Why Are Mutations Important?

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Mutations, the molecular clock, andmodels of sequence evolutionWhy are mutations important?Mutations canbe deleteriousMutations driveevolutionReplicative proofreading and DNA repair constrain mutation rate

UV damage to DNAUVThymine dimersWhat happens if damage is not repaired?Deinococcus radiodurans is amazinglyresistant to ionizing radiation 10 Gray will kill a human 60 Gray will kill an E. coli culture Deinococcus can survive 5000 Gray

DNA StructureOHAT5’Information polarityStrands complementaryATGAC3’3’G-C: 3 hydrogen bondsA-T: 2 hydrogen bondsCTGTwo base types:- Purines (A, G)- Pyrimidines (T, C)5’OHNot all base substitutions arecreated equal Transitions Purine to purine (A ! G or G ! A) Pyrimidine to pyrimidine (C ! T or T ! C) Transversions Purine to pyrimidine (A ! C or T; G ! C or T ) Pyrimidine to purine (C ! A or G; T ! A or G)Transition rate 2x transversion rate

Substitution rates differacross genomesSplice sitesStart of transcriptionPolyadenylation siteAlignment of 3,165 human-mouse pairsMutations vs. Substitutions Mutations are changes in DNA Substitutions are mutationsthat evolution has toleratedWhich rate is greater?How are mutations inherited?Are all mutations bad?

Selectionist vs. Neutralist sneutral Most mutations aredeleterious; removed vianegative selection Some mutations aredeleterious, manymutations neutral Advantageous mutationspositively selected Neutral alleles do notalter fitness Variability arises viaselection Most variability arisesfrom genetic driftWhat is the rate of mutations?Rate of substitutionconstant: implies thatthere is a molecular clockRates proportional toamount of functionallyconstrained sequence

Why care about a molecular clock?(1) The clock has important implications forour understanding of the mechanisms ofmolecular evolution.(2) The clock can help establish a time scalefor evolution.Dating evolutionary events with amolecular clockAncestral sequenceT years sincedivergenceK substitutionssince divergenceTTCan now datethis eventACsub. rate K/2TBWhat are the assumptions?

Properties of the molecular clock Clock is erratic Clock calibrations require geological times Many caveats - varying generation times,different mutation rates, changes in genefunction, natural selection Is the molecular clock hypothesis evenuseful at all?Measuring sequence divergence:Why do we care? Use in sequence alignments and homologysearches of databases Inferring phylogenetic relationships Dating divergence, correlating withfossil record

How do you measure how different twohomologous DNA sequences are?Sequence 0tSequence 1Sequence 2Seq1 ACCATGGAATTTTATACCCTSeq2 ACTATGGGATTGTATCCCCTp distance # differences / aligned lengthp distance 4/20 0.2A sequence mutating at random123456789101112112********9 substitutions*5 pairwise changesMultiple substitutions at one site can causeunderestimation of number of substitutions

Sequence distanceSimulating 10,000 random mutationsto a 10,000 base pair sequenceGraph of Distance vs.Substitutions is not linearSubstitutionsWouldn’t it be great to be able to correctfor multiple substitutions?True # subs (K) CF x p distanceWhat probabilities does this correctionfactor need to consider?

What is a model of nucleotidesequence evolution?!ATheoretical expression ofnucleotide composition andlikelihood of each possiblebase substitutionG!!!!C!TBase frequencies equal, allsubstitutions equally likelyJukes Cantor CorrectionStep 1 - Define rate matrix For any nt, #subs/time 3! In time t, therewill be 3!t subs ”instantaneous rate matrix”Q rate of substitution per siteWait! We don’tknow ! or t ! [A] [C] [G] [T]'&)[A]"###&)Q &[C] #"##)&)#"#)&[G] #&)##"(% [T] #!

But we do know relationshipbetween K, !, and t3!t3!t# subs K 2(3!t)K Correction factor x p distanceCan we express p distance in terms of ! and t ?Jukes Cantor CorrectionStep 2 - Derive Pnt(t 1) in terms of Pnt(t) and !(Rate of change to another nt !)PA(0) 1!APA(1) PA(0)-3! 1-3!PA(2) (1-3!) PA(1) (1-PA(1)) !G!!!!C!T prob. of staying A x prob. stayed A 1st time prob. A changed first time x prob. reverted to APA(t 1) (1-3!) PA(t) (1-PA(t)) !

Jukes Cantor CorrectionStep 3 - Derive probabilities of nt stayingsame or changing for time tPA(t 1) (1-3!) PA(t) (1-PA(t)) !Probability nt stays samePii(t) 1/4 3/4e-4!tProbability nt changesPij(t) 1/4 - 1/4e-4!tJukes Cantor CorrectionStep 4 - compute probability that twohomologous sequences differ at a given positionp 1 – prob. that they are identicalp 1 – (prob. of both staying the same prob. of both changing to the same thing)p 1 – { (PAA(t))2 (PAT(t))2 (PAC(t))2 (PAG(t))2 }p 3/4(1- e-8!t)

Jukes Cantor CorrectionStep 5 - calculate number of subs in terms ofproportion of sites that differ3!tp 3/4(1- e-8!t)8!t -ln(1- 4/3p)3!tNumber subs K 2(3!t)K -3/4 ln(1-4/3p)For p 0.25, K 0.304K Correction factor x p distanceDo we need a more complexnucleotide substitution model ? Different nucleotide frequencies Different transition vs. transversion rates Different substitution rates Different rates of change among nt positions Position-specific changes within codons Various curve fitting corrections

What about substitutions betweenprotein sequences? Model of DNA sequence evolution: 4x4 matrix What size matrix needed for all amino acids?20x20 p distance # differences / length Theoretical correction for single rate of aminoacid change: K -19/20 ln(1-20/19p)****But it’s more complicated to modelprotein sequence evolution Substitution paths between amino acidsnot a uniform length Amino acid changes have unpredictableeffects on protein function Solution: use empirical data on aminoacid substitutions

The PAM model of proteinsequence evolution Empirical data-based substitutionmatrix Global alignments of 71 families ofclosely related proteins. Constructed hypotheticalevolutionary trees Built matrix of 1572 a.a. pointaccepted mutationsOriginal PAM substitution matrixjiDayhoff, 1978Count number of times residue b was replaced with residue a Ai,j

Deriving PAM matricesFor each amino acid, calculaterelative mutabilities:mj # times a.a. j mutatedtotal occurrences of a.a.Likelihood a.a. will mutateDeriving PAM matricesCalculate mutation probabilitiesfor each possible substitutionMi,j relative mutability xproportion of all subs of j represented by change to iMi,j mj x Ai,j!Ai,jiMj,j 1- mj probability of j staying same

PAM1 mutation probability matrixjiDayhoff, 1978Probabilities normalized to 1 a.a. change per 100 residuesDeriving PAM matricesCalculate log odds ratio to convert mutationprobability to substitution scoreSi,j 10 x log10( )(Mi,j)fiMutation probability(Prob. substitution from j to iis an accepted mutation)Frequency of residue i(Probability of a.a. ioccurring by chance)

Deriving PAM matricesScoring in log odds ratio:-Allows addition of scores for residues in alignmentsInterpretation of score:- Positive: non-random (accepted mutation) favored- Negative: random model favoredUsing PAM scoring matricesPAM1 - 1% difference (99% identity)Can “evolve” the mutation probability matrix bymultiplying it by itself, then take log odds ratio(PAMn PAM matrix multiplied n times)

BLOSUM BLOCKS substitution matrix Like PAM, empirical proteins substitution matrices,use log odds ratio to calculate sub. scores Large database: local alignments of conservedregions of distantly related proteinsGaplessalignmentblocksBLOSUM uses clustering to reducesequence bias Cluster the most similar sequences together Reduce weight of contribution of clustered sequences BLOSUM number refers to clustering threshold used(e.g. 62% for BLOSUM 62 matrix)

BLOSUM and PAM substitution matricesBLOSUM 30changePAM 250 (80)BLOSUM 62PAM 120 (66)BLOSUM 90PAM 90 (50)% identity% changeBLAST algorithm uses BLOSUM 62 matrixPAMBLOSUM Smaller set of closelyrelated proteins - shortevolutionary period Larger set of moredivergent proteins-longerevolutionary period Use global alignment Use local alignment More divergent matricesextrapolated Each matrix calculatedseparately Errors arise fromextrapolation Clustering to avoid bias Errors arise fromalignment errors

Importance of scoring matrices Scoring matrices appear in all analysis involvingsequence comparison. The choice of matrix can strongly influence theoutcome of the analysis.

BLOSUM and PAM substitution matrices BLOSUM 30 BLOSUM 62 BLOSUM 90 % identity PAM 250 (80) PAM 120 (66) PAM 90 (50) % change change BLAST algorithm uses BLOSUM 62 matrix Smaller set of closely related proteins - short evolutionary period Use global alignment More divergent matrices

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