1. Combining RNA and Protein selection models
The Central Idea in Comparative Molecular Biology & Genomics
Three basic applications
Protein secondary structure
RNA secondary structure
Gene structure
Combining Evolution Constraints
Protein-Protein
RNA-Protein
Combining Structure Descriptions

2. Modelling Sequence Evolution
a - unknown
Biological setup
TGGTT
TCGTA
Pi,j(t) continuous time markov chain on the state space {A,C,G,T}. t1 A e t2 C C

3. Jukes-Cantor 69: Total Symmetry
Rate-matrix, R:
T O
A C G T
F A *a a a a
R C a *a a a
O G a a * a a
M T a a a * a
Transition prob. after time t, a = a*t:
P(equal) = ¼( e-4*a ) ~ a P(diff.) = ¼( e-4*a ) ~ 3a
Stationary Distribution: (1,1,1,1)/4.

4. Comparison of Evolutionary Objects.
Observable
Unobservable
Goldman, Thorne & Jones, 96 U C G A
Knudsen & Hein, 99
Eddy & others
Pedersen & Hein, 03
Haussler & others
Multiple levels of selection
Protein-protein
RNA-protein
Pedersen, Meyer, Forsberg, Hein,…
Observable
Unobservable

5. Finite Set of Rules Generating Strings
Structure Description: Grammars
Finite Set of Rules Generating Strings
A starting symbol:
A set of substitution rules applied to variables in the present string:
Regular
Context Free
finished – no variables
Protein secondary structure
Gene Structure
RNA secondary structure

6. Simple String Generators
Terminals (capital) Non-Terminals (small)
i. Start with S S --> aT bS
T --> aS bT 
One sentence – odd # of a’s:
S-> aT -> aaS –> aabS -> aabaT -> aaba
ii. S--> aSa bSb aa bb
One sentence (even length palindromes):
S--> aSa --> abSba --> abaaba

7. Stochastic Grammars i. Start with S. S --> (0.3)aT (0.7)bS
The grammars above classify all string as belonging to the language or not.
All variables has a finite set of substitution rules. Assigning probabilities to the use of each rule will assign probabilities to the strings in the language.
If there is a 1-1 derivation (creation) of a string, the probability of a string can be obtained as the product probability of the applied rules.
i. Start with S. S --> (0.3)aT (0.7)bS
T --> (0.2)aS (0.4)bT (0.2)
*0.2
S -> aT -> aaS –> aabS -> aabaT -> aaba
*0.3
*0.7
*0.3
*0.2
ii. S--> (0.3)aSa (0.5)bSb (0.1)aa (0.1)bb
S -> aSa -> abSba -> abaaba
*0.3
*0.5
*0.1

8. Gene Describers
Simple Prokaryotic Genes:
Simple Eukaryotic Genes:

9. Secondary Structure Generators
S --> LS L
F --> dFd LS
L --> s dFd
Vis alternative grammatikker
Put on Chomsky’s Normal Form
Knudsen & Hein, 99

10. Structure Dependent Evolution Models
Protein Secondary Structure Dependent (Goldman, Thorne & Jones)
a, b & Loop each has their own mutation rate matrix (20,20) , Ra,Rb & Rloop
2. RNA Secondary Structure Dependent
i. R singlet, singlet (4,4)
ii. R doublet,doublet (16,16)
(base pair conserving relative to
R singlet, singlet X R singlet, singlet )
3. Gene Structure Dependent
i. Rnon-coding{ATG-->GTG}
ii. Rcoding{ATG-->GTG}
iii-. Other structural categories, regulatory signals …..

11. The Genetic Code 3 classes of sites: 4 2-2 1-1-1-1 Problems:
4 (3rd)
(3rd)
ii. TA (2nd)
Problems:
i. Not all fit into those categories.
ii. Change in on site can change the status of another.

12. Kimura’s 2 parameter model & Li’s Model.
Probabilities:
Rates:
start b a
Selection on the 3 kinds of sites (a,b)(?,?)
(f*a,f*b)
(a,f*b)
(a, b)

13. alpha-globin from rabbit and mouse.
Ser Thr Glu Met Cys Leu Met Gly Gly
TCA ACT GAG ATG TGT TTA ATG GGG GGA
* * * * * * * **
TCG ACA GGG ATA TAT CTA ATG GGT ATA
Ser Thr Gly Ile Tyr Leu Met Gly Ile
Sites Total Conserved Transitions Transversions
(.8978) 12(.0438) (.0584)
(.6623) 21(.2727) (.0649)
(.6026) 16(.2051) (.1923)
Z(at,bt) = .50[1+exp(-2at) - 2exp(-t(a+b)] transition Y(at,bt) = .25[1-exp(-2bt )] (transversion)
X(at,bt) = .25[1+exp(-2at) + 2exp(-t(a+b)] identity
L(observations,a,b,f)=
C(429,274,77,78)* {X(a*f,b*f)246*Y(a*f,b*f)12*Z(a*f,b*f)16}* {X(a,b*f)51*Y(a,b*f)21*Z(a,b*f)5}*{X(a,b)47*Y(a,b)16*Z(a,b)15}
where a = at and b = bt.
Estimated Parameters: a = b = *b = (a + 2*b) = f =
Transitions Transversions
a*f = *b*f =
a = *b*f =
a = *b =
Expected number of: replacement substitutions synonymous
Replacement sites : (0.3742/0.6744)*77 =
Silent sites : = Ks = Ka = .1127

14. Three Questions HMM/Stochastic Regular Grammar: W WL WR j L 1 i i’ j’
What is the probability of the data?
What is the most probable ”hidden” configuration?
What is the probability of specific ”hidden” state?
HMM/Stochastic Regular Grammar:
O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 H1 H2 H3 W
Stochastic Context Free Grammars: WL WR j L 1 i i’ j’

15. Comparative Gene Finding Jakob Skou Pedersen & Hein, 2004

16. Knudsen & Hein, 99

17. From Knudsen & Hein (1999)

18. Knudsen and Hein, 2003

19. Why combine RNA & Protein Models?
Short Term/Long Term Evolution Discrepancies
Separating Selective Effects
Analyzing one level without interference from the other level
Predicting gene structure and RNA structure better.
Annotation of Viral Genomes

20. Combining Levels of Selection.
Assume multiplicativity: fA,B = fA*fB
Protein-Protein
Hein & Støvlbæk, 1995
Codon Nucleotide Independence Heuristic
Jensen & Pedersen, 2001
Contagious Dependence
Protein-RNA
Singlet
Doublets
Contagious Dependence

21. Overlapping Coding Regions
Hein & Stoevlbaek, 95
1st
2nd
sites
2-2 4
(f1f2a, f1f2b) (f2a, f1f2b) (f2a, f2b)
(f1a, f1f2b) (f2a, f1f2b) (a, f2b)
(f1a, f1b) (a, f1b) (a, b)
pol
gag
Example: Gag & Pol from HIV
Gag
Pol
sites
2-2 4
MLE: a= b= a+2b= fgag= fpol=.229
Ziheng Yang has an alternative model to this, were sites are lumped into the same category if they have the same configuration of positions and reading frames.

22. HIV2 Analysis Hasegawa, Kisino & Yano Subsitution Model Parameters:
a*t β*t pA pC pG pT
Selection Factors
GAG (s.d )
POL (s.d )
VIF (s.d )
VPR (s.d )
TAT (s.d )
REV (s.d )
VPU (s.d )
ENV (s.d )
NEF (s.d )
Estimated Distance per Site:

23. Evolution under double constraints
Codon Nucleotide Independence Heuristic
Singlet
Ri,j =f* qi,j
Doublet
R(i1,i2),(j1,j2) = f1 * f2 * q (i1,i2),(j1,j2)

24. Structure Prediction: Hepatitis C Analysis
A A
A C G - U C
C C –
U U
A G
U U
U A A – U G C
C C
U U
C U
C A
A C
A G U

25. Evolution Models: A hierarchy of hypotheses
Singlet
Doublets 1 2 3 1 2 3 1 2 3
ts/tv=2.00
3 (ts/tv)=1.50,1.26,3.05
3 (ts/tv, equil.)
Doublet/
singlet ratio L= L= L= L= L= L= 1 2 3 4 5
0.173
0.415
0.414
0.292
(f1:0.24,f2:0.14)
Codon
Factors
transversion
transition, ratio
Duplet
distortion
# parameters
Likelihood - + 7 9 15 17

26. Combined RNA & Protein Structure
Gene Structure Fixed, RNA Structure Stochastic
Presently being implemented with viral analysis in mind
Both RNA & Gene Structure Stochastic
Would imply Gene Finding as well.
Grammar for overlapping genes a new phenomena
Gene Structure Stochastic, RNA Structure Fixed
An untypical situation
A challenge for the future: structure evolution.

27. Open Problems Stacking Substitution Models
In principle a 44 times 44 matrix ( entries!!) is need, but proper parametrisation and symmetries is could reduce this substantially. N3 N4 N2 N1
Other Sets of Constraints: Regulatory Signals
Combining with Alignment A C G T A C T G T C T G T

28. References.
Hein,J & J.Stoevlbaek (1995) “A maximum-likelihood approach to analyzing nonoverlapping and overlapping reading frames” J.Mol.Evol
Jensen,JL & Pedersen (2001) “Probabilistic models of DNA sequence evolution with context dependent rates of subsitution” Adv. Appl.Prob
Katz and Burge (2003) “Widespread Selection for Local RNA Secondary Structure in Coding Regions of Bacterial Genes. Genome Research
Kirby, AK, SV Muse & W.Stephan (1995) “Maintenance of pre-mRNA secondary structure by epistatic selection” PNAS
Knudsen, Hein 99 “Predicting RNA Structure using Stochastic Context Free Grammars and Molecular Evolution” Bioinformatics
Knudsen and Hein (2003) “Pfold: RNA secondary structure prediction using stochastic context-free grammars. Nucleic Acid Research
New Influenza gene article???
Meyer and Durbin (2002) “Comparative Ab Initio prediction of Gene Structure using pair HMMs” Bioinformatics
Moulton, V., Zuker, M. Steel, M., Penny, D. and Pointon, R. “Metrics on RNA Structures”. J. Computational Biology, 7 (1): , (2000).
Pedersen, AMK & JL Jensen (2001) “A Dependent – Rates Model and an MCMC-Based Methodology for the Maximum-Likelihood Analysis of Sequences with Overlapping Reading Frames” Mol.Biol.Evol
Pedersen JS & J. Hein 2003 – “Gene finding with a Hidden Markov Model of genome structure and evolution” Bioinformatics
Pedersen, Forsberg, Meyer, Simmonds and Hein (2003) “An evolutionary model for protein coding regions with RNA secondary structure” Manuscript in Preparation
Pedersen, Forsberg, Meyer, Simmonds and Hein (2003) “Structure Models” Manuscript in Preparation
Schadt, E. & K.Lange (2002) “Codon and Rate Variation Models in Molecular Phylogeny” Mol.Biol.Evol
Savill, NJ et al (2001) “RNA Sequence Evolution With Secondary Structure Constraints: Comparison of Substituin Ratye Models Using Maximum-Likehood Methods” Genetics Jan
Simmonds, P. and DB Smith (July1999) “Structural Constraints on RNA Virus Evolution” J.of Virology
Tillier ERM & RA Collins (1998) “High Apparent Rate of Simultaneous Compensatory Base-Pair Substitutions in Ribosomal RNA” Genetics
Yang, Z. et al. (1995) “Molecular Evolution of the Hepatitis B Virus Genome” J.Mol.Evol

29. Acknowledgements 1. Comparative RNA Structure - Bjarne Knudsen
2. Comparative Gene Structure - Jakob Skou Pedersen
3. Integrating Levels of Selection & Structure:
Jakob Skou Pedersen, Irmtraud Meyer, Roald Forsberg
Bjarne Knudsen
Irmtraud Meyer
Roald Forsberg
Jakob Skou Pedersen