Download 91.510_ch06 - Computer Science

Information Theory, Statistical Measures and
Bioinformatics approaches
to gene expression
Friday’s Class
• Sei Hyung Lee will make a presentation on
his dissertation proposal at 1pm in this room
• Vector Support Clustering
• So I will discuss Clustering and other topics
Information Theory
• Given a probability distribution, Pi, for the
letters in an independent and identically
distributed (i.i.d.) message, the probability
of seeing a particular sequence of letters i, j,
k, ..., n is simply
Pi Pj Pk···Pn
or
elog Pi + log Pj + log Pk+ ··· + log Pn
Information Theory 2
• The information or surprise of an answer to a
question (a message) is inversely proportional to
its probability – the smaller the probability, the
more surprise or information
• Ask a child “Do you like ice cream?”
• If the answer is yes, you’re not surprised and the
information conveyed is little
• If the answer is no, you are surprised – more
information has been given with this lower
probability answer
Information Theory 3
Information H associated with probability p is
H(p) = log2 (1/p)
1/p is the information or surprise
and
log2 (1/p) = # of bits required
Information Theory 4
Log-probabilities and their sums represent
measures of information.
Conversely, information can be thought of as
log-probabilities (with the negative sign to
make the information increase with
increasing values)
H(p) = log2 (1/p) = - log2 p
Information Theory 5
If we have an i.i.d. with 6 values (a die), or 4 (A, C, T, G) or n
values (the distribution is flat) then the probability of any
particular symbol is
1/n
and the information in any such symbol is then
log2 n
and this value is also the average
If the symbols are not equally probable (not i.d.) we need to
weigh the information of each symbol by its probability of
occurring. This is Claude Shannon’s Entropy
H = Σ pi log2 (1/pi) = - Σ pi log2 pi
Information Theory 6
If we have a coin, assuming h and t have equal probabilities.
H = - ( (1/2) log2 (1/2) + (1/2) log2 (1/2) )
= - ( (1/2) (-1) + (1/2) (-1) )
= - ( -1)
= 1 bit
If the coin comes up heads ¾ of the time then the entropy should decrease
(we’re more certain of the outcome and there’s less surprise)
H = - ( (3/4) log2 (3/4) + (1/4) log2 (1/4) )
= - ( (0.75) (-0.415) + (0.25) (-2) )
= - ( -0.81)
= 0.81 bits
Information Theory 7
A random DNA source has an entropy of
H = - ( (1/4) log2 (1/4) + (1/4) log2 (1/4) + (1/4) log2 (1/4) + (1/4) log2 (1/4) )
= - ( (1/4) (-2) + (1/4) (-2) + (1/4) (-2) + (1/4) (-2))
= - ( -2)
= 2 bits
A DNA source that emits 45% A and T and 5% G and C has an entropy of
H = - ( 2*(0.45) log2 (0.45) + 2*(0.05) log2 (0.05))
= - ( (0.90) (-1.15) + (0.10) (-4.32) )
= - ( - 1.035 – 0.432)
= 1.467 bits
Natural Logs
• Using natural logarithms, the information is expressed in units of nats (a
contraction of Natural digits). Bits and nats are easily convertible as
follows
nats = bits · ln (2)
ln 2 or log 2 ≈ 0.693
1/ln 2 ≈ 1.44
• Generalizing, for a given base of the logarithm b
log x = log b · logb x
• Using logarithms to arbitrary bases, information can be expressed in
arbitrary units, not just bits and nats, such that
-logbP = -k log P , where 1/k=log b
So k is often ignored
Shannon’s Entropy
• Shannon's entropy, H = Σ pi log2 (1/pi) = - Σ pi log2 pi , is the expected
(weighted arithmetic mean) value of log Pi computed over all letters in
the alphabet, using weights that are simply the probabilities of the
letters themselves, the Pis
• The information, H, is expressed in units per letter
• Shannon's entropy allows us to compute the expected description
length of a message, given an a priori assumption (or knowledge) that
the letters in the message will appear with frequencies Pi
• If a message is 200 letters in length, 200H is the expected description
length for that message
• Furthermore, the theory tells us there is no shorter encoding for the
message than 200H, if the symbols do indeed appear at the prescribed
frequencies
• Shannon's entropy thus informs us of the minimum description length,
or MDL, for a message
Shannon Entropy
A DNA source that emits 45% A and T and 5% G
and C has an entropy of
H = - ( 2*(0.45) log2 (0.45) + 2*(0.05) log2
(0.05))
= - ( (0.90) (-1.15) + (0.10) (-4.32) )
= - ( - 1.035 – 0.432)
= 1.467 bits
Huffman Entropy (or Encoding)
If we build a binary Huffman code (tree) for the
same DNA
1 bit would be required to code for G
2 bits to code for T (or vice versa)
3 bits each to code for A and C
The "Huffman entropy" in this case is
1*0.45 + 2*0.45 + 3*0.05 + 3*0.05 = 1.65 bits
per letter -- which is not quite as efficient as the
previous Shannon code
Length of Message
• The description length of a message when using a
Huffman code is expected to be about equal to the
Shannon or arithmetic code length
• Thus, a Huffman-encoded 200 letter sequence will
average about 200H bits in length
• For some letters in the alphabet, the Huffman code
may be more or less efficient in its use of bits than
the Shannon code (and vice versa), but the
expected behavior averaged over all letters in the
alphabet is the same for both (within one bit)
Relative Entropy
• Relative entropy, H, is a measure of the expected coding
inefficiency per letter, when describing a message with an
assumed letter distribution P, when the true distribution is Q.
• If a binary Huffman code is used to describe the message, the
relative entropy concerns the inefficiency of using a Huffman
code built for the wrong distribution
• Whereas Shannon's entropy is the expected log-likelihood
for a single distribution, relative entropy is the expected
logarithm of the likelihood ratio (log-likelihood ratio or LLR)
between two distributions.
H(Q || P) = Σ Qi log2 (Qi /Pi)
The Odds Ratio
• The odds ratio Qi / Pi is the relative odds that
letter i was chosen from the distribution Q
versus P
• In computing the relative entropy, the logodds ratios are weighted by Qi
• Thus the weighted average is relative to the
letter frequencies expected for a message
generated with Q
H(Q || P) = Σ Qi log2 (Qi /Pi)
Interpreting the Log-Odds Ratio
• The numerical sign of individual LLRs log(Qi / Pi)
LLR > 0 => i was more likely chosen using Q than P
LLR = 0 => i was as likely selected using Q as it was using P
LLR < 0 => i was more likely chosen using P than Q
• Relative entropy is sometimes called the Kullback
Leibler distance between the distributions P and Q
H(P || Q) ≥ 0
H(P || Q) = 0 iff P = Q
H(P || Q) is generally ≠ to H(Q || P)
The Role of Relative Entropy
• Given a scoring matrix (or scoring vector, in this onedimensional case) and a model sequence generated i.i.d.
according to some background distribution, P, we can
write a program that finds the maximal scoring segment
(MSS) within the sequence (global alignment scoring)
• Here the complete, full-length sequence represents one
message, while the MSS reported by our program
constitutes another
• For example, we could create a hydrophobicity scoring
matrix that assigns increasingly positive scores to more
hydrophobic amino acids, zero score to amphipathic
residues, and increasingly negative scores to more
hydrophilic residues. (Karlin and Altschul (1990) provide
other examples of scoring systems, as well).
The Role of Relative Entropy
• By searching for the MSS - the "most
hydrophobic" segment in this case - we select for a
portion of the sequence whose letters exhibit a
different, hydrophobic distribution than the
random background
• By convention, the distribution of letters in the
MSS is called the target distribution and is
signified here by Q. (Note: some texts may signify
the background distribution as Q and the target
distribution as P).
The Role of Relative Entropy 2
• If the letters in the MSS are described using an optimal Shannon code
for the background distribution, we expect a longer description than if
a code optimized for the target distribution was used instead
• These extra bits -- the extra description length -- tell us the relative
odds that the MSS arose by chance from the background distribution
rather than the target
• Why would we consider a target distribution, Q, when our original
sequence was generated from the background distribution, P?
• Target frequencies represent the underlying evolutionary model
• The biology tells us that
– The target frequencies are indeed special
– The background and target frequencies are formally related to one another
by the scoring system (the scoring matrices don’t actually contain the
target frequencies but they are implicit in the score)
– The odds of chance occurrence of the MSS are related to its score
BLAST Scoring
Database similarity searches typically yield high-scoring pairwise sequence
alignments such as the following
Score = 67 (28.6 bits), Expect = 69., P = 1.0
Identities = 13/33 (39%), Positives = 23/33 (69%)
Query: 164 ESLKISQAVHGAFMELSEDGIEMAGSTGVIEDI 196
E+L + Q+ G+
ELSED ++ G +GV+E++
Subjct: 381 ETLTLRQSSFGSKCELSEDFLKKVGKSGVVENL 413
Scores:
+++-+-++--++--+++++-++- + +++++++
514121512161315445632110601643512
• The total score for an alignment (67 in the above case) is simply the sum
of pairwise scores
• The individual pairwise scores are listed beneath the alignment above (+5
on the left through +2 on the right)
Scoring Statistics
• Note that some pairs of letters may yield the same score
• For example, in the BLOSUM62 matrix used to find the
previous alignment, S(S,T) = S(A,S) = S(E,K) = S(T,S) =
S(D,N) = +1
• While alignments are usually reported without the
individual pairwise scores shown, the statistics of
alignment scores depend implicitly on the probabilities
of occurrence of the scores, not the letters.
• Dependency on the letter frequencies is factored out by the
scoring matrix.
• We see then that the "message" obtained from a similarity
search consists of a sequence of pairwise scores indicated
by the high-scoring alignment
Karlin-Altschul Statistics 1
If we search two sequences X and Y using a scoring
matrix Sij to identify the maximal-scoring segment
pair (MSP), and if the following conditions hold
1. the two sequences are i.i.d. and have respective
background distributions PX and PY (which may be
the same),
2. the two sequences are effectively "long" or infinite
and not too dissimilar in length,
3. the expected pairwise score Σ PX(i) PY(j) Sij is
negative,
4. a positive score is possible, i.e., PX(i)PY(j)Sij > 0 for
some letters i and j, then
Karlin-Altschul Statistics 2
• The scores in the scoring matrix are implicitly log-odds scores of
the form
Sij = log(Qij / (PX(i)PY(j))) / l
where Qij is the limiting target distribution of the letter pairs (i,j)
in the MSP and l is the unique positive-valued solution to the
equation ΣPX(i) PY(j) e l Sij = 1
• The expected frequency of chance occurrence of an MSP with
score S or greater is
E = K mn e-lS
where m and n are the lengths of the two sequences, mn is the size
of the search space, and K is a measure of the relative
independence of the points in this space in the context of
accumulating the MSP score
• While the complete sequences X and Y must be i.i.d., the letter
pairs comprising the MSP do exhibit an interdependency
Karlin-Altschul Statistics 3
• Since gaps are disallowed in the MSP, a pairwise
sequence comparison for the MSP is analogous to a
linear search for the MSS along the diagonals of a 2d search space. The sum total length of all the
diagonals searched is just mn
• Another way to express the pairwise scores is:
Sij = logb(Qij / (PX(i)PY(j)))
Where the log is to some base b and l = loge b, and is
often called the scale of the scoring matrix
Karlin-Altschul Statistics 4
•
•
•
•
The MSP score is the sum of the scores Sij for the aligned pairs of letters
in the MSP (the sum of log-odds ratios)
The MSP score is then the logb of the odds that an MSP with its score
occurs by chance at any given starting location within the random
background -- not considering yet how large an area, or how many starting
locations, were actually examined in finding the MSP
Considering the size of the examined area alone, the expected description
length of the MSP (measured in information) is log(K m n)
The relative entropy, H, has units of information per length (or letter pair),
the expected length of the MSP (measured in letter pairs) is
E(L) = log(K m n) / H
where H is the relative entropy of the target and background frequencies
H = Σ Qij log(Qij / (PX(i) PY(j)))
where PX(i) PY(j) is the product frequency expected for letter i paired
with j in the background search space; and Qij is the frequency at which
we expect to observe i paired with j in the MSP
Karlin-Altschul Statistics 5
•
•
•
•
By definition, the MSP has the highest observed score. Since this score is
expected to occur just once, the (expected) MSP score has an (expected)
frequency of occurrence, E, of 1
The appearance of MSPs can be modeled as a Poisson process with
characteristic parameter E, as it is possible for multiple, independent
segments of the background sequences to achieve the same high score
The Poisson "events" are the individual MSPs having the same score S or
greater
The probability of one or more MSPs having score S or greater is simply
one minus the probability that no MSPs appear having score S or greater
P = 1 - e-E
•
Note that in the limit as E approaches 0, P = E; and for values of E or P
less than about 0.05, E and P are practically speaking equal
Karlin-Altschul Statistics 6
•
For convenience in comparing scores from different database searches,
which may have been performed with different score matrices and/or
different background distributions, we can compute the normalized or
adjusted score
S' = lS - log K
•
Expressing the "Karlin-Altschul equation" as a function of the adjusted
score, we obtain
E = mn e-S'
•
Note how the search-dependent values for l and K have been factored out
of the equation by using adjusted scores
•
We can therefore assess the relative significance of two alignments found
under different conditions, merely by comparing their adjusted scores. To
assess their absolute statistical significance, we need only know the size of
the search space, mn.
Karlin-Altschul Statistics 7
•
•
•
•
•
•
Biological sequences have finite length, as do the MSPs found between
them
MSPs will tend not to appear near the outer (lower and right) edges of the
search space
The chance of achieving the highest score of all are reduced in that region
because the end of one or both sequences may be reached before a higher
score is obtained than might be found elsewhere
Effectively, the search space is reduced by the expected length, E(l), for
the MSP
We can therefore modify the Karlin-Altschul equation to use effective
lengths for the sequences compared.
m' = m - E(l) and n' = n - E(l)
E' = K m' n' e-lS
Since m' is less than m and n' is less than n, the edge-corrected E' is less
than E, indicating greater statistical significance.
Karlin-Altschul Statistics 8
•
•
•
•
•
•
A raw MSP or alignment score is meaningless (uninformative) unless we know the
associated value of the scaling parameter l, to a lesser extent K, and the size of the
search space
Even if the name of the scoring matrix someone used has been told to us (e.g.,
BLOSUM62), it might be that the matrix they used was scaled differently from the
version of the matrix we normally use
For instance, a given database search could be performed twice, with the second
search using the same scoring matrix as the first's but with all scores multiplied by
100
While the first search's scores will be 100-fold lower, the alignments produced by
the two searches will be the same and their significance should rightfully be
expected to be the same
This is a consequence of the scaling parameter l being 100-fold lower for the
second search, so that the product lS is identical for both searches
If we did not know two different scoring matrices had been used and hadn't
learned the lessons of Karlin-Altschul statistics, we might have been tempted to
say that the higher scores from the second search are more significant (at the same
time, we might have wondered: if the scores are so different, why are the
alignments identical?!)
Karlin-Altschul Statistics 9
• Karlin-Altschul statistics suggest we should be careful about
drawing conclusions from raw alignment scores
• When someone says they used the "BLOSUM62" matrix to
obtain a high score, it is possible their matrix values were
scaled differently than the BLOSUM62 matrix we have come to
know
• Generally in our work with different programs, and in
communications with other people, we may find "BLOSUM62"
refers to the exact same matrix, but this doesn't happen
automatically; it only happens through efforts to standardize
and avoid confusion
• Miscommunication still occasionally happens, and people do
sometimes experiment with matrix values and scaling factors,
so consider yourself forewarned!
• Hopefully you see how the potential for this pitfall further
motivates the use of adjusted or normalized scores, as well as
P-values and E-values, instead of raw scores
Karlin-Altschul Statistics 10
• Statistical interpretations of results often involves
weighing a null model against an alternative model
• In the case of sequence comparisons and the use of
Karlin-Altschul statistics, the two models being
weighed are the frequencies with which letters are
expected to be paired in unselected, random
alignments from the background versus the target
frequencies of their pairing in the MSP
• Karlin and Altschul tell us when we search for the
MSP we are implicitly selecting for alignments with
a specific target distribution, Q, defined for seeing
letter i paired with letter j, where
Qij = PX(i) PY(j) elSij
Karlin-Altschul Statistics 11
• We can interpret a probability (or P-value) reported by
BLASTP as being a function of the odds that the MSP was
sampled from the background distribution versus being
sampled from the target distribution
• In each case, one considers the MSP to have been created by
a random, i.i.d. process
• The only question is which of the two distributions was most
likely used to generate the MSP score: the background
frequencies or the target frequencies?
Karlin-Altschul Statistics 12
•
•
•
•
If the odds of being sampled from the background are low (i.e., much less
than 1), then they are approximately equal to the P-value of the MSP
having been created from the background distribution. Low P-values do
not necessarily mean the score is biologically significant, only that the
MSP was more likely to have been generated from the target distribution,
which presumably was chosen on the basis of some interesting biological
phenomena (such as multiple alignments of families of protein sequences)
Further interpretations, such as the biological significance of an MSP
score, are not formally covered by the theory (and are often made with a
rosy view of the situation)
Even if (biological) sequences are not random according to the conditions
required for proper application of Karlin-Altschul statistics, we can still
search for high-scoring alignments
It may just happen that the results still provide some biological insight, but
their statistical significance can not be believed. Even so, if the scoring
system and search algorithm are not carefully chosen, the results may be
uninformative or irrelevant -- and the software provides no warning.
Gene expression is regulated
in several basic ways
• by region (e.g. brain versus kidney)
• in development (e.g. fetal versus adult tissue)
• in dynamic response to environmental signals
(e.g. immediate-early response genes)
• in disease states
• by gene activity
Page 157
virus
bacteria
fungi
invertebrates
rodents
human
Disease
Cell types
Development
In response to stimuli
In mutant or wildtype cells
In virus, bacteria, and/or host
Organism
Gene expression changes measured...
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DNA
RNA
protein
phenotype
cDNA
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DNA
RNA
protein
DNA
cDNA
RNA
protein
cDNA
UniGene
SAGE
microarray
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DNA
RNA
protein
phenotype
cDNA
[1] Transcription
[2] RNA processing (splicing)
[3] RNA export
[4] RNA surveillance
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5’ exon 1
3’
intron
exon 2
3’
exon 3 5’
intron
transcription
5’
3’
RNA splicing
(remove introns)
3’
5’
polyadenylation
5’
AAAAA 3’
Export to cytoplasm
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Relationship of mRNA to genomic DNA for RBP4
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Analysis of gene expression in cDNA libraries
A fundamental approach to studying gene expression
is through cDNA libraries.
• Isolate RNA (always from a specific
organism, region, and time point)
insert
• Convert RNA to complementary DNA
• Subclone into a vector
vector
• Sequence the cDNA inserts.
These are expressed sequence tags
(ESTs)
Page 162-163
UniGene: unique genes via ESTs
• Find UniGene at NCBI:
www.ncbi.nlm.nih.gov/UniGene
• UniGene clusters contain many ESTs
• UniGene data come from many cDNA libraries.
Thus, when you look up a gene in UniGene
you get information on its abundance
and its regional distribution.
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Cluster sizes in UniGene
This is a gene with
1 EST associated;
the cluster size is 1
Page 164
Cluster sizes in UniGene
This is a gene with
10 ESTs associated;
the cluster size is 10
Page 164
Cluster sizes in UniGene
Cluster size
Number of clusters
1
34,000
2
14,000
3-4
15,000
5-8
10,000
9-16
6,000
17-32
4,000
500-1000
500
2000-4000
50
8000-16,000
3
>16,000
1
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Ten largest UniGene clusters (10/02)
Cluster
size
25,232
14,277
14,231
12,749
10,649
10,596
10,290
9,987
9,667
9,058
Gene
eukary. translation EF (Hs.181165)
GAPDH (Hs.169476)
ubiquitin (Ta.9227)
actin, gamma 1 (Hs.14376)
euk transl EF (Mm.196614)
ribosomal prot. S2 (Hs.356360)
hemoglobin, beta (Mm.30266)
mRNA, placental villi (Hs.356428)
actin, beta (Hs.288061)
40S ribosomal prot. S18 (Dr.2984)
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Digital Differential Display (DDD) in UniGene
• UniGene clusters contain many ESTs
• UniGene data come from many cDNA libraries
• Libraries can be compared electronically
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UniGene brain
libraries
UniGene lung
libraries
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CamKII
up-regulated
in brain
n-sec1 up-regulated
in brain
surfactant upregulated in lung
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Fisher’s Exact Test: deriving a p value
Gene 1
Pool A
g1A
All other genes
total
NA-g1A
NA
NB
Pool B
g1B
NB-g1B
total
c = g1A + g1B
C = (NA-g1A) + (NB-g1B)
Page 167
Pitfalls in interpreting cDNA library data
• bias in library construction
• variable depth of sequencing
• library normalization
• error rate in sequencing
• contamination (chimeric sequences)
Pages 166-168
Page 168-169
Serial analysis of gene expression (SAGE)
• 9 to 11 base “tags” correspond to genes
• measure of gene expression in different
biological samples
• SAGE tags can be compared electronically
Page 169
SAGE tags are mapped to UniGene clusters
Tag 1
Tag 1
Tag 2
Tag n
Cluster 1
Cluster 2
Cluster 3
Cluster 1
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Microarrays: tools for gene expression
A microarray is a solid support (such as a membrane
or glass microscope slide) on which DNA of known
sequence is deposited in a grid-like array.
RNA is isolated from matched samples of interest.
The RNA is typically converted to cDNA, labeled with
fluorescence (or radioactivity), then hybridized to
microarrays in order to measure the expression levels
of thousands of genes.
Page 173
Questions addressed using microarrays
• Wildtype versus mutant
• Cultured cells +/- drug
• Physiological states (hibernation, cell polarity formation)
• Normal versus diseased tissue (cancer, autism)
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Organisms represented on microarrays
• metazoans: human, mouse, rat, worm, insect
• fungi: yeast
• plants: Arabidopsis
• other: bacteria, viruses
Advantages of microarray experiments
Fast
Data on 15,000 genes in 1-4 weeks
Comprehensive
Entire yeast genome on a chip
Flexible
• As more genomes are sequenced,
more arrays can be made.
• Custom arrays can be made
to represent genes of interest
You can submit RNA samples
to a core facility for analysis
Easy
Cheap?
Chip representing 15,000 genes for $350;
robotic spotter/scanner cost $100,000
Page 175
Disadvantages of microarray experiments
Cost
Many researchers can’t afford to do
appropriate controls, replicates
RNA
The final product of gene expression is protein
significance
(see pages 174-176 for references)
Quality
control
Impossible to assess elements on array surface
Artifacts with image analysis
Artifacts with data analysis
Page 176
Sample
acquisition
RNA: purify, label
Data
acquisition
Microarray: hybridize,
wash, image
Data
analysis
Data
confirmation
Biological insight
Page 176
Stage 1: Experimental design
[1] Biological samples: technical and biological replicates
[2] RNA extraction, conversion, labeling, hybridization
[3] Arrangement of array elements on a surface
Page 177
Sample 1
Sample 2
Sample 3
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Samples 1,2
Samples 1,3
Sample 1, pool Sample 2, pool
Samples 2,3
Samples 2,1:
switch dyes
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Stage 2: RNA and probe preparation
For Affymetrix chips, need total RNA (about 10 ug)
Confirm purity by running agarose gel
Measure a260/a280 to confirm purity, quantity
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Basic sciences Affymetrix core
http://microarray.mbg.jhmi.edu/
Johns Hopkins Oncology Center
Microarray Core
http://www.hopkinsmedicine.org/microarray/
Johns Hopkins University
NIDDK Gene Profiling Center
http://www.hopkinsmedicine.org/
nephrology/microarray/
The Hopkins Expressionists
http://astor.som.jhmi.edu/hex/
Gene expression methodology
seminar series
http://astor.som.jhmi.edu/hex/gem.html
Stage 3: hybridization to DNA arrays
The array consists of cDNA or oligonucleotides
Oligonucleotides can be deposited by photolithography
The sample is converted to cRNA or cDNA
Page 178-179
Microarrays: array surface
Page 179
Microarrays: robotic spotters
See Nature Genetics microarray supplement
Stage 4: Image analysis
RNA expression levels are quantitated
Fluorescence intensity is measured with a scanner,
or radioactivity with a phosphorimager
Page 180
Differential Gene Expression on a cDNA Microarray
Control
Rett
a B Crystallin
is over-expressed
in Rett Syndrome
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Stage 5: Data analysis
This is the subject of Wednesday’s class
• How can arrays be compared?
• Which genes are regulated?
• Are differences authentic?
• What are the criteria for statistical significance?
• Are there meaningful patterns in the data
(such as groups)?
Page 180
Microarray data analysis
preprocessing
inferential
statistics
exploratory
statistics
Page 180
Microarray data analysis
preprocessing
global normalization
local normalization
scatter plots
inferential
statistics
t-tests
exploratory
statistics
clustering
Page 180
Matrix of genes versus samples
Metric (define distance)
principal
components
analysis
clustering
Trees
(hierarchical,
k-means)
supervised,
unsupervised
analyses
selforganizing
maps
Page 180
Stage 6: Biological confirmation
Microarray experiments can be thought of as
“hypothesis-generating” experiments.
The differential up- or down-regulation of specific
genes can be measured using independent assays
such as
-- Northern blots
-- polymerase chain reaction (RT-PCR)
-- in situ hybridization
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Stage 7: Microarray databases
There are two main repositories:
Gene expression omnibus (GEO) at NCBI
ArrayExpress at the European Bioinformatics
Institute (EBI)
See the URLs on page 184
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Gene expression omnibus (GEO)
NCBI repository for gene expression data
http://www.dnachip.org
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Microarrays: web resources
• Many links on Leming Shi’s page:
http://www.gene-chips.com
• Stanford Microarray Database
http://www.dnachip.org
• links at http://pevsnerlab.kennedykrieger.org/
Database Referencing of Array Genes Online
(DRAGON)
Database Referencing of Array Genes Online
(DRAGON)
Credit:
Christopher Bouton
Carlo Colantuoni
George Henry
Paste accession numbers
into DRAGON here
DRAGON relates genes
to KEGG pathways