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Explorations of Multidimensional Sequence Space

Explorations of Multidimensional Sequence Space. one symbol -> 1D. coordinate of dimension = pattern length. Two symbols -> Dimension = length of pattern. length 1 = 1D: . Two symbols -> Dimension = length of pattern. length 2 = 2D: . dimensions correspond to position

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Explorations of Multidimensional Sequence Space

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  1. Explorations ofMultidimensional Sequence Space

  2. one symbol -> 1D coordinate of dimension = pattern length

  3. Two symbols -> Dimension = length of pattern length 1 = 1D:

  4. Two symbols -> Dimension = length of pattern length 2 = 2D: dimensions correspond to position For each dimension two possibiities Note:Here is a possible bifurcation: a larger alphabet could be represented as more choices along the axis of position!

  5. Two symbols -> Dimension = length of pattern length 3 = 3D:

  6. Two symbols -> Dimension = length of pattern length 4 = 4D: aka Hypercube

  7. Two symbols -> Dimension = length of pattern

  8. Three Symbols (another solution is to use more values for each dimension)

  9. Four Symbols: I.e.: with an alphabet of 4, we have a hypercube (4D) already with a pattern size of 2, provided we stick to a binary pattern in each dimension.

  10. hypercubes at 2 and 4 alphabets 2 character alphabet, pattern size 4 4 character alphabet, pattern size 2

  11. Three Symbols Alphabet suggests fractal representation

  12. 3 fractal enlarge fill in outer pattern repeats inner pattern = self similar = fractal

  13. 3 character alphapet3 pattern fractal

  14. 3 character alphapet4 pattern fractal Conjecture: For n -> infinity, the fractal midght fill a 2D triangle Note: check Mandelbrot

  15. Same for 4 character alphabet 1 position 2 positions 3 positions

  16. 4 character alphabet continued(with cheating I didn’t actually add beads) 4 positions

  17. 4 character alphabet continued(with cheating I didn’t actually add beads) 5 positions

  18. 4 character alphabet continued(with cheating I didn’t actually add beads) 6 positions

  19. 4 character alphabet continued(with cheating I didn’t actually add beads) 7 positions

  20. Animated GIf 1-12 positions

  21. Protein Space in JalView

  22. Alignment of V F A ATPase ATP binding SU(catalytic and non-catalytic SU)

  23. UPGMA tree of V F A ATPase ATP binding SU with line dropped to partition (and colour) the 4 SU types (VA cat and non cat, F cat and non cat). Note that details of the tree $%#&@.

  24. PCA analysis of V F A ATPase ATP binding SU using colours from the UPGMA tree

  25. Same PCA analysis of V F A ATPase ATP binding SU using colours from the UPGMA tree, but turned slightly. (Giardia A SU selected in grey.)

  26. Same PCA analysis of V F A ATPase ATP binding SU Using colours from the UPGMA tree, but replacing the 1st with the 5th axis. (Eukaryotic A SU selected in grey.)

  27. Same PCA analysis of V F A ATPase ATP binding SU Using colours from the UPGMA tree, but replacing the 1st with the 6th axis. (Eukaryotic B SU selected in grey - forgot rice.)

  28. Problems • Jalview’s approach requires an alignment. • Solution: Use pattern absence / presence as coordinate • Which patterns? • GBLOCKS (new additions use PSSMs) • CDD PSSM profiles • It would be nice to stick to small words. • One could screen for words/motifs/PSSMs that have a good power of resolution: • PCA with all, choose only the ones that contribute to the main axis • probably better to do data bank search and find how often it is present. One could generate random motifs (or all possible motifs) and check them out (Criterion needs work). • Empirical orthogonality • Exhaustive vs random • How to judge discriminatory power (maybe 5% significance value) • Present absence - optimal discriminatory power?

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