Download Comparative Biology

Comparative Biology with focus on 8 examples
•Comparative Biology
•The Domain of Comparative Biology
•Co-modeling in Comparative Biology
•The purpose of Comparative Biology
•Examples of Stochastic Comparative Modeling
•Gene Frequencies in Populations
•Genome Structure Evolution
•Stemmatology: Manuscript Evolution
•RNA Secondary Structure Evolution
•Protein Structure Evolution
•Movement Evolution
•Shape Evolution
•Pattern Evolution
Comparative Biology
Most Recent
Common Ancestor
Time Direction
?
ATTGCGTATATAT….CAG
observable
Key Questions:
•Which phylogeny?
•Which ancestral states?
•Which process?
ATTGCGTATATAT….CAG
observable
ATTGCGTATATAT….CAG
observable
Key Generalisations:
•Homologous objects
•Co-modelling
•Genealogical Structures?
Comparative Biology: Evolutionary Models
Object
Nucleotides/Amino Acids/codons
Continuous Quantities
Sequences
Gene Structure
Genome Structure
Population
Structure
RNA
Protein
Networks
Metabolic Pathways
Protein Interaction
Regulatory Pathways
Signal Transduction
Macromolecular Assemblies
Motors
Shape
Patterns
Tissue/Organs/Skeleton/….
Dynamics
MD movements of proteins
Locomotion
Culture
Manuscripts (stemmatology)
Language
Vocabulary
Grammar
Phonetics
Semantics
Phenotype
Dynamical Systems
Type
CTFS continuous time finite states
CTNS continuous time continuous states
CTUS continuous time countable states
Matching
CTCS MM
Brownian Motion/Diffusion
SCFG-model like
non-evolutionary: extreme variety
CTCS
CTFS
CTCS
CTCS
CTCS
?
?
- (non-evolutionary models)
- (non-evolutionary models)
- (non-evolutionary models)
Reference
Jukes-Cantor 69 +500 others
Felsenstein 68 + 50 others
Thorne, Kishino Felsenstein,91 + 40others
DeGroot, 07
Miklos,
Fisher, Wright, Haldane, Kimura, ….
Holmes, I. 06 + few others
Lesk, A;Taylor, W.
Snijder, T (sociological networks)
Mithani, 2009a,b
Stumpf, Wiuf, Ideker
Quayle and Bullock, 06, Teichmann
Soyer et al.,06
Dryden and Mardia, 1998, Bookstein,
Turing, 52;
Grenander,
analogues to genetic models
analogous to sequence models
Biggins 05, Munz 10,
Cavalli-Sforza & Feldman, 83
Chris J Howe, http://www.cs.helsinki.fi/u/ttonteri/casc/
“Infinite Allele Model” (CTCS)
Swadesh,52, Sankoff,72, Gray & Aitkinson, 2003
Dunn 05
Bouchard-Côté 2007
Sankoff,70
Brownian Motion/Diffusion
-
Co-Modelling and Conditional Modelling
Observable
Unobservable
Goldman, Thorne &
Jones, 96
C C
A
Knudsen.., 99
Eddy & co.
U
C
A
G
U
A
AGGTATATAATGCG..... Pcoding{ATG-->GTG} or
AGCCATTTAGTGCG..... Pnon-coding{ATG-->GTG}
Meyer and Durbin 02
Pedersen …, 03
Siepel & Haussler 03
• Conditional Modelling
Pedersen, Meyer,
Forsberg…,
Simmonds 2004a,b
P ( Sequence Structure) P ( Structure) 
McCauley ….
Firth & Brown
P ( Structure Sequence ) P ( Sequence )
Footprinting -Signals (Blanchette)
Needs:
i. P(Sequence Structure)
Observable
Unobservable
ii. P(Structure)
The Purpose of Comparative Biology
To describe evolution:
• Make realistic model (pass goodness-of-fit (GOF) test)
• Estimate Parameters
• Make statements about the path of evolution – ancestral analysis
Analyse homologous pairs or sets
• What is the equilibrium distribution
• Integrate over histories
Biological Questions:
• Rate of Evolution
• Heterogeneity
Time
State Space
• Selection
• Co-Evolution of different components within a level
• Dependence among different levels (co-modelling)
Most of these questions have not been addressed beyond the sequence level:
• Primarily due to lack of data
• Secondarily due to lack of models
Xt is a diffusion with m(x)=0 and s(x)=x(1-x)
Reaction Coefficients:
• Continuous Time Continuous States Markov
Process - specifically Diffusion.
• For instance Ornstein-Uhlenbeck, which has
Gausssian equilibrium distribution
E. Thompson (1975) Human Evolutionary Trees CUP
Population Gene Frequencies
Genome Structure Evolution
• Evolutionary events:
Duplication
Inversion
1
1
1
1
2
3
Transposition
Deletion
1
2
3
1
2
3
1
2
1
3
3
k
• Inference Principles
• Shortest Path (Parsimony)
• Sum over paths with probabilities (ML)
2
k
3
1
• Extensions:
• Directions of Genes Unknown
• A set of chromosomes related by a phylogeny
Genome Structure Evolution
• Full graph for 5 genes
• Genomic reconstruction for
human, mouse and rat.
Ashmole 59
Buryed at Caane thus seythe the Croniculer
Digby 186
Beryed att Cane & thus says the cronyclere
BL Ad 31042
Beryed at caene so seyth the cronyclere
Lansd. 762
Buried at cane this saith the croneclere
de Worde
R. Wyer
And is buried at Cane as the Cronycle sayes
And buryed at cane as the Cronycle sayes
Phylogeny of “Canterbury Tales”:
Howe et al ,2001
Phylogenetics of Medieval Manuscripts by Christopher Howe
Stemmatology: Evolution of Manuscripts
Tree Representations of RNA Structure
Basic Edit Operations
A Tree Distance Pairwise Edit Algorithm
How Do RNA Folding Algorithms Work?. S.R. Eddy. Nature Biotechnology, 22:1457-1458, 2004.
Average complexity of the Jiang-Wang-Zhang pairwise tree alignment algorithm and of a RNA secondary structure alignment algorithmClaire
Herrbach, Alain Denise and Serge Dulucq
RNA Structure Evolution
Protein Structure Evolution
?
?
?
?
Known
a-globin
Unknown
300 amino acid changes
800 nucleotide changes
1 structural change
1.4 Gyr
Known
Myoglobin
1. Given Structure what are the possible events that could happen?
2. What are their probabilities? Old fashioned substitution + indel process with bias.
Bias: Folding(Sequence Structure) & Fitness of Structure
3. Summation over all paths.
Trajectories between two Secondary Structures
• Observation: two structures with sequence and secondary structure information
• Space of Protein Structures is large and complicated – both continuous and discrete
• Approximated by a series of stepping stones and a continuous time markov chain
S1
Sk
S2
3D Structure
Sn
S3
1 structure
2D Structure
1D Structure
Set of sequences
HQYWYWLLATIVVAWMCM
HSGHPPMCWFFWFLLIVIC
FYYRKKNQEDDNERPMTSG
QYYWWWFCTNSPPHYHRQ
DEEDNKRRKLWWAFFCCV
FIIAILLMVAGSTGVMMLMP
The Evolution/Comparison of Molecular Movements
Molecular Movements of Homologous Proteins are themselves homologous
The full problem: 2 times 1000 atoms observed at 106 time points.
Reductions:
i.
only a-carbons  100 space points
ii. Only correlated pairwise movements  1 dimensional summary for each aa pair
Dynamic Fingerprint Matrix (DFM)
The Evolution/Comparison of Molecular Movements
http://www.stats.ox.ac.uk/__data/assets/file/0015/3327/brooks.pdf
The Phylogenetic Turing Patterns I
The Phylogenetic Turing Patterns II
Reaction-Diffusion Equations:
Stripes: p small
Analysis Tasks:
1. Choose Class of Mechanisms
2. Observe Empirical Patterns
3. Choose Closest set of Turing Patterns T1, T2,.., Tk,
4. Choose parameters p1, p2, .. , pk (sets?) behind T1,..
Spots: p large
Evolutionary Modelling Tasks:
1. p(t1)-p(t2) ~ N(0, (t1-t2)S)
2. Non-overlapping intervals have independent increments
I.e. Brownian Motion
Scientific Motivation:
1. Is there evolutionary information on pattern mechanisms?
2. How does patterns evolve?
•
Landmarks
•
Semilandmarks
Gunz (2009) Early modern human diversity suggests subdivided population structure and a complex out-of-Africa scenario
Comparison of cranial ontogenetic trajectories among great apes and humans Philipp Mitteroeckera*,
Evolutionary Morphing David F. Wiley
http://graphics.idav.ucdavis.edu/research/projects/EvoMorph
Shapes and Shape Evolution
Summary
•Comparative Biology
•The Domain of Comparative Biology
•Co-modeling in Comparative Biology
•The purpose of Comparative Biology
•Examples of Stochastic Comparative Modeling
•Gene Frequencies in Populations
•Genome Structure Evolution
•Stemmatology: Manuscript Evolution
•RNA Secondary Structure Evolution
•Protein Structure Evolution
•Movement Evolution
•Shape Evolution
•Pattern Evolution