coat microscopic, magnetic beads with chemical baits with "TTTTT" tails hanging out.
When the contents of cells are washed past the beads, the RNA molecules will be trapped. A magnet is used to withdraw the bead and the RNAs out of the "soup".

7. Concatemer
Example of a concatemer: ATCTGAGTTC GCGCAGACTTTCCCCGTACAATCTGAGTTCTAGGACGAGG …
TAG TAG TAG TAG TAG 4
A computer program generates a list of tags and tells how many times each one has been found in the cell:
Tag_Sequence Count
ATCTGAGTTC
GCGCAGACTT 125
TCCCCGTACA 112
TAGGACGAGG 92
GCGATGGCGG 91
TAGCCCAGAT 83
GCCTTGTTTA 80
GCGATATTGT 66
TACGTTTCCA 66
TCCCGTACAT 66
TCCCTATTAA 66
GGATCACAAT 55
AAGGTTCTGG 54
CAGAACCGCG 50
GGACCGCCCC 48

8. Concatemer
The next step is to identify the RNA and the gene that produced each of the tags:
Tag Sequence Count Gene Name
ATATTGTCAA 5 translation elongation factor 1 gamma
AAATCGGAAT 2 T-complex protein 1, z-subunit
ACCGCCTTCG 1 no match
GCCTTGTTTA 81 rpa1 mRNA fragment for r ribosomal protein
GTTAACCATC 45 ubiquitin 52-AA extension protein
CCGCCGTGGG 9 SF1 protein (SF1 gene)
TTTTTGTTAA 99 NADH dehydrogenase 3 (ND3) gene
GCAAAACCGG 63 rpL21
GGAGCCCGCC 45 ribosomal protein L18a
GCCCGCAACA 34 ribosomal protein S31
GCCGAAGTTG 50 ribosomal protein S5 homolog (M(1)15D)
TAACGACCGC 4 BcDNA.GM12270

9. SAGE issues
At least 50,000 tags are required per sample to approach saturation, the point where each expressed gene (e.g. human cell) is represented at least twice (and on average 10 times)
Expensive: SAGE costs about $5000 per sample
Too expensive to do replicated comparisons as is done with microarrays

10. Transcript abundance in typical eukaryotic cell
<100 transcripts account for 20% of of total mRNA population, each being present in between 100 and 1000 copies per cell
These encode ribosomal proteins and other core elements of transcription and translation machinery, histones and further taxon-specific genes
General, basic and most important cellular mechanisms

11. Transcript abundance in typical eukaryotic cell (2)
Several hundred intermediate-frequency transcripts, each making 10 to 100 copies, make up for a further 30% of mRNA
These code for housekeeping enzymes, cytoskeletal components and some unusually abundant cell-type specific proteins
Pretty basic housekeeping things

12. Transcript abundance in typical eukaryotic cell (3)
Further 50% of mRNA is made up of tens of thousands low-abundance transcripts (<10), some of which may be expressed at less than one copy per cell (on average)
Most of these genes are tissue-specific or induced only under particular conditions
Specific or special purpose products

13. Transcript abundance in typical eukaryotic cell (4)
Get some feel for the numbers (can be a factor 2 off but order of magnitude about right) If
~80 transcripts * ~400 copies = 32,000 (20%)
~600 transcripts * ~75 copies = 45,000 (30%)
25,000 transcripts * ~3 copies = 75,000 (50%)
Then Total =150,000 mRNA molecules

14. Transcript abundance in typical eukaryotic cell (5)
This means that most of the transcripts in a cell population contribute less than 0.01% of the total mRNA
Say 1/3 of higher eukaryote genome is expressed in given tissue, then about 10,000 different tags should be detectable
Taking into account that half the transcriptome is relatively abundant, at least 50,000 different tags should be sequenced to approach saturation (so to get at least 10 copies per transcript on average)

15. SAGE analysis of yeast (Velculesco et al., 1997)
1.0
0.75
0.5
0.25
17% % %
Fraction of all transcripts
Number of transcripts per cell

16. SAGE quantitative comparison
A tag present in 4 copies in one sample of 50,000 tags, and in 2 copies in another sample, may be twofold expressed but is not going to be significant
Even 20 to 10 tags might not be statistically significant given the large numbers of comparisons
Often, 10-fold over- or under-expression is taken as threshold

17. SAGE quantitative comparison
A great advantage of SAGE is that the method is unbiased by experimental conditions
Direct comparison of data sets is possible
Data produced by different groups can be pooled
Web-based tools for performing comparisons of samples all over the world exist (e.g. SAGEnet and xProfiler)

18. Genome-Wide Cluster Analysis Eisen dataset
Eisen et al., PNAS 1998
S. cerevisiae (baker’s yeast)
– all genes (~ 6200) on a single array
– measured during several processes
human fibroblasts
– 8600 human transcripts on array
– measured at 12 time points during serum stimulation

19. The Eisen Data • 79 measurements for yeast data
• collected at various time points during
– diauxic shift (shutting down genes for metabolizing sugars, activating those for metabolizing ethanol)
– mitotic cell division cycle
– sporulation
– temperature shock
– reducing shock

20. The Data • each measurement represents Log(Redi/Greeni)
where red is the test expression level, and green is
the reference level for gene G in the i th experiment
• the expression profile of a gene is the vector of
measurements across all experiments [G1 .. Gn]

21. The Data m genes measured in n experiments: g1,1 ……… g1,n
gm,1 ………. gm,n
Vector for 1 gene

23. This is called ‘correlation coefficient with centering’

24. Basic correlation coefficient

25. Eisen et al. Results
redundant representations of genes cluster together
but individual genes can be distinguished from related genes by subtle differences in expression
genes of similar function cluster together
e.g. 126 genes strongly down-regulated in response to stress

26. Eisen et al. Results 126 genes down-regulated in response to stress
112 of the genes encode ribosomal and other proteins related to translation
agrees with previously known result that yeast responds to favorable growth conditions by increasing the production of ribosomes

27. Partitional Clustering
• divide instances into disjoint clusters
– flat vs. tree structure
• key issues
– how many clusters should there be?
– how should clusters be represented?

29. Partitional Clustering from a Hierarchical Clustering
we can always generate a partitional clustering from a hierarchical clustering by “cutting” the tree at some level

30. K-Means Clustering
• assume our instances are represented by vectors of real values
• put k cluster centers in same space as instances
• now iteratively move cluster centers

31. K-Means Clustering each iteration involves two steps:
assignment of instances to clusters
re-computation of the means

32. K-Means Clustering
in k-means clustering, instances are assigned to one and only one cluster
can do “soft” k-means clustering via Expectation Maximization (EM) algorithm
each cluster represented by a normal distribution
E step: determine how likely is it that each cluster “generated” each instance
M step: move cluster centers to maximize likelihood of instances

34. … … Ecogenomics Compatibility scores
Algorithm that maps observed clustering behaviour of sampled gene expression data onto the clustering behaviour of contaminant labelled gene expression patterns in the knowledge base:
Sample
Compatibility scores … …
Condition n
(contaminant n)
Condition 1
(contaminant 1)
Condition 2
(contaminant 2)
Condition 3
(contaminant 3)

35. Array-CGH (Comparative Genomics Hybridisation)
New microarray-based method to determine local chromosomal copy numbers
Gives an idea how often pieces of DNA are copied
This is very important for studying cancers, which have been shown to often correlate with copy events!
Also referred to as ‘a-CGH’

36. Tumor Cell Chromosomes of tumor cell:
Normal cells 23 pairs of chromosomes.
Each chromosome is built from two strands of bases labeled (ag tc)
Two connected bases are referred to as basepair
Male: XY
Female: XX
Some pieces of chromosomal DNA form genes. Processes in the cell ultimately form proteins from genes, which determine the way a cell behaves.
Each chromosome labeled with different color (SKY experiment).
You can see this cell does not at all have 2 copies of each chromosome… Pieces are lost, pieces have attached to other chromosomes, some pieces have more than 2 copies.

37. Example of a-CGH Tumor  V a l u e Clones/Chromosomes 
Estimated time: 1 minute
Explain axis.
About the data:
Normalized (average 1)
Log2 (why?)
“1It is preferable to work with logged intensities rather than absolute intensities for a number of reasons
including the facts that: (i) the variation of logged intensities and ratios of intensities is less dependent on
absolute magnitude; (ii) normalization is additive for logged intensities; (iii) taking logs evens out highly
skew distributions; and (iv) taking logs gives a more realistic sense of variation.”
Point out some gains, losses and amplifications
Clones/Chromosomes 

38. a-CGH vs. Expression a-CGH DNA DNA on slide
In Nucleus
Same for every cell
DNA on slide
Measure Copy Number Variation
Expression
RNA
In Cytoplasm
Different per cell
cDNA on slide
Measure Gene Expression
Estimated time: <= 2 minutes
This slide explains the difference between Array CGH and Microarray gene expression experiments.
Explain Copy Number: The copy number of a piece of DNA on the genome is the number of times this piece occurs in the nucleus of a cell.

39. CGH Data  C o p y # Clones/Chromosomes  Estimated time: 1 minute
Explain axis.
About the data:
Normalized (average 1)
Log2 (why?)
“1It is preferable to work with logged intensities rather than absolute intensities for a number of reasons
including the facts that: (i) the variation of logged intensities and ratios of intensities is less dependent on
absolute magnitude; (ii) normalization is additive for logged intensities; (iii) taking logs evens out highly
skew distributions; and (iv) taking logs gives a more realistic sense of variation.”
Point out some gains, losses and amplifications
Clones/Chromosomes 

40. Algorithms for Smoothing Array CGH data
Kees Jong (VU, CS and Mathematics)
Elena Marchiori (VU, CS)
Aad van der Vaart (VU, Mathematics)
Gerrit Meijer (VUMC)
Bauke Ylstra (VUMC)
Marjan Weiss (VUMC)

41. Naïve Smoothing

42. “Discrete” Smoothing
Copy numbers are integers

43. Why Smoothing ? Noise reduction
Detection of Loss, Normal, Gain, Amplification
Breakpoint analysis
Estimated time: about 1 minute
Explain and point at breakpoints: place where value changes.
Smoothing also makes it possible to do analysis on breakpoints.
Recurrent (over tumors) aberrations may indicate:
an oncogene or
a tumor suppressor gene

44. Is Smoothing Easy? Measurements are relative to a reference sample
Printing, labeling and hybridization may be uneven
Tumor sample is inhomogeneous
Estimated time: 2 minutes
Unfortunately there are some problems with the experiment just described that prevent us from simply reading the copy number from the ratio’s. 1)
- Not every spot on the slide has the same amount of clones on it. 2)
In a tumor not every cell is the same, normal cells may occur, tumor cells of a previous stadium of the tumor may occur.
The amounts of cells for a type of cell is unknown.
- The amount of DNA material taken from the tumor cells may not be exactly equal to the amount taken from normal cells.
- The “green” and “red” molecules do not stick equally well 3)
Not every labeled fragment can stick stick to a clone, because it is on a part of the chromosome that does not occur on a clone.
Not every part that can stick to a clone, does actually stick 4)
Every clone has three spots on the slide.
If we assume that red and green fragments same distribution over the spots, the three spots should have the same value. Which is almost the case, since there is only a small standard deviation.
Problem:
Assume lowest line is normal
What is the real situation?
1 Cell type, then the middle line is single gain, the highest line is a double gain
2 Cell types, then possibly
Type 1 occurs twice as much as type 2 and has a gain corresponding to the upper line
Type 2 has a gain corresponding to the middle line
vertical scale is relative
do expect only few levels

45. Smoothing: example
Estimated time: < 20 seconds.

46. Problem Formalization
A smoothing can be described by
a number of breakpoints
corresponding levels
A fitness function scores each smoothing according to fitness to the data
An algorithm finds the smoothing with the highest
fitness score.
Estimated time:
Details of function to optimize later.
What are we trying to model?
Do we want to find smoothings that resemble the expert or remove experimental noise?
Unfortunately not much known about the properties of the processes that take place during the experiments. We assume…
We do not have tumors with detailed data about the real composition of cell types, but the model seems to resemble the expert quite well as we will see.
We do have CGH data of a normal-normal experiment. A normal probability plot of that data shows that the noise in that experiment follows a normal distribution quite well.

47. Breakpoint Detection Identify possibly damaged genes:
These genes will not be expressed anymore
Identify recurrent breakpoint locations:
Indicates fragile pieces of the chromosome
Accuracy is important:
Important genes may be located in a region with (recurrent) breakpoints

48. Smoothing
breakpoints
variance
levels

49. Fitness Function
We assume that data are a realization of a Gaussian noise process and use the maximum likelihood criterion adjusted with a penalization term for taking into account model complexity
Estimated time:
Details of function to optimize later.
What are we trying to model?
Do we want to find smoothings that resemble the expert or remove experimental noise?
Unfortunately not much known about the properties of the processes that take place during the experiments. We assume…
We do not have tumors with detailed data about the real composition of cell types, but the model seems to resemble the expert quite well as we will see.
We do have CGH data of a normal-normal experiment. A normal probability plot of that data shows that the noise in that experiment follows a normal distribution quite well.
We could use better models given insight
in tumor pathogenesis

50. Fitness Function (2) likelihood: CGH values: x1 , ... , xn
breakpoints: 0 < y1< … < yN < xN
levels: m1, . . ., mN
error variances: s12, . . ., sN2
Estimated time: ?
Assume independence of all observations…
likelihood:

51. Fitness Function (3) Maximum likelihood estimators of μ and s 2
can be found explicitly
Need to add a penalty to log likelihood to
control number N of breakpoints
penalty
Estimated time: ?
* Goal: Add penalty to make sure not every index becomes a breakpoint.

52. Algorithms Maximizing Fitness is computationally hard
Use genetic algorithm + local search to find approximation to the optimum
Estimated time: ?

53. Algorithms: Local Search
choose N breakpoints at random
while (improvement)
- randomly select a breakpoint
- move the breakpoint one position to left
or to the right
Estimated time: ?

54. Genetic Algorithm Given a “population” of candidate smoothings
create a new smoothing by
- select two “parents” at random from population
- generate “offspring” by combining parents
(e.g. “uniform crossover” or “union”)
- apply mutation to each offspring
- apply local search to each offspring
- replace the two worst individuals with the offspring
Estimated time: ?
Encoding: 0/1 per clone. Label a clone as breakpoint.
Termination criterion (both GAs): best fitness in pool does not improve and “individuals” in pool are very similar (there is no pair of individuals that have (after smoothing) a pair of clones that differs at least epsilon in smooth cgh value (average of section))
The mutation is as follows: flip coin to either:
remove the breakpoint between 2 consecutive sections with best score afterwards.
Insert a breakpoint in the middle of the section with the highest standard deviation.

55. Comparison to Expert
algorithm
expert

56. Conclusion
Breakpoint identification as model fitting to search for most-likely-fit model given the data
Genetic algorithms + local search perform well
Results comparable to those produced by hand by the local expert
Future work:
Analyse the relationship between Chromosomal aberrations and Gene Expression
Estimated time: 1 minute

57. Breakpoint Detection Identify possibly damaged genes:
These genes will not be expressed anymore
Identify recurrent breakpoint locations:
Indicates fragile pieces of the chromosome
Accuracy is important:
Important genes may be located in a region with (recurrent) breakpoints
Estimated time: ?

58. Experiments Both GAs are Robust: Both GAs Converge:
Over different randomly initialized runs breakpoints are (mostly) placed on the same location
Both GAs Converge:
The “individuals” in the pool are very similar
Final result looks very much like (mean error = ) smoothing conducted by the local expert
Estimated time: ?

59. Genetic Algorithm 1 (GLS)
initialize population of candidate solutions randomly
while (termination criterion not satisfied)
- select two parents using roulette wheel
- generate offspring using uniform crossover
- apply mutation to each offspring
- apply local search to each offspring
- replace the two worst individuals with the offspring
Estimated time: ?
Encoding: 0/1 per clone. Label a clone as breakpoint.
Termination criterion (both GAs): best fitness in pool does not improve and “individuals” in pool are very similar (there is no pair of individuals that have (after smoothing) a pair of clones that differs at least epsilon in smooth cgh value (average of section))
The mutation is as follows: flip coin to either:
remove the breakpoint between 2 consecutive sections with best score afterwards.
Insert a breakpoint in the middle of the section with the highest standard deviation.

60. Genetic Algorithm 2 (GLSo)
initialize population of candidate solutions randomly
while (termination criterion not satisfied)
- select 2 parents using roulette wheel
- generate offspring using OR crossover
- apply local search to offspring
- apply “join” to offspring
- replace worst individual with offspring
Estimated time: ?
join:
Repeatedly select breakpoint whose removal results in biggest improvement of fitness, until fitness does not decrease anymore.