Understanding Molecular Evolution

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Understanding Molecular Evolution
Marco Salemi, Ph.D.
Dept. Pathology U.F. Gainesville, FL (U.S.A.)
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Before Darwin

• The first genealogy These are the generations
  of Shem Shem was an hundred years old, and begat
  Arphaxad two years after the flood And Shem
  lived after he begat Arphaxad five hundred years,
  and begat sons and daughters. And Arphaxad lived
  five and thirty years, and begat Salah
  Genesis 11
• Aristotle animal-plants classification
• Linnaeus (18th Century) familiar hierarchical
  classification scheme of life kingdom, family,
  class, order, genus and species

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The evolutionary thinking

• Russel Wallace writes to Charles Darwin (June
  17th 1858)

• Ernst Haeckel (mid-19th Century) the tree of
  life

• The neo-synthesis (Fisher, Heldane, and Wright,
  1930-1950)

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The molecular revolution

• Nuttal, 1904 Serological cross-reactions to
  study phylogenetic relationships among various
  group of animals.
• Watson and Crick beautiful helix!
• Zuckerland and Pauling, 1965 molecular clocks.
• Fitch Margoliash, 1967 Construction of
  phylogenetic trees.A method based on mutation
  distances as estimated from cytochrome c
  sequences is of general applicability (Science,
  155279-284).
• Kimura, 1968 Evolutionary rate at the molecular
  level (Nature, 217624-626).

The birth of molecular evolution
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FUNDAMENTALS OF MOLECULAR EVOLUTION
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Genetic information

• The phenotype of an organism is always the result
  of its genetic information and the interaction
  with the environment.
• Genetic information is stored in double stranded
  DNA for most organisms or RNA for some viruses.
• This genetic information can be coding (for
  proteins) or non-coding (e.g., rRNA, regulatory
  sequences).
• The genetic code is universal for all organisms,
  with only a few exceptions such as the
  mitochondrial code.

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Genetic code

• The genetic code is a triplet of 4 possible bases
  (AGCT), thus there are 64 codons 61 sense codes
  encoding 20 amino acids, and 3 non-sense codes
  encoding stop codons.
• The genetic code is degenerated in such a way
  that mutations at the 3rd cdp only in 30, at 2nd
  cdp always, and at 1st cdp in 96 of cases result
  in an amino acid change, causing a non-synonymous
  mutations. The other changes are silent or
  synonymous.

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Transitions and transversions
?
A
C
?
?
?
?
T
G
?

• Transitions (?) are purine (A, G) or pyrimidine
  (C, T) mutations Pu-Pu, Py-Py
• Transversions (?) are purine to pyrimidine
  mutations or the reverse (Pu-Py, or Py-Pu).

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Point mutations and the genetic code

• 4 possible transitions A?G, C?T
• 8 possible transversions A?C, A?T,
  G?C, G?T
• Thus if mutations were random, transversions are
  2 times more likely than transitions.
• Due to steric hindrance, the opposite is true,
  transitions occur in general more often than
  transversions (2-15 times more, depending on the
  gene region and the species).

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Transversions result in more disruptive amino
acid changes.
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Other mutations

• Insertions and deletions (indels). Usually by 3
  nucleotides in coding regions.
• Recombination. Often in viruses.
• Gene (or chromosome) duplication
• Lateral gene transfer

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Genetic variation in populations

• Polymorphism 2 (or more) mutations co-exist in a
  population of organisms.
• The variants at a particular position (or locus)
  are called alleles.
• Diploid organisms can be homozygous (2 identical
  alleles) or heterozygous (2 different alleles) at
  a particular locus.
• For viruses, the term quasispecies is often used.
• The variation in a population can be described in
  allele frequencies or gene frequencies

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Evolution and fixation of mutations

• Evolution is the consecutive fixation of
  mutations
• The fixation rate of such a polymorphism is in
  fact the evolutionary rate. This is dependant on
• Mutation rate
• Generation time
• Evolutionary forces, such as fitness, selective
  pressure, population size

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Population genetics

• Selective Pressure
• Effective Population size (Ne)
• Random Genetic drift

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Darwinian theory (neo-synthesis)

• A new mutation can quickly become FIXED in the
  population as a result of
• Natural Selection
• The differential reproduction of genetically
  distinct individuals or genotypes within a
  population
• Fitness
• Is a measure of the individual's ability to
  survive and reproduce

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Population dynamics
1
fixed mutation
polymorphism maintained
ALLELE FREQUENCY
lost mutation
0
TIME
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Selective pressure

• Positive selective pressure mutant is more fit
• Negative selective pressure mutant is less fit
• Balancing selection heterozygote is more fit
• Most synonymous mutations can be considered
  neutral
• Non-synonymous mutations are always subject to
  selective pressure

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Effective population size
1st generation N10, Ne5
2nd generation N10, Ne4
3rd generation N10, Ne3
4th generation N5, Ne2
Bottleneck event
5th generation N3, Ne2
Mutation event
6th generation N9, Ne4
7th generation N11
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Deterministic or stochastic model of evolution

• Deterministic fixation of mutations is entirely
  dependent on selective pressure. Alleles do not
  get lost or fixed by chance (by accident).
• Stochastic fixation is dependent on chance
  events. Chance effect is much larger than
  selective pressure, random genetic drift plays a
  big role.
• Whether or not selective pressure plays a role
  can be tested by comparing synonymous with
  non-synonymous rates of substitution.

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Neo-Darwinism vs Neutral evolution

• Neo-Darwinism
• Random mutations are source of variation.
• Selective pressure is cause of adaptive
  evolution survival of the fittest.
• Neutral evolution (Kimura)
• A majority of non-synonymous mutations are
  deleterious, there is a strong negative selective
  pressure.
• Most mutations that become fixed are neutral,
  rarely positive selective pressure is strong
  enough to fix adaptive mutations. Random genetic
  drift is strong.

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Adaptation by evolution in a fitness landscape
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Environmental factors

• Once an organism has reached the adaptive peak,
  evolution continues mainly according to the
  neutral model.
• Changes in the environment can reshape the
  adaptive landscape, and stimulate again adaptive
  evolution.
• Sudden changes in the environment often cause
  intense adaptive evolution and the origin of new
  species. Example mammalian diversification
  after the disappearance of dinosaurs.

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Adaptive evolution

• Neutral evolution is the major factor
  contributing to variation at the molecular level.
• The phenotypic effects of adaptive evolution can
  be more easily appreciated when long time periods
  are considered.
• Usually, only a minority of sites in a
  codingregion are subject to positive selection

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Mutation and evolutionary rate (1)

• New mutation in a diploid population of N
  individuals
• Fixation time t (Kimura and Otha 1969)
• t 2/s ln (2N) (s selective advantage)
• t 4N for neutral mutations
• Evolutionary Rate (or substitution rate), r
• number of mutants reaching fixation per unit time
• Mutation Rate, m
• rate of mutation at the DNA level (biochemical
  concept)

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Mutation and evolutionary rate (2)

• q 1/2N frequency of a new mutation
• m rate of neutral mutations
• 2Nm number of mutants arising per generation
• probability of fixation p
• p 1-exp(-4Nsq)/1-exp(-4Ns)
• when s?0, exp(-4Nsq) ? 1- 4Nsq, and exp(-4Ns) ?
  1- 4Ns
• p q 1/2N
• Evolutionary rate number of mutants arising per
  generation x probability of fixation
• r 2Nm 1/2N m (Kimura, 1968)

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The classic molecular clock

• The molecular clock hypothesis postulates that
  for any given macromolecule (a protein or a DNA
  sequence) the rate of evolution is approximately
  constant over time in all evolutionary lineages
  (Zuckerkandl and and Pauling 1962 and 1965)

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A global molecular clock?
The hypothesis known as global clock was based on
the observation that a linear relation seems to
exist between the number of amino acid
substitutions between homologous proteins of
different species, and the species divergence
times estimated from archaeological data.
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Why is the molecular clock attractive ?

• If macromolecules evolve at constant rates, they
  can be used to date species-divergence times and
  other types of evolutionary events, similar to
  the dating of geological time using radioactive
  elements
• Phylogenetic reconstruction is much simpler under
  constant rates that under nonconstant rates
• The degree of rate variation among lineages may
  provide much insight into the mechanisms of
  molecular evolution (e.g. Kimura 1983 Gillespie
  1991 Salemi et al., 1999).

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Estimating ancestral divergence times under the
clock hypothesis
knowing a divergence time T r dac/2T all the
other divergence dates in the internal nodes of
the tree can be estimated using the rate r
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Global vs Local clocks

• The molecular clock hypothesis is in perfect
  agreement with the neutral theory of evolution
  (Kimura 1968 Kimura 1983).
• The existence of a clock seems to be a major
  support of the neutral theory against natural
  selection
• The global clock hypothesis is today known to be
  untrue.
• Factors like different metabolic rates, different
  lifespan, and different efficiency in the DNA
  repair mechanisms between distantly related
  species are responsible for different
  evolutionary rates of homologous genes.

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Local clocks

• In general the evolutionary rate r can be
  expressed as
• r f m
• f fraction on neutral mutation
• m mutation rate
• If f is constant
• and
• m is constant
• The rate of evolution is constant (molecular
  clock)
• Local molecular clocks have been demonstrated
  for a number of closely related species (Li,
  1997), human and chimp mtDNA (Ingman et al,
  2000), and primate retroviruses (Salemi et al.,
  2000).

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Evolutionary rates of organisms
nucleotide substitutions per site per year
10 - 9
10 - 8
10 - 7
10 - 6
10 - 5
10 - 4
10 - 3
10 - 2
10 - 1
cellular genes
RNA viruses
DNA viruses
Human mtDNA
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Homology - Similarity

• Homology
• The tree of life implies one origin for all life
  on earth, thus all sequences are in fact
  descendant from the same sequence through
  mutations.
• The term homology is used when two sequences
  share a common ancestor recent enough such that
  this is still detectable in their sequence. An
  unambiguous sequence alignment can be obtained.
• Similarity
• Any 2 sequences can be compared and the
  similarity computed ( nt or aa identity).
• Allowing gaps, 2 non-homologous nt sequences can
  have a similarity of up to 50 for aa sequence
  this can be up to 20.

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The data used for phylogenetic analysis

• Morphological characters
• Fossils (not for viruses)
• Genetic data
• AA or NT sequences
• RFLP
• Allele frequencies
• ...
• A combination of these data

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Homoplasy

• When the linear relationship between time and
  evolution is disturbed
• convergent evolution (for example, HIV immune
  escape in the V3 loop)
• sequence reversal
• multiple hits
• parallel substitution

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Homology and Homoplasy

• Homology
• two identical nt in different sequences are
  homologous if and only if both sequences acquired
  that nt directly from a common ancestor

• Homoplasy
• two identical nt in different sequences are
  homoplasious when they evolved independently from
  different ancestors

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Alignments - Positional homology
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Pairwise sequence alignments

• Set up a matrix with the characters of the two
  sequences
• Score identities in the matrix with 1,
  differences with 0
• Gap penalties (GP) open gap penalty (e.g. -2)
  and extending gap penalty (e.g.-1). GP-2L(-1)
  with Llength of gap.
• End gaps are scored (global alignment) or not
  (local alignment)
• An alignment is a path through the matrix. Its
  overall score is the sum of the scores on its
  path, plus gap penalties
• The alignment with the best score is chosen as
  the optimal alignment

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Scoring a path in the matrix

• Take diagonal steps only
• Dont use characters twice
• Skipping characters results in insertions or
  deletions

G A A C T T A A 0 1 1 0 0 0 1 C 0 0 0 1 0 0 0
C 0 0 0 1 0 0 0 T 0 0 0 0 1 1 0 T 0 0 0 0 1 1 0
T 0 0 0 0 1 1 0
-1
GAACTTA-ACCTTT
Score 4-13
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Scoring another path
-2
G A A C T T A A 0 1 1 0 0 0 1 C 0 0 0 1 0 0 0
C 0 0 0 1 0 0 0 T 0 0 0 0 1 1 0 T 0 0 0 0 1 1 0
T 0 0 0 0 1 1 0
-1
GAAC-TTA--ACCTTT
Score 4-2-11
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Multiple sequence alignments

• Score all possible pairwise alignments Dij
• Find the best multiple alignment that gives the
  highest weighted sum of pairs (WSP)
• WSP??WijDij
• Wij is a weight that can be given e.g. to give
  less weight to overrepresented closely related
  sequences
• ClustalW
• sequences are aligned in pairs to create a
  distance matrix based on their alignment score
• scores are down-weighted according to how closely
  related they are
• this distance matrix is used to make a guide tree
  (see phylogenetic analysis methods)
• the guide tree is used to cluster the sequences
  during the stepwise alignment

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Phylogenetic analysis reconstructing the
history of a gene

• Only alignments of homologous positions can be
  used for phylogenetic analysis
• point mutations
• indels add gaps to achieve positional homology
• Recombinations disturb a phylogenetic analysis,
  since the two parts of the recombined gene have a
  different phylogenetic history.
• In case of gene duplication (paralogous genes)
  followed by speciation (orthologous genes)
  reconstruct the species tree from orthologous
  genes

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Rooted phylogenetic tree
Branches can rotate freely. Branching order is
called topology
External node or Operational Taxonomic Units
OTU (or Taxon)
A
G
node
H
B
J
C
K
Internal node or Hypothetical Taxonomic Units
HTU (or Ancestor)
D
I
root
E
branch
F
TIME
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Unrooted phylogenetic tree

• Root node K disappeared
• To root an unrooted tree
• root by outgroup, e.g. use F as outgroup
• midpoint rooting

Monophyletic taxa
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Coalescence time on a rooted tree
Most recent common ancestor of all taxa (MRCA)
TIME
Coalescence time of all taxa
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Trees combinatorial explosions

• Number of unrooted trees for n taxa
• NU(2n-5)!/2n-3(n-3)!
• Number of rooted trees for n taxa
• NR(2n-3)!/2n-2(n-2)!

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Phylogenetic tree using aligned sequences gene
tree

• When from orthologous genes the phylogenetic
  tree can be used to reconstruct the species tree
  (cladogram speciation over time).
• However, considering polymorphisms, the nodes do
  not necessarily coincide exactly with speciation.
  
• Similar for viruses if quasispecies variation
  exists, the coalescence time in a transmission
  case does not necessarily coincide with the
  transmission time.
• Molecular clock calculations to estimate the
  coalescence time can only be used if the clock
  holds

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Gene divergence may predate species divergence
Past Present
Gene splitting
Gene splitting
Population splitting
A B
C D
E F
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Gene trees vs Species trees

• Gene and species trees may be different

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Substitution models

• During evolution, multiple hits can have happened
  at a single position the evolutionary distance
  is almost always larger than the dissimilarity (
  nt or aa divergence)

Expected difference based on number of mutations
that happened
Correction
Sequence difference
Observed difference
Time/Evolutionary distance
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Phylogenetic signal / phylogenetic noise

• Before making any phylogenetic inference it is
  necessary to investigate the presence of
  phylogenetic signal in the data set of aligned
  sequences
• WHY ?
• Sequences could be not enough informative about
  the phylogeny of the taxa under study
  (phylogenetic signal too low)
• Sequences could be too divergent (positional
  homology is lost)
• Sequences could be saturated
• The data could not evolve according to a strictly
  bifurcating tree

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DNA dot matrix

• A fast way to evaluate whether or not two
  sequences can be unambiguously aligned is to
  perform a DNA dot matrix
• Homologous regions usually show a clear diagonal
  in the dot matrix

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DNA dot matrix
A T T C T G A
T C T G A A A
A T T C G G A
A T T C G G A

• Sequences that can be unambiguously aligned show
  a clear diagonal in the dot matrix

• Sequences that cannot be unambiguously aligned
  show no diagonal in the dot matrix

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HIV/SIV DNA env dot matrix (1)

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HIV/SIV DNA env dot matrix (2)
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Substitution Saturation

• If the sequences in the data set diverged long
  ago, the phylogenetic signal could be lost
• It can be proved that two random nucleotide
  sequences will share on average 25 similarity
  just by accident if gaps are not allowed, and up
  to 50 allowing gaps sequences with similar base
  composition will artificially cluster together,
  irrespective of the true phylogeny
• Third codon positions usually saturate much
  faster than first or second
• Transitions usually saturate much faster than
  transversions
• A fast way to check for substitution saturation
  in a set of aligned sequence is to plot the
  genetic distance for each pair wise comparison
  versus the number of transitions and
  transversions between each pair
• usually Ti occur more often than Tv. However,
  when the saturation point is reached, Tv tend to
  outnumber Ti

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d
Transitions A?G, C?T
- - - - - - -
Transversions A?C, T C?A, G
Divergence time (Mya)
5 10 15
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Implicit and explicit models of evolution

• Distance matrix methods and maximum likelihood
  methods can correct for homoplasy by defining
  evolutionary parameters such as a nucleotide
  substitution matrix (additional parameters can
  also be e.g. rate heterogeneity). These methods
  therefore use an explicit model of evolution
  whose parameters can be estimated from the data.
• Parsimony methods can not correct for homoplasy,
  they use an implicit model of evolution, they
  assume that the most parsimonious tree (that is
  the tree with the smallest number of mutations)
  is evolutionary also the most likely one.