Hidden Markov Models Probabilistic model of a Multiple

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

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 seen through the direct comparison of their sequences.

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

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.

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.

Match State with no Indels MSGL MTNL B M 1 M 2 M 3 M 4 Arrow indicates transition probability. In this case 1 for each step E

Match State with no Indels MSGL MTNL B M=1 S=0. 5 T=0. 5 M 1 M 2 M 3 M 4 E Also have probability of Residue at each positon

Typically want to incorporate small probability for all other amino acids. MSGL MTNL B M=1 S=0. 5 T=0. 5 M 1 M 2 M 3 M 4 E

Permit insertion states MS. GL MT. NL MSANI I 0 I 1 I 2 I 3 I 4 B M 1 M 2 M 3 M 4 Transition probabilities may not be 1 E

Permit insertion states MS. . GL MT. . NL MSA. NI MTARNL I 0 I 1 I 2 I 3 I 4 B M 1 M 2 M 3 M 4 E

DELETE PERMITS INCORPORATION OF LAST TWO SITES OF SEQ 1 MS. . GL-MT. . NLAG MSA. NIAG MTARNLAG D 1 D 2 D 3 D 4 D 5 D 6 D 7 I 4 I 5 I 6 I 7 I 0 I 1 I 2 I 3 B M 1 M 2 M 3 M 4 S T A A G N M M 5 M 6 I L A M 7 G 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. D 1 D 2 D 3 D 4 D 5 D 6 I 4 I 5 I 6 I 0 I 1 I 2 I 3 B M 1 M 2 M 3 M 4 M 5 M 6 E

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

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

Rotation around the peptide bond

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

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

From: http: //bioweb. ncsa. uiuc. edu/~bioph 254/Class-slides/Lect 12/figure 13. html

Longitudinal and Transverse image of alpha helix From: http: //bioweb. ncsa. uiuc. edu/~bioph 254/Class-slides/Lect 12/figure 14. html

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

Hemoglobin - ribbon representation

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

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

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

b sheet - longitudinal and transverse view. Side chains stick “out” http: //bioweb. ncsa. uiuc. edu/~bioph 254/Class-slides/Lect 12/figure 22. html

Superoxide dismutase - b sheet

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

CD 8 -all b

Thioredoxin a / b

Endonuclease Class a + b

Rhodopsin 7 TM proten

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

• 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.

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

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

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

Coiled Coil • Two or more adjacent a helices

Prediction of potential Coiled coil domain in Groucho

Potential Residues involved in Coiled Coil MMFPQSRHSGSSHLPQQLKFTTSDSCDRIKDEFQLLQAQYHSL KLECDKLASEKSEMQRHYVMYYEMSYGLNIEMHKQAEIVKR LNGICAQVLPYLSQEHQQQVLGAIERAKQVTAPELNSIIRQQL QAHQLSQLQALALPLTPLPVGLQPPSLPAVSAGTGLLSLSALG SQTHLSKEDKNGHDGDTHQEDDGEKSD

Triple helix coiled coil - built from a helices

Backbone of triple coiled coil

E. coli Nucleotide exchange factor

Domains • Single domain proteins • Epidermal growth factor • Serine Proteases - Trypsin • Multi domain proteins -Factor IX -one Ca 2+ binding, two EGF/ one protease domain. • Permit building of novel functions by swapping of domains

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

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

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

GOR prediction • Similar to Chou - Fassman – More recent (1988) tabulation of amino acid preferences. – Uses a larger window -17

More Recent Prediction Programs • Make use of library of 3 d structures to predict structure. • Most use a Neural Net approach for prediction. • Examples – Nnpredict – Predict. Protein

Neural Net • Programs “trained” on structures. • Window -within the window each position is predicted based upon knowledge. • Rules also applied (alpha helix 4 AA long) window a b coil Input Hidden Output

Predict. Protein • Uses an alignment approach. • Submitted sequence is compared to database and alignment is generated • Profile is generated for further database searching. • Alignment is then used for prediction of secondary structure. • Confidence predicted - based upon number of residues of given type at a given position in the alignment

Kyte and Doolittle Hydropathy • Average of hydropathy index for each residue. • Examle of Hydropathy index: • F +2. 8 • R -4. 5

Transmembrane Domain • Characteristics make them easier to predict: – – a helix structure Hydrophobic amino acids 19 or more amino acids long charged residue will typically have an opposing charge for neutralization. • Difficulty in predicted ends of transmembrane domains.

Caveat • Local secondary structure can be influenced by tertiary structure. • Identical string of residues can be an a helix in one protein but a b strand in another protein.

3 D structural prediction

>gi|14769656|ref|XP_010270. 4| coagulation factor IX [Homo sapiens] MQRVNMIMAESPGLITICLLGYLLSAECTVFLDHENANKILNRPKRYNSGKLEEFVQGNLERECMEEKCSFEEAREVFEN TERTTEFWKQYVDGDQCESNPCLNGGSCKDDINSYECWCPFGFEGKNCELDVTCNIKNGRCEQFCKNSADNKVVCSCTEG YRLAENQKSCEPAVPFPCGRVSVSQTSKLTRAETVFPDVDYVNSTEAETILDNITQSTQSFNDFTRVVGGEDAKPGQFPW QVVLNGKVDAFCGGSIVNEKWIVTAAHCVETGVKITVVAGEHNIEETEHTEQKRNVIRIIPHHNYNAAINKYNHDIALLE LDEPLVLNSYVTPICIADKEYTNIFLKFGSGYVSGWGRVFHKGRSALVLQYLRVPLVDRATCLRSTKFTIYNNMFCAGFH EGGRDSCQGDSGGPHVTEVEGTSFLTGIISWGEECAMKGKYGIYTKVSRYVNWIKEKTKLT Pfam Protein Information Resource KFHU

Tertiary Structure • Still challenging • Focus upon core structure for prediction Hydrophobic interactions that stabilize structure.

Approach • Determine “fit”of a query sequence to library of known structures. – Threading- examine compatibility of amino acid side groups with known structures – Two approaches: • Environmental template • Contact potential

Environmental Template • Each amino acid in known core evaluated for: – secondary structure – area of side chain buried – types of nearby AA side chains

Arginine - basic Aa Isoleucine Different propensity to be in a hydrophobic environment. Might accommodate charge by opposite charge

Environmental • Query sequence is submitted to previously analyzed database of structures – How well does your sequence fit these protein cores?

Contact Potential • Number and closeness between each AA pair determined. • Query sequence examined to determine if potential AA interactions match those of known cores.

Structural Profile • Structural position specific scoring matrix • Identify which amino acid fit into a specific position in the core of each known structure – each position is assigned to one of the 18 classes of structural environment – scores reflect suitability of AA for that position – log odds matrix • Use profile to examine query sequence

Z score • Many return an E value or a Z score • Z score the number of standard deviations from the mean score for all sequences. • The higher the Z score, the more significant the model -typical good score >5.