Lecture 21
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Lecture 21 Gene expression and the transcriptome II. Content. SAGE mRNA abundance and function Comparing expression profiles Eisen dataset Array CGH. 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

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Lecture 21 gene expression and the transcriptome ii

Lecture 21Gene expression and the transcriptome II


Content

Content

  • SAGE

  • mRNA abundance and function

  • Comparing expression profiles

  • Eisen dataset

  • Array CGH


Lecture 21 gene expression and the transcriptome ii

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.


Lecture 21 gene expression and the transcriptome ii

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


Concatemer

Concatemer

Example of a concatemer:ATCTGAGTTCGCGCAGACTTTCCCCGTACAATCTGAGTTCTAGGACGAGG …

TAG 1 TAG 2 TAG 3 TAG 1 TAG 4

A computer program generates a list of tags and tells how many times each one has been found in the cell:

Tag_SequenceCount

ATCTGAGTTC1075

GCGCAGACTT125

TCCCCGTACA112

TAGGACGAGG92

GCGATGGCGG91

TAGCCCAGAT83

GCCTTGTTTA80

GCGATATTGT66

TACGTTTCCA66

TCCCGTACAT66

TCCCTATTAA66

GGATCACAAT55

AAGGTTCTGG54

CAGAACCGCG50

GGACCGCCCC48


Concatemer1

Concatemer

The next step is to identify the RNA and the gene that produced each of the tags:

TagSequence CountGene Name

ATATTGTCAA5translation elongation factor 1 gamma

AAATCGGAAT2T-complex protein 1, z-subunit

ACCGCCTTCG1no match

GCCTTGTTTA81rpa1 mRNA fragment for r ribosomal protein

GTTAACCATC45ubiquitin 52-AA extension protein

CCGCCGTGGG9SF1 protein (SF1 gene)

TTTTTGTTAA99NADH dehydrogenase 3 (ND3) gene

GCAAAACCGG63rpL21

GGAGCCCGCC45ribosomal protein L18a

GCCCGCAACA34ribosomal protein S31

GCCGAAGTTG50ribosomal protein S5 homolog (M(1)15D)

TAACGACCGC4BcDNA.GM12270


Sage issues

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


Transcript abundance in typical eukaryotic cell

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


Transcript abundance in typical eukaryotic cell 2

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


Transcript abundance in typical eukaryotic cell 3

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


Transcript abundance in typical eukaryotic cell 4

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%)

  • ThenTotal =150,000 mRNA molecules


Transcript abundance in typical eukaryotic cell 5

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)


Sage analysis of yeast velculesco et al 1997

SAGE analysis of yeast (Velculesco et al., 1997)

1.0

0.75

0.5

0.25

0

17% 38% 45%

Fraction of all transcripts

1000 100 10 1 0.1

Number of transcripts per cell


Sage quantitative comparison

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


Sage quantitative comparison1

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)


Genome wide cluster analysis eisen dataset

Genome-Wide Cluster AnalysisEisen 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


The eisen data

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


The data

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]


The data1

The Data

  • m genes measured in n experiments:

    g1,1 ……… g1,n

    g2,1 ………. g2,n

    gm,1 ………. gm,n

Vector for 1 gene


Lecture 21 gene expression and the transcriptome ii

This is called ‘correlation coefficient with centering’


Lecture 21 gene expression and the transcriptome ii

Basic correlation coefficient


Eisen et al results

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


Eisen et al results1

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


Partitional clustering

Partitional Clustering

• divide instances into disjoint clusters

– flat vs. tree structure

• key issues

– how many clusters should there be?

– how should clusters be represented?


Partitional clustering from a hierarchical clustering

Partitional Clustering from aHierarchical Clustering

we can always generate a partitional clustering from ahierarchical clustering by “cutting” the tree at some level


K means clustering

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


K means clustering1

K-Means Clustering

  • each iteration involves two steps:

    • assignment of instances to clusters

    • re-computation of the means


K means clustering2

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


Lecture 21 gene expression and the transcriptome ii

Ecogenomics

Algorithm that maps observed clustering behaviourof sampled gene expression data onto the clusteringbehaviour ofcontaminant labelled gene expression patterns in theknowledge base:

Sample

Compatibility scores

Condition n

(contaminant n)

Condition 1

(contaminant 1)

Condition 2

(contaminant 2)

Condition 3

(contaminant 3)


Array cgh comparative genomics hybridisation

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’


Tumor cell

Tumor Cell

Chromosomes of tumor cell:


Example of a cgh tumor

Example of a-CGH Tumor

V

a

l

u

e

Clones/Chromosomes 


A cgh vs expression

a-CGH

DNA

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

a-CGH vs. Expression


Cgh data

CGH Data

C

o

p

y

#

Clones/Chromosomes 


Lecture 21 gene expression and the transcriptome ii

Algorithms forSmoothing 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)


Na ve smoothing

Naïve Smoothing


Discrete smoothing

“Discrete” Smoothing

Copy numbers are integers


Why smoothing

Why Smoothing ?

  • Noise reduction

  • Detection of Loss, Normal, Gain, Amplification

  • Breakpoint analysis

  • Recurrent (over tumors) aberrations may indicate:

    • an oncogene or

    • a tumor suppressor gene


Is smoothing easy

Is Smoothing Easy?

  • Measurements are relative to a reference sample

  • Printing, labeling and hybridization may be uneven

  • Tumor sample is inhomogeneous

  • vertical scale is relative

  • do expect only few levels


Smoothing example

Smoothing: example


Problem formalization

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.


Lecture 21 gene expression and the transcriptome ii

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


Smoothing

Smoothing

breakpoints

variance

levels


Fitness function

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

We could use better models given insight

in tumor pathogenesis


Fitness function 2

Fitness Function (2)

CGH values: x1 , ... , xn

breakpoints: 0 < y1< … < yN < xN

levels: m1, . . ., mN

error variances: s12, . . ., sN2

likelihood:


Fitness function 3

Fitness Function (3)

Maximum likelihood estimators of μ and s2

can be found explicitly

Need to add a penalty to log likelihood to

control number N of breakpoints

penalty


Algorithms

Algorithms

Maximizing Fitness is computationally hard

Use genetic algorithm + local search to find approximation to the optimum


Algorithms local search

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


Genetic algorithm

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


Comparison to expert

Comparison to Expert

algorithm

expert


Conclusion

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


Breakpoint detection

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


Experiments

Experiments

  • Both GAs are Robust:

    • 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 = 0.0513) smoothing conducted by the local expert


Genetic algorithm 1 gls

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


Genetic algorithm 2 glso

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


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