Saul B. Needleman & Christian D. Wuncsch (1969)

KAVINDRI DILSHANI

H.M.K.G BANDARA

PARINDA RAJAPAKSHE

ABOUT RESEARCH

Title

• “A General method applicable to the search for similarities

in the amino acid sequence of two proteins”

Authors

• Saul B. Needleman & Christian D. Wuncsch, Department of Biochemistry,

North-western University & Nuclear Medicine Service , V.A Research

Hospital ,Chicago, USA. (1969) [Cited by 8474]

S.B. Needleman & C.D. Wuncsch , “A General method applicable to the search for similarities in

the amino acid sequence of two proteins” , J. Mol . Biol .(1970) 48, 443- 453.

OUTLINE

• Introduction - Sequence Alignment

- Approaches

- Needleman-Wunch Algorithm vs. Dynamic Programming

• Example - Optimal Alignment Score

- Optimal Alignment

- Algorithm Cost

• Applications - Results & Discussion

- Methodology

- Usefulness

INTRODUCTION

SEQUENCE ALIGNMENT

• Sequence alignment is a way of arranging two or more sequences of characters to identify regions of similarity.

• Identification of residue-residue correspondences

• Sequence : Can be taken as ordered strings of letters.

• Sequences in Bio-Informatics ?

• DNA sequences

• RNA sequences

• Protein sequences

MOTIVATION

• Find homologous proteins

– Allows to predict structure and function

• Locate similar subsequences in DNA

– e.g.: Allows to identify regulatory elements

– Infer Biological similarities

• Locate DNA sequences that might overlap

– Helps in sequence assembly

SEQUENCE ALIGNMENT - RESULTS

• Input: Two sequences over the same alphabet. - GCGCATGGATTGAGCGA and TGCGCCATTGATGACCA

• Output: An alignment of the two sequences.

-GCGC-ATGGATTGAGCGA

TGCGCCATTGAT-GACC-A

• Input: Two sequences over the same alphabet. - GCGCATGGATTGAGCGA and TGCGCCATTGATGACCA

• Output: An alignment of the two sequences.

-GCGC-ATGGATTGAGCGA

TGCGCCATTGAT-GACC-A

• Input: Two sequences over the same alphabet. - GCGCATGGATTGAGCGA and TGCGCCATTGATGACCA

• Output: An alignment of the two sequences.

-GCGC-ATGGATTGAGCGA

TGCGCCATTGAT-GACC-A

Insertions / Deletions

(indel)

Perfect matches

Mismatches

APPROACHES

Sequence Alignment

Qualitative Quantitative

Dot-plot Global

Local

Multiple

QUALITATIVE

• Dot-plot

-Pictorial representation & relationship between two sequences

- Uses a Table or a Matrix

- Doesn’t quantifies the similarity figure !!

QUANTITATIVE

• Construction of the best alignment between

the sequences.

• Assessment of the similarity from the

alignment. ( Numerically Quantifies)

GLOBAL SEQUENCE ALIGNMENT

• The best alignment over the entire length of two

sequences.

• Suitable : Two sequences are of similar length,

with a significant degree of similarity throughout .

LOCAL SEQUENCE ALIGNMENT

• Compares short portions of sequence or a whole

library of sequences with short portions of

another.

• Suitable : Comparing substantially different

sequences, which possibly differ significantly in

length, and have only a short patches of similarity.

MULTIPLE SEQUENCE ALIGNMENT

• Simultaneous alignment of more than two

sequences.

• Suitable : Suitable when searching for subtle

conserved sequence patterns in a protein family,

and when more than two sequences of the protein

family are available.

EXAMPLE

S1 : SIMILARITY S2 : PILLAR S3 : MOLARITY

Global Local Multiple

SIMILARITY

PI-LLAR--- MILAR

ILLAR

SIMILARITY

PI-LLAR---

--MOLARITY

HOW TO QUANTIFY ?

• Introduces a Scoring Schema

• Set of rules which assigns the Alignment score to

any given alignment of two sequences.

• Alignment score : Goodness of Alignment

• Scoring Schema

Substitution scores

Gap penalties

THE SUBSITUTION MATRIX

• Simple scoring schema for Residue substitution

• Express the residue substitution costs can be achieved with

a N x N matrix (N is 4 for DNA and 20 for proteins).

C T A G

C 1 -1 -1 -1

T -1 1 -1 -1

A -1 -1 1 -1

G -1 -1 -1 1

EXAMPLE

• Consider the "best" alignment of ATGGCGT and

ATGAGT

• +1 as a reward for a match, -1 as the penalty for a mismatch,

and ignore gaps

ATGGCGT ATG_ AGT

Score: +1 + 1 + 1 + 0 - 1 + 1 + 1 = 4

Alternative alignment

ATGGCGT

A_TGAGT Score: +1 + 0 - 1 + 1 - 1 + 1 + 1 = 2

BETTER MATRIX

• Certain changes in DNA /Protein sequences are more

likely to occur naturally than the others.

• Proteins are composed of twenty amino acids, and

physico-chemical properties of individual amino acids

vary considerably.

• Important to incorporate evolutionary relationships

for this substitution schema.

EVOLUTIONARY SUBSTITUTION MATRIX

• PAM ("point accepted mutation") family

- PAM250, PAM120, etc.

• BLOSUM ("Blocks substitution matrix") family - BLOSUM62, BLOSUM50, etc.

• Derived from the analysis of known alignments of closely related proteins

• Assigns variable weights to different substitution operations.

BLOSUM 62

GAPS

• A Gap, indicates consecutive run of spaces in an

alignment , may be introduced in either sequence.

(insertion or a deletion of a residue)

• Objective :- Optimal sequence alignment with

meaningful alignments.

• Is it Good ?

– Interrupts the entire polymer chain

– In DNA shifts the reading frame Penalty

GAP PENALTIES

Constant Linear Affine

• Whatever size it is,

receives the constant

negative penalty : -g

• Depends linearly on

the size of a gap.

Parameter : -g, is the

penalty per unit

length of a gap.

• Gap introduction cost >

Gap extension cost

g = o + (L-1)e.

|e| < |o|

ENRICHED SCORING SCHEMA

• Scoring scheme provides us with the quantitative

measure of how good is some alignment relative to

alternative alignments .

• Does this scoring scheme tell us how to find the

best alignment ?

BASIC APPROACH

• Brute-force approach

- Generate the list all possible alignments between two

sequences, score them

- Select the alignment with the best score

– The number of possible global alignments between

two sequences of length N is

22𝑁

𝜋𝑁

- For two sequences of 250 residues this is ~ 10149

NEEDLEMAN WUNCH ALGORITHM

NEEDLEMAN-WUNCH ALGORITHM

• Reduce the massive number of possibilities that need to be considered, yet still guarantees that the best solution will be found.

• Global Sequence Alignment Technique.

• Build up the best alignment by using optimal alignments of smaller sub sequences.

• Dynamic Programming

DYNAMIC PROGRAMMING

• Dynamic Programming is an algorithmic

paradigm.

- Breaking problem into sub problems

- Stores results of sub problems

- Avoids computing the same results again.

• Main properties of the problem

- Overlapping Sub problems

- Optimal substructure

OVERLAPPING SUB PROBLEMS

• Segregate main problem into sub-problems.

• Mainly used when solutions of same sub problems are

needed again and again.

• Computed solutions to sub problems are stored in a

table/matrix so that these don’t have to recomputed.

• Dynamic Programming is not useful when there are no

common (overlapping) sub problems.

OPTIMAL SUBSTRUCTURE

• If an optimal solution can be constructed efficiently

from optimal solutions of its sub problems.

• Optimal global solution contains the optimal

solutions of all its sub problems.

• Dynamic Programming is not useful when there

isn’t optimal substructure in the problem.

HOW IT WORKS?

• Governed by three steps

- Break the problem into smaller sub problems.

- Solve the smaller problems optimally

- Use the sub-problem solutions to construct an

optimal solution for the original problem

• Needleman-Wunsch Algorithm incorporates

the Dynamic Algorithm paradigm Optimal global

alignment and the corresponding score.

WORKOUT

Definitions

• A scoring function (σ)

defines the score to give to a substitution mutation

eg. -1 for a match, -1 for mismatch

• A gap penalty

defines the score to give to an insertion or deletion

eg. -1

• A recurrence relation

defines what actions we repeat at each iteration (step) of the algorithm

T(i-1, j-1) + σ(S1(i), S2(j))

T(i, j) = max T(i-1, j) + gap penalty T(i, j-1) + gap penalty

Steps

• Step 1

– Fill up a matrix (table) T using the recurrence

relation

• Step 2

–The Trace back step use the filled-in matrix T to

work out the best alignment

Work Out

• Sequences

S1= TGGTG

S2= ATCGT

• Scoring function

For matches : +1

For mismatches : -1

A C G T

A +1 -1 -1 -1

C -1 +1 -1 -1

G -1 -1 +1 -1

T -1 -1 -1 +1

Substitution Matrix

Work Out cont..

• Initializing the table

T G G T G

A

T

C

G

T

i=0 i=1 i=2 i=3 i=4 i=5

j=0

j=1

j=2

j=3

j=4

j=5

Left to Right Top to Bottom

Step 1 - The value of T(0,0) is set to zero at the start

Work Out cont..

T G G T G

0

A

T

C

G

T

i=0 i=1 i=2 i=3 i=4 i=5

j=0

j=1

j=2

j=3

j=4

j=5

T(i-1, j-1) + σ(S1(i), S2(j))

T(i, j) = max T(i-1, j) + gap penalty

T(i, j-1) + gap penalty

previous column & row

previous column & same row

same column & previous row

Gap penalty = -2

A C G T

A +1 -1 -1 -1

C -1 +1 -1 -1

G -1 -1 +1 -1

T -1 -1 -1 +1

Work Out cont..

0 -2 -4 -6 -8 -10

-2 -1 -3 -5 -7 -9

i=0 i=1 i=2 i=3 i=4 i=5

j=0

j=1

j=2

j=3

j=4

j=5

A

T

C

G

T

T G G T G

A C G T

A +1 -1 -1 -1

C -1 +1 -1 -1

G -1 -1 +1 -1

T -1 -1 -1 +1

Gap penalty = -2

T(i-1, j-1) + σ(S1(i), S2(j))

T(i, j) = max T(i-1, j) + gap penalty

T(i, j-1) + gap penalty

Work Out cont..

0 -2 -4 -6 -8 -10

-2 -1 -3 -5 -7 -9

-4 -1 -2 -4 -4 -6

-6 -3 -2 -3 -5 -5

-8 -5 -2 -1 -3 -4

-10 -7 -4 -3 0 -2

i=0 i=1 i=2 i=3 i=4 i=5

j=0

j=1

j=2

j=3

j=4

j=5

A

T

C

G

T

T G G T G

Gap penalty = -2

Work Out cont..

0 -2 -4 -6 -8 -10

-2 -1 -3 -5 -7 -9

-4 -1 -2 -4 -4 -6

-6 -3 -2 -3 -5 -5

-8 -5 -2 -1 -3 -4

-10 -7 -4 -3 0 -2

i=0 i=1 i=2 i=3 i=4 i=5

j=0

j=1

j=2

j=3

j=4

j=5

A

T

C

G

T

T G G T G Trace Back

Work Out cont..

0 -2 -4 -6 -8 -10

-2 -1 -3 -5 -7 -9

-4 -1 -2 -4 -4 -6

-6 -3 -2 -3 -5 -5

-8 -5 -2 -1 -3 -4

-10 -7 -4 -3 0 -2

i=0 i=1 i=2 i=3 i=4 i=5

j=0

j=1

j=2

j=3

j=4

j=5

A

T

C

G

T

T G G T G Trace Back

Work Out cont..

0 -2 -4 -6 -8 -10

-2 -1 -3 -5 -7 -9

-4 -1 -2 -4 -4 -6

-6 -3 -2 -3 -5 -5

-8 -5 -2 -1 -3 -4

-10 -7 -4 -3 0 -2

i=0 i=1 i=2 i=3 i=4 i=5

j=0

j=1

j=2

j=3

j=4

j=5

A

T

C

G

T

T G G T G Trace Back

Work Out cont..

0 -2 -4 -6 -8 -10

-2 -1 -3 -5 -7 -9

-4 -1 -2 -4 -4 -6

-6 -3 -2 -3 -5 -5

-8 -5 -2 -1 -3 -4

-10 -7 -4 -3 0 -2

i=0 i=1 i=2 i=3 i=4 i=5

j=0

j=1

j=2

j=3

j=4

j=5

A

T

C

G

T

T G G T G Trace Back

Work Out cont..

0 -2 -4 -6 -8 -10

-2 -1 -3 -5 -7 -9

-4 -1 -2 -4 -4 -6

-6 -3 -2 -3 -5 -5

-8 -5 -2 -1 -3 -4

-10 -7 -4 -3 0 -2

i=0 i=1 i=2 i=3 i=4 i=5

j=0

j=1

j=2

j=3

j=4

j=5

A

T

C

G

T

T G G T G Trace Back

S1= TGGTG S2= ATCGT

-

A

T

|

T

G

C

G

|

G

T

|

T

G

-

→ Score = 3-1-4 = -2

Work Out cont..

W H A T

0 -2 -4 -6 -8

W -2 1 -1 -3 -5

H -4 -1 2 0 -2

Y -6 -3 0 1 -1

W H A T

0 -2 -4 -6 -8

W -2 1 -1 -3 -5

H -4 -1 2 0 -2

Y -6 -3 0 1 -1

W H A T

0 -2 -4 -6 -8

W -2 1 -1 -3 -5

H -4 -1 2 0 -2

Y -6 -3 0 1 -1

W

|

W

H

|

H

A

-

T

Y

(Pink traceback)

W

|

W

H

|

H

A

Y

T

-

(Orange traceback)

match:+1

mismatch:-1

gap:-2

Two possible trace backs ?

Work Out cont..

W H A T

0 -2 -4 -6 -8

W -2 1 -1 -3 -5

H -4 -1 2 0 -2

Y -6 -3 0 1 -1

W H A T

0 -2 -4 -6 -8

W -2 1 -1 -3 -5

H -4 -1 2 0 -2

Y -6 -3 0 1 -1

W H A T

0 -2 -4 -6 -8

W -2 1 -1 -3 -5

H -4 -1 2 0 -2

Y -6 -3 0 1 -1

W

|

W

H

|

H

A

-

T

Y

(Pink traceback)

W

|

W

H

|

H

A

Y

T

-

(Orange traceback)

Performance

• The N-W algorithm takes time proportion to n2

• Accessing all possible alignment one by one 2nCn

N2 < 2nCn

N-W is much faster than assessing all possible alignments one-

by-one

APPLICATIONS

Role of weighing factors in evaluating a maximum

match

Proteins not expected to exhibit homology

Proteins expected to exhibit homology

• Whale myoglobin

• Human β-hemoglobin

• Bovin pancreatic ribonuclease

• Hen’s egg lysozyme

APPLICATION OF THE METHOD

• Identification of the types of amino acid pairs

• Establish variable sets consisting of values to be assigned

to each type of pair

• Determine a value for the penalty

TYPES OF AMINO ACID PAIRS

• Pairs having a maximum of three corresponding bases in their codons Type 3

• Pairs having a maximum of two corresponding bases in their codons

Type 2

• Pairs having a maximum of one corresponding bases in their codons

Type 1

• Pairs having no possible corresponding bases in their codons Type 0

• Reading the amino acid sequences to be compared into the

computer

• Maximum-Correspondence array

– Contain all possible pairs of amino acids

– Identify each pair to the corresponding type

• Generating the two-dimensional array row-by-row

• Assigning the variable set containing the type values and

appropriate value from that set to the appropriate cell of the

comparison array

METHODOLOGY

Nucleotide sequences of

RNA codons recognized by

AA-tRNA*

*

Marshall RE, Caskey CT, Nirenberg M. Fine structure of RNA codewords recognized by bacterial, amphibian, and mammalian transfer RNA. Science. 1967 Feb 17;155(3764):820–826.

• Determination of the maximum-match by the procedure

of successive summations

• Randomizing the amino acid sequence of only one

member of the protein

– Sequences of β-hemoglobin and ribonuclease

– Randomization procedure: A sequence shuffling routine based

on computer-generated random

numbers

• Repeating the cycle of sequence randomization &

maximum-match determination

• Estimating the average and standard deviation for the

random values of each variable set

METHODOLOGY

RESULTS AND DISCUSSION

• A small random sample size (ten)

• Assumption: For each set of variables the random

values would be distributed in the fashion

of the normal-error curve

• The values of the first six random sets in the β-hemoglobin–

myoglobin comparison were converted to standard measures

• Probit plot

β-HEMOGLOBIN – MYOGLOBIN MAXIMUM MATCHES

RIBONUCLEASE – LYSOZYME MAXIMUM MATCHES

β-HEMOGLOBIN – MYOGLOBIN MAXIMUM MATCHES

β-HEMOGLOBIN – MYOGLOBIN MAXIMUM MATCHES

β-HEMOGLOBIN – MYOGLOBIN MAXIMUM MATCHES

β-HEMOGLOBIN – MYOGLOBIN MAXIMUM MATCHES

β-HEMOGLOBIN – MYOGLOBIN MAXIMUM MATCHES

• To detect homology and define its nature

• Assumption:

– Homologous proteins are the result of gene duplication and subsequent mutations

• Construct several hypothetical amino-acid sequences that would be expected to show homology

– Following the duplications, point mutations occur at a constant or variable rate

• After a relatively short period of time pairs will have nearly identical sequences

USEFULLNESS

DETECTION OF THE HIGH DEGREE OF HOMOLOGY PRESENT

• Use of values for non-identical pairs

• Assigning a relative high penalty for gaps

• Attaching substantial weight

• Reducing the penalty

• Assessing a very small or even negative penalty factor

THE NATURE OF HOMOLOGY

• Indication?

–Variables which maximize the significance of

the difference between real and random

proteins

EVOLUTIONARY DIVERGENCE

• Similar populations accumulate difference over

evolutionary time, and so become increasingly

distinct

EVOLUTIONARY DIVERGENCE

• “Divergent evolution" can be applied to molecular

biology characteristics.

• To genes and proteins derived from two or more

homologous genes

• Assignment of weight to type 2 pairs

–Enhances the significance of the results

– Substantial Evolutionary Divergence

EVOLUTIONARY DIVERGENCE

• Exception??

–Evolutionary divergence manifested by

cytochrome and other heme proteins

• Non-random mutations along the genes

THE DEGREE & TYPE OF HOMOLOGY

• Differ between protein pairs

• Due to the difference

–No a priori best set of cell and operation values

–No best set of value to detect only slight

homology

METHODS OF DETERMINING THE DEGREE OF HOMOLOGY

• Counting the number of non-identical pairs in the

homologous comparison

• Counting the number of mutations represented by the

non-identical pairs

• Measure of evolutionary distance

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