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CSE182-L6

Protein sequence analysis

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Possible domain queries

• Case 1: – You have a collection of sequences that belong to a

family (contain a functional domain).– Given an ‘orphan’ sequence, does it belong to the

family?– There are different solutions depending upon the

representation of the domain (patterns/alignments/HMM/profiles)

• Case 2: – You have an orphan sequence from an

uncharacterized family. Can you identify other members of the family, and create a representation of them (Harder problem).

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EX: Innexins

• The Macagno lab is studying Gap junction proteins, Innexins (invertebrate analogs of connexins) in Hirudo

• Innexins have been found in C. elegans, and Drosophila.

• In C. elegans, 25 members of this family have been found, and partially categorized.

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Innexins in Hirudo

• When certain Innexins are knocked out, they cause serious defects in cells in the ganglia.

• The EST database (partial gene sequences) contains a number of putative Innexins, discovered via BLAST.

• Project:• Q: Can you confirm that these are Innexins. Can you

find more members? (this lecture)• Q: Can you characterize them w.r.t known innexins in C.

elegans, and Drosophila?• Q: Use your method for other families of interest.

Netrins, and their receptors.

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Not all features(residues) are important

Skin patternsFacial Features

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Protein sequence motifs

• Premise: • The sequence of a protein sequence gives clues about its

structure and function.• Not all residues are equally important in determining

function.• Suppose we knew the key residues of a family. If our query

matches in those residues, it is a member. Otherwise, it is not.

• The key residues can be identified if we had structural information, or through conserved residues in an alignment of the family.

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Representation of domains/families.

• We will consider a number of representations that describe key residues, characteristic of a family– Patterns (regular expressions)– Alignments– Profiles– HMMs

• Start with the following:– A collection of sequences with the same function.– Region/residues known to be significant for maintaining structure and

function. • Develop a pattern of conserved residues around the

residues of interest• Iterate for appropriate sensitivity and specificity

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From alignment to patterns

* ALRDFATHDDF SMTAEATHDSI ECDQAATHEAS

ATH-[DE]

• Search a database with the resulting pattern• Refine pattern to eliminate false positives• Iterate

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Regular Expression Patterns

• Zinc Finger motif– C-x(2,4)-C-x(3)-[LIVMFYWC]-x(8)-H-x(3,5)-H – 2 conserved C, and 2 conserved H

• How can we search a database using these motifs?– The motif is described using a regular expression.

What is a regular expression?

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Regular Expressions

• Concise representation of a set of strings over alphabet .

• Described by a string over• R is a r.e. if and only if

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Σ,⋅,∗,+{ }

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R = {ε} Base caseR = {σ },σ ∈ ΣR = R1 + R2 Union of stringsR = R1 ⋅R2 ConcatenationR = R

1

* 0 or more repetitions

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Regular Expression

• Q: Let ={A,C,E}– Is (A+C)*EEC* a regular expression?– Is *(A+C) regular?

• Q: When is a string s in a regular expression?– R =(A+C)*EEC*– Is CEEC in R?– AEC?– ACEE?

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Regular Expression & Automata

Every R.E can be expressed by an automaton (a directed graph) with the following properties:– The automaton has a start and end node– Each edge is labeled with a symbol from , or

Suppose R is described by automaton AS R if and only if there is a path from start to end in A, labeled with s.

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Examples: Regular Expression & Automata

• (A+C)*EEC*

CA

C

start endE E

–Is CEEC in R?–AEC?–ACEE?–ACE?

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Constructing automata from R.E

• R = {}• R = {}, • R = R1 + R2

• R = R1 · R2

• R = R1*

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Regular Expression Matching

• Given a database D, and a regular expression R, is a substring of D in R?

• Is there a string D[l..c] that is accepted by the automaton of R?

• Simpler Q: Is D[1..c] accepted by the automaton of R?

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Alg. For matching R.E.

• If D[1..c] is accepted by the automaton RA

– There is a path labeled D[1]…D[c] that goes from START to END in RA

D[1] D[2] D[c]

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Alg. For matching R.E.

• If D[1..c] is accepted by the automaton RA

– There is a path labeled D[1]…D[c] that goes from START to END in RA

– There is a path labeled D[1]..D[c-1] from START to node u, and a path labeled D[c] from u to the END

D[1] .. D[c-1]

D[c]

u

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D.P. to match regular expression

• Define:– A[u,] = Automaton node

reached from u after reading

– Eps(u): set of all nodes reachable from node u using epsilon transitions.

– N[c] = subset of nodes reachable from START node after reading D[1..c]

– Q: when is v N[c]

uu vv

uu Eps(u)Eps(u)

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• Q: when is v N[c]?• A: If for some u N[c-1], w = A[u,D[c]],

• v {w}+ Eps(w)

D.P. to match regular expression

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Algorithm

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The final step

• We have answered the question:– Is D[1..c] accepted by R?– Yes, if END N[c]

• We need to answer – Is D[l..c] (for some l, and some c) accepted by R

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D[l..c]∈ R⇔ D[1..c]∈ Σ∗R

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Representation 2: Profiles

• Profiles versus regular expressions – Regular expressions are intolerant to an occasional

mis-match.– The Union operation (I+V+L) does not quantify the

relative importance of I,V,L. It could be that V occurs in 80% of the family members.

– Profiles capture some of these ideas.

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Profiles

• Start with an alignment of strings of length m, over an alphabet A,

• Build an |A| X m matrix F=(fki)

• Each entry fki represents the frequency of symbol k in position i

0.71

0.14

0.14

0.28

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Profiles

• Start with an alignment of strings of length m, over an alphabet A,

• Build an |A| X m matrix F=(fki)

• Each entry fki represents the frequency of symbol k in position i

0.71

0.14

0.14

0.28

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Scoring matrices

• Given a sequence s, does it belong to the family described by a profile?

• We align the sequence to the profile, and score it

• Let S(i,j) be the score of aligning position i of the profile to residue sj

• The score of an alignment is the sum of column scores.

s

sj

i

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Scoring Profiles

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S(i, j) = fkik

∑ M rk,s j[ ]

k

i

s

fki

Scoring Matrix

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Domain analysis via profiles

• Given a database of profiles of known domains/families, we can query our sequence against each of them, and choose the high scoring ones to functionally characterize our sequences.

• What if the sequence matches some other sequences weakly (using BLAST), but does not match any Profile?

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Psi-BLAST idea

• Iterate:– Find homologs using Blast on query– Discard very similar homologs– Align, make a profile, search with profile.– Why is this more sensitive?

Seq Db

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Psi-BLAST speed

• Two time consuming steps.1. Multiple alignment of homologs2. Searching with Profiles.

1. Does the keyword search idea work?

• Multiple alignment:– Use ungapped multiple

alignments only

• Pigeonhole principle again: – If profile of length m must score >= T– Then, a sub-profile of length l must

score >= lT|/m– Generate all l-mers that score at least

lT|/M– Search using an automaton

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Representation 3: HMMs

• Question:• your ‘friend’ likes to gamble. • He tosses a coin: HEADS, he gives you a dollar.

TAILS, you give him a dollar.• Usually, he uses a fair coin, but ‘once in a

while’, he uses a loaded coin. • Can you say what fraction of the times he

loads the coin?

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Representation 3: HMMs

• Building good profiles relies upon good alignments.– Difficult if there are gaps in the

alignment.– Psi-BLAST/BLOCKS etc. work

with gapless alignments.

• An HMM representation of Profiles helps put the alignment construction/membership query in a uniform framework.

V

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The generative model

• Think of each column in the alignment as generating a distribution.

• For each column, build a node that outputs a residue with the appropriate distribution

0.71

0.14

Pr[F]=0.71Pr[Y]=0.14

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A simple Profile HMM

• Connect nodes for each column into a chain. Thie chain generates random sequences.

• What is the probability of generating FKVVGQVILD?• In this representation

– Prob [New sequence S belongs to a family]= Prob[HMM generates sequence S]

• What is the difference with Profiles?

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Profile HMMs can handle gaps

• The match states are the same as on the previous page.

• Insertion and deletion states help introduce gaps.

• A sequence may be generated using different paths.

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Example

• Probability [ALIL] is part of the family?• Note that multiple paths can generate this sequence.

– M1I1M2M3

– M1M2I2M3

• In order to compute the probabilities, we must assign probabilities of transition between states

A L - LA I V LA I - L

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Profile HMMs

• Directed Automaton M with nodes and edges. – Nodes emit symbols according to ‘emission

probabilities’– Transition from node to node is guided by ‘transition

probabilities’

• Joint probability of seeing a sequence S, and path P– Pr[S,P|M] = Pr[S|P,M] Pr[P|M]– Pr[ALIL AND M1I1M2M3]

= Pr[ALIL| M1I1M2M3,M] Pr[M1I1M2M3| M]

• Pr[ALIL | M] = ?

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Protein structure basics

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Side chains determine amino-acid type

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• The residues may have different properties.• Aspartic acid (D), and Glutamic Acid (E) are acidic

residues

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Bond angles form structural constraints

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Various constraints determine 3d structure

• Constraints– Structural constraints due to physiochemical

properties– Constraints due to bond angles– H-bond formation

• Surprisingly, a few conformations are seen over and over again.

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Alpha-helix

• 3.6 residues per turn• H-bonds between 1st

and 4th residue stabilize the structure.

• First discovered by Linus Pauling

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Beta-sheet

• Each strand by itself has 2 residues per turn, and is not stable.• Adjacent strands hydrogen-bond to form stable beta-sheets, parallel or anti-parallel.• Beta sheets have long range interactions that stabilize the structure, while alpha-helices have local

interactions.

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Domains

• The basic structures (helix, strand, loop) combine to form complex 3D structures.

• Certain combinations are popular. Many sequences, but only a few folds

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3D structure

• Predicting tertiary structure is an important problem in Bioinformatics.

• Premise: Clues to structure can be found in the sequence.• While de novo tertiary structure prediction is hard, there are

many intermediate, and tractable goals.• The PDB database is a compendium of structures

PDB

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Searching structure databases

• Threading, and other 3d Alignments can be used to align structures.

• Database filtering is possible through geometric hashing.

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Trivia Quiz

• What research won the Nobel prize in Chemistry in 2004?

• In 2002?

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How are Proteins Sequenced? Mass Spec 101:

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Nobel Citation 2002

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Nobel Citation, 2002

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Mass Spectrometry

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Sample Preparation

Enzymatic Digestion (Trypsin)

+Fractionation

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Single Stage MS

MassSpectrometry

LC-MS: 1 MS spectrum / second

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Tandem MS

Secondary Fragmentation

Ionized parent peptide