Human Population Genomics

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• Human Population Genomics
• ?Man, ?Woman, ? Birth, ? Death,
• ? Infinity, Plus
• ? Altruism, ? Cheap Talks,
• ? Bad Behavior, Money, ? God and
• ? Diversity on Steroids

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Jack Schwartz (1930 2009)
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Lord Jeffrey (misattributed badly paraphrased)

• Damn the Human Genomes.
• Small populations
• Genes too distant
• Pestered with duplications
• Feeble contrivance
• Could make a better one myself!

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Small Populations

• Non-equilibrium Models
• Population Bottlenecks
• Not Well-mixed
• Migration/Colonization Patterns
• Catastrophic Infections
• Heterozygous Advantages

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Wright-Fisher Process
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Moran Process
death
time

• Overlapping generations
• Distribution of time to replication

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Forces in Population Genetics

• How to understand forces that produce and
  maintain inherited genetic variation
• Forces
• Mutation
• Recombination
• Natural Selection
• Population Structure/Migration
• Random birth/death (drift)

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(No Transcript)
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Genes Too Distant

• 20,000 Genes (Estimate in 80s 120,000)
• Occurring about every 150 Kb
• Many more functional ncRNA
• snoRNA, siRNA, piRNA, etc.
• Uncharacterized

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Y

• From a genes point of view, reshuffling is a
  great restorative
• The Y, in its solitary state disapproves of such
  laxity. Apart from small parts near each tip
  which line up with a shared section of the X, it
  stands aloof from the great DNA swap. Its genes,
  such as they are, remain in purdah as the
  generations succeed. As a result, each Y is a
  genetic republic, insulated from the outside
  world. Like most closed societies it becomes both
  selfish and wasteful. Every lineage evolves an
  identity of its own which, quite often, collapses
  under the weight of its own inborn weaknesses.
• Celibacy has ruined mans chromosome.
• Steve Jones, Y The descent of Men, 2002.

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DAZ locus on Y Chromosome
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Optical Mapping

1. Capture and immobilize whole genomes as massive
   collections of single DNA molecules

Cells gently lysed to extract genomic DNA
DNA captured in parallel arrays of long single
DNA molecules using microfluidic device
Genomic DNA, captured as single DNA molecules
produced by random breakage of intact chromosomes
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?
2. Interrogate with restriction
endonucleases 3. Maintain order of restriction
fragments in each molecule
Digestion reveals 6-nucleotide cleavage sites as
gaps
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??

• Single molecule maps are aligned to
  sequence-based in silico maps to validate an
  assembly
• The Bayesian likelihood function leads to
  long-range haplotypic score function.
• Later we will see how to perform a shotgun map
  assembly

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• Sizing Error
• (Bernoulli labeling, absorption cross-section,
  PSF)
• Partial Digestion
• False Optical Sites
• Orientation
• Spurious molecules, Optical chimerism, Calibration

Image of restriction enzyme digested YAC clone
YAC clone 6H3, derived from human chromosome 11,
digested with the restriction endonuclease Eag I
and Mlu I, stained with a fluorochrome and imaged
by fluorescence microscopy.
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Various combinations of error sources lead to
NP-hard Problems
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Pestered with duplications

• Complex Genome Structures
• Segmental Duplications
• Many types of Polymorphisms
• (SNPs, CNVs, SVs, etc.)
• Models of Genome Dynamics
• GOD (Genome Organizing Devices)
• Models of Coalescence

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Segmental Duplications

• Segmental duplications have been found to be
  associated with genomic disorders.
• Deletions Williams-Beuren syndrome
• Duplications Charcot-Marie-Tooth disease type 1A
• Inversions Haemophilia A
• Translocations Derivative 22 der(22) syndrome.
• Segmental duplications may be related to cancer
  development by causing copy number fluctuations
• Duplication of myc in lung cancer, and ERBB2 in
  breast cancer.

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Recent Segmental Duplications
Human

• 3.5 5 of the human genome is found to contain
• segmental duplications, with length gt 5 or 1kb,
  identity gt 90.
• August, 2001 assembly,
• Bailey, et al. 2002.
• April, 2003 assembly,
• Cheung, et al. 2003.
• These duplications are estimated to have emerged
  about 40Mya under neutral assumption.
• The duplications are mostly interspersed
  (non-tandem), and happen both inter- and
  intra-chromosomally.

From Bailey, et al. 2002
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Recent Segmental Duplications
Mouse

• 1.2 of the mouse genome is found to contain
  segmental duplications, with length gt 5kb,
  identity gt 90.
• February, 2003 mouse assembly,
• Cheung, et al. 2003.
• These duplications are estimated to have emerged
  about 25Mya under neutral assumption.
• The duplications happen both inter- and
  intra-chromosomally.

From Cheung, et al. 2003
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Duplication Flanking Sequences

• What are the molecular mechanisms that caused the
  recent segmental duplications in the human and
  mouse genomes?
• Thermodynamic instability in the DNA sequences
• Recombination between homologous repeat elements
• Other unknown mechanisms.

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Thermodynamics
Control
Data
5-breakpoint
3-breakpoint
5
3
512bp
-512bp
duplicated region
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?
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??

• The duplication flanking regions contain more
  repeats than the control sequences SINE, LINE,
  MaLR and HERV.
• Only the repeats from the younger subfamilies
  (with lower sequence divergence levels) are
  over-represented in the duplication flanking
  sequences.

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The Model
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The Mathematical Model
Time after duplication
1-a-2ß
1-a-2ß
1-a-2ß
h0--
a
a
a
a
f - -
h1--
?
2ß
?
2ß
2ß
?
h0-
h0
H0
a
a
a
a
f -
1-a-ß/2-?
1-a-ß/2-?
1-a-ß/2-?
2?
ß/2
2?
ß/2
2?
ß/2
h0
a
a
a
a
H1
f
h1
h1
1-a-2?
1-a-2?
1-a-2?
0 d lt e
e d lt 2e
(k-1)e d lt ke
h1 proportion of duplications by repeat
recombination h1 proportion of
duplications by recombination of the specific
repeat h1- - proportion of duplications
by recombination of other repeats h0 proportion
of duplications by other repeat-unrelated
mechanism h0 proportion of h0 with
common specific repeat in the flanking regions
h0- proportion of h0 with no common
specific repeat in the flanking regions
h0- - proportion of h0 with no specific repeat
in the flanking regions
a mutation rate in duplicated sequences ß
insertion rate of the specific repeat ?
mutation rate in the specific repeat d
divergence level of duplications e divergence
interval of duplications.
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Model Fitting
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Mer Frequencies
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Copy Number Variation Data
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CNVs in Unique regions
OR
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CNVs in Unique regions
Yoruba Japanese Chinese Ceph
No polymorphism 810 817 817 799
Amplifications only 43 43 46 55
Deletions only 46 37 36 44
Mixed 1 321 1 211
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CNVs in SD regions
AND
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CNV in SD regions
Yoruba Japanese Chinese Ceph
No polymorphism 786 794 785 741
Amplifications only 124 135 141 129
Deletions only 101 86 101 141
Mixed 43 40 27 44
Unique and SD regions show completely different
behavior of CNVs!
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Distance-dependent recombination

• The chance of recombination depends on the
  distance between Allele A and its copy

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Simulation (probabilistic model)
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Simulation (probabilistic model)
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Observations Conclusions

• Mutation rate of 0.0001 and recombination rate of
  0.001 in SD regions constitute the best fit to
  observed real life data.
• Single mutations cannot explain observed data,
  but can be explained by convergence via
  recombination.
• Evolution-by-Duplication (EBD) appears to play a
  crucial role in evolution and molds the genetic
  circuitry in a rather constrained way, before it
  is subject to selection pressure

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Feeble Contrivance

• GWAS (Genome-Wide Association Studies)
• Common Variants vs. Rare Variants
• Haplotype Phasing/Linkage Analysis
• Poor Experiment Design
• Reference Sequences
• Genotypic vs. Haplotypic References
• Weak Technologies

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Common vs. Rare Disease Variants

• From Ionita-Laza (2009)
• There are two disease models
• CDCV - common disease, common variants
• CDRV - common disease, rare variants
• The current genome-wide association studies only
  consider common variants (frequency at least 5).
• Feasible with available resources
• The common loci identified so far have small
  effects (ORs 11 -15) and only explain a small
  percentage of the estimated heritability.
• Rare susceptibility variants are expected to play
  an important role
• population genetics theory (Pritchard, 2001)
• empirical evidence (BMI, blood pressure, autism,
  Mendelian diseases etc.)

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Effect Size Distribution
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Capture-Recapture Model

• Suppose we have sequence data on Nind individuals
  in a genomic region.
• An individual shows variation at a position if
  the corresponding allele is different from the
  ancestral one.
• A position is variable or is a variant if there
  is at least one individual in the dataset with a
  variation at that position.
• Let xs be the number of individuals with
  variation at position s xs gt 0.
• What is N the total, unknown number of variants
  in the region.

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One can estimate the following

• ?(t) NEW variants expected to be found in a
  FUTURE dataset of size t . Nind.
• t is a multiplier of initial dataset size, Nind.
• ?f(t) new variants with frequency at least f
  . . .

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ENCODE dataset

• Ten 500Kb genomic regions were sequenced in
  several unrelated DNA samples
• 8 Yoruba (YRI)
• 16 CEPH European (CEPH)
• 7 Han Chinese (CHB)
• 8 Japanese (JPT)
• To make results comparable across the four
  populations (YRI, CEPH, CHB and JPT), they
  considered only 7 of the sequenced individuals
  for each dataset.

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ENCODE - ?f(t)

• From Ionita-Laza et al. 2009

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How to Make a Better Human?

• Debugging a human better
• Sequencing a genome
• Sequencing a population

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S ?M ? A ? S ? H

• Single
• Molecule
• Approach to
• Sequencing-by-
• Hybridization

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SMASH

• Sequence a human size genome of about 6
  Gbinclude both haplotypes.
• Integrate
• Optical Mapping (Ordered Restriction Maps)
• Hybridization (with short nucleobase probes PNA
  or LNA oligomers with dsDNA on a surface, and
• Positional Sequencing by Hybridization (efficient
  polynomial time algorithms to solve localized
  versions of the PSBH problems)

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?

• Genomic DNA is carefully extracted

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??

• LNA probes of length 6 8 nucleotides are
  hybridized to dsDNA (double-stranded genomic DNA)
• The modified DNA is stretched on a 1 x 1 chip.

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???

• DNA adheres to the surface along the channels and
  stretches out.
• Size from 0.3 3 million base pairs in length.
• Bright emitters are attached to the probes and
  imaged (Fig 3).

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????

• A restriction breaks the DNA at specific sites.
• The cut fragments of DNA relax like entropic
  springs, leaving small visible gaps

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?????

• The DNA is then stained with a fluorogen (Fig 5)
  and reimaged.
• The two images are combined in a composite image
• suggesting the locations of a specific short word
  (e.g., probes) within the context of a pattern of
  restriction sites.

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??????

• The integrated intensity measures the length of
  the DNA fragments.
• The bright-emitters on probes provides a profile
  for locations of the probes.

The restriction sites are represented by a tall
rectangle The probe sites by small circles
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• These steps are repeated for all possible probe
  compositions
• (modulo reverse complementarity).
• Software assembles the haplotypic ordered
  restriction maps with approximate probe locations
  superimposed on the map.

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SMASH

• Local clusters of overlapping words are combined
  by our PSBH (positional sequencing by
  hybridization) algorithm

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Probe Map (lambda DNA)
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Final Probe Map

• Consensus map with 2 probe locations
• 14.8 and 52.4 of the DNA length.
• In close agreement with the correct map
• 50.2 and 85.7 (known from the sequence)
• Implied probe hybridization rate 42.
• Significantly better than the needed 30

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Four AFM images of lambda DNA with PNA probes
A
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Combinatorial Structure
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Discretization
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Prediction
The probability of successfully computing the
correct restriction map as a function of the
number of cuts in the map and number of molecules
used in creating the map
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Gentig Bayesian Approach
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Bayesian Model
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Robustness

• BAC Clones with 6-cutters
• Average Clone size 160 Kb Average Fragment
  Size 4 Kb, Average Number of Cutsites 40.
• Parameters
• Digestion rate can be as low as 10
• Orientation of DNA need not be known.
• 40 foreign DNA
• 85 DNA partially broken
• Relative sizing error up to 30
• 30 spurious randomly located cuts

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Single Molecule HapoltypingCandida Albicans

• The left end of chromsome-1 of the common fungus
  Candida Albicans (being sequenced by Stanford).
• Three 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.

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Problem to Solve

• Given probe maps of some small region of the
  genome for all N-bp hybridization probes (e.g.
  all 2080 probes of 6-bp).
• With known error rates (false positive, false
  negatives and sizing errors).
• Can we reconstruct the complete sequence ?

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Basic reconstruction algorithm

• Keep track of multiple sequence assemblies.
• Initialize with all possible 5-bp sequences.
• Try all 4 possible extensions of each sequence.
• Check if probe is present in corresponding map
  if not add a penalty score to the sequence
  involved.
• Periodically delete sequences with high penalty.
• Stop when missing probe rate jumps significantly
  from False Negative rate (2) to (100 - false
  extension rate) 55.
• Return highest scoring sequence.

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Anomalies

• Irresolvable Ambiguities
• From assemblies based on 6bp probes
• Error Pattern s w sRC
• Correct Pattern s wRC sRC
• s tcgcc (any 5 bases)
• sRCggcga (Reverse compliment of X)
• w CCCCTAAC (any short sequence under 50bp)
• wRC GTTAGGGG (Reverse compliment of Y)

AssemblytcgccCCCCTAAC ggcga
Correct
tcgccGTTAGGGGggcga
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Directed Eulerian Graph
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?

• Mixing solid bases with wild-card bases
• E.g., xx-x-x-xx (9-mers) or xxx- -x- -x- -xxx (14
  mers)
• An inert base
• Universal In terms of its ability to form base
  pairs with the other natural DNA/RNA bases.
• Examples
• The naturally occurring base hypoxanthine, as its
  ribo- or 2'-deoxyribonucleoside
  2'-deoxyisoinosine 7-deaza-2'-deoxyinosine
  2-aza-2'-deoxyinosine

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Simulation Results
UNGAPPED
GAPPED
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1000 Rupees Genome
22.67 US for 6 billion bases 135 billion US
for the entire human population
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Who we are

• Population
• David Albers (Columbia)
• Eric Aslakson (NYU)
• Mickey Atwal (CSHL)
• Ivan Iossifov (CSHL)
• Hossein Khiabanian (Columbia)
• Samantha Kleinberg (NYU)
• Partha Mitra (CSHL)
• Michaela Oswald (CSHL)
• Raul Rabadan (Columbia)
• Vladimir Trifonov (Colmbia)
• Daniel Valente (CSHL)
• Chris Wiggins (Columbia)

• Polymorphims
• Iuliana Ionita-Laza (Harvard)
• Antonina Mitrofanova (NYU)
• Joey Zhao (Princeton)
• SMASH
• TS Anantharaman (OpGen)
• Charles Cantor (Sequenom)
• Vladimir Demidov (BU)
• Pierre Franquin (NYU)
• Alex Lim (Ex-NYU)
• Toto Paxia (Ex-NYU)
• Jason Reed (UCLA)
• Andrew Sundstrom (NYU)
• SUTTA
• Giusepe Narzisi (NYU)
• Alessio Narzisi (NYU/Catania)

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Lord Jeffrey

• Beware prejudices.
• They are like rats, and men's minds are like
  traps prejudices get in easily, but it is
  doubtful if they ever get out.