Introduction to Bioinformatics-5

7/24/2019 Introduction to Bioinformatics-5

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Introduction to

Bioinformatics


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Introduction to Bioinformatics.

LECTURE 5: Variation within and betweenspecies

* Chapter 5: re Neanderthals among us?


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!eanderta"# $erman%# &'5(

Initia" interpretations:

* bear skull

* pathological idiot

* )"d utchman...
http://upload.wikimedia.org/wikipedia/commons/3/37/Neandertal_1856.jpg


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Introduction to Bioinformatics

LEC!"E #$ I%E"& '%( I%"')ECIE) +'"I'I,%


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5.& Variation in DNA sequences

* E/en closel0 related indi/iduals differ in genetic seuences

* point mutations $ cop0 error at certain location

* )eual reproduction 5 diploid genome


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#.1 +'"I'I,% I% (%' )E7!E%CE)

ip"oid chromosomes


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#.1 +'"I'I,% I% (%' )E7!E%CE)

+itosis: dip"oid reproduction


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#.1 +'"I'I,% I% (%' )E7!E%CE)

+eiosis: dip"oid ,-double / hap"oid ,-single


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#.1 +'"I'I,% I% (%' )E7!E%CE)

* t0ping error rate /er0 good t0pist$ 1 error : 1; t0ped letters

* all our diploid cells constantl0 reproduce billion letters

* t0pical cell cop0ing error rate is < 1 error :1 =bp


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#.1 +'"I'I,% I% (%' )E7!E%CE)

$ER+ LI!E

Re0erse time and fo""ow %our ce""s:

>%o? 0ou count < 1913cells

>,ne generation ago 0ou had 2 cells @some?hereA in 0our parents bod0>)mall Tgenerations ago 0ou had 2T5 multiple ancestorscells

>Large Tgenerations ago 0ou counted fertile ancestorscells>Congratulations$ 0ou are 3.4 billion 0ears old

1ast2forward time and fo""ow %our ce""s:

>,nl0 a fe? cells in 0our reproducti/e organs ha/e a chance to li/e on

in the net generations

>he rest including 0ou ?ill die D


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#.1 +'"I'I,% I% (%' )E7!E%CE)

$ER+ LI!E +UTTI)!3

This potentia""% immorta" "inea4e of ,4erm ce""s is

ca""ed the $ER+ LI!E

"" mutations that we ha0e accumu"ated are en routeon

the 4erm "ine


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#.1 +'"I'I,% I% (%' )E7!E%CE)

* o"%morphism$ multiple possibilities for a nucleotide$ a""e""e

* )ingle %ucleotide ol0morphism 5 )% snipF point mutation

eample$ '''''' /s '''C'''

* Gumans$ )% H 1:1#99 bases H 9.9-

* )" H )hort andem "epeats microsatelites

eample$ C'C'C'C'C'C'C'C'C' D

* ransition & trans/ersion


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urines 6 %rimidines


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#.1 +'"I'I,% I% (%' )E7!E%CE)

Transitions 6 Trans0ersions


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5.7 Mitochondrial DNA

* mitochondriae are inherited onl0 /ia the maternal line

* +er0 suitable for comparing e/olutionJ not reshuffled


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#.2 KI,CG,%("I'L (%'

H.sapiensmitochondrion

I d i Bi i f i


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#.2 KI,CG,%("I'L (%'

E+ photo4raph of 8. 3apiens mt!

I t d ti t Bi i f ti


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#.2 KI,CG,%("I'L (%'



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5.9 Variation between species

* 4enetic 0ariationaccounts for morpho"o4ica"2

ph%sio"o4ica"2beha0iora"0ariation

* $enetic/ariation c.. distance relates to ph%"o4enetic

re"ationHrelationship

* %ecessit0 to measure distances bet?een seuences$ ametric



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#.3 +'"I'I,% BEEE% )ECIE)

3ubstitution rate

* Kutations originate in single indi/iduals

* Kutations can become fiedin a population

* +utation rate$ rate at ?hich ne? mutations arise

* 3ubstitution rate$ rate at ?hich a species fies ne? mutations

* Mor neutra" mutations



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#.3 +'"I'I,% BEEE% )ECIE)

3ubstitution rate and mutation rate

* Mor neutra" mutations

* N H 2%O*1:2% H O

* N H ;:2



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5.; Estimating genetic distance

* )ubstitutions are independent P

* )ubstitutions are random

* Kultiple substitutions ma0 occur

* Back&mutations mutate a nucleotide back to an earlier /alue



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#.4 E)IK'I%= =E%EIC (I)'%CE

Kultiple substitutions and Back&mutations

concealthe real genetic distance

GACTGATCCACCTCTGATCCTTTGGAACTGATCGT

TTCTGATCCACCTCTGATCCTTTGGAACTGATCGT

TTCTGATCCACCTCTGATCCATCGGAACTGATCGT

GTCTGATCCACCTCTGATCCATTGGAACTGATCGTobser0ed : 7 ,- d

actua" : ; ,- K



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* 3aturation$ on a/erage one substitution per site

* ?o random seuences of eual length ?ill match

for approimatel0 Q of their sites

* In saturation therefore the proportional genetic

distance is Q



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* Truegenetic distance proportion$ K

* )bser0edproportion of differences$ d

* (ue to back&mutations K d



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3E


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!he "u#es$%antor modelCorrection for multiple substitutions

)ubstitution probabilit0persitepersecond is >

)ubstitution means there are 3 possible replacements

e.g. C R S'J=JT

%on&substitution means there is 1 possibilit0e.g. C R C



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#.4 GE U!;E)&C'%," K,(EL

hereforeJ the one&step Karko/ process has the follo?ingtransition matri$

MJC=

A C G T

A 1- /3 /3 /3

C /3 1- /3 /3

G /3 /3 1- /3

T /3 /3 /3 1-



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#.4 GE U!;E)&C'%," K,(EL

'fter tgenerations the substitution probabilit0 is$

Mt= MJCt

Ei4en20a"uesand ei4en20ectorsof Mt$

V1H 1Jmultiplicit0 1$ 01H 1:4 1 1 1 1

V2..4

H 1&4W:3Jmultiplicit0 3$ 02

H 1:4 &1 &1 1 1

03H 1:4 &1 &1 &1 1

04H 1:4 1 &1 1 &1



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#.4 GE U!;E)&C'%," K,(EL3pectra" decompositionof Mt$

MJCt= ii

t0i0i

(efine Mt as$

MJCt=

hereforeJ substitution probabilit0 st per site after t

generations is$

st= Q & Q1 & 4W:3t

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)



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#.4 GE U!;E)&C'%," K,(EL

substitution probabilit0 st per site after t generations$

st= Q & Q1 & 4W:3t

obser&edgenetic distance dafter t generations X st $

d = Q & Q1 & 4W:3t

Mor small W$( )dt

341ln

4

3



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#.4 GE U!;E)&C'%," K,(EL

Mor small Wthe obser0edgenetic distance is$

he actua"genetic distance is of course$

K = t

)o$

his is the ?u=es2Cantor formu"a$ independent of and t.

( )dt341ln

4

3

( )dK34

43 1ln



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#.4 GE U!;E)&C'%," K,(EL

he ?u=es2Cantor formu"a$

Mor sma""dusing ln1Yx Xx$ K d)o$ actual distance observed distance

Mor saturation$ dZ [ $ K R\)o$ if observed distancecorresponds to random seuence&distance then the actual distance becomes indeterminate

( )dK 3443 1ln


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?u=es2Cantor



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#.4 GE U!;E)&C'%," K,(EL

Variance in K

If$K = f(d)then$

)o$

=eneration of a seuence of length n ?ith substitution rate

dis a binomial process$

and therefore ?ith /ariance$ Var(d) = d(1-d)/n

Because of the Uukes&Cantor formula$

knk ddk

nk

= )1()(Prob

dd

K

341

1

=

)(Var)(Var

2

dd

KK

=

2

2

2d

d

KKd

d

KK

=

=



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#.4 GE U!;E)&C'%," K,(EL

Variance in K

+ariance$ Var(d) = d(1-d)/n

Uukes&Cantor$

)o$

dd

K

341

1

=

2

34 )1(

)1()(Var dn

dd

K


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Var,K



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#.4 GE U!;E)&C'%," K,(EL

E'AM()E *.+ on page ,-

* Create artificial data ?ith nH 1999$ generate K*mutations

* Count d

* ith Uukes&Cantor relation reconstruct estimate Kd

* lot Kd K



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#.4 E]'KLE #.4 on page 89



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#.4 E]'KLE #.4 on page 89 H 1I$ 5.9



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!he Kimura $parameter model

Include substitution bias in correction factor

Transitionprobabilit0 =^' and ^Cpersitepersecondis /

Trans0ersionprobabilit0 =^J =^CJ '^J and '^Cper

sitepersecond is0



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#.4 GE ;IK!"' 2&'"'K K,(EL

he one&step Karko/ process substitution matrino? becomes$

MK!"=

A C G TA 1--

C 1--

G 1--

T 1--



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#.4 GE ;IK!"' 2&'"'K K,(EL

'fter tgenerations the substitution probabilit0 is$

Mt= MK!"t

(etermine of Mt$

ei4en20a"uesSiT

and ei4en20ectorsS&iT



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#.4 GE ;IK!"' 2&'"'K K,(EL

3pectra" decompositionof Mt$

MK!"t= ii

t0i0i

(etermine fraction of transitionsper site after tgenerations $P(t)

(etermine fraction of transitionsper site after t

generations $ Q(t)

=enetic distance$K - ln(1-2P-Q) ln(1 2Q)

Mraction of substitutionsd = P + Q Jukes-Cantor



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1ther models 2or nucleotide e&olution* (ifferent t0pes of transitions:trans/ersions

* air?ise substitutions =" H =eneral ime "e/ersible model

* 'mino&acid substitutions matrices

* D



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1ther models 2or nucleotide e&olution

E1ICIT$

all abo/e models assume s0mmetric substitution probs_

prob'R H probR'

%o? strong e/idence that this assumption is nottrue

Cha""en4e: incorporate this in a se"f2consistent mode"



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5.5 %A3E 3!4D56 Neanderthals

* mt(%' of 29- #$ sapiensfrom different regions

* Mragments of mt(%' of 2 #$ neandert%aliensis& includingthe original 16#- specimen.

* all 296 samples from =enBank

* ' homologous seuence of 699 bp of the G+" could befound in all 296 specimen.



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#.# C')E )!(`$ 'eandert%als

* air?ise genetic difference 5 corrected ?ith Uukes&Cantor

formula

* di&( is UC&corrected genetic difference bet?een pair i&()*

* dH d

K() Multi +i,ensional caling$ translate distance table

d to a n(&map.J here 2(&map



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distance map d,i#7



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MDS

H. sapiens

H. neanderthaliensiswe""2se

parated



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phylogentic tree


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E! of LECTURE 5



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Introduction to Bioinformatics-5