CSE280a: Algorithmic topics in bioinformatics

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CSE280a Algorithmic topics in bioinformatics

• Vineet Bafna

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The scope/syllabus

• We will cover topics from the following areas
• Population genetics
• Computational Mass Spectrometry
• Biological networks (emphasis on comparative
  analysis)
• ncRNA
• The focus will be on the use of algorithms for
  analyzing data in these areas
• Some background in algorithms (mathematical
  maturity) is helpful.
• Relevant biology will be discussed on a need to
  know basis

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Logisitics

• This class has little required homework.
• All reading is optional, but recommended.
• 1 Final Exam (20), and 1 research project (70)
• Students help edit class notes in latex (10)
• At most one topic per student
• Groups of lt 2 per topic
• Project Goal
• Address research problems with minimum
  preparation
• Lectures will be given by instructors and by
  students.
• Most communication is electronic.
• Check http//www.cse.ucsd.edu/classes/wi08/cse280a

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From an individual to a population

• Individual genomes vary by about 1 in 1000bp.
• These small variations account for significant
  phenotype differences.
• Disease susceptibility.
• Response to drugs
• How can we understand genetic variation in a
  population, and its consequences?
• It took a long time (10-15 yrs) to produce the
  draft sequence of the human genome.
• Soon (within 10-15 years), entire populations can
  have their DNA sequenced. Why do we care?

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Population Genetics

• Individuals in a species (population) are
  phenotypically different.
• Often these differences are inherited (genetic).
  Understanding the genetic basis of these
  differences is a key challenge of biology!
• The analysis of these differences involves many
  interesting algorithmic questions.
• We will use these questions to illustrate
  algorithmic principles, and use algorithms to
  interpret genetic data.

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Population genetics

• We are all similar, yet we are different. How
  substantial are the differences?
• What are the sources of variation?
• As mutations arise, they are either neutral and
  subject to evolutionary drift, or they are
  (dis-)advantageous and under selective pressure.
  Can we tell?
• If you had DNA from many sub-populations, Asian,
  European, African, can you separate them?
• How can we detect recombination?
• Why are some people more likely to get a disease
  then others? How is disease gene mapping done?
• Phasing of chromosomes

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Computational mass spectrometry

• Mass Spectrometry is a key technology for
  measuring active proteins, their interactions,
  and their post-translational modifications
• Computation plays a key role in interpreting mass
  spectrometry data.

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Back to the genome

• Recall that the genome contains protein-coding
  genes (1 of the genome)
• Another 5 might encode RNA, and regulatory sites
• How do we find regions of functional interest?

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Population genetics basics
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Scope of genetics lectures

• Basic terminology
• Key principles
• Sources of variation
• HW equilibrium
• Linkage
• Coalescent theory
• Recombination/Ancestral Recombination Graph
• Haplotypes/Haplotype phasing
• Population sub-structure
• Structural polymorphisms
• Medical genetics basis Association
  mapping/pedigree analysis

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Terminology allele

• Allele A specific variant at a location
• The notion of alleles predates the concept of
  gene, and DNA.
• Initially, alleles referred to variants that
  described a measurable trait (round/wrinkled
  seed)
• Now, an allele might be a nucleotide on a
  chromosome, with no measurable phenotype.
• As we discuss source of variation, we will have
  different kinds of alleles.

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Terminology

• Locus The location of the allele
• A nucleotide position.
• A genetic marker
• A gene
• A chromosomal segment

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Terminology

• Genotype genetic makeup of (part of) an
  individual
• Phenotype A measurable trait in an organism,
  often the consequence of a genetic variation
• Humans are diploid, they have 2 copies of each
  chromosome.
• They may have heterozygosity/homozygosity at a
  location
• Other organisms (plants) have higher forms of
  ploidy.
• Additionally, some sites might have 2 allelic
  forms, or even many allelic forms.
• Haplotype genetic makeup of (part of) a single
  chromosome

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What causes variation in a population?

• Mutations (may lead to SNPs)
• Recombinations
• Other crossover events (gene conversion)
• Structural Polymorphisms

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Single Nucleotide Polymorphisms

• Small mutations that are sustained in a
  population are called SNPs
• SNPs are the most common source of variation
  studied
• The data is a matrix (rows are individuals,
  columns are loci). Only the variant positions are
  kept.

A-gtG
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Single Nucleotide Polymorphisms
Infinite Sites Assumption Each site mutates at
most once
00000101011 10001101001 01000101010 01000000011 00
011110000 00101100110
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Short Tandem Repeats
GCTAGATCATCATCATCATTGCTAG GCTAGATCATCATCATTGCTAGTT
A GCTAGATCATCATCATCATCATTGC GCTAGATCATCATCATTGCTAG
TTA GCTAGATCATCATCATTGCTAGTTA GCTAGATCATCATCATCATC
ATTGC
4 3 5 3 3 5
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STR can be used as a DNA fingerprint

• Consider a collection of regions with variable
  length repeats.
• Variable length repeats will lead to variable
  length DNA
• Vector of lengths is a finger-print

4 2 3 3 5 1 3 2 3 1 5 3
individuals
loci
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Structural polymorphisms

• Large scale structural changes (deletions/insertio
  ns/inversions) may occur in a population.
• Copy Number variation
• Certain diseases (cancers) are marked by an
  abundance of these events

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Personalized genome sequencing

• These variants (of which 1,288,319 were novel)
  included
• 3,213,401 single nucleotide polymorphisms (SNPs),
  
• 53,823 block substitutions (2206 bp),
• 292,102 heterozygous insertion/deletion events
  (indels)(1571 bp),
• 559,473 homozygous indels (182,711 bp),
• 90 inversions, as well as numerous segmental
  duplications and copy number variation regions.
• Non-SNP DNA variation accounts for 22 of all
  events identified in the donor, however they
  involve 74 of all variant bases. This suggests
  an important role for non-SNP genetic alterations
  in defining the diploid genome structure.
• Moreover, 44 of genes were heterozygous for one
  or more variants.

PLoS Biology, 2007
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Recombination
00000000 11111111 00011111

• Not all DNA recombines!

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Human DNA

• Not all DNA recombines.
• mtDNA is inherited from the mother, and
• y-chromosome from the father

http//upload.wikimedia.org/wikipedia/commons/b/b2
/Karyotype.png
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Gene Conversion

• Gene Conversion versus single crossover
• Hard to distinguish in a population

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Topic 1 Basic Principles

• In a stable population, the distribution of
  alleles obeys certain laws
• Not really, and the deviations are interesting
• HW Equilibrium
• (due to mixing in a population)
• Linkage (dis)-equilibrium
• Due to recombination

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Hardy Weinberg equilibrium

• Consider a locus with 2 alleles, A, a
• p (respectively, q) is the frequency of A (resp.
  a) in the population
• 3 Genotypes AA, Aa, aa
• Q What is the frequency of each genotype

• If various assumptions are satisfied, (such as
  random mating, no natural selection), Then
• PAAp2
• PAa2pq
• Paaq2

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Hardy Weinberg why?

• Assumptions
• Diploid
• Sexual reproduction
• Random mating
• Bi-allelic sites
• Large population size,
• Why? Each individual randomly picks his two
  chromosomes. Therefore, Prob. (Aa) pqqp 2pq,
  and so on.

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Hardy Weinberg Generalizations

• Multiple alleles with frequencies
• By HW,
• Multiple loci?

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Hardy Weinberg Implications

• The allele frequency does not change from
  generation to generation. Why?
• It is observed that 1 in 10,000 caucasians have
  the disease phenylketonuria. The disease
  mutation(s) are all recessive. What fraction of
  the population carries the mutation?
• Males are 100 times more likely to have the red
  type of color blindness than females. Why?
• Conclusion While the HW assumptions are rarely
  satisfied, the principle is still important as a
  baseline assumption, and significant deviations
  are interesting.

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Recombination
00000000 11111111 00011111
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What if there were no recombinations?

• Life would be simpler
• Each individual sequence would have a single
  parent (even for higher ploidy)
• The genealogical relationship is expressed as a
  tree. This principle is used to track ancestry of
  an individual

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The Infinite Sites Assumption
0 0 0 0 0 0 0 0
3
0 0 1 0 0 0 0 0
5
8
0 0 1 0 1 0 0 0
0 0 1 0 0 0 0 1

• The different sites are linked. A 1 in position
  8 implies 0 in position 5, and vice versa.
• Some phenotypes could be linked to the
  polymorphisms
• Some of the linkage is destroyed by
  recombination

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Infinite sites assumption and Perfect Phylogeny

• Each site is mutated at most once in the history.
  
• All descendants must carry the mutated value, and
  all others must carry the ancestral value

i
1 in position i
0 in position i
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Perfect Phylogeny

• Assume an evolutionary model in which no
  recombination takes place, only mutation.
• The evolutionary history is explained by a tree
  in which every mutation is on an edge of the
  tree. All the species in one sub-tree contain a
  0, and all species in the other contain a 1. Such
  a tree is called a perfect phylogeny.

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Handling recombination

• A tree is not sufficient as a sequence may have 2
  parents
• Recombination leads to loss of correlation
  between columns

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Quiz 1

• Allele, locus, genotype, haplotype
• Hardy Weinberg equilibrium?
• Today Linkage (dis)-equilibrium

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Quiz 2

• Recall that a SNP data-set is a binary matrix.
• Rows are individual (chromosomes)
• Columns are alleles at a specific locus
• Suppose you have 2 SNP datasets of a contiguous
  genomic region.
• One from an African population, and one from a
  European Population.
• Can you tell which is which?
• How long does the genomic region have to be?

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Recombination, and populations

• Think of a population of N individual
  chromosomes.
• The population remains stable from generation to
  generation.
• Without recombination, each individual has
  exactly one parent chromosome from the previous
  generation.
• With recombinations, each individual is derived
  from one or two parents.
• We will formalize this notion later in the
  context of coalescent theory.

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Linkage (Dis)-equilibrium (LD)

• Consider sites A B
• Case 1 No recombination
• Each new individual chromosome chooses a parent
  from the existing haplotype

A B 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0
1 0
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Linkage (Dis)-equilibrium (LD)

• Consider sites A B
• Case 2 diploidy and recombination
• Each new individual chooses a parent from the
  existing alleles

A B 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0
1 1
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Linkage (Dis)-equilibrium (LD)

• Consider sites A B
• Case 1 No recombination
• Each new individual chooses a parent from the
  existing haplotype
• PrA,B0,1 0.25
• Linkage disequilibrium
• Case 2 Extensive recombination
• Each new individual simply chooses and allele
  from either site
• PrA,B(0,1)0.125
• Linkage equilibrium

A B 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0
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LD

• In the absence of recombination,
• Correlation between columns
• The joint probability PrAa,Bb is different
  from P(a)P(b)
• With extensive recombination
• Pr(a,b)P(a)P(b)

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Measures of LD

• Consider two bi-allelic sites with alleles marked
  with 0 and 1
• Define
• P00 PrAllele 0 in locus 1, and 0 in locus 2
• P0 PrAllele 0 in locus 1
• Linkage equilibrium if P00 P0 P0
• D abs(P00 - P0 P0) abs(P01 - P0 P1)

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LD over time

• With random mating, and fixed recombination rate
  r between the sites, Linkage Disequilibrium will
  disappear
• Let D(t) LD at time t
• P(t)00 (1-r) P(t-1)00 r P(t-1)0 P(t-1)0
• D(t) P(t)00 - P(t)0 P(t)0 P(t)00 - P(t-1)0
  P(t-1)0 (Why?)
• D(t) (1-r) D(t-1) (1-r)t D(0)

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Other measures of LD

• D is obtained by dividing D by the largest
  possible value
• Dmax max P1P1, P0P1, P1P0, P0P0
• Ex D abs(P11- P1 P1)/ Dmax
• ? D/(P1 P0 P1 P0)1/2
• Let N be the number of individuals
• Show that ?2N is the ?2 statistic between the two
  sites

1
0
P00N
0
P0N
Site 1
1
Site 2
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LD over distance

• Assumption
• Recombination rate increases linearly with
  distance
• LD decays exponentially with distance.
• The assumption is reasonable, but recombination
  rates vary from region to region, adding to
  complexity
• This simple fact is the basis of disease
  association mapping.

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LD and disease mapping

• Consider a mutation that is causal for a disease.
  
• The goal of disease gene mapping is to discover
  which gene (locus) carries the mutation.
• Consider every polymorphism, and check
• There might be too many polymorphisms
• Multiple mutations (even at a single locus) that
  lead to the same disease
• Instead, consider a dense sample of polymorphisms
  that span the genome

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LD can be used to map disease genes
LD
0 1 1 0 0 1
D N N D D N

• LD decays with distance from the disease allele.
• By plotting LD, one can short list the region
  containing the disease gene.

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(No Transcript)
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• 269 individuals
• 90 Yorubans
• 90 Europeans (CEPH)
• 44 Japanese
• 45 Chinese
• 1M SNPs

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LD and disease gene mapping problems

• Marker density?
• Complex diseases
• Population sub-structure

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Topic 2 Simulating population data

• We described various population genetic concepts
  (HW, LD), and their applicability
• The values of these parameters depend critically
  upon the population assumptions.
• What if we do not have infinite populations
• No random mating (Ex geographic isolation)
• Sudden growth
• Bottlenecks
• Ad-mixture
• It would be nice to have a simulation of such a
  population to test various ideas. How would you
  do this simulation?