IPM-POLYTECHNIQUE-WPI Workshop on

Bioinformatics and Biomathematics

April 11-21, 2005 IPM

School of Mathematics Tehran

Prediction of protein surface accessibility based on residue

pair types and accessibility state using dynamic

programming algorithm

R. Zarei1, M. Sadeghi2, and S. Arab3

1,2) NRCGEB, Tehran, Iran 3) IBB, University of Tehran

Proteins & structure of proteins

Prediction of protein structure

Prediction of protein accessible surface area

Method

conclusion

Flow of information

DNA

RNA

PROTEIN SEQ

PROTEIN STRUCT

PROTEIN FUNCTION

……….

Proteins are the Machinery of life

Proteins have Structural & functional roles in cells

No other type of biological macromolecule could possibly assume all of the functions that proteins have amassed over billions of

years of evolution.

Proteins structure leads to protein function

Precise placement of chemical groups allows proteins to have :

Catalysis function Structural roleTransport functionRegulatory function

Then the determination of 3-dimentional structure of proteins is important.

4 levels of protein structures

The Primary structure of proteins (A string of 20 different Amino acids)

The secondary structure of proteins (Local 3-D structure)

The Tertiary structure of proteins (Global 3-D structure)

The Quaternary structure of proteins (Association of multiple polypeptide chains)

The Primary structure of proteins

The secondary structure of proteins α-helix α- helices 310-helix

Π-helix

parallel β- sheets

anti parallel Hairpin loops

Loops Ώ loops Other secondary structures Extended loops

Coils random coil

The Tertiary structure of proteins

There are a wide variety of ways in which the various helix, sheets & loop elements can combine to produce a complete structure.

At the level of tertiary structure, the side chains play a much more active role in creating the final structure.

Why predict protein structure?

Structural knowledge brings understanding of function and mechanism of action

Protein structure is determined experimentally by X-ray and NMR

The sequence- structure gap is rapidly increasing.

1000 000 known sequences, 20 000 known structures

What is protein structure prediction?

In its most general form

A prediction of the (relative) spatial position of each atom in the tertiary structure generated from knowledge only of the primary structure (sequence)

Hypotheses of Prediction

No general prediction of 3D structure from sequence yet.

Sequence determines structure determines function

The 3D structure of a protein (the fold) is uniquely determined by the specificity of the sequence(Afinsen,1973)

Methods of structure prediction

Comparative (homology) modelling

Fold recognition/threading

Ab initio protein folding approaches

3D structure prediction of proteins

0 10 20 30 40 50 60 70 80 90 100

Existing folds

ThreadingBuilding by homology

similarity (%)

New folds

Ab initio prediction

Levels of structure prediction

1D secondary structure, accessibility,……

2D contact map of residues

3D Tertiary structure

Prediction in 1D

Structure prediction in 1D is To project 3D structure onto strings of structural assignments.

Secondary Structure prediction

Prediction of Accessible Surface Area

Prediction of Membrane Helices

What is prediction in 1D?

Given a protein sequence (primary structure)

GHWIATHWIATRGQLIREAYEDYGQLIREAYEDYRHFSSSSECPFIP

Assign the residues

(C=coils H=Alpha Helix E=Beta Strands)

CEEEEEEEEEECHHHHHHHHHHHHHHHHHHHHHHCCCHHHHCCCCCC

secondary structure prediction in 1D

less detailed resultsonly predicts the H (helix), E (extended) or C

(coil/loop) state of each residue, does not predict the full atomic structure

Accuracy of secondary structure predictionThe best methods have an average accuracy of just

about 73% (the percentage of residues predicted correctly)

History of prediction of protein structure in 1D methods

First generation

– How: single residue statistics– Accuracy: low

Second generation– How: segment statistics– Accuracy: ~60%

Third generation

– How: long-range interaction, homology based– Accuracy: ~70%

Protein surface

Accessible Surface Area

Solvent ProbeAccessible Surface

Van der Waals Surface

Reentrant Surface

The accessible surface is traced out by the probe sphere center as it rolls over the protein. It is a kind of expanded

van der waalse surface.

Accessibility

Accessible Surface Area (ASA)

in folded protein Accessibility =

Maximum ASA

Two state = b (buried) ,e (exposed)

e.g. b<= 16% e>16% Three state = b (buried), I (intermediate), e (exposed)

e.g. b<=16% 16%>i,<36% e>36%

Use of Solvent Accessibility

studies of solvent accessibility in proteins have led to many insight into protein structure like:

Protein function

Sequence motifs

Domains

Formulating antigenic determinants & site-directed mutagenesis

Why Predict Solvent Accessibility?Helpful for :

Predicting the arrangement of secondary structure segments in 3-D structure

Estimating the number of protein-protein & protein- solvent contacts of residues

Threading procedure to find putative remote homologues

Improving prediction of glycosylation sites

Predicting epitops

Problems of predicting solvent Accessibility

Prediction of solvent accessibility is less accurate than that of secondary structure

Problem of approximation for residue accessibility (a projection of surface area onto 2 states leads to reduce of information )

The problem of how to define the threshold

ASA Calculation

DSSP - Database of Secondary Structures for Proteins (swift.embl-heidelberg.de/dssp)

VADAR - Volume Area Dihedral Angle Reporter (http://redpoll.pharmacy.ualberta.ca/vadar/)

GetArea - www.scsb.utmb.edu/getarea/area_form.html

Other ASA sites

Connolly Molecular Surface Home Pagehttp://www.biohedron.com/

Naccess Home Page http://sjh.bi.umist.ac.uk/naccess.html

ASA Parallelizationhttp://cmag.cit.nih.gov/Asa.htm

Protein Structure Database http://www.psc.edu/biomed/pages/research/PSdb/

Methods of Accessibility prediction

MethodCCAccuracyYearScientists

1Decision treeDT0.4371 ~ 72%1998Salzberg

2Bayesian statistics

BS0.4371 ~ 72%1996Tompson, Goldstein

3Multiple linear regression

MLR0.4371 ~ 72%2001Li, Pan

4Support vector Machine

SVM2~4 %79%2002Yuan, et al

5Neural network

2~4%79%1994Rost, sander

6A method Based on information theory

2001Sadeghi et al

PHD Prediction of rCD2

Accessibility Prediction

PredictProtein-PHDacc (58%)http://cubic.bioc.columbia.edu/predictprotein

PredAcc (70%?)http://condor.urbb.jussieu.fr/PredAccCfg.html

QHTAW... QHTAWCLTSEQHTAAVIWBBPPBEEEEEPBPBPBPB

THEORY &

METHOD

Data sets

A set of 230 nonredundant protein structures in the PDB with mutual sequence similarity <25% were selected to construct the training and testing sets from the PDBSELECT and with 2.5 Å resolution determined by x-ray and without chain breaks

ASA calculation

Surface area and accessibility for dataset proteins were calculated by software developed in our group

Accessibility states defined as two states and three states with different threshold

Two states B and E ( 5%, 9%, and 16%)

Three states B , I , E ( 4,9% - 9, 16% - 4,16% )

Conformation(State) of a residue is affected by:

Short range interactions(between near residues)Long range interactions(between far residues)

Most efforts have been focused on the analysis of near residues(local effects).

our method is based on :

Residue type (R)Residue conformation (state of neighbor

residues S & S’):

different neighbor residue types cause that residue adopt to different states.

E B I

E B I

E B I E B I E B I

E B I E B I

n1

n2

n3

3n Branch

n=length of protein

Branch with maximum information

Single residue prediction

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10

s1

s2

s3

s4

s5

s6

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10

S S

S S

S S

S S

S S S S S S

S S S S S

Double residue prediction

S S

Where P(SS’= XX’ ) is the probability of the occurrence of an event P(SS’=XX’ RiRj) is the conditional probabilityof SS’= XX’ if residues Ri and Rj have occurred.

The complementary event of

Complexity & problems of method

Considering pairwise residue type:20*20 entry

considering both types of Pair residues & pair residue states simultaneously :For two states : 20*20*2 entryFor three states : 20*20*3 entry

Note:

because of sample limitation we can’t analyze triplets or more.

Problems that we encountered for considering pairwise residue types & states simultaneously was: Each residue in a window with length of L predicts L times.

for example in a window with length of two residues, each residue predicts 2 times and so on.

If we consider the state of each residue in a window with the length of L , there are L times prediction for each residue.

Result : the ambiguity in answering the question or Which state stands for each residue ?

Solution: Use of dynamic programming

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10

S S

S S

S S

S S

S S S S S S

S S S S S

Double residue prediction

S S

n1 n2 n3 n4 n5 n6 n7 n8 n9

S S S S S

double residue prediction for long length wndows

S S S S S

S S S S S

S S S S S

S S S S S

S S S S

S S S

S S

S

information content I of a sequence length L, amino acid types Ri and Ri+m and accessibility states S and S’ (E,I,B) in window size L calculate as follow:

Dynamic programming algorithm

Build an optimal solution from optimal solutions to sub problems

Decompose a large problem into number of small problems. Solve the small problems and use these to solve the large problem.

Three basic components

The development of a dynamic programming algorithm has three basic components:– The recurrence relation (for defining the value of

an optimal solution);– The tabular computation (for computing the value

of an optimal solution);– The trace back (for delivering an optimal solution).

Dynamic programming algorithm

Dynamic programming algorithm

Three states accessibility for two residues length window

n1 n2 n3 n4 n5 n6

n1 n2 n3 n4

n1n2

n2

n3 n2n3

n4 n3n4

n1

n2

n3

n2 n3 n4

EE EB EI

BB BIBE

IIIBIE

EE EB EI

BB BIBE

IIIBIE

EE EB EI

BB BIBE

IIIBIE

EE II

Results&

discussion

Window length

threshold

2

3

4

5

6

7

5%9%16%

66.77

68.51

69.34

70.2

70.96

71.93

68.2

69.37

70.22

71.29

71.34

72.1

65.2

66.37

66.42

67.29

67.34

68.3

Two states accuracy

60

62

64

66

68

70

72

74

2 3 4 5 6 7

5%

9%

16%

Two states accuracy

Three states accuracy

Window length

thresholds

2

3

4

5

6

7

4, 9 %9, 16%4,16%

63.81

64.21

64.56

65.3

65.8

66.18

64.79

65.54

66.74

67.36

68.15

69.3

62.79

63.54

63.74

64.26

64.85

65.1

58

60

62

64

66

68

70

2 3 4 5 6 7

4,9%

9,16%

4,16

Three states accuracy

Suggestions

• Taking longer windows surely increases prediction accuracy

• Analysis and scoring of amino acid pairs by other statistical methods such as markov chain

• Using larger data sets and analysis of amino acid triplets (8000* 27 states)

Thank You