5 Open Problems in Bioinformatics. Pedigrees from Genomes Comparative Genomics of Alternative Splicing Viral Annotation Evolving Turing Patterns Protein Structure Evolution. From genomes to pedigrees. Coalescent Rebombination process. Seqeunce/Individual Boundary. Pedigree process.
Coalescent Rebombination process
From Yun Song
Elston-Stewart (1971) -Temporal Peeling Algorithm:
Condition on parental states
Recombination and mutation are Markovian
Lander-Green (1987) - Genotype Scanning Algorithm:
Condition on paternal/maternal inheritance
Recombination and mutation are Markovian
Comment: Obvious parallel to Wiuf-Hein99 reformulation of Hudson’s 1983 algorithm
Genomes with r and m/r --> infinity
r - recombination rate, m - mutation rate
From Phylogenies to Pedigrees
Mike’s counter example, linkage and individuals
Gluing Phylogenies together
Sibling Sequences come from different parents.
A recombinants’ parent are sister sequences.
Classes of Gene Structures
Diarrhoea Causing Arrangements
Illustrating the 3 main classes of gene structures: Unidirectional, Convergent and Divergent.
Our 8 State HMM which allows for Unidirectional overlapping gene structures
Assume multiplicativity: fA,B = fA*fB
Hein & Støvlbæk, 1995
Codon Nucleotide Independence Heuristic
Jensen & Pedersen, 2001
Table illustrating the performance benefit in Sensitivity we obtain utilizing a Phylogenetic HMM. We extend the HMM model to include evolutionary information from 13 aligned HIV2 sequences.
GenBank: Centralized resource for publicly available viral sequence data.
Entrez Genomes currently contains 2120 Reference Sequences for 1510 viral genomes and 36 Reference Sequences for viroids.
Properties of overlapping genes are conserved across microbial genomes.Genome Res. 2004 Nov;14(11):2268-72.
Within microbial genomes, one third of annotated genes contain some degree of overlap, and one third of these are either Convergent or Divergent.
Krakauer, D.C. Stability and evolution of overlapping genes.
Evolution 54: 731-739 (2000) Genome Res. 2004 Nov;14(11):2268-72.
General preponderance of overlapping gene structures is roughly a 90:9:1 ratio split across Unidirectional, Convergent and Divergent arrangements.
From Maini’s Home Page: http://www.maths.ox.ac.uk/~maini
Stripes: p small
Spots: p large
[From: Leppanen et al. Dimensionality effects in Turing pattern formation, Int. J. Mod. Phys. B 17, 5541-5553 (2003)]
Networks and Turing Patterns
2. Stochastic Partial Differential Equations
3. Phylogenetically related Turing Patterns
300 amino acid changes
800 nucleotide changes
1 structural change
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(SequenceStructure) & Fitness of Structure
3. Summation over all paths.
A. Structure (Homology Modelling, Topology)
As a first approximation similar structures should be compared and the problem could be solved by comparative modelling.
Fast Homology Modelling
Using Protein Topology as Hidden Variable
Fitness of Structure – such functions are common place in guiding prediction programs.
Protein Structure Analysis is much harder than Sequence Analysis. Much of the first hand impression will remain: “Structures are either trivially similar or highly dissimilar” – the middle ground is empty.
At Gyr scale other rearrangements occur.
Positive Note: If it works
Test of smooth/catastrophic structure evolution
Separation of analogous/homologous similarities
Protein Evolution in General
How closely linked are homologous and structurally equivalent sites?
Pedigrees from Genomes
Does infinite genomes determine pedigrees?
How many pedigrees are there?
Comparative Genomics of Alternative Splicing
How well do you know the ASG?
How do you measure selection on the ASG?
How well can you annotate viruses from observed evolution?
Evolving Turing Patterns
Turing Patterns and Networks
Stochastic Turing Patterns
Phylogenetically Related Turing Patterns
Protein Structure Evolution
Full Model of Structure Evolution
Model of Protein Topology Evolution