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Protein Folding Pathway Prediction
by
Haitham Ahmad Gamal
Supervised by
Prof. Ibrahim M.El-Henawy
Dr. Ahmed H.Kamal
Dr. Hisham Al-Shishiny
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Problem Statement
Motivation
Approach
Previous Work
Biological Background
What Affects Folding
Why is it difficult
Data Set
Methodology (the 4 stages)
Hypothesis (formally stated)
Results
Conclusion
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Proteins are the most vital agents in living bodies.
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Their function is what concerns scientists
Function
3D
Structure
Hydrophobicity
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Much effort in structure prediction but limited success:
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Result are:
• premature due to the huge conformations search space.
• or, insufficiently accurate due to simplifications.
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In this study we try to limit this search space to the most
likely possible conformations of a protein by answering the
following questions:
1. Do angle measures depend on the hydrophobicity of the
amino-acids?
2. If the answer of question (1) is "yes", how many neighbors
shall be used?
3. If the answer of question (1) is "yes", what are the most
likely values of the protein final structure angles?
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Knowledge of how a protein can fold enables us to
understand how it is functioning.
With this level of understanding we can affect a
protein either by enhancement or by suppression.
Drugs can be built to affect certain proteins directly
or through other proteins interacting with the
protein under investigation.
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The approach used in this study is a statistical, machine
learning approach. We try using this approach to answer
the previous questions.
Clustering
Distribution
Fitting
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In our study we are not developing a prediction algorithm.
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Our
study
fits in the
coloured
classes
across
these criteria.
We are
proving
some
hypothesis
that
can all
improve
several
types of prediction algorithms.
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Prediction algorithms/techniques can be classified based on
Ab intio
Homology
different criteria.
On-lattice
Off-lattice
Heuristic
Statistics
Protein-based
Subsequence-based
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The tertiary structure is the minimum free energy structure of a
protein (for single chain proteins)
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It has been proven that the function of a protein
depends on its 3D structure not its primary structure.
The most effective factor is folding proteins (specially
globular proteins) is the hydrophobicity of its
constituents amino acids.
Amino acids are either charged(soluble) or contains
aromatic groups(insoluble).
Hydrophobicity of all the 20 known amino acids is
called the Hydrophobicity scale.
Residue Type
Hydrophobicity
Ile
4.5
Val
4.2
Leu
3.8
Phe
2.8
Cys
2.5
Met
1.9
Ala
1.8
Gly
-0.4
Thr
-0.7
Ser
-0.8
Trp
-0.9
Tyr
-1.3
Pro
-1.6
His
-3.2
Glu
-3.4
Gln
-3.5
Asp
-3.5
Asn
-3.5
Lys
-3.9
Arg
-4.5
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An exact simulation of a short peptide folding may take
months on a super computer.
The number of possible conformations is huge.
such that
20l  l is the length of the peptidebond
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Scientists proved that solving the problem for the HP model
(simplified model) is NP-Complete.
Current technologies cannot keep pace with this God created
miracle.
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A collection of more than 1000 proteins is taken
randomly from the SCOP protein databank
Each SCOP entry (file) represents one protein with
all its features including its exact atom
coordinates.
Angles are extracted using the three dimensional
coordinates of each Cα atom
Angle
Extraction
Chopping to
Subsequences
K-means
Clustering
Distribution
Fitting
X - coordinate
the 3rd residue
Atom Serial
Number
Residue
Residue
Name
Sequence Number
Y - coordinate
the 4th residue
Z - coordinate
the 5th residue
Continue doing the same until the end
The angle that lies between each
consecutive Cα atoms
is ,called
angle
θ.
(
,
)
i-1
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three
Cα
θ1
θ2
θ3
Let (a) be a vector such that: a = (Cαi,Cαi-1)
Cαi-1
.
Cα.i
.
.
(
,
,
)
θ
can
then
be
calculated using the
cosine
law:a vector such that: b = (Cαi,Cαi+1θ)
Let (b) be
Cαi+1
Cαi are calculated
As shown in the figure the angles
Cαi+1 at each Cα atom starting
(
, from, Cα1 ) until CαL-1, such
that (L)is the protein length.
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After all the angles of all of the proteins are extracted in
each protein sequence is divided into subsequences of
length n.
A subsequence must contain an odd number of
residues.
A sliding window technique is used to chop the whole
protein sequence into pieces.
The value of n is crucial in our study as will be shown in
the results section.
Let’s take n = 5 as an example
aa0
aa1
aa3
Θ0
Θ2
Θ1
aa2
Θ3
aa4
aa7
aa5
Θ4
Θ7
Θ6
aa6
aa8
The
first subsequence
effect
Similarity
the effect of starts
all thefrom
nextaa
subsequences
starting
0 to aa4 and the
of this subsequence
on
the
angle Θ1 is what
generally
from aai to aa
oncentral
the measurement
of the
i+n-1
concerns
us
in this study.
central
angle Θ
is studied.
i+floor(n/2)-1
Let’s take n = 3 as an example
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Since hydrophobicity is the main factor affecting
No. determined
of
proteinAll Hydrophillic
folding. The centroids were
initial centroids is
accordingly.
2n
The choice of centroids is meant to cover all the
possible hydrophobicity patterns of a subsequence
of length n.
Hydrophobic
Hydrophillic
All Hydrophobic
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Clustered as well as the unclustered data are compared using
Kolmogrov-Smirnov test against 66 continuous probability
distributions, which are:
Beta, Burr, Burr (4P), Cauchy, Chi-Squared, Chi-Squared (2P),
Dagum, Dagum (4P), Erlang, Erlang (3P), Error, Error Function,
Exponential, Exponential (2P), Fatigue Life, Fatigue Life (3P), Frechet,
Frechet (3P), Gamma, Gamma (3P), Gen. Extreme Value,
Gen. Gamma, Gen. Gamma (4P), Gen. Logistic, Gen. Pareto,
Gumbel Max, Gumbel Min, Hypersecant, Inv. Gaussian,
Inv. Gaussian (3P), Johnson SB, Johnson SU, Kumaraswamy, Laplace,
Levy, Levy (2P), Log-Gamma, Log-Logistic, Log-Logistic (3P), LogPearson 3, Logistic, Lognormal, Lognormal (3P), Nakagami, Normal,
Pareto, Pareto 2, Pearson 5, Pearson 5 (3P), Pearson 6,
Pearson 6 (4P), Pert, Phased Bi-Exponential, Phased Bi-Weibull,
Power Function, Rayleigh, Rayleigh (2P), Reciprocal, Rice, Student's t,
Triangular, Uniform, Wakeby, Weibull and Weibull (3P).
Through conducting this study we try to argue about
two assumptions:
I.
The first part of the hypothesis suggests that the
angles measurements of a protein sequences
follow some sort of pattern based on the
hydrophobicity of the surrounding
amino acid
residues.
II.
The second part suggests that the
these patterns
as the
neighboring amino acid residues taken
consideration
.
of
of
into
n=3
Distribution
Burr
Centroids in this distribution (i = Ci)
1, 4
Burr(4p)
7
Gen. Extreme Value
6
Gen. Pareto
2, 3, 5
Johnson SB
0
n=5
Distribution
Dagum(4p)
Gumbel Min.
Gen. Extreme Value
Burr(4p)
Weibull(3p)
Centroids in this distribution (i = Ci)
0, 5, 7, 19
1, 2, 3, 17, 20
4, 32
6, 8, 10, 11, 14, 18, 21, 22, 23, 24, 27, 30, 31
9, 12, 13, 15, 16, 25, 26, 28, 29
n=7
Distribution
Weibull(3p)
Burr(4p)
Dagum
Dagum(4p)
Gen. Gamma(4p)
Gen. Logistic
Gumbel Min.
Log-Logistic
Wakeby
Centroids in this distribution (i = Ci)
3, 21, 79
20, 32, 40, 60, 67, 71, 74, 75, 83, 85, 105
4, 80
41, 90
69, 84, 106
2, 6, 7, 9, 12, 14, 15, 19, 33, 34, 35, 36, 37, 45, 46, 47,
49, 79, 87, 89, 94, 95, 107, 117, 125
66
42, 116, 118
1, 5, 8, 10, 11, 13, 16, 17, 18, 22, 23, 24, 25, 26, 27,
28, 29, 30, 31, 38, 39, 43, 44, 48, 50, 51, 52, 53, 54,
55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 68, 70, 72, 73,
76, 77, 78, 81, 82, 86, 88, 91, 92, 93, 96, 98, 99, 100,
101, 102, 103, 104, 108, 109, 110, 111, 112, 113, 114,
115, 119, 120, 121, 122, 123, 124, 126, 127
Tricky KS-statistic value are not enough for complete
interpretation
KS statistic for
Unclustered data
KS statistic for
Clustered data
n=3
0.09041
0.0937
n=5
0.012
0.0243
n=7
0.013
0.0202
The number of rejected critical values shows that the
fits of Un-clustered data are fake fits
No. of rejected values for
Un-Clustered data
No. of rejected values
for Clustered data
n=3
All 5 values
All 5 values
n=5
All 5 values
2.94
n=7
All 5 values
Zero
Number of tested critical values is 5
Obviously the KS-statistic shows that the
larger the value of n the better the fit.
Looking deeper at the rejected value test, all the 5 test values are rejected
for n = 3 while n = 7 gives ZERO rejected values, the thing that emphasizes
the truth of our hypothesis.
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it is now clear that there exists a direct relationship
between the hydrophobicity of the residues of a
subsequence (local neighbours) and the measurements
of the backbone angles. Classifying a subsequence into
one of the available clusters will give a good insight of
the angles measurements and consequently the
structure of the subsequence.
Also the length of the subsequence is an effective factor
in angle measurement prediction process. Longer
subsequences achieve better fits in one of the standard
continuous probability distributions.
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These results can be used to guide the search process in a
complete protein structure prediction algorithm.
Local angle-hydrophobicity relationship can be used
combined with heuristic techniques like genetic algorithm to
restrict the initial population to statistically familiar
conformation.
Approximations of our results can be applied to crystalline
lattices protein models like cube octahedron lattice model
which allows the use of several possible angles 60", 90", 120"
and 180".
it is possible to investigate applying the same approach on
subsequences of length more than 7 residues and try to
minimize the required processing time.
Title
A CENTRAL-3-RESIDUES-BASED CLUSTERING APPROACH FOR
STUDYING THE EFFECT OF HYDROPHOBICITY ON PROTEIN
BACKBONE ANGLES
Authors
Prof. Ibrahim M.El-Henawy
Dr. Hisham Al-Shishiny
Dr. Ahmed H.Kamal
Haitham Gamal
Has been published in Egyptian Computer Science Journal (ECS
Journal), ISSN-1110-2586, Volume 32, Number 1, May, 2009