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Introduction to. Bioinformatics. Introduction to Bioinformatics. LECTURE 5: Variation within and between species * Chapter 5: Are Neanderthals among us?. Neandertal, Germany, 1856. Initial interpretations: * bear skull * pathological idiot * Old Dutchman.

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**Introduction to**Bioinformatics**Introduction to Bioinformatics.**LECTURE 5: Variation within and between species * Chapter 5: Are Neanderthals among us?**Neandertal, Germany, 1856**Initial interpretations: * bear skull * pathological idiot * Old Dutchman ...**Introduction to BioinformaticsLECTURE 5: INTER- AND**INTRASPECIES VARIATION**Introduction to BioinformaticsLECTURE 5: INTER- AND**INTRASPECIES VARIATION**Introduction to BioinformaticsLECTURE 5: INTER- AND**INTRASPECIES VARIATION**Introduction to BioinformaticsLECTURE 5: INTER- AND**INTRASPECIES VARIATION • 5.1 Variation in DNA sequences • * Even closely related individuals differ in genetic sequences • * (point) mutations : copy error at certain location • * Sexual reproduction – diploid genome**Diploid chromosomes**Introduction to Bioinformatics5.1 VARIATION IN DNA SEQUENCES**Mitosis: diploid reproduction**Introduction to Bioinformatics5.1 VARIATION IN DNA SEQUENCES**Meiosis: diploid (=double) → haploid (=single)**Introduction to Bioinformatics5.1 VARIATION IN DNA SEQUENCES**Introduction to Bioinformatics5.1 VARIATION IN DNA SEQUENCES*** typing error rate very good typist: 1 error / 1K typed letters * all our diploid cells constantly reproduce 7 billion letters * typical cell copying error rate is ~ 1 error /1 Gbp**GERM LINE**• Reverse time and follow your cells: • Now you count ~ 1013 cells • One generation ago you had 2 cells ‘somewhere’ in your parents body • Small T generations ago you had (2T – multiple ancestors) cells • Large T generations ago you counted #(fertile ancestors) cells • Congratulations: you are 3.4 billion years old !!! • Fast-forward time and follow your cells: • Only a few cells in your reproductive organs have a chance to live on in the next generations • The rest (including you) will die … Introduction to Bioinformatics5.1 VARIATION IN DNA SEQUENCES**Introduction to Bioinformatics5.1 VARIATION IN DNA SEQUENCES**GERM LINE MUTATIONS This potentially immortal lineage of (germ) cells is called the GERM LINE All mutations that we have accumulated are en route on the germ line**Introduction to Bioinformatics5.1 VARIATION IN DNA SEQUENCES*** Polymorphism : multiple possibilities for a nucleotide: allelle * Single Nucleotide Polymorphism – SNP (“snip”) point mutation example: AAATAAA vs AAACAAA * Humans: SNP = 1/1500 bases = 0.067% * STR = Short Tandem Repeats (microsatelites) example: CACACACACACACACACA … * Transition - transversion**Purines – Pyrimidines**Introduction to Bioinformatics5.1 VARIATION IN DNA SEQUENCES**Introduction to Bioinformatics5.1 VARIATION IN DNA SEQUENCES**Transitions – Transversions**Introduction to BioinformaticsLECTURE 5: INTER- AND**INTRASPECIES VARIATION • 5.2 Mitochondrial DNA • * mitochondriae are inherited only via the maternal line!!! • * Very suitable for comparing evolution, not reshuffled**Introduction to Bioinformatics 5.2 MITOCHONDRIAL DNA**H.sapiens mitochondrion**Introduction to Bioinformatics 5.2 MITOCHONDRIAL DNA**EM photograph of H. Sapiens mtDNA**Introduction to BioinformaticsLECTURE 5: INTER- AND**INTRASPECIES VARIATION • 5.3 Variation between species • * genetic variation accounts for morphological-physiological-behavioralvariation • * Genetic variation (c.q. distance) relates to phylogeneticrelation (=relationship) • * Necessity to measure distances between sequences: a metric**Substitution rate*** Mutations originate in single individuals * Mutations can become fixed in a population * Mutation rate: rate at which new mutations arise * Substitution rate: rate at which a species fixes new mutations * For neutral mutations Introduction to Bioinformatics5.3 VARIATION BETWEEN SPECIES**Introduction to Bioinformatics5.3 VARIATION BETWEEN SPECIES**Substitution rate and mutation rate * For neutral mutations * ρ = 2Nμ*1/(2N) = μ * ρ = K/(2T)**Introduction to BioinformaticsLECTURE 5: INTER- AND**INTRASPECIES VARIATION 5.4 Estimating genetic distance * Substitutions are independent (?) * Substitutions are random * Multiple substitutions may occur * Back-mutations mutate a nucleotide back to an earlier value**Introduction to Bioinformatics 5.4 ESTIMATING GENETIC**DISTANCE Multiple substitutions and Back-mutations conceal the real genetic distance GACTGATCCACCTCTGATCCTTTGGAACTGATCGT TTCTGATCCACCTCTGATCCTTTGGAACTGATCGT TTCTGATCCACCTCTGATCCATCGGAACTGATCGT GTCTGATCCACCTCTGATCCATTGGAACTGATCGT observed : 2 (= d) actual : 4 (= K)**Introduction to Bioinformatics 5.4 ESTIMATING GENETIC**DISTANCE * Saturation: on average one substitution per site * Two random sequences of equal length will match for approximately ¼ of their sites * In saturation therefore the proportional genetic distance is ¼**Introduction to Bioinformatics5.4 ESTIMATING GENETIC**DISTANCE * True genetic distance (proportion): K * Observed proportion of differences: d * Due to back-mutations K ≥ d**Introduction to Bioinformatics 5.4 ESTIMATING GENETIC**DISTANCE SEQUENCE EVOLUTION is a Markov process: a sequence at generation (= time) t depends only the sequence at generation t-1**Introduction to Bioinformatics 5.4 ESTIMATING GENETIC**DISTANCE The Jukes-Cantor model Correction for multiple substitutions Substitution probability per site per second is α Substitution means there are 3 possible replacements (e.g. C → {A,G,T}) Non-substitution means there is 1 possibility (e.g. C → C)**Introduction to Bioinformatics 5.4 THE JUKES-CANTOR MODEL**Therefore, the one-step Markov process has the following transition matrix: MJC = A C G T A 1-αα/3 α/3 α/3 C α/3 1-αα/3 α/3 G α/3 α/3 1-αα/3 T α/3 α/3 α/3 1-α**Introduction to Bioinformatics 5.4 THE JUKES-CANTOR MODEL**After t generations the substitution probability is: M(t) = MJCt Eigen-values and eigen-vectors of M(t): λ1 = 1, (multiplicity 1): v1 = 1/4 (1 1 1 1)T λ2..4 = 1-4α/3, (multiplicity 3): v2 = 1/4 (-1 -1 1 1)T v3 = 1/4 (-1 -1 -1 1)T v4 = 1/4 (1 -1 1 -1)T**Spectral decomposition of M(t):**MJCt = ∑iλitviviT Define M(t) as: MJCt = Therefore, substitution probability s(t) per site after t generations is: s(t) = ¼ - ¼(1 - 4α/3)t Introduction to Bioinformatics 5.4 THE JUKES-CANTOR MODEL r(t) s(t) s(t) s(t) s(t) r(t) s(t) s(t) s(t) s(t) r(t) s(t) s(t) s(t) s(t) r(t)**Introduction to Bioinformatics 5.4 THE JUKES-CANTOR MODEL**substitution probability s(t) per site after t generations: s(t) = ¼ - ¼(1 - 4α/3)t observed genetic distance dafter t generations ≈s(t) : d = ¼ - ¼(1 - 4α/3)t For small α:**Introduction to Bioinformatics 5.4 THE JUKES-CANTOR MODEL**For small α the observed genetic distance is: The actual genetic distance is (of course): K = αt So: This is the Jukes-Cantor formula : independent of αand t.**Introduction to Bioinformatics 5.4 THE JUKES-CANTOR MODEL**The Jukes-Cantor formula : For smalld using ln(1+x) ≈ x : K ≈ d So: actual distance ≈ observed distance For saturation: d↑ ¾ : K →∞ So: if observed distance corresponds to random sequence-distance then the actual distance becomes indeterminate**Introduction to Bioinformatics 5.4 THE JUKES-CANTOR MODEL**Variance in K If: K = f(d) then: So: Generation of a sequence of length n with substitution rate d is a binomial process: and therefore with variance: Var(d) = d(1-d)/n Because of the Jukes-Cantor formula:**Introduction to Bioinformatics 5.4 THE JUKES-CANTOR MODEL**Variance in K Variance: Var(d) = d(1-d)/n Jukes-Cantor: So:**Introduction to Bioinformatics 5.4 THE JUKES-CANTOR MODEL**EXAMPLE 5.4 on page 90 * Create artificial data with n = 1000: generate K* mutations * Count d * With Jukes-Cantor relation reconstruct estimate K(d) * Plot K(d) – K***Introduction to Bioinformatics 5.4 EXAMPLE 5.4 on page 90 (=**FIG 5.3)**Introduction to Bioinformatics 5.4 ESTIMATING GENETIC**DISTANCE The Kimura 2-parameter model Include substitution bias in correction factor Transition probability (G↔A and T↔C) per site per second is α Transversion probability (G↔T, G↔C, A↔T, and A↔C) per site per second is β**Introduction to Bioinformatics 5.4 THE KIMURA 2-PARAM MODEL**The one-step Markov process substitution matrix now becomes: MK2P = A C G T A 1-α-ββαβ C β 1-α-ββα G αβ1-α-ββ T βαβ1-α-β**Introduction to Bioinformatics 5.4 THE KIMURA 2-PARAM MODEL**After t generations the substitution probability is: M(t) = MK2Pt Determine of M(t): eigen-values {λi} and eigen-vectors {vi}**Introduction to Bioinformatics 5.4 THE KIMURA 2-PARAM MODEL**Spectral decomposition of M(t): MK2Pt = ∑iλitviviT Determine fraction of transitions per site after t generations : P(t) Determine fraction of transitions per site after t generations : Q(t) Genetic distance: K ≈ - ½ ln(1-2P-Q) – ¼ ln(1 – 2Q) Fraction of substitutionsd = P + Q → Jukes-Cantor**Introduction to Bioinformatics 5.4 ESTIMATING GENETIC**DISTANCE Other models for nucleotide evolution * Different types of transitions/transversions * Pairwise substitutions GTR (= General Time Reversible) model * Amino-acid substitutions matrices * …**Introduction to Bioinformatics 5.4 ESTIMATING GENETIC**DISTANCE Other models for nucleotide evolution DEFICIT: all above models assume symmetric substitution probs; prob(A→T) = prob(T→A) Now strong evidence that this assumption is not true Challenge: incorporate this in a self-consistent model

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