1. 5 Open Problems in Bioinformatics Pedigrees from Genomes Comparative Genomics of Alternative Splicing Viral Annotation Evolving Turing Patterns Protein Structure Evolution

2. Three Processes 1.Recombination 2.Choosing Parents 3.The Mutational Process Pedigree process Coalescent Rebombination process Seqeunce/Individual Boundary From Yun Song From genomes to pedigrees

3. Probability of Data given a pedigree. Elston-Stewart (1971) -Temporal Peeling Algorithm: Lander-Green (1987) - Genotype Scanning Algorithm: Mother Father Condition on parental states Recombination and mutation are Markovian Mother Father Condition on paternal/maternal inheritance Recombination and mutation are Markovian Comment: Obvious parallel to Wiuf-Hein99 reformulation of Hudson’s 1983 algorithm

4. Genomes with  and  --> infinity  recombination rate,  mutation rate Counting within a small interval would reveal the length of the path connecting the two segments. Siblings are readily revealed, since they will have segments with 2  density of mutations The distribution of path lengths are readily observable between two sequences All embedded phylogenies are observable Benevolent Mutation and Recombination Process

5. From Phylogenies to Pedigrees Mike’s counter example, linkage and individuals 12 12 12 12 12 12 12 12 Pedigree 1Pedigree 2 grandparents Individual 1 Individual 2 Different Pedigrees Same Phylogenies Gluing Phylogenies together ? Sibling Sequences come from different parents. A recombinants’ parent are sister sequences.

6. Comparative Genomics of Alternative Splicing

7. From Transcripts to the AS-Graph EES S 1.How well known is the AS-graph as a function number of transcripts? 2.A family and distribution of transcripts, can they be explained an AS-graph with probabilities at donor sites or do we need probabilities for (donor,acceptor) pairs? Or possibly even more complicated situations. And is sampling transcripts good enough to distinguish these situations.

8. Mini-project: reliability of AS-detection. Choose Idealized AS-Graph: 1.Genome 2.Choose donor and acceptor sites in random pairs. 3.For each possible splice pair assign probability for choosing it. This should define a probability for all transcripts. Generate a set of transcripts. Reconstruct AS-Graph. Key questions: 1.How many transcripts must be sampled to detect AS. 2.How well will the AS-Graph be recovered?

9. Optimal DAG (directed acyclic graph) under restrictions Optimal Paths: Sub-optimal Paths: Finding a set of annotations: 1.Find set of paths, maximizing sum of scores. 2.The score of minimal path must be above threshold. Two paths must differ significantly: An enclosed area, the maximal height must be d higher than the boundary defining it. Height(i,j) = d i,j + d i,j 1.Does known AS genes have more CTO structure than non-AS genes? 2.Do the AS correspond to the CTO structure 3.Is the CTO structure evolutionary conserved?

10. Phylogenetically related ASGs 1.Is ASG conserved? 2.What is conserved? 3.How is selection along position dependent on splicing status? E E S S E E S S E E S S

11. http://www.tulane.edu/~dmsander/WWW/335/Diarrhoea.html http://www.tulane.edu/~dmsander/WWW/335/Papovaviruses.html http://www.tulane.edu/~dmsander/WWW/335/Retroviruses.html Virus Annotation Classes of Gene Structures Retroviridae Arrangements Papoviridae Arrangement Diarrhoea Causing Arrangements Illustrating the 3 main classes of gene structures: Unidirectional, Convergent and Divergent.

12. The Problems of Viral Annotation HMM gene structure generator (McCauley) Gene Structure Evolution (de Groot) Alignment (Caldeira, Lunter, Rocco) Recombination (Lyngsø, Song) Multiple constraints: RNA secondary structure, gene conservation, binding/transcriptional instructional sites.

13. Our 8 State HMM which allows for Unidirectional overlapping gene structures HMM States Non-coding Coding RF1 Coding RF2 Coding RF3 Coding RF1,2 Coding RF1,3 Coding RF2,3 Coding RF1,2,3

14. Combining Levels of Selection. Protein-Protein Hein & Støvlbæk, 1995 Codon Nucleotide Independence Heuristic Jensen & Pedersen, 2001 Contagious Dependence Assume multiplicativity: f A,B = f A *f B Protein-RNA DoubletsSinglet Contagious Dependence

15. HIV2 Genomes SS HMM Sensitivity PHMM Sensitivity Del Sensitivity SS HMM Specificity PHMM Specificity Del Specificity M305020.89130.97650.08520.98780.9753-0.0125 J045420.84580.91730.07141.00000.9956-.0044 D008350.87960.94320.06360.99200.9733-0.0187 M153900.93100.99710.06611.00000.9869-0.0131 J036540.82610.99710.17091.00000.9865-0.0135 AY5092590.86970.92560.05591.00000.9886-0.0114 AY5092600.82570.91010.08440.99280.9792-0.0136 J044980.89610.97370.07761.00000.9911-0.0089 AF0823390.90740.96500.05770.98420.9773-0.0069 U220470.90280.98740.08470.98650.9744-0.0121 U272000.87690.94530.06840.99280.9748-0.0180 LO76250.83400.96800.13401.00000.9607-0.0393 L368740.86530.99570.13030.99800.9766-0.0214 MEANS0.87320.96170.08850.99490.9800-0.0149 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.

16. http://www.ncbi.nlm.nih.gov/Genbank/ http://www.ncbi.nlm.nih.gov/genomes/VIRUSES/viruses.html Entrez Genomes currently contains 2120 Reference Sequences for 1510 viral genomes and 36 Reference Sequences for viroids.2120 Reference Sequences 1 469469 9595 6 Properties of overlapping genes are conserved across microbial genomes. Genome Res. 2004 Nov;14(11):2268-72. GenBank: Centralized resource for publicly available viral sequence data. 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.

17. Turing Patterns

18. From Maini’s Home Page: http://www.maths.ox.ac.uk/~mainihttp://www.maths.ox.ac.uk/~maini Mathematical models to understand biological patterns Turing Model

19. [From: Leppanen et al. Dimensionality effects in Turing pattern formation, Int. J. Mod. Phys. B 17, 5541-5553 (2003)] Different parameters lead to different patterns Stripes: p smallSpots: p large

20. 3 suggestions 1.Networks and Turing Patterns 2. Stochastic Partial Differential Equations 3. Phylogenetically related Turing Patterns

21. Evolutionary Models of Protein Structure Evolution Known Unknown  -globin Myoglobin 300 amino acid changes 800 nucleotide changes 1 structural change 1.4 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.

22. 2 suggestions Folding(Sequence  Structure) As a first approximation similar structures should be compared and the problem could be solved by comparative modelling. Fitness of Structure – such functions are common place in guiding prediction programs. Fast Homology Modelling B. MCMC A. Structure  (Homology Modelling, Topology) Using Protein Topology as Hidden Variable

23. Questions to be asked 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. Test of smooth/catastrophic structure evolution Separation of analogous/homologous similarities Protein Evolution in General How closely linked are homologous and structurally equivalent sites? Negative Note: Positive Note: If it works http://www.biochem.ucl.ac.uk/bsm/cath/ http://scop.mrc-lmb.cam.ac.uk/scop/

24. Summary 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? Viral Annotation 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