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### Advanced Hidden Markov Models for Sequence Alignment: Theory and Applications ###

This text elaborates on the application of Hidden Markov Models (HMMs) for multiple sequence alignment without the need for indel penalties. It emphasizes the utility of HMMs to synthesize experimentally derived information and adjust parameters that reflect observed variations across at least 20 sequences. The document explores evolutionary aspects of sequences, including the introduction of mutations and divergence over time, and highlights how HMMs can act as intermediates to uncover relationships among sequences, enhancing our understanding of sequence evolution and protein structure. ###

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### Advanced Hidden Markov Models for Sequence Alignment: Theory and Applications ###

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  1. Hidden Markov Models • Probabilistic model of a Multiple sequence alignment. • No indel penalties are needed • Experimentally derived information can be incorporated • Parameters are adjusted to represent observed variation. • Requires at least 20 sequences

  2. The Evolution of a Sequence • Over long periods of time a sequence will acquire random mutations. • These mutations may result in a new amino acid at a given position, the deletion of an amino acid, or the introduction of a new one. • Over VERY long periods of time two sequences may diverge so much that their relationship can not see seen through the direct comparison of their sequences.

  3. Hidden Markov Models • Pair-wise methods rely on direct comparisons between two sequences. • In order to over come the differences in the sequences, a third sequence is introduced, which serves as an intermediate. • A high hit between the first and third sequences as well as a high hit between the second and third sequence, implies a relationship between the first and second sequences.Transitive relationship

  4. Introducing the HMM • The intermediate sequence is kind of like a missing link. • The intermediate sequence does not have to be a real sequence. • The intermediate sequence becomes the HMM.

  5. Introducing the HMM • The HMM is a mix of all the sequences that went into its making. • The score of a sequence against the HMM shows how well the HMM serves as an intermediate of the sequence. • How likely it is to be related to all the other sequences, which the HMM represents.

  6. B M1 M2 M3 M4 E Match State with no Indels MSGL MTNL Arrow indicates transition probability. In this case 1 for each step

  7. B M1 M2 M3 M4 E Match State with no Indels MSGL MTNL S=0.5 T=0.5 M=1 Also have probability of Residue at each positon

  8. B M1 M2 M3 M4 E Typically want to incorporate small probability for all other amino acids. MSGL MTNL S=0.5 T=0.5 M=1

  9. B M1 M2 M3 M4 E Permit insertion states MS.GL MT.NL MSANI I0 I1 I2 I3 I4 Transition probabilities may not be 1

  10. B M1 M2 M3 M4 E Permit insertion states MS..GL MT..NL MSA.NI MTARNL I0 I1 I2 I3 I4

  11. DELETE PERMITS INCORPORATION OF LAST TWO SITES OF SEQ1 MS..GL-- MT..NLAG MSA.NIAG MTARNLAG AA GN IL ST A M D1 D2 D3 D4 D5 D6 D7 I7 I0 I1 I2 I3 I4 I5 I6 M4 E M2 M3 M5 M6 B M1 M7 G

  12. D1 D2 D3 D4 D5 D6 I0 I1 I2 I3 I4 I5 I6 B M1 M2 M3 M4 M5 M6 E • The bottom line of states are the main states (M) • These model the columns of the alignment • The second row of diamond shaped states are called the insert states (I) • These are used to model the highly variable regions in the alignment. • The top row or circles are delete states (D) • These are silent or null states because they do not match any residues, they simply allow the skipping over of main states.

  13. Dirichlet Mixtures • Additional information to expand potential amino acids in individual sites. • Observed frequency of amino acids seen in certain chemical environments • aromatic • acidic • basic • neutral • polar

  14. STRUCTURES a helix b sheet coils turns Structures are used to build domains.-Legos of evolution

  15. Rotation around the peptide bond

  16. Ramachandran plot for Glycine Areas not permitted for other amino acids Psi Angles Phi angles

  17. Introduction to Protein Structure, Branden and Tooze Garland Publishing Co.1991 p.13

  18. From: http://bioweb.ncsa.uiuc.edu/~bioph254/Class-slides/Lect12/figure13.html

  19. Longitudinal and Transverse image of alpha helix From: http://bioweb.ncsa.uiuc.edu/~bioph254/Class-slides/Lect12/figure14.html

  20. Turn connecting two helices Introduction to Protein Structure, Branden and Tooze Garland Publishing Co.1991 p. 17

  21. Hemoglobin - ribbon representation

  22. Proline • Because of its structure, proline is typically excluded from a helices except in the first three positions at the amino end.

  23. b Structure b strand - single run of amino acids in b conformation b sheet- multiple b strands which are hydrogen bonded to yield a sheet like structure. b bulge - disruption of normal hydrogen bonding in a b sheet by amino acid(s) that will not fit into the sheet -for example: proline

  24. b sheets- Parallel Introduction to Protein Structure, Branden and Tooze Garland Publishing Co.1991 p.17.

  25. b sheet - longitudinal and transverse view. Side chains stick “out” http://bioweb.ncsa.uiuc.edu/~bioph254/Class-slides/Lect12/figure22.html

  26. Superoxide dismutase - b sheet

  27. Superoxide dismutase - b sheet

  28. Six classes of structure • Class a- bundled a helices connected by loops. • Class b- sandwich or barrel comprised entirely of b sheets typically anti-parallel. • Class a / b mainly parallel b sheets with intervening a helices. • Class a + b - segregated a helices and anti-parallel b sheets • Multi-domain • Membrane proteins

  29. CD8 -all b

  30. Thioredoxin a / b

  31. Endonuclease Class a + b

  32. Rhodopsin 7TM proten

  33. Common Hairpin Loop between two b Strands Introduction to Protein Structure, Branden and Tooze Garland Publishing Co.1991 p. 17

  34. Turn - short, regular loop. • Difference in frequency of amino acids at positions 1-4 of the turn. • Coils (not coiled coil) • Random turns or irregular structure.

  35. Disulfide bridges • Crosslink of two cysteine residues. • Distance between sulfur = 3 Angstroms.

  36. Coiled coil -two a helices bundled side by side From: http://catt.poly.edu/~jps/coilcoil.html

  37. a,d are internal, remaining amino acids are solvent exposed From: http://catt.poly.edu/~jps/coilcoil.html

  38. Coiled Coil • Two or more adjacent a helices

  39. Prediction of potential Coiled coil domain in Groucho

  40. Potential Residues involved in Coiled Coil MMFPQSRHSGSSHLPQQLKFTTSDSCDRIKDEFQLLQAQYHSL KLECDKLASEKSEMQRHYVMYYEMSYGLNIEMHKQAEIVKR LNGICAQVLPYLSQEHQQQVLGAIERAKQVTAPELNSIIRQQL QAHQLSQLQALALPLTPLPVGLQPPSLPAVSAGTGLLSLSALG SQTHLSKEDKNGHDGDTHQEDDGEKSD

  41. Triple helix coiled coil - built from a helices

  42. Backbone of triple coiled coil

  43. E. coli Nucleotide exchange factor

  44. Domains • Single domain proteins - • Epidermal growth factor • Serine Proteases - Trypsin • Multi domain proteins -Factor IX -one Ca2+ binding, two EGF/ one protease domain. • Permit building of novel functions by swapping of domains

  45. Factor IX Domain Structure Ca EGF EGF CT Ca - Calcium binding domain EGF - Epidermal growth factor domain CT - Chymotrypsin domain

  46. Chou - Fasman Prediction of Secondary Structure • Based upon analysis of known structures (1974). • Frequency of occurrence of each amino acid in: • a helix • b strand • turn

  47. Chou - Fasman Prediction • List is then analyzed for stretches of amino acids that have a common tendency to form a given secondary structure. • Extend until a region of high probability for either a turn or region with a low probability of both a or b is encountered. • Window is typically <10

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