Comparative Biology observabl e observabl e Parameters:tim e rates, selection Unobservable Evolutionary Path observabl e Most Recent Common Ancestor ? ATTGCGTATATAT….CAG ATTGCGTATATAT….CAG ATTGCGTATATAT….CAG T i m e D i r e c t i o n •Which phylogeny? •Which ancestral states? •Which process? Key Questions: •Homologous objects •Co-modelling • Genealogical Key Generalisations:
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Comparative Biology observable Parameters:time rates, selection Unobservable Evolutionary Path observable Most Recent Common Ancestor ? ATTGCGTATATAT….CAG.
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membrane Single molecules measurem ents, X-ray diffraction of crystals, N MR
Classical potentials and Newtonian Dynamics, Quantum Mechanics,
Molecular complexes Ribosome, hemoglobin, single molecule measu rements Mechanical analo gues models, Continuous Time Markov Chain with finite state space
Molecule concentrations
Concentration of meta bolites, fate of isotopes in different molecules,
ODEs (many molecules/c oncentrations), kinetics,
Metabolic Network Citric Acid Cycle Enzyme and metabolite concentrations and metabonomics
ODEs, Kinetic Models, Flux Analysis,
Regulatory Network -globins and their regulators
Expression data Boolean networks, Petri Nets, ODEs
Signal Transduction Mitogen-activated protein -kinase (MAPK)
Protein Interaction and Expression Data
ODEs, Continuous Time Markov Chains,
Protein Interaction Network
Yeast PIN Mass Spectroscopy No dynamics involved, i.e. a data type.
Motors Flagellar Motor, Microscopy, single molecule flourescen ce
Mechanical Analog ue Models
Cell(s) B-Cell, zygote, E.coli, Microscopy, expressi on data, proteomics,..
Integration of genetic, mechanical and network models.
Tissue Cancer, Partial differentia l equation (PDEs), cellular automata.
Organ Liver, lung, heart Mechanical measurem ents, Multilevel integrated modelling, including mechanics.
How to Compare?Examples
Protein Structures Networks Craniums/Shape
Homologous - Non-Homologous?
Homologous components A C G TA - T T
Matching - Similarity - Distance
Distance from shortest paths
The ideal: The probability of 1 observation * Summing over possible evolutionary trajectories to the second observation.
Informal
A set:
AG
T
AC
CT
AC
CTP( ) P( )
A pair:
“Natural” Evolutionary Modeling
Components: Birth and Death Process. Components are born with rate and die with rate.
Discrete states: Continuous Time Finite States Markov Chains. Initially all rates the same.
p0
p1
p2
p3
Continuous states: Continuous Time Continuous States Markov Process - specifically Diffusion. Initially simplest Diffusion: Brownian Motion, then Ornstein-Uhlenbeck.
Comparative BiologyNucleotides/Amino Acids
Continuous Quantities
Sequences
Gene Structure
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
Language Vocabulary Grammar Phonetics Semantics
• Observed or predicted?
• Choice of Representation.
Comparative Biology: Evolutionary Models
Nucleotides/Amino Acids/codons CTFS continuous time finite state Jukes-Cantor 69 +500 otherContinuous Quantities CTCS Felsenstein 68 + 50 otherSequences CT countable S Thorne, Kishino Felsenstein,91 + 40Gene Structure Matching DeGroot, 07Genome Structure CTCS MMStructure RNA SCFG-model like Holmes, I. 06 + few others ProteinNetworks CT countable S Snijder, T Metabolic Pathways Protein Interaction Regulatory Pathways Signal Transduction Macromolecular Assemblies Motors IShapePatternsTissue/Organs/Skeleton/….Dynamics MD movements of proteins LocomotionCultureLanguage Vocabulary “Infinite Allele Model” (CTCS) Swadesh,52, Sankoff,72,… Grammar - Phonetics Semantics Phenotype
Object Type Reference
“Natural” Co-Modeling
• Joint evolutionary modeling of X(t),Y(t).
The ideal, rarely if ever done.
• Conditional evolutionary modeling of X(t) given Y(t). The standard in comparative genomics. The distribution of Y(t) is not derived from evolution, but from practicality.
A-U + C-G can base pair. Some other pairings can occur + triple interactions exists.
Pseudoknot – non nested pairing: i < j < k < l and i-k & j-l.
Simple String Generators
Context Free Grammar S--> aSa bSb aa bb
One sentence (even length palindromes):S--> aSa --> abSba --> abaaba
Variables (capital) Letters (small)
Regular Grammar: Start with S S --> aT bS T --> aS bT
One sentence – odd # of a’s:S-> aT -> aaS –> aabS -> aabaT -> aaba
Reg
ula
rC
on
text
Fre
e
Stochastic GrammarsThe 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.
S -> aSa -> abSba -> abaaba
i. Start with S. S --> (0.3)aT (0.7)bS T --> (0.2)aS (0.4)bT (0.2)
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.
S -> aT -> aaS –> aabS -> aabaT -> aaba
ii. S--> (0.3)aSa (0.5)bSb (0.1)aa (0.1)bb
*0.3
*0.3 *0.2 *0.7 *0.3 *0.2
*0.5 *0.1
S --> LS L .869 .131F --> dFd LS .788 .212L --> s dFd .895 .105