‫تقرير نهائي لمشروع بحث‬
Research project final report /
Rapport final du projet de recherche
1
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
‫مستند إداري‬
Administrative Document
--------
Administrative information / ‫المعلومات اإلداري‬
71-70-11
:‫المرجع‬
Project Title - )‫عنوان المشروع (عربي وأجنبي‬
Computational evaluation of protein energy functions
‫ت ق ي يم حا سوب ي ل نماذج طاق ة ال بروت ين‬
Principal Investigator - ‫الباحث الرئيسي‬
‫العنوان‬
rthsta
tahsaN
‫االسم والشهرة‬
Address
nmansour@lau.edu.lb
‫العنوان االلكتروني‬
e-mail
01-786456
03-379647
‫رقم الهاتف‬
Telephone
Name &
surname
Lebanese American
University
‫المؤسسة‬
Institution
rooommorPooProsseforP
mrnoiro
‫الوظيفة‬
Post
Co-investigators - ‫الباحثون المشاركون‬
‫العنوان االلكتروني‬
e-mail
mirvat.elsibai@lau.edu.lb
‫المؤسسة‬
Institution
Lebanese American
University
‫االسم والشهرة‬
Name and surname
Mirvat Sibai
2
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
.1
Duration and starting date of the research / ‫المدة التعاقدي للمشروع وتاريخ بدء البحث‬
PPfwoPsoarmP
Duration (year) / ‫المدة التعاقدية للمشروع‬
rrfotorP4100
Starting date of the research /‫وتاريخ بدء البحث‬
Scientific Information / ‫العلمي‬
‫ المعلومات‬.2
ّ
Objectives - ‫الهدف‬
(mandatory field to fill 5-8 lines) – )‫ أسطر‬8-5 : ‫( معلومات إلزامية‬
The objective is to study the energy functions commonly used in the computational
protein structure prediction methods in order to improve the capability of these functions,
leading to better protein structures. More specifically, the objectives are: to determine
which energy function is more appropriate for ab initio computational methods; whether
different energy functions suit different protein types and sizes; and how the energy
functions may be amended to provide better guidance to ab initio computational
algorithms.
Achievements - ‫أالنجازات المحقق‬
(mandatory field to fill 5-8 lines) – )‫ أسطر‬8-5 : ‫( معلومات إلزامية‬
Our results show that the CHARMM energy model tends to yield better protein structures
than the other two energy functions, next is AMBER without polarization, followed by
LINUS and the polarization version of AMBER.
We have also found that it is more favorable for computational protein prediction
methods to assign unequal weights to the terms in the energy function. As a result, we
recom-mend the following weight values for the CHARMM energy function: 0.1-0.3 for
the electrostatic term, 0.1-0.2 for the Vander Waals term, and 0.6-0.8 for the Torsion
term, when applied to small to medium size proteins.
Perspectives - ‫آفاق البحث‬
(mandatory field to fill 5-8 lines) – )‫ أسطر‬8-5 : ‫( معلومات إلزامية‬
We have carried out a computational assessment of the ability of three energy models for
predicting the tertiary structure of proteins. We have also investigated the merit of
assigning unequal weights to the terms included in energy functions employed for ab
initio protein structure prediction (PSP). Our experimental results have validated our
hypotheses. They showed that energy functions have different capabilities in guiding the
PSP algorithms and that the energy terms should not have equal coefficient values. In fact,
our work did yield some achievements, as mentioned above. However, we have also
found that further experimental work, perhaps accompanied with some adjustments to the
approach, still needs to be carried out in order to reach more solid conclusions. The
3
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
volume of the work requires more time to complete it since it involves heavy
programming and very long execution times.
Publications & Communications - ‫المنشورات والمساهمات في المؤتمرات‬
Mansour, N., Mohsen, H.: Computational Evaluation of Protein Energy Functions.
Proceedings of the International Conference on Intelligent Computing; in Intelligent
Computing in Bioinformatics, 288-299, Springer (2014).
Abstract - ‫موجز عن نتائج البحث‬
(mandatory field to fill 5-8 lines) – )‫ أسطر‬8-5 : ‫( معلومات إلزامية‬
Predicting protein structures is guided by the requirement of minimizing the associated
energy value. However, the energy functions proposed so far are still in the exploration
phase. Also, assigning equal weights to different terms in energy has not been wellsupported. In this project, we carry out a computational evaluation of putative protein
energy functions. Our findings show that the CHARMM energy model tends to be more
appropriate for ab initio computational techniques that predict protein structures. Also,
we propose an approach based on a simulated annealing algorithm to find a better
combination of energy terms, by assigning different weights to the terms, for the purpose
of improving the capability of the computational prediction methods.
P
‫توقيع الباحث‬
4
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
Final report /
Rapport Final
Warning / Avertissement
1. The final report must be limited to results directly related to the research project
supported by the Council excluding any other activity carried out by the investigator
otherwise the report will be rejected.
2. Appendices may be added or attached to the report.
1. Le rapport final doit être limité aux résultats directement liés au projet de recherche
soutenu par le Conseil à l'exclusion de toute autre activité menée par le chercheur
sous peine de rejet.
2. Des annexes peuvent être ajoutées ou attachées au rapport.
1. Principal investigator / Chercheur principal
Name and surname /
Nom et prénoms
Nashat Mansour
Institution of affiliation /
Institution d'affiliation
Lebanese American University
2. Title of the project as proposed in the original application /
Titre du projet tel qu'il a été proposé dans la demande originale
(English and French / Anglais et Français)
Computational evaluation of protein energy functions
5
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
3. Purpose of the project / Objectifs du projet
(1page)
Proteins are organic compounds made up of chains of amino acids that fold into
complex 3-dimensional structures based on their chemical and physical
properties. A protein is characterized by its 3D structure, which defines its
biological function. Proteins fold into 3D structures in a way that leads to lowenergy state. Predicting these structures is guided by the requirement of
minimizing the energy value associated with the protein structure. However, the
energy functions proposed so far by biophysicists and biochemists are still in
the exploration phase and their usefulness has been demonstrated only
individually. Also, assigning equal weights to different terms in energy has not
been well-supported.
In this project, we carry out a computational evaluation of putative protein
energy functions. We investigate the energy functions commonly used in the
computational ab initio protein structure prediction (PSP) methods. The
objectives are: to determine which energy function is more appropriate for ab
initio PSP methods and how the energy functions may be amended to provide
better guidance to these PSP algorithms. In particular, we explore the possibility
of finding ‘optimal’, different weights to be assigned to the terms of the energy
functions.
The ultimate, strategic goal is to discover misfolded proteins and hence the
reason for some relevant diseases in order to guide treatment.
6
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
4. Expected outputs / Résultats attendus
1 page max / 1 page au maximum
The expected / achieved outputs are the following :
1. Finding one (or more) energy model that is more appropriate to guide the
ab initio PSP algorithm in evolving better tertiary protein structures. The
main metric used for this indentification is the Root mean square
deviation (RMSD) value.
2. Developing suboptimal, unequal weights that can be assigned to the terms
of the selected energy function and, thus, lead to improved guidance of
the ab initio PSP algorithms.
7
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
5.
Résultats obtenus / Obtained results
5 to 10 pages / 5 à 10 pages
Appendices can be added a the end of this document / Des annexes peuvent être ajoutées à
la fin de ce document
Introduction
Proteins are organic compounds that are made up of combinations of amino acids and are of different types and
roles in living organisms. Initially a protein is a linear chain of amino acids, ranging from a few tens up to
thousands of amino acids. Proteins fold, under the influence of several chemical and physical factors, into their
3-dimensional structures which determine their biological functions and properties. Misfolding occurs when the
protein folds into a 3D structure that does not represent its correct native structure, which can lead to many
diseases such as Alzheimer, several types of cancer, etc… [1]. Using computational methods for predicting the
native structure of a protein from its primary sequence is an important and challenging task especially that this
protein structure prediction (PSP) problem is computationally intractable. The protein’s sequence of amino
acids defines a unique native fold which normally corresponds to a minimum energy value [2]. In theory, this
free energy minimum can be computed from quantum mechanics and, thus, should help in predicting the
structure from the sequence. In practice, the theoretical foundation of such functions has not been fully
established and several energy functions have been proposed.
The energy function models proposed so far depend on a number of biophysical factors. Their usefulness has
been relatively demonstrated by different researchers. But, previous work has also shown that the precision of
these energy models is not well-established [3]. Also, no serious comparative evaluation of these energy
functions has been reported. Furthermore, limited work has been reported on the relative importance of the
terms of the energy function; many decoys per protein, for a number of proteins, were generated from
molecular dynamics trajectories and conformational search using the A-TASSER program minimizing the
AMBER potential [4], [5].
In this work, we carry out a computational comparison of important energy functions that have appeared in
the protein structure prediction literature in association with ab initio algorithms. We also design a simulated
annealing algorithm for deriving values that should be used as weights for the energy terms based on the native
structure knowledge on existing golden proteins in the ‘protein data bank’. The ultimate goal is to yield better
prediction of the tertiary structure of proteins.
This paper is organized as follows. Section 2 presents our methodology. Section 3 describes the energy
models used for the comparative work. Section 4 explains the algorithm used for optimizing the weights of the
energy terms. Section 5 presents the experimental results. Section 6 concludes the paper.
Methodology
The primary structure of a protein is a linear sequence of amino acids connected together via peptide bonds.
Proteins fold due to hydrophobic effect, Vander Waals interactions, electrostatic forces, Hydrogen bonding,
etc…. The protein structure prediction (PSP) problem is intractable [6]. Hence, the main computational
approaches are heuristics for finding good suboptimal solutions and can be classified as: Homology modeling,
threading, and ab initio methods [7]. For the latter methods, the only required input is the amino acid sequence
whereas for the first two methods, data of previously predicted protein structures are used.
Ab initio methods predict the 3D structure of proteins given their primary sequences without relying on
protein databases. The underlying strategy is find the best possible structure based on a chosen energy function.
Based on the laws of physics, the most stable structure is the one with the lowest possible energy. We have
identified three energy models/force fields as the most recognized models for pure ab initio PSP methods: the
CHARMM model [8], the LINUS energy function [9], and AMBER [10]. The different energy functions
include different terms and make a variety of assumptions. But, the relative merits of these functions in guiding
computational protein structure prediction methods have not been well-studied. In particular, a computational
8
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
investigation of their applicability has not been carried out. We believe that conducting such an investigation
will serve the PSP research community by providing guidelines regarding the applicability of the recognized
force fields.
Our methodology is based on the following steps and activities. We employ our recently developed
computational method for PSP, namely the adapted scatter search metaheuristic [3], [11], as the basic platform
for analyzing the behavior of the different energy functions. The selected energy functions are simulated and
incorporated into the scatter search algorithm to create different versions of the scatter search based program.
Then, real-world proteins are selected from a protein databank. The impact of the energy functions will be
evaluated by computing the widely used root mean square deviation (RMSD) of the target structure with
respect to the reference/golden protein structure. Then, we computationally derive sub-optimal weights for the
energy terms in order to further improve the prediction. Then, for the ‘winner’ energy function, we find
alternative weights for its terms to replace the commonly-used equal weights. This is done by adapting a
simulated annealing algorithm that aims to simultaneously minimize the energy values of several (golden)
proteins whose structure is already known.
Energy Functions/Models
The stability of the three-dimensional structure for protein is determined by the intramolecular interactions and
interactions with the external environment. The search for stable conformations of proteins is based on the
minimum total energy of interaction. The three recognized energy models, which are selected for our
experimental study, are described in the following subsections.
CHARMM Energy Model
The Chemistry at HARvard Molecular Mechanics (CHARMM) function [12] is based on the dihedral planes
representation of proteins that can be defined by the degrees of freedom given by the torsion angles. There are
four torsion angles present in each amino acid in a protein: phi φ, psi ψ, omega ω, and chi χ. Phi is the angle
between the planes C-N-Cα and N-Cα-C, where N-Cα is the axis of rotation. This angle decides the distance of
C-C of two amino acids. The chi angle is between the planes formed by the atoms of the side chains, and side
chains can have as many as five chi angles. Fig. 1 shows a segment of a protein backbone.
H
R1
H
Cα
φ
O
O
H
C
N
C
NH2
ψ
R3
Cα
Cα
N
H
R2
plane A
COOH
H
plane B
Fig. 1. Segment of a protein backbone with planes of bonds N-Cα and Cα-C, plane A and plane B, respectively.
The CHARMM energy function is given by
E (c ) 
 K b (b  bo )
2

bonds
K
 K (   o )
(   o ) 2 
 K  (1  cos( n   ))
dihedrals
 Aij
Bij 

 12   
10

rij  electrostatic
hydrogen  rij
  ij 12  ij 6 

 4 ij  r 12  r 6 
van der waals
ij 
 ij


angles
imp
improper dihedrals

2
qi q j
4o  r rij
9
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
AMBER Energy Model
The AMBER99 model is composed of several all-atom force fields. These fields include parameters for bonded
potential energy terms (stretching, bending, and torsion) and nonbonded terms (charge and van der Waals). The
original version was AMBER94, which was developed to improve on peptide backbone torsion parameters;
Kollman and co-workers used RESP charges derived from high-level ab initio calculations to parameterize
energies [13]. The subsequent force field, denoted as AMBER99, is intended for use both with and without
polarization effects [14]. AMBER99 includes the following terms:
Vbounded =
å Kr (r - r
eq
bonds
)2 +
å Kq (q - qeq )
2
angles
+
Vn
[1+ cos(nj - g )]
dihedrals 2
å
ìïé A
B ù q q üï
Vnonbounded = åíê 12ij - ij6 ú + i j ý
ïêë Rij Rij ûú 4pe Rij þï
i< j î
Vpol = -
1
mi Eio
å
2 i
The total energy includes the sum of all the potential fields and the polarization potential energy added in
AMBER99. In the first equation , three terms represent contribution to the total energy from “bond stretching,
bond angle bending, and torsion angle”, in the second one Vnonbonded is the sum of non-bonded energy as “van
der Waals and electrostatic energies”. In the third equation, V pol the polarization value is calculated for each
pair of point charge and induced point dipole moment as μ i and Ei is the electrostatic field at the ith atom
generated by all other point charges qj.
LINUS Energy Model
LINUS (Local Independently Nucleated Units of Structure) is an ab initio method for simulating the folding of
a protein on the basis of simple physical principles. LINUS involves a Metropolis Monte Carlo procedure,
represents a protein by including all its heavy atoms (i.e., non-hydrogen atoms). LINUS developed by
Srinivasan and Rose in 1995 is based on simple scoring function includes three components: hydrogen bonding,
scaled contacts, and backbone torsion. The hydrogen bonding and the hydrophobic contact scores are calculated
between pairs of atoms from residues. The contact energy is given by
é
Contact energy = maximum value x ê1.0 -
ë
ù
ú
(s +1.4)2 - s 2 û
dij2 - s 2
The scaled contact has both “Repulsive and attractive” terms. The repulsive term is implemented by
rejecting conformations when the interatomic distance between any two atoms is less than the sum of their van
der Waals radii. All pairwise interactions are evaluated except those involving carbonyl carbons and the
attractive term is applied between the side chain pseudo-atoms. The total energy of the LINUS function scoring
is given by the negative sum of the three preceding terms: hydrogen bonding, scaled contact, and backbone
torsion [9].
Simulated Annealing Algorithm for Energy Terms’ Weights
Simulated Annealing (SA) is a metaheuristic that deals with optimization problems with large search space to
find near-optimal solutions. In this paper, simulated annealing is employed to assign appropriate weights to
different energy terms. SA aims to yield a good solution with a minimized objective function value.
Algorithm Steps
The outline of the SA algorithm is shown in Fig. 2
10
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
Initialize Solution X and initial Temperature T
while (T > Steady State Temperature
and iteration < MAX_ITERATIONs)
for (NUMBER_OF_PERTURBATIONS)
Y = Perturb(X)
if (F(Y) < F(X) or e (-delta E/T) > random (0,1))
X=Y
// end if
// end for
Update (T)
// end while
Fig. 2. Outline of the SA algorithm.
Solution Representation
Each energy term is given a random weight between 0 and 1, where the sum of weights must be 1 in any
solution. The weight given to ES is called , that to VW is called β, and to Torsion energy is . Thus, the
obtained total energy for all solution is calculated according to the following formula:
Eprotein = .Golden-ESprotein + β.Golden-VWprotein + .Golden-Torsionprotein
Initial Solution
The initial solution is randomly generated. α, β, and  are randomly generated with values between 0 and 1,
such that α + β +  = 1 and no single value falls below 0.1.
Initial Temperature, Maximum Iterations, and Number of Perturbation
Initial temperature is chosen as 400,000 and that of steady state is 15. The maximum number of iterations is
chosen to be 200 with 3 perturbations in the ‘for’ loop of each iteration.
Perturbation Method
The implemented perturbation method alters the weights distribution among the energy terms. It either takes a
certain percentage (0.1) from a target weight factor and distributes it to the other 2 weight factors or takes this
percentage from two factors and adds it to the target third one.
The method has 3 decisions to take randomly. The first one is which of the weight factors (α, β, and ) to
target (whether to take from or add to). The second decision is whether to take from the chosen factor or give it
more energy. The third decision is how to distribute the amount of energy taken/given.
For example, the algorithm may randomly first choose α as the target, then randomly choose to take from it
0.1 of its value, and then randomly chooses to give 0.3 of the amount to be taken from α to β and 0.7 to .
Objective Function
The objective function to be minimized is the following:
∑ (Ei – AvgEi)2,
for i=1 to n
where n is the number of the selected proteins, Ei (defined in subsection 4.2) is the total energy obtained
according to the weights distribution by α, β, and , and AvgEi is the average of the calculated energies, Ei for
i=1..n, in the set of proteins according to weight distributions. Effectively, we are minimizing the mean square
deviation in the values of Ei over the n proteins as the values of the weights vary.
The SA metaheuristic algorithm enforces a lower bound of 0.1 for each of α, β, and  in order not to prevent
making any of the energy terms negligible. Thus, in any perturbed combination of values, the SA algorithm
rejects any perturbation that yields weight values below 0.1.
11
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
Experimental Results
In this section, we demonstrate the performance of our proposed methods using the 3 different energy models
for generating native-like structures for the backbones of the three target proteins.
Experimental procedure for energy functions
In our experiments, we use three subject proteins with known structures in PDB. Our reference PDB is the
Brookhaven database [15]. The 3 proteins are: 1CRN (CRAMBIN) is Plant seed protein (46 AAs); 1ROP (ROP
Protein) is Transcription Regulation (56 AAs); 1UTG (UTEROGLOBIN) is Steroid Binding (70 AAs).
We run the scatter search program for predicting protein structures based on each of the three energy models.
The results are evaluated by computing the target protein’s structural difference from the reference/golden
protein. This is accomplished by calculating the root mean square deviation (RMSD), in Angstrom, of the Cα
atoms of the two proteins [16].
Experimental results for energy functions
Table 1 gives the RMSD values by Scatter Search using the 3 types of potential energy function. These results
show that CHARMM generates the lowest RMSD values for the 3 proteins. Also, the limited experiments
reveal that the polarization term added in AMBER99 may not cause an improvement in the predicted protein
structure. CHARMM also runs faster than AMBER and has comparable execution time to LINUS.
Although the results in Table 1 demonstrate a rather clear tendency in favor of CHARMM, this does not
yield a final conclusion since the number of proteins that are used in the experiment is small. Future work
should employ many proteins with various sizes and functions in order to establish whether our result may vary
with protein size and type.
Experimental procedure for energy weights
In order to experiment with weights for energy terms, the real energy values have to be obtained. These are the
golden energy values obtained from the data retrieved from the Protein Data Bank (PDB) file of each protein.
The data are the 3D coordinates of atoms, torsion angles and amino acids. The total energy value of a protein is
the sum of the terms of the CHARMM energy function.
Two sets of non-homologous proteins have been chosen, where each is made up of 5 different proteins. The
first set contains proteins each with less than 100 amino acids (AAs), whereas the second contains proteins with
more than 100 AAs in each. We run the SA algorithm on the data obtained from each set of proteins to generate
values for the weights of the energy terms. The variation in the weights is also plotted over the SA iterations
until convergence. Finally, to give an indication of the validity of the weight results, we rerun the scatter search
program of Mansour et al. [11] to predict the structure of a protein, by using the new weights, and compare the
resulting RMSD with that of the structure produced by using equal weights for the energy terms.
Table 1. Experimental results for SS on 3 energy functions
Energy function
CHARMM
AMBER96
AMBER99 with
Polarization
LINUS
1CRN (46 AAs, 326
atoms)
1ROP(56 AAs, 420
atoms)
1UTG(70 AAs, 547
atoms)
Time (min)
964
1140
3600
RMSD
9.39
11.80
14.39
Time (min)
1059
1320
4200
RMSD
11.52
15.84
16.04
Time (min)
1182
1800
5005
RMSD
13.56
16.21
18.07
960
13.05
1005
15.22
1200
18.36
12
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
Results for energy weights
Results of SA for proteins of less than 100 amino acids. For proteins with less than 100 amino acids (1RPO,
1UBQ, 1CRN, 1ROP, and 1UTG), SA converged after 20 iterations to the objective function value of
5.159x1015. The initial randomly generated solution was of objective function value of 2.178x10 17. Fig. 3 shows
the variations of , β, and  as a function of iterations of the SA. The values of the three weights at convergence
are: α = 0.352; β = 0.105;  = 0.543.
Fig. 3. Variations of , β, and  (x10-1) as a function of iterations
Comparing the energy values obtained by using these weights with those obtained from the equal weights for
the 1ROP protein show that the former ones (using the new weights) are lower. Equal weights (0.333) give the
energy value of 1.125x106, whereas the obtained solution (with α, β, and  values) gives the value of 426,072.
Fig. 4 shows the values of ES, VW and Torsion energy terms as a function of iterations and the corresponding
values of , β, and .
After running the scatter search code, the obtained 1ROP protein structure has an RMSD with respect to the
golden protein of 7 Angstrom in comparison with about 12 Angstrom, obtained with equal weights [11].
Fig. 4. Variations of ES, VW and Torsion Energies for 1ROP (in 10 5 charge units) as a function of iterations
Results of SA for proteins of more than 100 amino acids. For proteins with more than 100 amino acids
(1AAJ, 1BP2, 1RPG, 1RRO, and 1YCC), SA converged after 43 iterations to the objective function value of
1.457x1012. The initial randomly generated solution was of objective function value of 3.278x10 13. Fig. 5
shows the variations of , β, and  as a function of iterations of the SA. The values of the three weights at
convergence are: α = 0.104; β = 0.108;  = 0.788.
Comparing the energy values obtained by using these weights with those obtained from the equal weights for
13
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
the 1AAJ protein shows that the new weights yield lower values. Specifically, equal weights for all energy
terms give the value of: 2.305x106. The obtained solution (with different α, β, and ) gives the value of:
742,844. Fig. 6 shows the values of ES, VW and Torsion energy terms as a function of iterations and the
corresponding values of , β, and .
After running the Scatter Search code, the obtained 1AAJ protein structure has an RMSD with the golden of
5.84 Angstroms, which is a promising result.
By inspecting the values of each of the 3 energy terms, it is clear that in the case of equal weights, the VW
term used to dominate the energy function and, consequently, the resulting protein structure. The change in the
weight values provides fairer shares to the other two terms and, thus, allows them to influence the evolution of
the predicted structure. We also note that the relative weights are different for different protein sizes.
These results show that assigning equal weights to the energy terms does not yield the best possible protein
structure prediction. But, more experiments are required to establish what weights should be assigned for what
size-category of proteins. Also, it will be useful to apply our approach to other recognized energy functions.
Fig. 5. Variations of , β, and  (x10-1) as function of iterations
Fig. 6. Variations of ES, VW and Torsion Energies in 1AAJ (in 105 charge units) as a function of iterations
Conclusions
We have carried out a computational assessment of the ability of three recognized energy models for predicting
the tertiary structure of proteins using a pure ab initio algorithm. We have also investigated the merit of
assigning unequal weights to the terms included in energy functions employed for ab initio protein structure
prediction.
Our experimental results show that the CHARMM energy model tends to yield better protein structures than
14
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
the other two energy functions, next is AMBER without polarization, followed by LINUS and the polarization
version of AMBER. We have also found that it is more favorable for computational protein prediction methods
to assign unequal weights to the terms in the energy function. As a result, we recommend the following weight
values for the CHARMM energy function: 0.1-0.3 for the electrostatic term, 0.1-0.2 for the Vander Waals term,
and 0.6-0.8 for the Torsion term, when applied to small to medium size proteins.
This work has established the merit of the proposed approach. Further work can focus on extending the
experimental work to a larger number of protein sets that include proteins with different sizes and functions and
on extending to other energy models.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Prusiner, S.B.: Prions. Proceedings of the National Academy of Sciences of the United States of America 95,
13363–13383 (1998)
Anfinsen, C.B.: Principles that Govern the Folding of Proteins. Science, 181-187 (1973)
Mansour, N., Kehyayan, C., Khachfe, H.: Scatter Search Algorithm for Protein Structure Prediction. Int. J.
Bioinformatics Res. Appl. 5, 501-515 (2009)
Wroblewska L., Skolnick J.: Can a Physics-Based, All-Atom Potential Find a Protein's Native Structure Among
Misfolded Structures? J Comput Chem. 28, 2059-2066 (2007)
Wroblewska, L., Jagielska, A., Skolnick, J.: Development of a Physics-Based Force Field for the Scoring and
Refinement of Protein Models. Biophysical J. 94, 3227–3240 (2008)
Unger, R. Moult, J.: Genetic Algorithms for Protein Folding Simulations. J. Mol. Biol. 231, 75–81 (1993)
Sikder, A.R. Zomaya, A.Y.: An Overview of Protein-Folding Techniques: Issues and Perspectives. Int. J.
Bioinformatics Res. Appl. 1, 121-143 (2005)
Vanommeslaeghe, K., Hatcher, E., Acharya, C., Kundu, S., Zhong, S., Shim, J., Darian, E., Guvench, O., Lopes,
P., Vorobyov, I., Mackerell Jr., A. D.: CHARMM General Force Field: A Force Field for Drug-Like Molecules
Compatible with the CHARMM All-Atom Additive Biological Force Fields. J. Comput. Chem. 31, 671–90
(2009)
Srinivasan, R., Fleming, P.J., Rose, G.D.: Ab Initio Protein Folding Using LINUS. Methods in Enzymology 383,
48–66 (2004)
Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz, K.M., Ferguson, D.M., Spellmeyer, D.C., Fox, T.,
Caldwell, J.W., Kollman, P.A.: A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids,
and Organic Molecules. J. Am. Chem. Soc. 117, 5179-5197 (1995)
Mansour, N., Ghalayini, I., Rizk, S., El- Sibai, M.: Evolutionary Algorithm for Predicting All-Atom Protein
Structure. Int. Conf. on Bioinformatics and Computational Biology, New Orleans (2011)
Brooks, B.R., Bruccoleri, R.E., Olafson, B.D., States, D.J., Swaminathan, S., Karplus, M.: CHARMM: a Program
for Macromolecular Energy, Minimization, and Dynamics Calculations. Journal of Computational Chemistry 4,
187–217 (1983)
Kollman P.A.: Advances and Continuing Challenges in Achieving Realistic and Predictive Simulations of the
Properties of Organic and Biological Molecules. American Chemical Society (1996)
Wang, J., Cieplak, P., Kollman, P.A.: How Well Does a Restrained Electrostatic Potential (RESP) Model
Perform in Calculating Conformational Energies of Organic and Biological Molecules?. J. Comp. Chem. 21,
1049–1074 (2000)
Bernstein F.C., Koetzle T.F., Williams G.J., Meyer E.F. Jr, Brice M.D., Rodgers J.R., Kennard O., Shimanouchi
T., Tasumi M.: The Protein Data Bank: a computer-based archival file for macromolecular structures. J. Mol.
Biol. 112, 535-542 (1977)
Carugo, O., Pongor, S.: A Normalized Root-Mean-Square Distance for Comparing Protein Three-Dimensional
Structures. Protein Sci. 10, 1470–1473 (2001)
15
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
6. Summary table of expected and obtained results / Tableau récapitulatif
des résultats attendus et des résultats obtenus
Expected outputs / Résultats attendus
Obtained results / Résultats obtenus
1. Finding one (or more) energy model
that is more appropriate to guide the ab
initio PSP algorithm in evolving better
tertiary protein structures.
1. Our experimental results show that
the CHARMM energy model tends to
yield bet-ter protein structures than
the other two energy functions, next
is AMBER without polarization,
followed by LINUS and the
polarization version of AMBER.
2. Developing suboptimal, unequal 2. We have also found that it is more
weights that can be assigned to the favorable for computational protein
terms of the selected energy function
prediction methods to assign unequal
weights to the terms in the energy
function. As a result, we recommend
the following weight values for the
CHARMM energy function: 0.1-0.3
for the electrostatic term, 0.1-0.2 for
the Vander Waals term, and 0.6-0.8
for the Tor-sion term, when applied
to small to medium size proteins.
7. Possible encountered difficulties / Difficultés éventuelles rencontrées
1. Technical challenge, which resulted from the extensive programming that
was required for the experimental work and the very long execution times
that were required for running the program even on small size proteins.
This challenge prevented us from conducting further experiments,
especially on large proteins.
2. Operational challenge due to the difficulty of finding qualified and
committed students to assist in the programming and experimentation.
Unfortunately, a few students had to contribute to the work which led to
project instablity and a lot of management time during the handover
periods (from a student to another).
16
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
3. Scientific publications )articles in peer review journals, books,
communications, etc …) / Publications scientifiques (articles dans des
revues à comité de lecture, livres, communications, etc …)
Attach a copy of each publication as it appeared in the journal) / (Joindre une copie de
chaque publication telle qu'elle a paru dans la revue)
Related publications :






Scatter search algorithm for protein structure prediction. International Journal of Bioinformatics
Research and Applications, Vol. 5, No. 5, 2009, 501-515. (with C. Kehyayan, H. Khachfe).
Evolutionary Algorithm for Predicting All-Atom Protein Structure. Proceedings of the Int.
Conference on Bioinformatics and Computational Biology, New Orleans, March 23-25, 2011 (with
I. Ghalayini, S. Rizk, M. El- Sibai).
Particle swarm optimization approach for protein structure prediction in the 3D HP model. Journal
of Interdisciplinary Sciences: Computational Life Sciences, Vol. 4, 1-11, 2012, Springer (with F.
Kanj, H. Khachfe)
Ab initio Protein Structure Prediction: Methods and Challenges. Book Chapter in Biological
Knowledge Discovery Handbook: Preprocessing, Mining and Postprocessing of Biological Data,
M. Elloumi and A. Y. Zomaya (Eds.), Wiley Book Series on Bioinformatics: Computational
Techniques and Engineering, IEEE-Wiley, John Wiley & Sons Ltd., New Jersey, USA; 2013 (with
J. Abbass and J.-C. Nebel)
MMLD based Genetic algorithm for tag SNP selection. Journal of Interdisciplinary Sciences:
Computational Life Sciences, Vol. 6, 1-9, 2014 Springer (with A. Mouawad)
Computational Evaluation of Protein Energy Functions. Proceedings of the International
Conference on Intelligent Computing; in Intelligent Computing in Bioinformatics, 288-299,
Springer, 2014 (with H. Mohsen)
8. Oral presentations or posters in national, regional and international
conferences / Présentations orales ou affichées à des congrès nationaux,
régionaux ou internationaux.
(Attach a copy of each presentation as it was presented or published in refereed
conference proceedings)/ (Joindre une copie de chaque présentation telle qu'elle a été
affichée ou publiée dans les comptes rendus des congrès)
Presenting a paper, entitled «Computational Evaluation of Protein Energy
Functions » at the 10th International Conference on Intelligent Computing,
Taiyuan, August 3-6, 2014.
17
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
How to submit the final report ?
Comment soumettre le rapport final ?
-------The final report must be submitted to Council in two versions :
 A hard copy which can be mailed or delivered directly to the Council
administrative seat;
 An electronic version, Word document, on CD-ROM or USB drive or email sent to the Council at the following address : grp@cnrs.edu.lb
Le rapport final doit parvenir au Conseil en deux versions :
 Une version sur papier qui peut être envoyée par la poste ou déposée
directement au siège administratif du Conseil ;
 Une version électronique en format Word sur CD-ROM ou sur clé USB, ou
envoyée au Conseil par e-mail à l'adresse suivante : grp@cnrs.edu.lb
18
4102 ‫برنامج دعم البحوث العلمية‬
Grant Program for Scientific Research in Lebanon – 2012
Programme de subvention à la recherche scientifique au Liban – 2012
‫برنامج دعم البحوث العلمي في لبنان لعام ‪2712‬‬
‫صفح ‪8‬‬
‫‪--------‬‬‫‪ .17‬تقديم التقرير النهائي‪:‬‬
‫‪ .0100‬في نهاية المشروع (سنة أو سنتين)‪ ،‬على الباحث تقديم تقرير نهائي (نسخة ورقية ونسخة‬
‫إلكترونية بصيغة ‪ Word‬على ‪P‬قرص مدمج أو ‪ USB‬أو ترسل إلى المجلس بواسطة البريد‬
‫االلكتروني على العنوان التالي‪ ،grp@cnrs.edu.lb :‬وذلك ‪P‬وفقاً للنموذج المعتمد في المجلس‬
‫والموجود على موقع المجلس ‪ http://www.cnrs.edu.lb‬مرفقاً بالتصفية المالية لمشروع‬
‫يبين فيه ما‬
‫البحث‪ .‬ال يقبل التقرير النهائي إالّ إذا عرض الباحث بشكل واضح جدوالً مفصالً ّ‬
‫تم إنجازه مقارن مع تصوره لمخرجات المشروع عند قبوله‪ ،‬على أن ال يتضمن سوى ما له‬
‫عالقة مباشرة بمشروع البحث المدعوم من المجلس دون إغراقه بأية تفاصيل أو نشاطات أخرى‬
‫والتركيز حص اًر على النتائج التي توصل اليها الباحث‪.‬‬
‫‪ .0104‬يعتمد المجلس في تقييم التقرير النهائي على األهمية العلمية للمقاالت الصادرة عن الباحث‬
‫وذات العالقة بمشروع البحث المدعوم من المجلس من خالل عدد من المعايير والمؤشرات‬
‫الدولية نذكر من بينها على سبيل المثال ‪Impact Factor, Citation Index:‬‬
‫‪19‬‬
‫برنامج دعم البحوث العلمية ‪4102‬‬
‫‪Grant Program for Scientific Research in Lebanon – 2012‬‬
‫‪Programme de subvention à la recherche scientifique au Liban – 2012‬‬