Comparative Biology with focus on 8 examples•Comparative Biology

•The Domain of Comparative Biology

•The purpose of Comparative Biology

•Co-modeling in Comparative Biology

•Examples of Stochastic Comparative Modeling

•Shape Evolution

•Protein Structure Evolution

•Movement Evolution

•RNA Secondary Structure Evolution

•Genome Structure Evolution

•Gene Frequencies in Populations

•Pattern Evolution

•Stemmatology: Manuscript Evolution

Comparative Biology

observable observable

Parameters:tim

e

rates, selection

Unobservable

Evolutionary Path

observable

Most Recent

Common Ancestor

?

ATTGCGTATATAT….CAG ATTGCGTATATAT….CAG ATTGCGTATATAT….CAG

Tim

e Direction

•Which phylogeny?

•Which ancestral states?

•Which process?

Key Questions:•Homologous objects•Co-modelling•Genealogical Structures?

Key Generalisations:

Comparative Biology: Evolutionary Models

Nucleotides/Amino Acids/codons CTFS continuous time finite states Jukes-Cantor 69 +500 othersContinuous Quantities CTNS continuous time continuous states Felsenstein 68 + 50 othersSequences CTUS continuous time countable states Thorne, Kishino Felsenstein,91 + 40othersGene Structure Matching DeGroot, 07Genome Structure CTCS MM Miklos,Population Brownian Motion/Diffusion Fisher, Wright, Haldane, Kimura, ….Structure RNA SCFG-model like Holmes, I. 06 + few others Protein non-evolutionary: extreme variety Lesk, A;Taylor, W.Networks CTCS Snijder, T (sociological networks) Metabolic Pathways CTFS Mithani, 2009a,b Protein Interaction CTCS Stumpf, Wiuf, Ideker Regulatory Pathways CTCS Quayle and Bullock, 06, Teichmann Signal Transduction CTCS Soyer et al.,06 Macromolecular Assemblies ?Motors ?Shape - (non-evolutionary models) Dryden and Mardia, 1998, Bookstein, Patterns - (non-evolutionary models) Turing, 52; Tissue/Organs/Skeleton/…. - (non-evolutionary models) Grenander, Dynamics MD movements of proteins - Biggins 05, Munz 10, Locomotion -Culture analogues to genetic models Cavalli-Sforza & Feldman, 83Manuscripts (stemmatology) analogous to sequence models Chris J Howe, http://www.cs.helsinki.fi/u/ttonteri/casc/

Language Vocabulary “Infinite Allele Model” (CTCS) Swadesh,52, Sankoff,72, Gray & Aitkinson, 2003

Grammar Dunn 05 Phonetics Bouchard-Côté 2007 Semantics Sankoff,70 Phenotype Brownian Motion/DiffusionDynamical Systems -

Object Type Reference

Co-Modelling and Conditional Modelling

Observable

Observable Unobservable

Unobservable

Goldman, Thorne & Jones, 96

UC G

AC

AU

AC

Knudsen.., 99

Eddy & co.

Meyer and Durbin 02 Pedersen …, 03 Siepel & Haussler 03

Pedersen, Meyer, Forsberg…, Simmonds 2004a,b

McCauley ….

Firth & Brown

i. P(Sequence Structure)

ii. P(Structure)

)()(

)()(

SequencePSequenceStructureP

StructurePStructureSequenceP

• Conditional Modelling

Needs:Footprinting -Signals (Blanchette)

AGGTATATAATGCG..... Pcoding{ATG-->GTG} orAGCCATTTAGTGCG..... Pnon-coding{ATG-->GTG}

The Purpose of Comparative Biology

• Primarily due to lack of data

• Secondarily due to lack of models

• Make realistic model (pass goodness-of-fit (GOF) test)• Estimate Parameters• Make statements about the path of evolution – ancestral analysis

• Co-Evolution of different components within a level

• Rate of Evolution

• Heterogeneity

Time

State Space

• Selection

• Dependence among different levels (co-modelling)

To describe evolution:

Biological Questions:

Most of these questions have not been addressed beyond the sequence level:

Analyse homologous pairs or sets• What is the equilibrium distribution• Integrate over histories

Population Gene Frequencies

Xt is a diffusion with (x)=0 and (x)=x(1-x)

E. T

hompson (1975) H

uman E

volutionary Trees C

UP

Reaction Coefficients:

• Continuous Time Continuous States Markov Process - specifically Diffusion.

• For instance Ornstein-Uhlenbeck, which has Gausssian equilibrium distribution

Genome Structure Evolution

1 2 3 k

12 3k

• Evolutionary events:

• Extensions:

• Directions of Genes Unknown

• A set of chromosomes related by a phylogeny

Duplication1

1 1

Inversion1 2 3

1 2 3

TranspositionDeletion

1 3

1 2 3

• Inference Principles

• Shortest Path (Parsimony)

• Sum over paths with probabilities (ML)

Genome Structure Evolution

• Full graph for 5 genes

• Genomic reconstruction for human, mouse and rat.

Stemmatology: Evolution of ManuscriptsP

hylogenetics of Medieval M

anuscripts by Christopher H

owe

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 And is buried at Cane as the Cronycle sayes

R. Wyer And buryed at cane as the Cronycle sayes

Phylogeny of “Canterbury Tales”:

Howe et al ,2001

RNA Structure Evolution

Tree Representations of RNA Structure

How

Do R

NA

Folding A

lgorithms W

ork?. S.R

. Eddy. N

ature Biotechnology, 22:1457-1458, 2004.

Average com

plexity of the Jiang-Wang-Z

hang pairwise tree alignm

ent algorithm and of a R

NA

secondary structure alignment algorithm

Claire

Herrbach, A

lain Denise and S

erge Dulucq

A Tree Distance Pairwise Edit AlgorithmBasic Edit Operations

Known KnownUnknown

-globin Myoglobin

300 amino acid changes800 nucleotide changes1 structural change1.4 Gyr

?

?

?

?

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.

Protein Structure Evolution

Trajectories between two Secondary Structures

HQYWYWLLATIVVAWMCMHSGHPPMCWFFWFLLIVICFYYRKKNQEDDNERPMTSG

QYYWWWFCTNSPPHYHRQDEEDNKRRKLWWAFFCCVFIIAILLMVAGSTGVMMLMP

1D Structure

3D Structure

2D Structure

S1

S2

Sn

Sk

1 structure

Set of sequences

S3

• 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

• Observation: two structures with sequence and secondary structure information

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:

ii. Only correlated pairwise movements 1 dimensional summary for each aa pair

i. only a-carbons 100 space points

Dynamic Fingerprint Matrix (DFM)

The Evolution/Comparison of Molecular Movements

The Phylogenetic Turing Patterns Ihttp://w

ww

.stats.ox.ac.uk/__data/assets/file/0015/3327/brooks.pdf

Stripes: p small Spots: p large

The Phylogenetic Turing Patterns II

Reaction-Diffusion Equations:

Analysis Tasks:1. Choose Class of Mechanisms2. Observe Empirical Patterns

3. Choose Closest set of Turing Patterns T1, T2,.., Tk,

4. Choose parameters p1, p2, .. , pk (sets?) behind T1,..

Evolutionary Modelling Tasks:

1. p(t1)-p(t2) ~ N(0, (t1-t2)) 2. Non-overlapping intervals have independent incrementsI.e. Brownian Motion

Scientific Motivation:1. Is there evolutionary information on pattern mechanisms?2. How does patterns evolve?

Shapes and Shape EvolutionG

un

z (2009) Early m

od

ern h

um

an d

iversity sug

gests su

bd

ivided

po

pu

lation

structu

re and

a com

plex o

ut-o

f-Africa scen

arioC

omparison of cranial ontogenetic trajectories am

ong great apes and humans P

hilipp Mitteroeckera*,

Evolutionary M

orphing David F

. Wiley http://graphics.idav.ucdavis.edu/research/projects/E

voMorph

• Landmarks

• Semilandmarks

Summary•Comparative Biology

•The Domain of Comparative Biology

•The purpose of Comparative Biology

•Co-modeling in Comparative Biology

•Examples of Stochastic Comparative Modeling

•Shape Evolution

•Protein Structure Evolution

•Movement Evolution

•RNA Secondary Structure Evolution

•Genome Structure Evolution

•Gene Frequencies in Populations

•Pattern Evolution

•Stemmatology: Manuscript Evolution