rna structure, evolution and...

RNA Structure, Evolution and Phylogenetics

Dr. P. Higgs, U. Manchester (ITP 5/15/01) 1

Supported by BBSRC


School of Biological Sciences

Paul Higgs

David Hoyle

Cendrine Hudelot

Daniel Jameson

Stephen Morgan

Nick Savill

Dept of Computer Science

MagnusRattray

Howsun Jow



Secondary S tructure: small subunit ribosomal RNA

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132 4 5 687 9 9 :; <�= > ?A@ @ B

5 '

3 '

UUUCAACGGAG A G U U U G

AUCCUGGCUCAGGAU

GAACGCUGGCGGCG

UGC

UUA

ACAC AUGC

A

A

G U CG A

A C G A UG A

U C C G G U G CUU

GCACCGGGGAUUAGUGGC

GA

ACGGGUG A

GU

AACA

CGUGAGUA

ACC

UG

CCCUU

GACU C U G G GA U A A G C C U G G G

AA

ACUGGGUCUAAU

ACCGGAUA

UG

ACUCCUCAUCG

CAUGGUGGGGGGU

GG

AAAGCUU

UU U G U G

GUU

UUGG

AU

GGACUCGCGGC

CUA

UC

AG

CUU

GUU

GGU

GAGG

UAAUG

G CUC

A CC

A AG

GCGACG A C

GG

GU

A GCCGGCCUG

AG A G G G U

G AC

C G GC CA

CA

CUGGGACUGAGACA C GG

C C C A GAC

UCC

UA

C GG

GAG G C A G

CAGUGG

GGA A

UAUU

GCACAA

UGGGCGAA

A G C C U G A U G C A GCGA CG CCGCGUGAGG

GAUGA

CGGCCU

UC

G G G U UG U A A A

C C U CUU

UCA

GUA

GGGAAGAAG

CGA

A A G UGAC G G

UAC

CUG

C AGA

AGAA G

CGCCGGC

U A A CUACGUGC

CAGCA G C C GC

GGU

AAU

ACGUAG

GGCGCAA G CGUU

A UC CGGAA

UU A U

UGGGCGU

AA

AGAGCUCGU

AGGCGGUUUGUC

GCGUCUGCCGUG

AAAG

UCCGGGGCU

CA A C U C C G G

A U CU G C G G U G G G

U AC G G G C A G A C

UA

GAGUGAUGU

AGG

GGAGACUGGAAUUCCUGGUGUAGCGGU

GA

A A U G CGC A G A

UA U C A G G A G G A A C A C C G A

U GG C G

AA

GGCAGGUCUCUGG

GCAUUAACUG

ACG CU G A

GGA G CG

AA

A GCAUGGGG

AG CGAA

CAGG

AUU

A G AUA

CCCUG

GUA

G

UCCAUGC C G U

AAAC

GUU

G G G C A C UA GGU

GUG

GGG

GAC

AU U C

CA

CGU

UUU

CCG

CGCC GU

AG

CUA

ACGCAU

UAAGUGCCC

CGCCUGG G G A G UA C G G C C G

CA

AGGCUAAA

ACUCAAA G G A A U U G A C G

GG G G C C C G C A C A A G CG G C

GGAGCAUGCGGAU

UAAUU

CGA

UGCA

AC G CG

AAGA

AC C U U

A CCAAGGCU

UGA

CAUG

GACCGGACCGCCGCAG

AA

A U G U G G U U U CUCCU

U UUGGGGC

CGGUU

CA C AGG

UGGUGC

A UG

GUUG

UCGUCA

GCUCGUGUCG

UGAGAUGUUGGG

UU

A AGU

CCCG C

AA C G A G C

GC A A CC C U C G U U C C A U G U U G C C

A GC G C G U

AA

UGGCGGGGACU

CAUGGGAG

ACUG

CC

GGG

GU

CAAC

UC

GGA

GG

AAG

GUGGGGA

CGACG

UC AAAU C

AUC

AUGCCCCU U

AUG

UCUUGG

GC

UUC

ACGCAUGCUA CA A UG GCCGGU

AC

A A A G GGUU GC

GA U A C U G U

GAGGU

GGA

GCU

AAUCCC

AA

AAAGCCGGUCUCA

GU

UCGGAU

UGGGGUC U

GC

AACUCGA

CC

CCA

UG

AAGU

CG

GAGUCGCU

AGUA

A UCGCA

G A UCA

GCAAC

GCU

GCGGUGAAUA

CG

UUC

CCGGGCCUUGU

ACA

CACCGC

CCG

UC

AAGUC

ACGA

AAGUUGGU

AACACC

CGAA

GCCGGUG

GCCUA

A CCC

CU U G

UGGGA

GGGA

GCCG

UC

GAA

GGUG

GG

ACUGGC

GA

UUG

GGACUA

AGU

CGU

AAC

A AG

G

U A G C C G U A C C GGA

AGGUGCGGCUGGAUCACCUCCUUUCU

Typical transfer RNA structure



G

G

G

C

A

A C

U

U AA

C

C G

A

C

U

U

A

CG C

G

A

C

U A

C

C

G C

U

A

C

G

A

A B

1

2

3

4

5

6

7

8

9

10

∆E = 3

∆E = 5

A B

A B

∆E = 1

A B

Trailer No. 2 RNA as a Disordered System Measure Barriers Between Groundstates

The relevant barrier height controlling kinetics at low temperature is the highest point on the lowest route



1234567 7654321((((((( )))))))

Bacillus subtilis GGCUCGG CCGAGCCEscherichia coli GCCCGGA UCCGGGCSaccharomyces cerevisiae GCGGAUU AAUUCGCDrosophila melanogaster GCCGAAA UUUCGGCHomo sapiens GCCGAAA UUUCGGC

Compensatory Substitutions

Two sides of the acceptor stem from a tRNA are shown.

Due to structure conservation alignment is possible in widely different species.

Two possible mechanisms of compensatory substitutions

Frequency in population

GC GU AUAUGC

GU

time time

Two single substitutions

One double substitution



Second site

A C G U

A

C

G

U

Population genetics model

First

site

Selection

Watson Crick Pairs Fitness 1

Mismatches Fitness 1-s

GU and UG pairs

Population size N Mutation rate u

Solve diffusion equation.

Higgs (1998) Genetica

Probability F(x) of observing a fraction x of AU sequences

F(x) is controlled by a parameter α = 8Nu2/s

α >> 1 all 4 WC pairs present simultaneously (curve a)

α << 1 population is monomorphic but switches between the 4 WC states (curve c)



29680212121Number of pairs

4558464754884Number of sequences

0.3520.2980.1220.1730.0200.0210.014

0.3850.2960.1170.1040.0500.0220.026

0.4730.3200.0570.0770.0310.0200.022

0.3720.2600.1280.1420.0430.0250.030

0.2660.1210.2570.2330.0460.0300.046

Frequencies GCCGAUUAGUUG

MM

0.5450.674

0.5940.730

0.6360.829

0.5320.681

0.3390.448

G+C averageG+C heli cal regions

SSUrRNA

RnasePtRNAarchaea

tRNAgeneral

tRNAmitoch.

Analysis of RNA sequence databases

Selection for thermodynamically stable structures

Higgs (2000) Quart. Rev. Biophysics

A Substitution Rate Model for RNA Stems for use with Molecular Phylogenetics

Pij(t) = probabilit y of being in state j at time t

given that ancestor was in state i at time 0.

States label pairs (AU, GC etc.) not single bases.

i

t

j

kjk

ikij

rPdt

dP∑=



*7

*6

*5

*4

*3

*2

*1

7654321

676575474373272171

677565464363262161

577566454353252151

477466455343242141

377366355344232131

277266255244233121

177166155144133122

απαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπαπ

MM

CG

UG

UA

GC

GU

AU

MMCGUGUAGCGUAU

Model 7A is a General Reversible 7-state Model

7 frequencies πi + 21 rate parameters αij

- 2 constraints = 26 free parameters

Probability of remaining in same state Pii

SSU rRNA sequences from Eubacteria



Probability Pij of changes from CG to other pairs

SSU rRNA from Eubacteria

AU

GC

GU

CG

UA

UG

slow

fastfast

Selection against GU and UG is weaker than against mismatches.

Double transitions are faster than double transversions.

Double transitions are faster than single transitions to GU and UG states. This is explained by the theory of compensatory substitutions.

What is going on?



2.83.68.92.01.6Double transitions /Transitions to GU or UG

2.13.12.31.74.7Double transitions / Double transversions

0.550.661.400.933.924.367.84

0.650.601.461.091.722.845.24

0.450.894.011.781.853.000.86

0.490.831.461.241.965.010.99

0.670.840.860.772.443.322.32

Mutabilities GCCGAUUAGUUG

MM

SSUrRNA

RnasePtRNAarchaea

tRNAgeneral

tRNAmitoch.

Analysis of RNA Substitution Rates

Thermodynamic properties influence Evolutionary properties

Model Selection

Savill , Hoyle & Higgs (2001) Genetics

How complex must a model be to explain the data?

How many parameters are justified?

Many other rate models have been proposed:

• Schöniger & von Haeseler• Muse• Rzhetsky• Till ier & Collins

Use likelihood-based statistical tests to distinguish between models.



*MM

*CG

*UG

*UA

*GC

*GU

*AU

MMCGUGUAGCGUAU

sd

ss

ds

sd

ss

ds

γπγπγπγπγπγπγπαπαπβπβπβπγπαπαπβπβπβπγπαπαπβπβπβπγπβπβπβπαπαπγπβπβπβπαπαπγπβπβπβπαπαπ

654321

754321

764321

765321

765421

765431

765432

7

6

5

4

3

2

1

7654321

AU

GC

GU

αs

αs

MM

CG

UA

UG

αs

αsαd αd

β

γ γ

Model 7D

Also called OTRNA by

Tillier & Collins (1998)

*UU

*UC

*GG

*GA

*CU

*CC

*CA

*AG

*AC

*AA

/////*/CG

/////*/UG

//////*UA

/////*/GC

/////*/GU

//////*AU

UUUCGGGACUCCCAAGACAACGUGUAGCGUAU

CCGAGA

UCAGAG

AACUCU

GCAUCU

UCAGGA

UUAAGG

GUCAGU

GCACUU

CCGAGU

GCGCUU

GUCAAU

UCGACA

UCGCAG

UGACAU

UGACCA

UCGCAG

απαπφβπλβπφβπλβπαπαπβπφβπλβπλβπ

απαπλβπφβπλβπφβπαπβπαπλβπλβπφβπ

απαπβπλβπφβπλβπαπαπβπβπλβπλβπ

βπβπβπβπλαπλαπαπβπαπλβπφβπλβπ

βπβπβπβπλαπλαπαπβπαπβπλβπλβπ

λβπλβπλβπλαπλβπλφαπφβπφβπφβπφβπφλαπϕλαπλβπλβπλβπλαπλβπλφαπ

λβπλβπλβπλβπλαπλφαπφβπφβπφβπφβπφλαπϕλαπλβπλβπλβπλαπλβπλφαπ

000000000

000000000

000000000

000000000

000000000

000000000

000000000

000000000

000000000

000000000

000000000

000000000

000000000

000000000

000000000

000000000

Model 16D and related models

Proposed by Muse (1995)

Considers all 16 states.

Only single substitutions allowed. Distinguishes between paired and mismatch states.



6A

6C

6B

6D

7A

7C 7D 7B

7E 7F

16H

16F16E

16G

16D

16B 16C

16A

Families of Nested Models

Bacill us subtili sRhodomicrobium vannielii

Sphingomonas capsulata

Pseudomonas aeruginosa

Escherichia coliT1

T2

T3

T6

T7

T4

T5

Test models using “known” phylogeny of five bacteria.

Small sub-unit ribosomal RNA sequences.



Likelihood Ratio Test shows that rates of double substitutions are non-zero.

Likelihood Ratio Test shows General Reversible Model 7A is preferable to 7D.



C o n d y lu ra *

C h o l o e p us d id . * C h o l o e p u s h o f.Ta m a n d u aM yrm e co p h a g aE u p h ra c tu s * C h a e to p h ra c tu sTr ich e ch u s *L o xo d o n ta * P ro c a v ia * E ch in o p s * O r yc te ro p u s *M a c ro sce l id e sE le p h a n tu lu s *D i d e lp h is * M a c ro p u s *

S ire n iaP ro b o sc i d e aH y ra c o id e aTe n re c id a eTu b u lid e n ta t a

X e n a rth ra

M a c r o sce l id e a

M arsup ia lia

Tethy theria

Paenungulata

Afrotheria

100 77 99

94< 50 99

97 63

< 50 79

< 50< 50 50

< 50< 50

85 62

< 50

656479

100100100

100100100

100100

100100

100100

100100100

100100

936485

100100 C a v ia *

H y d ro c h a e ru sA g o u tiE re th izo nM yo c a s to rD i n o m ysH y s tr ixH e te ro ce p h a lu s *M u s *R a tt u sC r ic e tu sP e d e te sC a s to rD i p o d o m ysTa m ia s *M u sca rd in u sS y lv ila g u s *O ch o to n a *H y lo b a te sH o m o *M a ca ca *A te le s *C a ll im icoC y n o ce p h a lu s * / * * L e m u r *Ta rs iu s *Tu p a ia *

Cavio-morpha Hystrico-

gnathi

Anthropoidea P ri m a te s

D e rm o p te ra * *

S ca n d e n tia

R o d e n ti a

L a g o m o rp h a

Glires

Lemuriform esTarsiiform es

P ri m a te s

88< 50

5398

90100

995295

97 87100

7287

9784

988099

60< 50< 50

67< 50< 50

9070

100100

100100100

100100

100100100

100100100

100100

100100

7183

100100100

9995

100100

III

749999

M e g a p te ra *Tu rs io p sH i p p o p o ta m u s *Tra g e la p h u sO ka p i aS u sL a m a * C e ra to th e r iu m *Ta p iru sE q u u s *F e lis * L e o p a rd u sP a n th e raC a n i s * U rsu sM a n is *A rti b e u s *N y c te r isP te ro p u s * R o u s e ttu sE ri n a ce u s *S o re x *A s io sca lo p s

Cetacea

C e ta r t i o d a c ty la

P e ri sso d a c ty l a

C a rn ivo ra

P h o lid o ta

C h i ro p te raM egachiroptera

Microchiroptera

'E u l ip o typ h la '

6677

9199

637267

92100 90

100100

9693

5270

100100100

100100100

100 97 98

100 96100

100100

100 99

100100100

100100

96 97100

1 0 01 0 0

1 0 01 0 0

IV

II

I

100100

< 50< 50 63

< 50< 50 55

< 50< 50

72

Murphy et al.

Nature (2001)

Afrotheria / Laurasiatheria



RNA Phylogeny Package

Soon to be released …

Uses a range of evolutionary models designed specifically for RNA paired regions (as well as standard single site models).

Secondary structure is specified in the alignment as bracket notation.

Exhaustive Maximum Likelihood search for small numbers of species or small numbers of clusters.

Statistical tests to distibuish between proposed trees: Kishino-Hasegawa (important to consider correlation between sites)

Markov Chain Monte Carlo methods for tree searching.



Sub-trees in theLaurasiatheria Group

Carnivora

(((Harbour Seal, Gray Seal), Dog), Cat)

Perissodactyla

((Donkey, Horse),(Indian Rhino, White Rhino))

Cetartiodactyla

((((Blue Whale, Sperm Whale), Hippo),(Cow, Sheep)), Pig)

Chiroptera

((Long-tailed Bat, Fruit-eating Bat),(Flying Fox, Flying Fox))

Insectivora

(Hedgehog, Mole)

Outgroup: Rabbit

Maximum Likelihood Cluster Arrangements



Preliminary Results with MCMC

43 mammals with completely sequenced mitochondrial genomes

SSU + LSU + 14 tRNAs on the same strand

Study paired regions using the 7D model

Well -defined groups: 100% support

e.g. Primates, Marsupials, Rodents, Carnivores.

Four large-scalecladeswell -defined

Afrotheria (100%), Laurasiatheria (97%), Primates+Glires (86%), Xenarthra (100%)

Insectivores+Bats (87%)

A few wandering species: e.g. Pig

Thoughts for the day…

Thermodynamic parameters affect evolutionary parameters.

Rate models for phylogenies need to be tailored to the sequences studied.

rna structure, evolution and...

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