2006.2.24

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• 2006.2.242006.6.16
• ?????????????

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???? I

• Week 1 Course Overview, Basic Knowledge of
  Genome Biology, Basic Principles of Population
  Genetics
• Week 2 Linkage Analysis for Family Data I
• Week 3 Linkage Analysis for Family Data II
• Week 4 Introduction to Microarray Data Analysis
• Week 5 Nature of Discrete Genetic data
  Estimating Frequencies
• Week 6 Disequilibrium Diversity
• Week 7 Population Structure, Individual
  Identification Outcrossing And Selection
• Week 8 Linkage
• Week 9 Midterm

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???? II

• Week 10. Phylogeny Reconstruction Quantitative
  Genetics I
• Week 11 Quantitative Genetics II
• Week 12 QTL mapping I
• Week 13 QTL mapping II
• Week 14 Population-based Association Analysis
• Week 15 Family-based Association Analysis
• Week 16 Multipoint Association Analysis
• Week 17 Genomewide Association Analysis

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Thomas Andrew Knight (1759-1838)
Thomas Andrew Knight, the first man to practice
large-scale, systematic strawberry breeding,
which produced two famous varieties the Downton
and the Elton. As a founder and long-time
president of England's Royal Horticultural
Society, he encouraged others to breed better
varieties of fruits and vegetables.
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Thomas Andrew Knight

• Knight's father was a Herefordshire clergyman who
  died when his son was five years old. The boy's
  education was neglected, and until he was nine he
  remained almost illiterate. Since he was unable
  to read as a child, he concentrated his curiosity
  on the plant and animal life on the family
  estate. One day, says a story, he saw a gardener
  planting beans. The boy asked why the man was
  planting sticks of wood and was told they would
  grow up to be beans. The gardener's prediction
  came true. Knight immediately planted his pocket
  knife and waited in anticipation for the
  miraculous growth of new knives. When the
  experiment failed he sat down to consider the
  difference in the two cases. Already he was
  engrossed with the mysteries of the vital
  processes in plants, a preoccupation which would
  lead later to his reputation as a brilliant plant
  physiologist.

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Downton (1817)
Elton (1828)
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• Knight didnt count,
• Mendel did count.

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By the 1890's, the invention of better
microscopes allowed biologists to discover the
basic facts of cell division and sexual
reproduction.  The focus of genetics research
then shifted to understanding what really happens
in the transmission of hereditary traits from
parents to children.  A number of hypotheses were
suggested to explain heredity, but Gregor Mendel,
a little known Central European monk, was the
only one who got it more or less right.  His
ideas had been published in 1866 but largely went
unrecognized until 1900, which was long after his
death.  His early adult life was spent in
relative obscurity doing basic genetics research
and teaching high school mathematics, physics,
and Greek in Brno (now in the Czech Republic). 
In his later years, he became the abbot of his
monastery and put aside his scientific work.
Gregor Mendel    1822-1884 
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James Watson 1928--
Francis Crick 1916--2004
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Slides 1536 are edited from
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and
Bonnie Berger MIT
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The human genome

• The cell is the fundamental working
• unit of every living organism.
• Humans trillions of cells (metazoa)
• other organisms like yeast one cell
• (protozoa).
• Cells are of many different types (e.g.
• blood, skin, nerve cells), but all can be
• traced back to a single cell, the
• fertilized egg.

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Nucleus
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Eukaryota More on Morphology
                                                  
                                                  
                                   
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The human genome in numbers

• 23 pairs of chromosomes
• 2 meters of DNA
• 3,000,000,000 bp
• 35 M (males 27M, females 44M)
• 30,000-40,000 genes.

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The human genome

• The genome, or blueprint for all
• cellular structures and activities in our
• body, is encoded in DNA molecules.
• Each cell contains a complete copy of
• the organisms genome.

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The human genome

• The human genome is distributed
• along 23 pairs of chromosomes
• 22 autosomal pairs
• the sex chromosome pair, XX for
• females and XY for males.
• In each pair, one chromosome is
• paternally inherited, the other
• maternally inherited (cf. meiosis).

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The human genome

• Chromosomes are made of compressed
• and entwined DNA.
• A (protein-coding) gene is a segment
• of chromosomal DNA that directs the
• synthesis of a protein.

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DNA

• A deoxyribonucleic acid or DNA molecule is a
• double-stranded polymer composed of four
  basic
• molecular units called nucleotides.
• Each nucleotide comprises a phosphate group, a
• deoxyribose sugar, and one of four nitrogen
  bases
• adenine (A), guanine (G), Cytosine (C), and
• thymine (T)
• The two chains are held together by hydrogen
• bonds between nitrogen bases.
• Base-pairing occurs according to the following
• rule G pairs with C, and A pairs with T.

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Genes control the making of cell parts

• The gene is a fundamental unit of inheritance
• DNA molecule contains tens of thousands of genes
• Each gene governs the making of one functional
  element,
• one part of the cell machine
• Every time a part must be made, a piece of the
  genome
• is copied, transported, and used as a
  blueprint
• RNA is a temporary copy
• The medium for transporting genetic information
  from
• the DNA information repository to the
  protein-making
• machinery is and RNA molecule
• The more parts are needed, the more copies are
  made
• Each mRNA only lasts a limited time before
  degradation

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The genetic code

• DNA sequence of four different nucleotides.
• Protein sequence of twenty different amino
• acids.
• The correspondence between DNAs four-letter
• alphabet and a proteins twenty-letter
  alphabet is
• specified by the genetic code, which relates
• nucleotide triplets or codons to amino acids.

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Big Picture
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Basic human genetics

• 46 chromosomes
• 22 pairs of autosomal chromosomes and
• 2 sex chromosomes
• Double stranded DNA
• 4 bases A Adenine

p-arm T Thymine q-arm G
Guanine Centromere C Cytosine Approximat
ely 3 000 000 000 basepairs in the human genome
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The Central Dogma of Molecular Biology

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Basic Principles of Population Genetics

• Reference Kenneth Lange
• Mathematical and Statistical Methods for Genetic
  Analysis

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Mendels experiment data
Trait           Characteristics          Dominant
     Recessive
stem length tall short 787 277 277
pod shape inflated constricted 882 299 299
seed shape round wrinkled 5474 1850 1850
seed colour yellow green 6022 2001 2001
flower position axial terminal 651 207 207
flower colour purple white 705 224 224
pod colour green yellow 428 152
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Mendels First Law

• First Generation RR x rr
• Second Generation Rr x Rr (self cross)
• Third generation RRRr (3/4)
• rr (1/4)

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Mendels Second LawIndependent two traits
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What if the traits are not independent?
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Genetic and physical maps

• Physical distance number of base pairs
• (bp).
• Genetic distance expected number of
• crossovers between two loci, per chromatid,
• per meiosis.
• Measured in Morgans (M) or centiMorgans
• (cM).
• 1cM 1 million bp (1Mb).

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Definition

• The genetic map distance (in units of Morgans)
  between two loci is defined as the expected
  (average) number of crossovers occuring on a
  single chromosome (in a gamete) between two loci.
• Ex Chromosome 1 Physical length 263 Mb
• Female map length 3.76 M 376 cM
• Male map length 2.21 M 221 cM
• Note 1 Mb . 1 cM

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Crossover, Recombination
Mothers Chromosomes
Fathers Chromosomes
Sibling 1
Crossover
Recombination crossover occurs odd number of
times
Haldane Mapping Fun. A Recombination freq. Fun
between 2 genes Q(d)(1-exp(-2ld))/2 Assume that
the event of Crossover across a Chromosome is a
Poisson Process
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Haldane Mapping Function

• Assume crossover happens as a Poisson Process
  along the chromosome
• rate
• physical distance d

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Haldane Mapping Function

• P( Recombination between A and B)
• P( of crossover odd number
• between A, B)

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Haldane Mapping Function
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• The following 5 slides are to help you
• keep a reference for the basic human genetics
  terminologies.

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1.2 Genetics Background

• The cells of all organisms, from bacteria to
  humans, contain one or more sets
• of a basic DNA complement that is unique to the
  species. This fundamental
• complement of DNA is called a genome. The genome
  may be subdivided
• into chromosomes, each of which is a very long
  single continuous DNA
• molecule. In its turn, a chromosome can be
  demarcated along its length
• into thousands of functional regions called
  genes. The word gene is used
• originally as the unit factor of heredity. In
  modern terminology, a gene
• is a specific coding sequence of DNA. The
  alternate forms of a gene are
• called alleles. Two persons who share alleles
  from a common ancestor are
• called Identical by Descent, abbreviated as IBD.
  The pair of alleles in
• an individual constitutes that individuals
  genotype. The expression of a
• particular genotype is called a phenotype.

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• Sperm and egg are created in a process called
  meiosis by splitting
• the chromosome pairs in half and creating cells
  with only twenty-three single
• chromosomes. When an embryo is formed from an egg
  and a sperm cell,
• it again has a full set of twenty-three pairs,
  with half of each pair coming
• from mother and half from the father. In meiosis,
  homologous chromosomes
• pair up, and they may exchange genetic material
  between them during a
• process called crossover. A chromosome in a
  gamete, which is a mixture
• of the two homologous chromosomes in the parent,
  can be modeled in the

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• following way. It starts with either homologous
  chromosome randomly, moves
• a random distance along this chromosome and then
  switches to the other
• chromosome. It moves another random distance, and
  switches again. This
• process continues untill the end of the
  chromosome is reached.

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• There are two kinds of distance metric for
  chromosome. Physical dis-
• tances are measured in terms of number of base
  pairs (abbreviated as bp)
• Between two points. The units for physical
  distances are bp and kb (1000
• bp). Genetic distances are defined as the
  expected numbers of crossovers
• between two points with unit Morgan. Another
  common unit for genetic
• distances is cM (centi-Morgan). Different models
  underlying the crossover
• process will give different genetic distances.
  The most popular one is Hal-
• dane model, saying that the random distance
  waiting for a crossover to occur
• is an exponential R.V. this implies that the
  number of crossovers along the
• chromosomes is a Poisson process. The genetic
  length of a a human genome is
• about 35 Morgans. See Ott (1991).

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• If two alleles on the same parental
  chromosomes are passed to the offspring
• together, one says that there is no recombination
  between them otherwise,
• one says that there is recombination. Another way
  to explain recombination
• Is that there is odd number of crossovers between
  two genes. When two genes
• are inherited independently of each other, the
  probabilities for recombination
• and no recombination are equal, i.e., ½. Two
  genes are linked if the
• recombination frequency between them is smaller
  than ½. (Notice that the
• recombination frequency is never greater than ½.)
  A mapping function
• is a mapping between the recombination frequency
  and genetic distance for
• two loci. For example, under the Haldane model,
  the mapping function for

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Hardy-Weinberg Equilibrium

• The genotype frequencies reach steady states
  through the generations.
• Assumptions
• 1)Infinite population size
• 2)Discrete generations
• 3)Random Mating
• 4)No Selection
• 5)No migration
• 6) No mutation
• 7) Equal initial genotype frequencies in 2 sexes.
  

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Hardy-Weinberg Equilibrium

• Consider a single locus with two alleles (A, a),
  the possible genotypes are (AA, Aa, aa)
• Question How the genotype frequencies propagate
  through the generation?

genotype freq.
P0 P(A) U0V0 Q0 P(a) W0V0 1- P0
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H.W. Equilibrium
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HW Equilibrium for X-linked loci

• Assume at generation n
• gene frequency for female
• gene frequency for male
• gt

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HW Equilibrium for X-linked loci

• Proof Under the similar conditions,
• we have
• gt

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HW Equilibrium for X-linked loci

• a 2
• a -1

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Linkage Equilibrium

• alleles
• frequency
• haplotype frequency of
  in the
• generation
• recombination frequency(
  ),

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Linkage Equilibrium

• 
  if

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Selection reproduction capacity

• E.g.
• let (fitness) be the
  expected genetic contributions to the next
  generation for the given genotypes.
• W.L.O.G.
• let
  
• where

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Selection

• Let be the allele frequency of A at
  generation n. for allele a

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Selection
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Selection

• To reach equilibrium state
• or 0 or
• Assume r, s different sign
• if r gt 0, if
• gt extinction of
  A
• if , s gt 0 gt extinction of a

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Selection

• if r, s have the same sign

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Selection

• if r lt 0, s lt 0,
• 
  unstable equilibrium
• 
  

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Selection

• If r gt 0, s gt 0,
• stable equilibrium
  

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Heterozygote advantage (r, s both positive)

• Geneticists have suggested that reverse recessive
  diseases are maintained at high frequency by the
  mechanism of Heterozygote advantage.
• The best evidence favoring this hypothesis exists
  for sickle cell anemia. A single dose of the
  sickle cell gene appears to confer protection
  against malaria.

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Sickle Cell Anemia
normal hemoglobin Hb 2 alpha and 2 beta
chains form a 4 chain tetramer
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Sickle Cell Anemia
beta chains bind with other beta chains in RBC
when deoxygenatedpolymerization occursHb
polymers distort RBC into sickled
shapesvaso-occlusion