Human Cancer Genome Project Computational Systems Biology of
Cancer: (II) Slide 2 Human Cancer Genome Project Bud Mishra
Professor of Computer Science, Mathematics and Cell Biology Courant
Institute, NYU School of Medicine, Tata Institute of Fundamental
Research, and Mt. Sinai School of Medicine Slide 3 Human Cancer
Genome Project The New Synthesis Genome Evolution Selection
perturbed pathways micro-environment epigenomics transcriptomics
proteomic metabolomics signaling genetic instability Part-lists,
Annotation, Ontologies DNA RNA Protein TranscriptionTranslation
Genotype Phenotype Slide 4 Human Cancer Genome Project Is the
Genomic View of Cancer Necessarily Accurate ? If I said yes, that
would then suggest that that might be the only place where it might
be done which would not be accurate, necessarily accurate. It might
also not be inaccurate, but I'm disinclined to mislead anyone. US
Secretary of Defense, Mr. Donald Rumsfeld, Once again quoted
completely out of context. Slide 5 Human Cancer Genome Project
Cancer Initiation and Progression Genomics (Mutations,
Translocations, Amplifications, Deletions) Epigenomics (Hyper &
Hypo-Methylation) Transcriptomics (Alternate Splicing, RNA)
Proteomics (Synthesis, Post-Translational Modification,
Degradation) Signaling Proliferation, Motility, Immortality,
Metastasis, Signaling Slide 6 Human Cancer Genome Project Mishras
Mystical 3Ms Rapid and accurate solutions Bioinformatic,
statistical, systems, and computational approaches. Approaches that
are scalable, agnostic to technologies, and widely applicable
Promises, challenges and obstacles Measure Mine Model Slide 7 Human
Cancer Genome Project Measure What we can quantify and what we
cannot Slide 8 Human Cancer Genome Project Microarray Analysis of
Cancer Genome Representations are reproducible samplings of DNA
populations in which the resulting DNA has a new format and reduced
complexity. We array probes derived from low complexity
representations of the normal genome We measure differences in gene
copy number between samples ratiometrically Since representations
have a lower nucleotide complexity than total genomic DNA, we
obtain a stronger specific hybridization signal relative to
non-specific and noise Normal DNA Normal LCR Tumor DNA Tumor LCR
Label Hybridize Slide 9 Human Cancer Genome Project Minimizing
Cross Hybridization (Complexity Reduction) Slide 10 Human Cancer
Genome Project A1 A2 A3 B1 B2 B3 C1 C2 C3 Copy Number Fluctuation
Slide 11 Human Cancer Genome Project Critical Innovations Data
Normalization and Background Correction for Affy-Chips 10K, 100K,
500K (Affy); Generalized RMA Multi-Experiment-Based
Probe-Characterization (Kalman + EM) A novel genome segmenter
algorithm Empirical Bayes Approach; Maximum A Posteriori (MAP)
Generative Model (Hierarchical, Heteroskedastic) Dynamic
Programming Solution Cubic-Time; Linear-time Approximation using
Beam-Search Heuristic Single Molecule Technologies Optical and
Nanotechnologies Sequencing: SMASH Epigenomics Transcriptomics
Slide 12 Human Cancer Genome Project Background Correction &
Normalization Slide 13 Human Cancer Genome Project Oligo Arrays:
SNP genotyping Given 500K human SNPs to be measured, select 10
25-mers that over lap each SNP location for Allele A. Select
another 10 25-mers corresponding to SNP Allele B. Problem : Cross
Hybridization DNA 25-mers Slide 14 Human Cancer Genome Project
Using SNP arrays to detect Genomic Aberrations Each SNP probeset
measures absense/presence of one of two Alleles. If a region of DNA
is deleted by cancer, one or both alleles will be missing! If a
region of DNA is duplicated/amplified by cancer, one or both
alleles will be amplified. Problem : Oligo arrays are noisy. Slide
15 Human Cancer Genome Project 90 humans, 1 SNP (A=0.48) Allele A
Allele B Slide 16 Human Cancer Genome Project 90 humans, 1 SNP
(A=0.24) Allele B Allele A Slide 17 Human Cancer Genome Project 90
humans, 1 SNP (A=0.96) Allele B Allele A Slide 18 Human Cancer
Genome Project Background Correction & Normalization Consider a
genomic location L and two similar nucleotide sequences s L,x and s
L,y starting at that location in the two copies of a diploid
genomes E.g., they may differ in one SNP. Let x and y be their
respective copy numbers in the whole genome and all copies are
selected in the reduced complexity representation. The gene chip
contains four probes p x 2 s L,x ; p y 2 s L,y ; p x, p y :2 G.
After PCR amplification, we have some K x x amount of DNA that is
complementary to the probe p x, etc.K' ( K x ) amount of DNA that
is additionally approximately complementary to the probe p x. Slide
19 Human Cancer Genome Project Normalize using a Generalized RMA I
= U - n [ n 2 - N(0,1) (a/b)/ N(0,1) (a/b)] {(1 + B n / N(0,1)
(a/b)} -1 + [b n /B n ] )] {(1 + N(0,1) (a/b)/( B n )} -1, Where a
= U- n - n 2 ; b = n, and b n = [I i,j U + n ] N(0,1) ([I i,j U + n
] ) B n = N(0,1) ([I i,j U + n ] ) Slide 20 Human Cancer Genome
Project Background Correction & Normalization If the probe has
an affinity x, then the measured intensity is can be expressed as
[K x x + K] x +noise = [ x + K/K x ] x + noise With Exp[ + a
multiplicative logNormal noise, [ + an additive Gaussian noise, and
x = K x x an amplified affinity. A more general model: I x = [ x +
K/K x ] x e + + Slide 21 Human Cancer Genome Project Mathematical
Model In particular, we have four values of measured intensities: I
x = [ x x + N x ]e + + 2 I x = [N x ] e + + 2 I y = [ y y + N y ] e
+ + 2 I y = [N y ] e + + 2 Slide 22 Human Cancer Genome Project
Bioinformatics: Data modeling Good news: For each 25-bp probe, the
fluorescent signal increases linearly with the amount of
complementary DNA in the sample (up to some limit where it
saturates). Bad news: The linear scaling and offset differ for each
25-bp probe. Scaling varies by factors of more than 10x. Noise :
Due to PCR & cross hybridization and measurement noise. Slide
23 Human Cancer Genome Project Scaling & Offset differ Scaling
varies across probes: Each 25-bp sequence has different
thermodynamic properties. Scaling varies across samples: The
scanning laser for different samples may have different levels. The
starting DNA concentrations may differ; PCR may amplify
differently. Offset varies across probes: Different levels of Cross
Hybridization with the rest of the Genome. Offset varies across
samples: Different sample genomes may differ slightly (sample
degradation; impurities, etc.) Slide 24 Human Cancer Genome Project
Linear Model + Noise Slide 25 Human Cancer Genome Project Noise
minimization Slide 26 Human Cancer Genome Project Final Data Model
Slide 27 Human Cancer Genome Project MLE using gradients Slide 28
Human Cancer Genome Project Data Outliers Our data model fails for
few data points (bad probes) Soln (1): Improve the model Soln (2):
Discard the outliers Soln (3): Alternate model for the outliers
Weight the data approprately. Slide 29 Human Cancer Genome Project
Outlier Model Slide 30 Human Cancer Genome Project Problem with
MLE: No unique maxima Slide 31 Human Cancer Genome Project Scaling
of MLE estimate Slide 32 Human Cancer Genome Project Segmentation
to reduce noise The true copy number (Allele A+B) is normally 2 and
does not vary across the genome, except at a few locations
(breakpoints). Segmentation can be used to estimate the location of
breakpoints and then we can average all estimated copy number
values between each pair of breakpoints to reduce noise. Slide 33
Human Cancer Genome Project Allelic Frequencies: Cancer &
Normal Slide 34 Human Cancer Genome Project Allelic Frequencies:
Cancer & Normal Slide 35 Human Cancer Genome Project
Segmentation & Break-Point Detection Slide 36 Human Cancer
Genome Project Algorithmic Approaches Local Approach Change-point
Detection (QSum, KS-Test, Permutation Test) Global Approach HMM
models Wavelet Decomposition Bayesian & Empirical Bayes
Approach Generative Models (One- or Multi-level Hierarchical)
Maximum A Posteriori Slide 37 Human Cancer Genome Project HMM 2 3 4
5 6 0 1 Model with a very high degree of freedom, but not enough
data points. Small Sample statistics a Overfitting, Convergence to
local maxima, etc. Slide 38 Human Cancer Genome Project HMM,
finally Model with a very high degree of freedom, but not enough
data points. Small Sample statistics a Overfitting, Convergence to
local maxima, etc. 2 3 1 Slide 39 Human Cancer Genome Project HMM,
last time We will simply model the number of break-points by a
Poisson process, and lengths of the aberrational segments by an
exponential process. Two parameter model: p b & p e =2 2 pbpb
1-p b 1-p e pepe Advantages: 1.Small Number of parameters. Can be
optimized by MAP estimator. (EM has difficulties). 2.Easy to model
deviation from Markvian properties (e.g., polymorphisms, power-law,
Polyas urn like process, local properties of chromosomes, etc.)
Slide 40 Human Cancer Genome Project Generative Model
Amplification, c=4Amplification, c=3 Deletion, c=0Deletion, c=1
Breakpoints, Poisson, p b Segmental Length, Exponential, p e Copy
number, Empirical Distribution Noise, Gaussian, , Slide 41 Human
Cancer Genome Project A reasonable choice of priors yields good
segmentation. Slide 42 Human Cancer Genome Project A reasonable
choice of priors yields good segmentation. Slide 43 Human Cancer
Genome Project A MAP (Maximum A Posteriori) Estimators Priors:
Deletion + Amplification Data: Priors + Noise Goal: Find the most
plausible hypothesis of regional changes and their associated copy
numbers Generalizes HMM:The prior depends on two parameters p e and
p b. p e is the probability of a particular probe being normal. p b
is the average number of intervals per unit length. (pe,pb) max at
(0.55,0.01) Slide 44 Human Cancer Genome Project Likelihood
Function The likelihood function for first n probes: L( h i 1, 1, ,
i k, k i ) = Exp(-p b n) (p b n) k (2 2 ) (-n/2) i=1 n Exp[-(v i -
j ) 2 /2 2 ] p e (#global) (1-p e ) (#local) Where i k = n and i
belongs to the j th interval. Maximum A Posteriori algorithm
(implemented as a Dynamic Programming Solution) optimizes L to get
the best segmentation L( h i* 1, 1, , i* k, k i ) Slide 45 Human
Cancer Genome Project Dynamic Programming Algorithm Generalizes
Viterbi and Extends. Uses the optimal parameters for the generative
model: Adds a new interval to the end: h i 1, 1, , i k, k i h i
k+1, k+1 i = h i 1, 1, , i k, k, i k+1, k+1 i Incremental
computation of the likelihood function: Log L( h i 1, 1, , i k, k,
i k+1, k+1 i ) = Log L( h i 1, 1, , i k, k i ) + new-res./2 2 Log(p
b n) +(i k+1 i k ) Log (2 2 ) (i k+1 i k ) [ I global Log p e + I
local Log(1 p e )] Slide 46 Human Cancer Genome Project Prior
Selection: F criterion For each break we have a T 2 statistic and
the appropriate tail probability ( p value) calculated from the
distribution of the statistic. In this case, this is an F
distribution. The best (p e,p b ) is the one that leads to the
maximum min p -value. (pe,pb) max at (0.55,0.01) Slide 47 Human
Cancer Genome Project Segmentation Analysis Slide 48 Human Cancer
Genome Project 13q13.113q31.3 CGH Explorer v.2.43 DNAcopy GLAD vMAP
Olshen, AB et al. Biostatistic s 5 : 557-72 Lingjaerde, OC et al.
Bioinformatics 21 : 821-2 Hupe, P et al. Bioinformatics 20 :
3413-22 Daruwala et al. Proc Natl Acad Sci U S A. 2004 Comparison
of chromosome 13 tumor using 4 different segmentation algorithm
Comparison of chromosome 13 tumor using 4 different segmentation
algorithm Slide 49 Human Cancer Genome Project Comparative
Analysis: BAC Array Slide 50 Human Cancer Genome Project
Comparative Analysis: Nimblegen Slide 51 Human Cancer Genome
Project Comparative Analysis: Affy 10K Slide 52 Human Cancer Genome
Project Simulated Data Array CGH simulations and an ROC analysis
Using the same scheme as Lai et al. Weil R. Lai, Mark D. Johnson,
Raju Kucherlapati, and Peter J. Park (2005), Comparative analysis
of algorithms for identifying amplifications and deletions in array
CGH data, Bioinformatics, 21(19): 3763-3770. Segmented by Vmap and
DNAcopy Vmap algorithm was tested at 11 segmentation Pvalues of:
0.1, 5 10 -2, 10 -2, 10 -3, 10 -4, , 10 -10. DNAcopy algorithm was
tested at 9 segmentation alpha values of:.9,.5,.1, 10 -2, 10 -3, 10
-4, , 10 -7. Analysis by Alex Pearlman et al. (2006) Slide 53 Human
Cancer Genome Project VMAP Slide 54 DNACopy Slide 55 Slide 56 Log
ratio Prostate Tumor Gains and Losses Genome view of 19K BAC CGH
Prostate Tumor Gains and Losses Genome view of 19K BAC CGH Slide 57
Human Cancer Genome Project Normal 1,2,3 Tumor1 Tumor2 Tumor3
Proximal breakpoints were identical for T1 and T3. Distal
breakpoints overlapped for T1, T2, and T3. Segmentation of
Multi-BAC Events On Chromosome 13 Slide 58 Human Cancer Genome
Project Further Improvement We employed a hierarchical Bayesian
model in which global false discovery rates can be calculated using
the different levels of the model. Noise processes are also
estimated using the appropriate global parameters. Slide 59 Human
Cancer Genome Project Specific Features of the Model We build a
model in which, given the region segmentations, we assume that the
copy numbers I j = region j, (1 j k) in that regions are mutually
independent Gaussian X i,j N ( j, j 2 ), (1 i n j ) random
variables with mean j and variance j 2. We further assume that each
copy region mean parameter j is in one of a small number of states
2 {1,,S} with respective probabilities, 1, , S of being in state s.
j is in state s (with probability s ) if it has a Gaussian
distribution with state mean s and state variance s 2. States serve
to characterize regions. The state means and variances are the
hyperparameters of the model. Slide 60 Human Cancer Genome Project
Implementation: Dynamic Programming Given the hyperparameters, we
segment regions using a dynamic programming approach. This consists
in constructing probe regions as follows: After the (j-1) st region
has been constructed: A) we choose the next two contiguous regions
to the right of those already constructed by optimizing the
corresponding log likelihood, subject to the condition that the
p-value of the t-statistic distinguishing between these two
(aforementioned) regions is above a given threshold. B) Having
chosen these (aforementioned) regions, the probe regions already
constructed, contiguous to them, may also need to be altered. Slide
61 Human Cancer Genome Project Segmentation (ROMA,chr3) Slide 62
Human Cancer Genome Project S*M*A*S*H Single Molecule Approaches to
Sequencing by Hybridization ~Extensions to Optical Mapping~ Slide
63 Human Cancer Genome Project S*M*A*S*H Genomic DNA is carefully
extracted from small number of cells of an organism (e.g., human)
in normal or diseased states. (Fig 1 shows a cancer cell to be
studied for its oncogeneomic characterization.) Fig 1 Slide 64
Human Cancer Genome Project S*M*A*S*H LNA probes of length 6 8
nucleotides are hybridized to dsDNA (double-stranded genomic DNA)
in a test tube (Fig 2) and the modified DNA is stretched on a 1 x 1
chip that has microfluidic channels manufactured on its surface.
These surfaces have been chemically treated to create a positive
charge. Fig 2 DNA samples are prepared for analysis with LNA probes
and restriction enzymes. Slide 65 Human Cancer Genome Project
S*M*A*S*H Since DNA is slightly negatively charged, it adheres to
the surface as it flows along these channels and stretches out.
Individual molecules range in size from 0.3 3 million base pairs in
length. Next, bright emitters are attached to the probes on the
surface and the molecules are imaged (Fig 3). Fig 3 Slide 66 Human
Cancer Genome Project S*M*A*S*H A restriction enzyme 1 is added to
break the DNA at specific sites. Since DNA molecules are under
slight tension, the cut fragments of DNA relax like entropic
springs, leaving small visible gaps corresponding to the positions
of the restriction site (Fig 4). 1. A restriction enzyme is a
highly specific molecular scissor that recognizes short nucleotide
sequences and cuts the DNA at only those recognition sites. Fig 4
Slide 67 Human Cancer Genome Project S*M*A*S*H The DNA is then
stained with a fluorogen (Fig 5) and reimaged. The two images are
combined to create a composite image suggesting the locations of a
specific short word (e.g., probes) within the context of a pattern
of restriction sites. Fig 5 Slide 68 Human Cancer Genome Project
S*M*A*S*H The intensity of the light emitted by the dye at one
frequency provides a measure of the length of the DNA fragments.
The intensity of the light emitted by the bright-emitters on probes
provides an intensity profile for locations of the probes. Images
of each DNA molecule are then converted into ideograms, where the
restriction sites are represented by a tall rectangle and probe
sites by small circles (Fig 6). Fig 6 Slide 69 Human Cancer Genome
Project S*M*A*S*H The steps above are repeated for all possible
probe compositions (modulo reverse complementarity). Sutta software
then uses the data from all such individual ideograms to create an
assembly of the haplotypic ordered restriction maps with
approximate probe locations superimposed on the map. ATAT TATC ATCA
TCAT CATA ATATCATAT Fig 7 Slide 70 Human Cancer Genome Project
S*M*A*S*H Local clusters of overlapping words are combined by
Suttas PSBH (positional sequencing by hybridization) algorithm to
overlay the inferred haplotypic sequence on top of the restriction
map (Fig 7). ATAT TATC ATCA TCAT CATA ATATCATAT Fig 7 Slide 71
Human Cancer Genome Project Gapped Probes Mixing solid bases with
`wild-card bases: E.g., xx*x**x*xx (10-4-mers) or xx*x****x*xx
(12-6-mers) An wild-card base Universal: In terms of its ability to
form base pairs with the other natural DNA/RNA bases. Applications
in primers and in probes for hybridization Examples: The naturally
occurring base hypoxanthine, as its ribo- or 2'-
deoxyribonucleoside 2'-deoxyisoinosine 7-deaza-2'-deoxyinosine
2-aza-2'-deoxyinosine Slide 72 Human Cancer Genome Project
Simulation Results Probe Map Assumptions: For single DNA molecules:
Probe location Standard Deviation = 240 bases; Data coverage per
probe map = 50x; Probe hybridization rate = 30%, and false positive
rate of 10 probes per megabase, uniformly distributed. Analytically
estimation of the average error rate in the probe consensus map:
Probe location SD = 60 bases; False Positive rate < 2.4%; False
Negative rate < 2.0%. Slide 73 Human Cancer Genome Project
Simulation Results UNGAPPEDGAPPED Slide 74 Human Cancer Genome
Project Simulation Results Simulation based on non-random sequences
from the human genome: 96 blocks of 1 Kb (from chromosome 1)
concatenated together along with its in silico restriction map.
Error summary for the gapped probe pattern xx*x **** x*xx: Error
count excluding repeats or near repeats: 0.32bp / 10Kb There is no
error due to incorrect rearrangements. There is no loss of
information at haplotypic level. Assembly failed in 2 of 96 blocks
of 1kb = 2.1% failure rate (out of memory). Slide 75 Human Cancer
Genome Project GENomic conTIG Gentig uses a purely Bayesian
Approach. It models all the error processes in the prior. FAST: It
initially starts with a conservative but fast pairwise overlap
configuration, computed efficiently using Geometric Hashing.
ACCURATE: It iteratively combines pairs of maps or map contigs,
while optimizing the likelihood score subject to a constraint
imposed by a false- positive constraint. It has special heuristics
to handle non-local errors. Slide 76 Human Cancer Genome Project
HAPTIG: HAPlotypic conTIG Candida Albicans The left end of
chromsome-1 of the common fungus Candida Albicans (being sequenced
by Stanford). You can clearly see 3 polymorphisms: (A) Fragment 2
is of size 41.19kb (top) vs 38.73kb (bottom). (B) The 3rd fragment
of size 7.76kb is missing from the top haplotype. (C)The large
fragment in the middle is of size 61.78kb vs 59.66kb. FAST &
ACCURATE BAYESIAN ALGORITHM Slide 77 Human Cancer Genome Project
Lambda DNA with probes 10 m Slide 78 Human Cancer Genome Project
500 nm A Fig. A : Four AFM images of lambda DNA with PNA probes
hybridized to the distal recognition site, located 6,900 bp or 2.28
microns from the end (green arrow). Non-specifically bound probes
indicated by the red arrows. Z- scale is +/- 1.5 nm. Slide 79 Human
Cancer Genome Project E. coli Figure 3. Two optical images of E
coli K12 genomic DNA after restriction digestion with 6-cutter
restriction enzyme Xho 1 and hybridization with an 8-mer PNA probe.
Bound probes are indicated by blue arrows and non- specifically
bound probes by the red arrows. Scale bar shown is 10 micron. Slide
80 Human Cancer Genome Project Discussions Q&A Slide 81 Human
Cancer Genome Project Answer to Cancer If I know the answer I'll
tell you the answer, and if I don't, I'll just respond, cleverly.
US Secretary of Defense, Mr. Donald Rumsfeld. Slide 82 Human Cancer
Genome Project To be continued Break
