A Metaheuristic Approach To Protein Structure Prediction Algorithms and Insights From Fitness Landscape Analysis 1st Edition Nanda Dulal Jana

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Emergence, Complexity and Computation ECC
Nanda Dulal Jana · Swagatam Das

Jaya Sil
A Metaheuristic
Approach to
Protein Structure
Prediction
Algorithms and Insights from Fitness
Landscape Analysis
Emergence, Complexity and Computation
Volume 31
Series editors
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e-mail: ivan.zelinka@vsb.cz
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e-mail: adamatzky@gmail.com
Guanrong Chen, City University of Hong Kong, Hong Kong, China

e-mail: eegchen@cityu.edu.hk
Editorial Board
Ajith Abraham, MirLabs, USA
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Alegre, RS, Brazil
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The Emergence, Complexity and Computation (ECC) series publishes new
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from international experts.
More information about this series at http://www.springer.com/series/10624

Nanda Dulal Jana Swagatam Das
•
Jaya Sil
A Metaheuristic Approach
to Protein Structure
Prediction
Algorithms and Insights from Fitness
Landscape Analysis
123
Nanda Dulal Jana Jaya Sil
Department of Computer Science Department of Computer Science
and Engineering and Technology
National Institute of Technology Indian Institute of Engineering Science
Durgapur and Technology
Durgapur, West Bengal Howrah, West Bengal
India India
Swagatam Das
Indian Statistical Institute
Electronics and Communication
Sciences Unit
Kolkata, West Bengal
India
ISSN 2194-7287 ISSN 2194-7295 (electronic)

Emergence, Complexity and Computation
ISBN 978-3-319-74774-3 ISBN 978-3-319-74775-0 (eBook)
https://doi.org/10.1007/978-3-319-74775-0
Library of Congress Control Number: 2017964439
© Springer International Publishing AG 2018

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Foreword
Slightly over 50 years ago, pioneering bioinformaticist Margaret Dayhoff published

her first Atlas of Protein Sequences and Structure. At the time, the sequences for only
65 proteins were available in the literature, and just a handful of x-ray structures like
those of myoglobin or hemoglobin were available. Dayhoffs database led to the
development of the Protein Information Resource, which also was the first database
that could be accessed by remote computers. Her landmark effort also led to an
improved understanding of protein structure and evolution. However, a central
problem remained. While it was understood that proteins fold from primary to
secondary to tertiary and even quaternary levels, the rules associated with that
process remained unknown. Over time and through considerable worldwide
experimental effort, the number of protein sequences grew exponentially as did the
number of known protein structures. Current databases such as UniProtKB/TrEMBL
contain 93,000,000 protein sequences while the Protein Data Bank holds roughly
135,000 known structures. In light of this impressive rapid increase in information,
we have learned about structural domains, supersecondary structure, and superdo-
mains. We understand considerably more about the process of folding than ever
before. Despite that knowledge, and despite similar exponential gains in computing
power over roughly the same time frame, we remain unable to consistently and
accurately fold long protein sequences into their native structures via ab-initio
simulation. We can choose to use supercomputers to calculate all-atom models of the
folding process, but these are useful only to a certain time horizon or protein length.
We can thread protein sequences onto known structure information through a pro-
cess of homology modeling to see how well a new sequence maps to a known
structure yet this is not ab-initio folding. Another promising approach is the use of
metaheuristics such as evolutionary computation to iteratively search for improved
folds in light of an objective function. But this requires knowledge of the right
objective function for the protein and its environment, which may in some cases be
difficult to define. This book offered by Nanda Dulal Jana, Swagatam Das, and Jaya
Sil focuses on metaheuristic approaches and improved understanding of the fitness
landscape that is used as the objective function for search. As our knowledge about
sequences, structures, and their mapping improves, we are faced with the realization
v
vi Foreword
that proteins in living systems are likely to be in constant motion. Our inability to
faithfully recapitulate the correct structure may itself be an artifact of the fuzziness
of the actual process, or our inability to capture the fitness function in a manner that
makes it possible for either physics-based or metaheuristic approaches to succeed.
While we await the exciting decades of experimental protein structural biology
ahead of us, we explore and improve our use of computers to help solve these
problems. This book by Jana, Das, and Sil continues us on that journey that Dayhoff
and others started over 50 years ago.
San Diego, CA, USA Gary B. Fogel, Ph.D., FIEEE

November 2017 Chief Executive Officer, Natural Selection, Inc.
Preface
Proteins are the main building blocks of the dry mass of cells in living organisms.
Proteins perform a huge variety of tasks such as catalyzing certain processes and
chemical reactions, transporting molecules to and from the cell, delivering mes-
sages, sensing signals, and countless other useful functions which are essential for
the preservation of life. Protein is a macromolecule combining with amino acids
that are connected by peptide bonds. During synthesis, protein is folded into a
three-dimensional structure. However, sometimes protein may fold into an incorrect
structure (known as misfolding) leading to a protein substance with the different
properties which can be harmful to organisms. Misfolding of a protein causes many
critical human diseases such as Alzheimer’s disease, cystic fibrosis, amyotrophic
lateral sclerosis, cancer, and neurodegenerative disorders. Therefore, the knowledge
of protein structure and its prediction by analyzing the amino acid sequences is a
challenging task in computational biology.
Biologists define a hierarchy of protein structures with four levels in order to
more accurately characterize the structure properties. The primary structure is
simply the linear protein chain, i.e., a sequence of amino acids. The secondary
structure is the local conformation of protein structures. There are two types of
major secondary structures, known as alpha-helix and beta-sheet. The tertiary
structure is the global three-dimensional structures. Sometimes, multiple protein
chains united together and form hydrogen bonds between each other, resulting in
the quaternary structures. Therefore, the protein structure prediction (PSP) is the
process of determining the three-dimensional structure of a protein from its
sequence of amino acids.
The experimental techniques such as X-ray crystallography and nuclear mag-
netic resonance (NMR) have been used to determine a protein structure from its
sequence of amino acids. For instance, it may take months of concerted efforts to
crystallize a single protein in order to enable X-ray diffraction methods that
determine its 3D structure. The major limitations of experimental techniques are
extremely time-consuming and labor-intensive, strict laboratory setup, and heavy
operational burdens. As a result, the gap between the protein sequences and the
known structures is increasing rapidly day by day. For example, there are 78028152
vii
viii Preface
protein sequences but the structure is known only for 117184 of them as of January
2017. Therefore, researchers from multiple disciplines and with diverse domains of
knowledge are involved in predicting protein structure from its sequence of amino
acids using computational methods.
Computational approaches have the potential to predict the structure of a protein
from its primary sequence in order to overcome the difficulties associated with the
experimental approaches. Basically, a computational technique is a process of
finding a three-dimensional structure by arranging a sequence of basic structural
elements. Depending on the database information, computational methods are
divided into three category: homology or comparative, threading or fold recogni-
tion, and ab-initio or denovo PSP. Homology modeling is based on the similarity
comparison of the sequence while threading approach is a process to thread together
likely short sub-conformation of the corresponding subsequence. These two tech-
niques fully depend on the availability of similar sequence information exists in the
database. i.e.. these are template-based methods and the results may become
unconvincing for dissimilar sequences. On the other hand, ab-initio method predicts
three-dimensional structure of a protein from its primary sequence directly based on
the intrinsic properties (namely, hydrophobic, and hydrophilic) of amino acids, so it
is a template-free approach. The concept of ab-initio method is based on the
Anfinsen’s thermodynamic hypothesis where the theory of thermodynamics states
that conformation of a protein corresponds to the global minimum free energy
surface and the conformation is called a native structure of the protein. A native
structure is a stable structure of a protein which always consumes minimum energy
among all the conformations of the protein. Therefore, ab-initio based PSP
approach is transformed into a global optimization problem where energy function
would be minimized.
The ab-initio based PSP has two important key parts. The first part is to state the
simplified mathematical model that corresponds to a protein energy function, i.e.,
the objective function. The second part is to develop a computationally efficient
searching or optimization algorithm which can find the global minimum of the
energy function. A number of a computational model have been proposed and
developed that derive the protein energy function for the PSP problem. Among
these physical models, hydrophobic-polar (HP) lattice model is a simple model
widely used for structure prediction. It can be represented in two dimension or three
dimension and consumes less computation time, but the level of accuracy of the
predicted structure is not enough to use in rational drug designing. The off-lattice
model is also a computational model that brings good interactions between amino
acid residues and their environments. The AB off-lattice is such a type of model
where amino acid residues are characterized as hydrophobic (A) and hydrophilic
(B) residues. It represents the intramolecular interactions between residues which
are connected by rigid unit length bonds, and the angles between the bonds change
freely in two or three dimension. So, the AB off-lattice model provides a structure of
a protein at much higher atomic details than the lattice model. The energy function
for the AB off-lattice model is expressed as a weighted sum of bending energy of
protein backbone, independent of the sequence. The non-bonded potential energy
Preface ix
among nonadjacent residues is known as Lennard-Jones 12, 6 potentials. The two

components of the energy function are defined by bond and torsional angles
between two consecutive amino acids. All angles are limited in an interval ½p; p.
Thus, the objective is to find the optimal angles associated with the energy function
that provides the minimal free energy value. In this way, a PSP mission is trans-
formed into a numerical optimization problem. It is widely accepted that ab-initio
based structure prediction using AB off-lattice model belongs to a class of difficult
optimization problem known as NP-complete problem. Therefore, in order to solve
such problem, search and optimization algorithms are usually developed using
certain heuristic or metaheuristic that, though lacking in strong mathematical
foundations, are nevertheless good at reaching an approximate solution in a rea-
sonable amount of time.
Metaheuristics denote a collective name for a range of problem-solving tech-
niques based on principles of biological evolution, swarm intelligence, and physical
phenomenon. These techniques are based on iterative progress, such as growth or
development in a population of candidate solutions for a given problem. The
population is then selected in a guided random search to achieve the desired end.
Since the past few decades, algorithms from this domain have attracted the
researchers to the field of ab-initio based PSP. However, the characteristics or
complexity of the optimization problem play an important role in determining the
optimization technique to be used for problem-solving and influence the perfor-
mance of the algorithm. Therefore, a fundamental question arises: how to select and
configure a best-suited algorithm for solving the PSP problem? This book attempts
to determine the structural features associated with the PSP problem and configured
some widely used promising metaheuristic methods based on the structural features
to find near-optimal and acceptable solutions. The structural properties are deter-
mined using fitness landscape analysis (FLA) which provides a better under-
standing of the relationship between the problem nature and the algorithm in order
to choose the most appropriate algorithm for solving the problem.
Extensive research on metaheuristic algorithms have been proved their potential
in solving complex optimization problems like PSP. However, it is not easy to
choose the best metaheuristic technique for solving a particular problem. FLA is
used for understanding the problem characteristics based on which the best-suited
algorithm can be chosen. In the literature, it has been shown that more research on
landscape analysis in discrete search space have been considered compared to
landscape analysis on continuous search space. Since the PSP problem is defined as
a continuous optimization problem, continuous FLA for the PSP problem has
remained uncovered till date. In this book, we determine the structural features
of the PSP problem and configured some well-known metaheuristic techniques
based on the structural properties. Toward this end, we first undertake an analysis
of the continuous search space of the PSP problem for generating the landscape
structure and proposed a random walk algorithm. Taking the cue from the analysis
of the search space, we generated protein landscape structure based on sampling
technique for determining the structural properties of the protein landscape. Next,
we developed a variant of the differential evolution (DE) algorithm in order to
x Preface
overcome the difficulties associated with the PSP problem without imposing any
serious additional computational burden. Drop Developed Variants of particle
swarm optimization (PSO), bees algorithm (BA), biogeography-based optimization
(BBO), and harmony search (HS) algorithms are developed in order to overcome
the difficulties associated with the landscape structure while solving the PSP
problem. The proposed algorithms are compared with several state-of-the-art PSP
algorithms over many artificial and real data sets reflect the superior performance
of the proposed schemes in terms of final accuracy, speed, and robustness. We also
study the implication of the proposed hybrid technique which is configured based
on the structural features for obtaining the better minimum energy value of the PSP
problem.
The book is divided into eight chapters. Chapter 1 presents the overview of the
PSP problem and discusses the importance to the research community in the
domain of computational biology. The chapter begins with a discussion of the basic
concepts of proteins structure and gradually elaborates the various terminology
about the structure prediction of a protein. It also discusses the computational
models. Next, the chapter provides the basic fundamentals and different types of
metaheuristic algorithms. It explains some widely used metaheuristic techniques
such as DE, PSO, BA, BBO, and HS in details.
Chapter 2 presents a literature review of metaheuristic techniques based PSP, a
scope of the work and contribution to the book chapters. Initially, a critical analysis
of the existing metaheuristic techniques employed in PSP problem are presented.
Next, we explain the scope of the work. The main contributions of the book are
briefly outlined at the end of the chapter.
Chapter 3 investigates continuous fitness landscape structure with random walk
(RW) algorithm. The chapter develops two chaos-based random walk (CRW)
algorithm for generating sample points in the search space and fitness landscape is
created based on the relative fitness of the neighboring sample points. The chaotic
map is used to generate the chaotic pseudo-random numbers (CPRN) for deter-
mining variable scaled step size and direction of the proposed RW algorithm.
Histogram analysis provides better coverage of the search space by the CRW
algorithm compared to the existing random walk algorithms in the literature. The
chapter also presents empirical results over complex benchmark functions and PSP
problem to validate the efficiency of the proposed method.
Chapter 4 determines the characteristics of PSP problem or its structural features
using FLA based on which the most appropriate algorithm can be recommended for
solving the problem. The chapter describes protein landscape structure generated by
using the quasi-random sampling technique and city block distance. The structural
properties of the PSP problem are analyzed with the help of information and
statistical landscape measures. The chapter also reports an important investigation
of six well-known real-coded optimization algorithms over the same set of protein
sequences and the performances are subsequently analyzed based on the structural
features. Finally, it suggests the most appropriate algorithms for solving the PSP
problem.
Preface xi
Chapter 5 describes a DE-based metaheuristic algorithm for solving the PSP

problem. In the proposed method, parameters of the DE algorithm are controlled
adaptively using Lévy distribution. The distribution function is used to made a
possible changes in the control parameters of DE adaptively in order to achieve
balance between exploration and exploitation strategy in the search space. The
performance of the proposed method has been extensively compared with some
parameter control techniques over a test-suite of expanded multimodal, hybrid
composite functions and the different protein instances. It is apparent from the
computer simulations that proposed method provides significant performance in
terms of accuracy and convergence speed to obtain global minimum energy.
Chapter 6 provides four variants of metaheuristic algorithms for solving the PSP
problem in both two-dimensional and three-dimensional AB off-lattice model. The
proposed algorithms are configured in order to tackle the structural features reported
in Chap. 4. The chapter begins with a modified version of the classical PSO
algorithm which uses a local search technique. Use of local search makes it possible
to jump out from the local optima and prevent the premature convergence. Next, a
mutation-based BA is developed for enhancing the diversity in the search space to
solve the complex problem like the PSP problem. The chapter also describes
chaos-based BBO and perturbation-based HS algorithms which are configured to
prevent the loss of diversity in the search space and being trapped in local optima
when dealing with PSP problem. Experimental results over the artificial and real
protein sequences of varying range of protein lengths indicate that the proposed
algorithms are very efficient to solve the PSP problem.
Chapter 7 explains a hybrid technique that combines the merits of algorithms to
improve the performance of an optimizer when dealing with multimodal problem.
The chapter develops a synergism of the improved version of the PSO and DE
algorithm. The proposed method is executed in an interleaved fashion for balancing
exploration and exploitation dilemma in the evolution process. Experiments are
carried out on the real protein sequences with different lengths taken from Protein
Data Bank (PDB) and the results indicate that the proposed method outperforms the
state-of-the-art algorithms.
Finally, Chap. 8 concludes with the self-review of the book chapters and scope
of the future research.
Durgapur, West Bengal, India Nanda Dulal Jana

November 2017 Swagatam Das
Jaya Sil
Contents
1 Backgrounds on Protein Structure Prediction and Metaheuristics . . 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Proteins and Amino Acids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Level of Protein Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 Primary Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.2 Secondary Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.3 Tertiary Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.4 Quaternary Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Protein Structure Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Protein Structure Prediction Methods . . . . . . . . . . . . . . . . . . . . . . 6
1.5.1 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5.2 Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Computational Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6.1 HP Lattice Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6.2 AB Off-Lattice Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.7 Population Based Metaheuristic Techniques . . . . . . . . . . . . . . . . . 12
1.7.1 An Optimization Problem . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.7.2 The Metaheuristic Family . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.7.3 The Evolutionary Algorithms . . . . . . . . . . . . . . . . . . . . . . 14
1.7.4 Swarm Intelligence Algorithms . . . . . . . . . . . . . . . . . . . . . 20
1.7.5 Physical Phenomena Based Algorithms . . . . . . . . . . . . . . . 23
1.8 Innovation and Research: Main Contribution of This Volume . . . . 28
2 Metaheuristic Approach to PSP—An Overview of the Existing
State-of-the-art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Evolution Based Metaheuristic Algorithms . . . . . . . . . . . . . . . . . . 30
2.3 Swarm Intelligence Based Metaheuristic Algorithms . . . . . . . . . . . 32
2.4 Physical Phenomena Based Metaheuristic Algorithms . . . . . . . . . . 34
2.5 Hybrid Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
xiii
xiv Contents
2.6 Protein Structure Prediction Using Metaheuristics: A Road

Map of This Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.7 Potential Applications Areas for the Metaheuristics Based
Structure Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3 Continuous Landscape Analysis Using Random Walk
Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Simple Random Walk (SRW) . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 Random Walks for Fitness Landscapes Analysis . . . . . . . . . . . . . 43
3.4 Chaotic Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.4.1 Logistic Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.2 Tent Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.3 Chebyshev Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.4 Cubic Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.5 ICMIC Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Landscape Measure Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5.1 Entropy Based Measure . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5.2 Fitness Distance Correlation (FDC) . . . . . . . . . . . . . . . . . . 47
3.6 The Chaotic Random Walk (CRW) Algorithm . . . . . . . . . . . . . . . 47
3.6.1 Chaotic Pseudo Random Number (CPRN) Generation . . . . 48
3.6.2 Chaos Based Random Walk Algorithm . . . . . . . . . . . . . . . 48
3.6.3 Coverage Analysis of the Walks . . . . . . . . . . . . . . . . . . . . 51
3.7 Experiments for the Benchmark Functions . . . . . . . . . . . . . . . . . . 54
3.7.1 Benchmark Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.7.2 Simulation Configurations . . . . . . . . . . . . . . . . . . . . . . . . 54
3.7.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.7.4 Landscape Analysis for 20-Dimension . . . . . . . . . . . . . . . 63
3.8 Application to PSP Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4 Landscape Characterization and Algorithms Selection
for the PSP Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 Fitness Landscape Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.1 Information Based Measure . . . . . . . . . . . . . . . . . . . . . . . 90
4.2.2 Statistical Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3 Energy Function Landscape Structure . . . . . . . . . . . . . . . . . . . . . 94
4.3.1 Quasi-Random Sampling . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.3.2 Landscape Path Creation . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.4 Landscape Analysis for PSP Problem . . . . . . . . . . . . . . . . . . . . . 97
4.4.1 Experimental Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Contents xv
4.5 Performance Analysis of the Metaheuristic Algorithms . . . . . . . . . 124

4.5.1 Simulation Configurations . . . . . . . . . . . . . . . . . . . . . . . . 124
4.5.2 Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5 The Lévy Distributed Parameter Adaptive Differential
Evolution for Protein Structure Prediction . . . . . . . . . . . . . . . . . . . . 151
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.2 Lévy Distributed DE (LdDE) . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.2.1 Lévy Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.2.2 The Lévy Distributed DE Algorithm . . . . . . . . . . . . . . . . . 155
5.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.3.1 Benchmark Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.3.2 Simulation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.4 Application to Protein Structure Prediction . . . . . . . . . . . . . . . . . . 163
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6 Protein Structure Prediction Using Improved Variants
of Metaheuristic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.2 Particle Swarm Optimization with Local Search . . . . . . . . . . . . . . 170
6.2.1 Hill Climbing: A Local Search Algorithm . . . . . . . . . . . . . 171
6.2.2 PSOLS Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.2.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.3 The Mutation Based Bees Algorithm . . . . . . . . . . . . . . . . . . . . . . 177
6.3.1 Adaptive Polynomial Mutation Based BA . . . . . . . . . . . . . 179
6.3.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.4 The Chaos-Based Biogeography Based Optimization
Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
6.4.1 Chaotic Mutation in BBO . . . . . . . . . . . . . . . . . . . . . . . . 184
6.4.2 Experiments and Results . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.5 The Difference Mean Based Harmony Search Algorithm . . . . . . . 189
6.5.1 Difference Mean Based Perturbation (DMP) Method . . . . . 189
6.5.2 The DMP-HS Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 189
6.5.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
xvi Contents
7 Hybrid Metaheuristic Approach for Protein Structure

Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
7.2 The Hybridization Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
7.2.1 Improved PSO (IPSO) . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
7.2.2 Improved DE (IDE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
7.2.3 The HPSODE Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 200
7.3 Experiments for PSP Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8 Conclusions and Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
8.1 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
8.2 Future Research Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Abbreviations and Symbols
Abbreviations
ABC Artificial Bee Colony
APM Adaptive Polynomial Mutation
BA Bees Algorithm
BBO Biogeography-Based Optimization
CLPSO Comprehensive Learning Particle Swarm Optimization
CMA-ES Covariance Matrix Adaptation Evolution Strategy
CR Crossover Ratio
CRW Chaotic Random Walk
DE Differential Evolution
DMP-HS Difference Mean-based Perturbation Harmony Search
EA Evolutionary Algorithm
FDC Fitness Distance Correlation
FLA Fitness Landscape Analysis
GA Genetic Algorithm
HM Harmony Memory
HMCR Harmony Memory Considering Rate
HMS Harmony Memory Size
HP Hydrophobic-Polar
HPSODE Hybrid PSO and DE
HS Harmony Search
HSI Habitat Suitability Index
LdDE Lévy distributed Differential Evolution
NMR Nuclear Magnetic Resonance
PAR Pitch Adjusting Rate
PSL Protein Sequence Length
PSO Particle Swarm Optimization
PSOLS Particle Swarm Optimization with Local Search
PSP Protein Structure Prediction
QPSO Quantum-based Particle Swarm Optimization
xvii
xviii Abbreviations and Symbols
RW Random Work
SI Swarm Intelligence
SIV Suitability Index Variable
TS Tabu Search
TSM Tabu Search Mechanism
TSR Tabu Search Recombination
Symbols
H Hydrophobic or nonpolar amino acid
P Hydrophilic or polar amino acid
hi The ith bend angle
bi The ith torsion angle
rij The distance between ith and jth amino acid of the chain
ni The ith amino acid
tmax The maximum generations or iterations
xi;t The ith vector at tth generation
xmin
j The lower bound of the jth component of a vector
xmax
j The upper bound of the jth component of a vector
D Dimensions of the problem
NP The population size
ki The ith immigration rate
li The ith emigration rate
vi ðtÞ The velocity of the ith particle at generation t
x An inertia weight
F Fitness landscape
x Vector
fi The ith fitness value
N/ ðxi Þ Neighborhood of xi
x The global minimum
R
P Real number
Q Sum
Product
List of Figures
Fig. 1.1 Basic structure of an amino acid . . . . . . . . . . . . . . . . . . . . . . . .. 3

Fig. 1.2 Peptide bonds between two amino acids . . . . . . . . . . . . . . . . . .. 4
Fig. 1.3 Dihedral and bond angles in protein . . . . . . . . . . . . . . . . . . . . .. 4
Fig. 1.4 Different levels of structures of a protein (Figures are adopted
from http://goo.gl/images/KPbnr0) . . . . . . . . . . . . . . . . . . . . . .. 5
Fig. 1.5 An example of conformation of 20 amino acids using
the 2D-HP lattice model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10
Fig. 1.6 An example of a 2D AB off-lattice model for a protein
sequence AABBABAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10
Fig. 1.7 An example of a 3D AB off-lattice model for a protein
sequence ABBA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11
Fig. 1.8 Flowchart of general evolutionary algorithm . . . . . . . . . . . . . . .. 15
Fig. 1.9 Migration model of species . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
Fig. 3.1 Three independent simple random walks of 50 steps each
with variable step size of simple random walk algorithm . . . . .. 42
Fig. 3.2 Different chaotic behaviors of chaotic maps . . . . . . . . . . . . . . .. 45
Fig. 3.3 One independent sample walk of 200 steps with variable
step size using tent chaotic random walk . . . . . . . . . . . . . . . . .. 50
step size using CCRW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50
step size using ICRW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50
Fig. 3.6 Visualization of different independent sample walks of 200
steps with step size 20 by CCRW algorithm. . . . . . . . . . . . . . .. 51
Fig. 3.7 Visualization of different independent sample walks of 200
steps with step size 20 by ICRW algorithm . . . . . . . . . . . . . . .. 51
Fig. 3.8 Histogram of three random walk algorithms for a sample
of 10,000 points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52
Fig. 3.9 Mean of HðeÞ over different values of e for all the functions
in 10-dimension using CCRW . . . . . . . . . . . . . . . . . . . . . . . . .. 63
xix
xx List of Figures
in 20-dimension using CCRW . . . . . . . . . . . . . . . . . . . . . . . . .. 70
in 30-dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77
Fig. 3.12 Ruggedness characteristics for selected benchmark functions
in different dimensions using four random walk algorithms . . .. 81
Fig. 3.13 Ruggedness characteristics for real protein sequences over
different values of e using four RW algorithms. . . . . . . . . . . . .. 84
Fig. 4.1 An example of a rugged landscape structure . . . . . . . . . . . . . . .. 90
Fig. 4.2 An example of a funnel landscape structure . . . . . . . . . . . . . . .. 94
Fig. 4.3 Distributions of pseudo random sampling and quasi
random sampling. The quasi random sampling points
do not form clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 96
Fig. 4.4 Mean entropy, HðeÞ for ASs in 2D model: a AS1 - AS6 2 GA1 ,
b AS6 - AS10 2 GA2 , c AS11 - AS19 2 GA3 , d AS20 - AS25
2 GA4 , e AS26 - AS35 2 GA5 and f AS2, AS8, AS18, AS22
and AS35 taken from each group . . . . . . . . . . . . . . . . . . . . . . . . 105
Fig. 4.5 Mean entropy, HðeÞ for RSs in 2D model: a RS1 - RS6 2 GR1 ,
b RS7 - RS12 2 GR2 , c RS13 - RS17 2 GR3 , d RS18 - RS23
2 GR4 , e RS24 - RS30 2 GR5 and a RS3, RS9, RS15, RS22
and RS28 taken from each group . . . . . . . . . . . . . . . . . . . . . . . . 105
Fig. 4.6 Mean partial information content measure, MðeÞ curves for
artificial protein sequences in 2D AB off-lattice model:
a AS1 - AS6 2 GA1 , b AS6 - AS10 2 GA2 , c AS11 - AS19
2 GA3 , d AS20 - AS25 2 GA4 , e AS26 - AS35 2 GA5
and f AS2, AS8, AS18, AS22 and AS35 taken from
each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Fig. 4.7 Mean partial information content measure, MðeÞ curves for real
protein sequences in 2D AB off-lattice model: a RS1 - RS6
2 GR1 , b RS7 - RS12 2 GR2 , c RS13 - RS17 2 GR3 ,
d RS18 - RS23 2 GR4 , e RS24 - RS30 2 GR5 and a RS3, RS9,
RS15, RS22 and RS28 taken from each group . . . . . . . . . . . . . . 107
Fig. 4.8 Scatter plots of fitness versus distance to the global minimum
ðX Þ for artificial protein sequence in 2D AB off-lattice model:
a AS4 with length 23, b AS7 with lenght 34, c AS21 with
lenght 50, d AS24 with lenght 60, e AS34 with lenght 64
and f AS2, AS8, AS18, AS22 and AS35 taken
from each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
ðx Þ for real protein sequences in 2D AB off-lattice model:
a RS1 with lenght 13, b RS10 with lenght 25, c RS15 with
lenght 29, d RS23 with lenght 46, e RS30 with lenght 98
and f RS3, RS9, RS15, RS22 and RS28 taken
from each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
List of Figures xxi
Fig. 4.10 Correlograms for artificial protein sequences in 2D AB

off-lattice model: a AS1 - AS6 2 GA1 , b AS6 - AS10 2 GA2 ,
c AS11 - AS19 2 GA3 , d AS20 - AS25 2 GA4 , e AS26 - AS35
2 GA5 and f AS2, AS8, AS18, AS22 and AS35 taken
from each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Fig. 4.11 Correlograms for real protein sequences in 2D AB off-lattice
model: a RS1 - RS6 2 GR1 , b RS7 - RS12 2 GR2 ,
c RS13 - RS17 2 GR3 , d RS18 - RS23 2 GR4 , e RS24 - RS30
2 GR5 and a RS3, RS9, RS15, RS22 and RS28 taken
from each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Fig. 4.12 Dispersion for artificial protein sequences in 2D AB off-lattice
model: a AS1 - AS6 2 GA1 , b AS6 - AS10 2 GA2 ,
2 GA5 and f AS2, AS8, AS18, AS22 and AS35 taken from
each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Fig. 4.13 Dispersion for real protein sequences in 2D AB off-lattice
2 GR5 and a RS3, RS9, RS15, RS22 and RS28 taken
from each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Fig. 4.14 Mean entropy measure, HðeÞ curves for artificial protein
sequences in 3D AB off-lattice model: a AS1 - AS6 2 GA1 ,
b AS6 - AS10 2 GA2 , c AS11 - AS19 2 GA3 , d AS20 - AS25
2 GA4 , e AS26 - AS35 2 GA5 and f AS2, AS8, AS18, AS22
and AS35 taken from each group . . . . . . . . . . . . . . . . . . . . . . . . 117
Fig. 4.15 Mean entropy measure, HðeÞ curves for real protein sequences
in 3D AB off-lattice model: a RS1 - RS6 2 GR1 , b RS7 - RS12
2 GR2 , c RS13 - RS17 2 GR3 , d RS18 - RS23 2 GR4 ,
e RS24 - RS30 2 GR5 and a RS3, RS9, RS15, RS22 and RS28
taken from each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Fig. 4.16 Mean partial information content measure, MðeÞ curves for
artificial protein sequences in 3D AB off-lattice model:
a AS1 - AS6 2 GA1 , b AS6 - AS10 2 GA2 , c AS11 - AS19
2 GA3 , d AS20 - AS25 2 GA4 , e AS26 - AS35 2 GA5
from each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Fig. 4.17 Mean partial information content measure, MðeÞ curves for real
protein sequences in 3D AB off-lattice model: a RS1 - RS6
2 GR1 , b RS7 - RS12 2 GR2 , c RS13 - RS17 2 GR3 ,
d RS18 - RS23 2 GR4 , e RS24 - RS30 2 GR5 and a RS3,
RS9, RS15, RS22 and RS28 taken from each group . . . . . . . . . 118
xxii List of Figures
ðX Þ for artificial protein sequences in 3D AB off-lattice
model: a AS4 with lenght 23, b AS7 with lenght 34, c AS21
with lenght 50, d AS24 with lenght 60, e AS34 with lenght 64
from each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
ðX Þ for real protein sequence in 3D AB off-lattice model:
a RS1 with lenght 13, b RS10 with lenght 25, c RS15 with
lenght 29, d RS23 with lenght 46, e RS30 with lenght 98
and f RS3, RS9, RS15, RS22 and RS28 taken
from each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Fig. 4.20 Correlograms for artificial protein sequences in 3D AB
off-lattice model: a AS1 - AS6 2 GA1 , b AS6 - AS10 2 GA2 ,
each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Fig. 4.21 Correlograms for real protein sequences in 3D AB off-lattice
2 GR5 and a RS3, RS9, RS15, RS22 and RS28 taken from
each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Fig. 4.22 Dispersion for artificial protein sequences in 3D AB off-lattice
model: a AS1 - AS6 2 GA1 , b AS6 - AS10 2 GA2 ,
each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Fig. 4.23 Dispersion for real protein sequences in 3D AB off-lattice
2 GR5 and a RS3, RS9, RS15, RS22 and RS28 taken from
each group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Fig. 4.24 Convergence curve of algorithms for ASs in 2D AB off-lattice
model: a AS1 with length 13, b AS6 with length 25, c AS8
with length 36, d AS15 with length 48, e AS23 with length 58
and f AS35 with length 64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Fig. 4.25 Convergence curve of algorithms for RSs in 2D AB off-lattice
model: a RS1 with length 13, b RS8 with length 24, c RS15
with length 29, d RS22 with length 38, e RS26 with length 64
and f RS30 with length 98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Fig. 4.26 Convergence curve of algorithms for ASs in 3D AB off-lattice
model: a AS1 with length 13, b AS6 with length 25, c AS8
with length 36, d AS15 with length 48, e AS23 with length 58
and f AS35 with length 64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
List of Figures xxiii
Fig. 4.27 Convergence curve of algorithms for RSs in 3D AB off-lattice

model: a RS1 with length 13, b RS8 with length 24, c RS15
with length 29, d RS22 with length 38, e RS26 with length
64 and f RS30 with length 98. . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Fig. 5.1 Convergence characteristics of LdDE and other algorithms
on nine real protein sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Fig. 6.1 Convergence characteristics of PSOLS, PSO and CPSO
on artificial protein sequences with different lengths . . . . . . . . . . 176
Fig. 6.2 Convergence characteristics of PSOLS, PSO and CPSO
on real protein sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Fig. 6.3 Convergence characteristics of the algorithms on artificial
protein sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Fig. 6.4 Convergence characteristics of the algorithms for real protein
sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Fig. 6.5 Convergence characteristics of the algorithms over artificial
protein sequences based on 3D AB off-lattice model . . . . . . . . . 187
Fig. 6.6 Convergence characteristics of the algorithms for real protein
sequences based on 3D AB off-lattice model . . . . . . . . . . . . . . . 188
Fig. 6.7 Convergence curves of best objective value for the algorithms
on the real protein sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Fig. 7.1 Flow diagram of the improved PSO and improved DE
algorithm. Here, lbest: local best of particle, gbest: global best
in the swarm, r: random number, sl : mutation probability, TM:
trigonometry mutation, APM: adaptive polynomial mutation
and GBS: global best solution . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Fig. 7.2 Convergence characteristics of comparable algorithms over
nine real protein sequences based on 2D AB off-lattice
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
List of Tables
Table 1.1 Summary of the most representative metaheuristic

algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26
Table 3.1 Average standard deviation of the mean frequency
in a bin over 30 runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53
Table 3.2 The CEC 2013 real-parameter Benchmark Functions. Please
refer to the details of the website http://www.ntu.edu.
sg/home/EPNSugan/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55
Table 3.3 The entropic measure HðeÞ for all functions in
10-Dimensions with different values of e using CCRW . . . . .. 56
Table 3.4 The entropic measure, HðeÞ for all functions in 10-
Dimensions with different values of e using ICRW . . . . . . . .. 58
Table 3.5 Results of landscape measures for all functions using CCRW
and ICRW in 10-Dimension . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
Table 3.6 The entropic measure HðeÞ for all functions
in 20-Dimensions with different values of e using CCRW . . .. 64
Table 3.7 The entropic measure HðeÞ for all functions
in 20-Dimensions with different values of e using ICRW . . .. 66
Table 3.8 Results of landscape measures for all test functions using
CCRW and ICRW in 20-Dimension . . . . . . . . . . . . . . . . . . .. 68
Table 3.9 The entropic measure HðeÞ for all functions in 30-Dimension
with different values of e using CCRW . . . . . . . . . . . . . . . . .. 71
Table 3.10 The entropic measure HðeÞ for all functions in 30-
Dimensions with different values of e using ICRW . . . . . . . .. 73
Table 3.11 Results of landscape measures for all functions using CCRW
and ICRW in 30-Dimension . . . . . . . . . . . . . . . . . . . . . . . . . .. 75
Table 3.12 Mean of maximum HðeÞ value over 30 runs for selected
benchmark functions in different dimensions . . . . . . . . . . . . .. 79
Table 3.13 Results of landscape measures (LM) for four real protein
sequences using CCRW, ICRW, PRW and SRW
algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83
xxv
xxvi List of Tables
Table 4.1 Encoding and class labels of a landscape path with

neighbor fitness values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91
Table 4.2 Artificial protein sequences . . . . . . . . . . . . . . . . . . . . . . . . . .. 98
Table 4.3 Real protein sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Table 4.4 Results of information and statistical landscape measures
for 35 artificial protein instances in 2D AB off-lattice
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Table 4.5 Results of information and statistical landscape measures
for 30 real protein instances in 2D AB off-lattice model . . . . . 103
Table 4.6 Pearson correlation coefficients ðqx;y Þ between landscape
measures for all artificial protein sequences in 2D AB
off-lattice model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
measures for all real protein sequences in 2D AB off-lattice
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Table 4.8 Results of information and statistical measures for 35
artificial protein landscapes in 3D AB off-lattice model . . . . . . 113
Table 4.9 Results of information and statistical measures for 30 real
protein landscapes in 3D AB off-lattice model . . . . . . . . . . . . . 115
measures for all artificial protein sequences in 3D AB
off-lattice model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
measures for all real protein sequences in 3D AB off-lattice
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Table 4.12 Parametric set-up for the algorithms compared. . . . . . . . . . . . . 126
Table 4.13 Results for six optimization algorithms on 35 artificial
protein sequences using 2D AB off-lattice model . . . . . . . . . . . 128
Table 4.14 Results for six optimization algorithms on 30 real protein
sequences using 2D AB off-lattice model . . . . . . . . . . . . . . . . . 132
Table 4.15 Results for six optimization algorithms on 35 artificial
protein sequences using 3D AB off-lattice model . . . . . . . . . . . 136
Table 4.16 Results for six optimization algorithms on 30 real protein
sequences using 3D AB off-lattice model . . . . . . . . . . . . . . . . . 140
Table 4.17 Summary of landscape features and most appropriate
algorithm for protein sequences in 2D AB off-lattice
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Table 4.18 Summary of landscape features and most appropriate
algorithm for protein sequences in 3D AB off-lattice
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Table 5.1 The CEC 2005 real-parameter Benchmark Functions. Please
refer to the details of the website http://www.ntu.edu.sg/
home/EPNSugan/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
List of Tables xxvii
Table 5.2 Results of the LdDE and other compared algorithms

over fifteen test functions in 10-Dimension . . . . . . . . . . . . . . . 158
Table 5.3 Results of unpair t-test on the data of Table 5.2 . . . . . . . . . . . 160
Table 5.4 Results of the LdDE and other compared algorithms over
fifteen test functions in 30-Dimension . . . . . . . . . . . . . . . . . . . 161
Table 5.5 Results of unpair t-test for the data on Table 5.4 . . . . . . . . . . . 163
Table 5.6 Details of amino acid sequences used in the experiment . . . . . 164
Table 5.7 Best, Mean and Standard deviation values obtained by LdDE
compared to other algorithms on RPs . . . . . . . . . . . . . . . . . . . 165
Table 6.1 Artificial protein sequences of length 5 . . . . . . . . . . . . . . . . . . 173
Table 6.2 Artificial protein sequences with different lengths . . . . . . . . . . 173
Table 6.3 Real protein sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Table 6.4 Results for artificial protein sequences with length 5 . . . . . . . . 175
Table 6.5 Results for artificial protein sequences with different
lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Table 6.6 Results for real protein sequences with different lengths . . . . . 177
Table 6.7 APM-BA learning parameters . . . . . . . . . . . . . . . . . . . . . . . . . 181
Table 6.8 Results for artificial protein sequences . . . . . . . . . . . . . . . . . . . 182
Table 6.9 Results for real protein sequences . . . . . . . . . . . . . . . . . . . . . . 183
Table 6.10 Results for artificial protein sequences . . . . . . . . . . . . . . . . . . . 187
Table 6.11 Results of real protein sequences with different algorithms
based on 3D AB off-lattice model . . . . . . . . . . . . . . . . . . . . . . 188
Table 6.12 Details of amino acid sequences used in the experiment . . . . . 191
Table 6.13 Comparisons of best, mean and standard deviation results
for RPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Table 7.1 Details information about amino acid sequences
used in the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Table 7.2 The parameter settings of the algorithms . . . . . . . . . . . . . . . . . 204
Table 7.3 Results of the algorithms on real protein sequences
with different lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
List of Algorithms
Algorithm 1 Differential Evolution (DE) . . . . . . . . . . . . . . . . . . . . . . . . . 18

Algorithm 2 Biogeography Based Optimization (BBO) . . . . . . . . . . . . . . 19
Algorithm 3 Particle Swarm Optimization (PSO) . . . . . . . . . . . . . . . . . . . 22
Algorithm 4 Bees Algorithm (BA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Algorithm 5 Harmony Search (HS) algorithm . . . . . . . . . . . . . . . . . . . . . 25
Algorithm 6 SRW Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Algorithm 7 CRW Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Algorithm 8 LdDE Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Algorithm 9 Hill Climbing (HC) Algorithm . . . . . . . . . . . . . . . . . . . . . . . 172
Algorithm 10 PSOLS Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Algorithm 11 APM-BA Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Algorithm 12 Chaotic Mutation Implementation . . . . . . . . . . . . . . . . . . . . 185
Algorithm 13 BBO-CM algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Algorithm 14 DMP implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Algorithm 15 DMP-HS algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Algorithm 16 HPSODE Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
xxix
Chapter 1
Backgrounds on Protein Structure
Prediction and Metaheuristics
Abstract This chapter provides a comprehensive overview of the protein structure

prediction problem based on metaheuristic algorithms. At first, the basic concepts
of proteins, the level of protein structure have been presented in a formal way. A
computational model, as well as techniques, have been addressed for solving protein
structure prediction (PSP) problem. The chapter discusses the basic fundamentals of
metaheuristics algorithms in detail and finally ends with a discussion of techniques
are used in the book towards solving the problem.
1.1 Introduction
Proteins are the main building blocks of dry mass cells in all living organisms. All
cell activities are performed with the help of proteins. Proteins are complex macro-
molecules combining with amino acids that are connected by peptide bonds. During
synthesis, an individual protein is folded into a three-dimensional structure [1], pro-
vides essential biological functions and properties which are playing important role in
biological science, medicine, drug design and carries disease prediction, pharmaceu-
ticals and much more [2, 3]. Sometimes, proteins may fold into an incorrect structure
(known as misfolding) leads to a protein with the different properties which can be
harmful to the organisms [4–8]. The knowledge of protein structure is, therefore,
crucial in protein research.
Biologists have defined a hierarchy of protein structures with four levels in order
to better characterize the structure properties. The primary structure is simply the
linear protein chain, i.e. a sequence of amino acids. The secondary structure is
the local conformation of protein structures. There are three types of major sec-
ondary structures, known as alpha-helix, beta-sheet, and coils (or loops). The tertiary
structure is the global three-dimensional structures. Sometimes, multiple protein
chains unit together and form hydrogen bonds between each other, resulting in the
© Springer International Publishing AG 2018 1

N. D. Jana et al., A Metaheuristic Approach to Protein Structure
Prediction, Emergence, Complexity and Computation 31,
https://doi.org/10.1007/978-3-319-74775-0_1
2 1 Backgrounds on Protein Structure Prediction and Metaheuristics
quaternary structures. Thus, the protein structure prediction (PSP) is the meaning of
determining the three-dimensional structure of a protein from its primary structure
i.e. a sequence of amino acids.
In general, the experimental techniques such as X-ray crystallography and Nuclear
Magnetic Resonance (NMR) have been used to determine a protein structure from
its sequence of amino acids [9, 10]. However, these experimental techniques are not
always feasible due to very expensive, time-consuming, strict laboratory require-
ments and heavy operational burdens [11]. As a result, the gap between the protein
sequences and the known structures are increasing rapidly day by day [12]. For
example, there are 78028152 protein sequences but the structure is known only for
117184 of them as of January 2017 [13]. As a rough estimation of a protein structure
is usually more useful than no structure at all, a number of computational methods
have been developed for PSP in the last two decades [14–16].
The computational approaches are based on utilization of computer resources
and free from laboratory activities. These methods have the potential to correlate
and predict the structure of a protein from its primary sequence in order to overcome
the difficulties associated with the experimental approaches. Based on template or
template-free modeling, computational approaches are dived into three category [15]:
homology or comparative modeling, threading or fold recognition and ab-initio or
denovo method. Homology modeling is based on the similarity comparison of the
sequence while threading approach is a process to thread together likely short sub-
conformation of the corresponding sub-sequence. These two techniques are totally
depended on the availability of similar sequence in the database i.e. these are template
based methods and the results may become unconvincing for dissimilar sequences
[17]. Consequently, the ab-initio method predicts three-dimensional structure of an
individual protein from its primary sequence directly based on intrinsic properties
(namely, hydrophobic and hydrophilic) of amino acids i.e. template-free approach.
The concept of ab-initio structure prediction method is based on the Anfinsen’s
thermodynamic hypothesis where the theory of thermodynamics [18] states that con-
formation of a protein corresponds to the global minimum free energy surface which
is called a native structure of the protein. Thus, a native structure is a stable structure
of a protein which always consume minimum energy among all the conformations
of the protein. Therefore, PSP based on ab-initio approach can be transformed into
a global optimization problem where energy function would be minimized.
The ab-initio based protein structure prediction has two important key parts. The
first part is to state the simplified mathematical model that corresponds to a protein
energy function. The second part is to develop a computationally efficient optimiza-
tion algorithm which can find the global minimum of the potential energy function.
A number of simplified models that derived the protein energy function for the PSP
have been proposed in [19–22]. The simplest computational model for the PSP prob-
lem is known as Hydrophobic-Polar (HP) or lattice model, both are two and three
dimensions. Another widely used physical model that extended from former model
known as the AB off-lattice model. The off-lattice model reveals the structure of pro-
teins at much higher atomic details and represents in both two and three dimensions
[21]. Unfortunately, the models are used in computational techniques that belong to
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GRASMERE.
The wandering minstrel and his sister—that great-hearted, most beautiful,
and devoted sister, whom we cannot help loving so devoutly,—went in the
spring of 1799 to visit their friends, the Hutchinsons, at Stockton-on-Tees,
and remained there, with occasional exceptions, until the close of the year.
Here dwelt Miss Mary Hutchinson, for whom the poet had begun to
conceive such passion as he was capable of from the time of her visit to him
and his sister, at Alfoxden. For although Dr. Wordsworth is silent also
respecting this visit, De Quincy tells us that it actually took place.—And
now the lovers—in their saturnine way—had leisure to cement their
attachment, and what is more, they took advantage of it, as their subsequent
marriage, about the commencement of the present century, sufficiently
proves.—Many other things, however, occupied the poet’s attention beside
this, and we find him, September 20, planning another tour, and this time
through the lake district, with his friends Cottle and Coleridge. It was the
first time that the latter had seen the lake country, and he, in writing to Miss
Wordsworth, thus speaks of it:—
“At Temple Sowerby we met your brother John, who accompanied us to
Hawes-water, Ambleside, and the divine sisters, Rydal and Grasmere. Here
we stayed two days. We accompanied John over the fork of Helvellyn, on a
day when light and darkness co-existed in contiguous masses, and the earth
and sky were but one. Nature lived for us in all her grandest accidents. We
quitted him by a wild turn, just as we caught a sight of the gloomy
Ullswater.
“Your brother John is one of you; a man who hath solitary usings of his
own intellect, deep in feelings, with a subtle tact, a swift instinct of truth
and beauty; he interests me much.
“You can feel what I cannot express for myself, how deeply I have been
impressed by a world of scenery, absolutely new to me. At Rydal and
Grasmere I received, I think, the deepest delight; yet Hawes-water, through
many a varying view, kept my eyes dim with tears; and the evening
approaching, Derwent-water, in diversity of harmonious features, in the
majesty of its beauties, and in the beauty of its majesty ... and the black
crags close under the snowy mountains, whose snows were pinkish with the
setting sun, and the reflections from the rich clouds that floated over some,
and rested over others!—it was to me a vision of a fair country: why were
you not with us?”
It was in this tour that Wordsworth resolved to settle at Grasmere. First
he thought of building a house by the lake side, and to enable him to do
this, his brother John offered to give him £40 to buy the land. There was a
small house to let, however, at Grasmere, which, after much deliberation
with his sister, he finally hired, and the two inseparables entered upon it on
St. Thomas’s Day, 1799.
One of the very finest of all Wordsworth’s letters—written to Coleridge
four days after the settlement at Grasmere—details, with a graphic and truly
poetic power, the wanderings of the sister and brother from Sockburn to
their new home. It is too long, however, to quote here, and for a perusal of it
the reader is referred to the Memoirs.[H]
The poet lived at Grasmere with his sister for eight years.[I] “The
cottage,” says Dr. Wordsworth, in which Wordsworth and his sister took up
their abode, and which still retains the form it wore then, stands on the right
hand, by the side of what was then the coach road, from Ambleside to
Keswick, as it enters Grasmere, or, as that part of the village is called,
“Town End.” The front of it faces the lake; behind is a small plot of orchard
and garden-ground, in which there is a spring, and rocks; the enclosure
shelves upward towards the woody sides of the mountain above it.—Many
of his poems, as the reader will remember, are associated with this fair spot:
“This spot of orchard ground is ours;

My trees they are, my sister’s flowers.”
In the first book of the “Recluse,” still unpublished, he thus expresses his
feelings in settling in this house at Grasmere, and in looking down from the
hills which embosom the lake.
“On Nature’s invitation do I come,

By reason sanctioned. Can the choice mislead,
That made the calmest, fairest spot on earth,
With all its unappropriated good,
My own, and not mine only, for with me
Entrenched—say rather peacefully embowered—
Under yon orchard, in yon humble cot,
A younger orphan of a home extinct
The only daughter of my parents, dwells;
Aye, think on that, my heart, and cease to stir;
Pause upon that, and let the breathing frame
No longer breathe, but all be satisfied.
O, if such silence be not thanks to God
For what hath been bestowed, then where, where then,
Shall gratitude find rest? Mine eyes did ne’er
Fix on a lovely object, nor my mind
Take pleasure in the midst of happy thoughts,
But either she, whom now I have, who now
Divides with me that loved abode was there,
Or not far off. Where’er my footsteps turned,
Her voice was like a hidden bird that sung;
The thought of her was like a flash of light
Or an unseen companionship, a breath
Or fragrance independent of the wind.
In all my goings, in the new and old
Of all my meditations, and in this
Favourite of all, in this the most of all....
Embrace me then, ye hills, and close me in.
Now in the clear and open day I feel
Your guardianship; I take it to my heart;
’Tis like the solemn shelter of the night,
But I would call thee beautiful; for mild,
And soft, and gay, and beautiful thou art,
Dear valley, having in thy face a smile,
Though peaceful, full of gladness. Thou art pleased,
Pleased with thy crags, and woody steeps, thy lake
Its one green island, and its winding shores,
The multitude of little rocky hills,
Thy church, and cottages of mountain stone
Clustered like stars, some few, but single most,
And lurking dimly in their shy retreats,
Or glancing at each other cheerful looks,
Like separated stars with clouds between.”
All this is a burst of quiet, yet beautiful, and almost ecstatic, enthusiasm
—the like of which is not to be met with elsewhere, I think, in poetry.
Surely, Wordsworth was worthy of his sweet cottage, and sweeter and
dearer sister, and his glorious lake, with its one green island,—his
mountains, and woods, and dales,—his church, and the cottages, “clustered
like stars,” around it; for he had the great heart, and large brain, which
Nature makes the condition for all those who would share her communion.
And, then, his tastes were so simple, natural, and unaffected; he lived so
close to Nature, and knew so many of her secrets, and loved her too, with
the passion of a first and only love. Yes, surely, he was worthy of all he
enjoyed.
During the three years which elapsed, between the poet’s entering upon
the cottage at Grasmere, and his marriage, he was very industriously, and
even laboriously, employed in cultivating his art; for he had resolved that
poetry should be the business and not the pastime of his life. We find
Coleridge urging him to continue the “Recluse,”—by which he meant, as
Dr. Wordsworth informs us, the “Prelude;”—in the summer of 1799, and
again in October of the same year, he says he will hear of nothing else but
the “Recluse;” for in the mood he was in at that time, he was wholly against
the publication of any small poems. He desired that his friend should build,
what my friend J. H. Stirling calls an “Opus;” but Wordsworth, though still
at work upon the foundations of his opus, cannot rest without making little
oratories—holy cells—in the pauses of his labour. Hence a new volume of
poems was soon ready for publication; and as the 12mo. edition of the
“Lyrical Ballads,” was by this time exhausted, Wordsworth determined to
reprint them, and add this new volume to the work, calling the two
conjointly “Lyrical Ballads, in two Volumes.” The pieces now presented to
the public, included some of his finest lyrical effusions. Amongst others,
“Lucy Gray,” “Nutting,” “The Brothers,” “Ruth,” “Poor Susan,” “The
Waterfall, and the Eglantine.” This new edition was published, in 1800, by
Messrs. Longmans, who offered the poet £100 for two editions of the two
volumes.
In 1801, Wordsworth presented a copy of the “Lyrical Ballads” to the
Right Hon. C. J. Fox, accompanied by a characteristic letter; in reply to
which, Mr. Fox expresses his high admiration of many of the poems,
particularly of “Harry Gill,” “We are Seven,” “The Mad Mother,” and “The
Idiot Boy.” Mr. Fox, however, takes exception to blank verse, as a vehicle
for subjects which are to be treated with simplicity.
Other poems of deep interest succeeded these new lyrics; and I will
name “The Leech Gatherer,” and the “Ode to Immortality,” because these
poems have always been great favourites with me; and, further, because I
wish to add here the notes which the poet has furnished respecting them.
And first of all “The Leech Gatherer:”—speaking of this poem to his
friends he says,—
“I will explain to you in prose, my feelings in writing that poem. I
describe myself as having been exalted to the highest pitch of delight by the
joyousness and beauty of Nature; and then as depressed, even in the midst
of these beautiful objects, to the lowest dejection and despair. A young poet
in the midst of the happiness of Nature is described as overwhelmed by the
thoughts of the miserable reverses which have befallen the happiest of all
men—viz., poets. I think of this till I am so deeply impressed with it, that I
consider the manner in which I was rescued from my dejection and despair
almost as an interposition of Providence. A person reading the poem with
feelings like mine, will have been awed and controlled, expecting
something spiritual or supernatural. What is brought forward? A lonely
place, ‘a pond by which an old man was, far from all house and home;’ not
stood, nor sat, but was. The figure presented in the most naked simplicity
possible. This feeling of spirituality or supernaturalness is again referred to
as being strong in my mind in this passage. How came he here? thought I,
or what can he be doing? I then describe him, whether ill or well is not for
me to judge with perfect confidence; but this I can confidently affirm, that
though I believe God has given me a strong imagination, I cannot conceive
a figure more impressive than that of an old man like this, the survivor of a
wife and children, travelling alone among the mountains, and all lonely
places, carrying with him his own fortitude in the necessities which an
unjust state of society has laid upon him. You speak of his speech as
tedious. Everything is tedious when one does not read with the feelings of
the author. The ‘Thorn’ is tedious to hundreds; and so is the ‘Idiot Boy.’ It
is in the character of the old man to tell his story, which an impatient reader
must feel tedious. But, good heavens! should he ever meet such a figure in
such a place; a pious, self-respecting, miserably infirm old man telling such
a tale!”
Having thus shown the feelings of the poet in writing “The Thorn,” I
will quote, secondly and lastly, the note to the celebrated “Ode.” “This,” he
says, “was composed during my residence at Town End, Grasmere. Two
years at least passed between the writing of the first four stanzas and the
remaining part. To the attentive and competent reader the whole sufficiently
explains itself; but there may be no harm in adverting here to particular
feelings or experiences of my own mind on which the structure of the poem
partly rests. Nothing was more difficult for me in childhood than to admit
the notion of death as a state applicable to my own being. I have said
elsewhere—
“A simple child
That lightly draws its breath,
And feels its life in every limb,
What should it know of death?”
But it was not so much from the source of animal vivacity that my
difficulties came, as from a source of the indomitableness of the spirit
within me. I used to brood over the stories of Enoch and Elijah, and almost
to persuade myself that, whatever might become of others, I should be
translated in something of the same way to heaven. With a feeling congenial
to this, I was often unable to think of external things as having externally
existence, and I communed with all that I saw as something not apart from,
but inherent in my own immaterial nature. Many times, when going to
school, have I grasped at a wall or tree to recall myself from this abyss of
idealism to the reality. At that time I was afraid of such processes. In later
periods of life I have deplored, as we have all reason to do, a subjugation of
an opposite character, and have rejoiced over the remembrances, as is
expressed in the lines “Obstinate Questionings,” &c. To that dream-like
vividness of splendour which invests objects of sight in childhood, every
one, I believe, if he would look back, could bear testimony, and I need not
dwell upon it here; but having in the poem regarded it as presumptive
evidence of a prior state of existence, I think it right to protest against such
a conclusion which has given pain to some good and pious persons, that I
meant to inculcate such a belief. It is far too shadowy a notion to be
recommended to faith as more than an element in our instincts of
immortality. But let us bear in mind that, though the idea is not advanced in
revelation, there is nothing there to contradict it, and the fall of man
presents an analogy in its favour. Accordingly, a pre-existent state has
entered into the popular creeds of many nations, and among all persons
acquainted with classic literature is known as an ingredient in Platonic
philosophy. Archimedes said that he could move the world if he had a point
whereon to rest his machine. Who has not felt the same aspirations as
regards the world of his own mind? Having to wield some of its elements
when I was impelled to write this poem on the ‘Immortality of the Soul,’ I
took hold of the notion of pre-existence, as having sufficient foundation in
humanity for authorising me to make for my purpose the best use of it I
could as a poet.”
Now, in this note, and in the “Ode” which it illustrates, will be found the
key to all Wordsworth’s philosophy, and to the secret of his mind as a poet.
The mystic spiritualism which imbues all his writings, is the great
distinguishing feature which marks and separates him from merely didactic
and descriptive poets; and, were this element wanting in him, we should
have a fine reporter of Nature’s doings—a fine painter of objective effects
—but no creator—no idealist, and therefore, properly speaking, no poet, in
the high signification of that term. Luckily, however, for Wordsworth and
for the world, he possessed the spiritual faculty, and kept it always active;
so that his eye, even in the presence of the meanest objects, was open to the
ideal things of which the symbols they were. The infinite was ever present
to his mind, and he saw all objects through that medium of light and
relationship. But the great band of critics outside the fine region in which
Wordsworth dwelt, could not of course understand this “Ode,” or the
general tone of Wordsworth’s poetry, and therefore they denounced it, as
incomprehensible, mystic, and absurd. But because they had no faculty with
which to appreciate spiritual representation, or even to believe in spirituality
as a fact belonging to the nature of man, that was no reason in the
estimation of our poet, that he should cease to sing his wonted strains in his
wonted manner. In alluding to this depreciation of his poems, he very
sorrowfully says, somewhere in his letters or notes, that it is a fact that
“nineteen out of every twenty persons are unable to appreciate poetry;” and
we are bound to confess that this hard judgment is truth. Even the better sort
of “Reviews,” in which we should have expected at least a recognition of
the genius and noble aims of the poet, stood out dead against him; and
Jeffrey’s “This will never do,” in speaking of “The Excursion,” shows how
blindly bigotted and intolerant were such critics in those days. As a sample
of the abuse, and utter want of judgment which characterised Wordsworth’s
critics, take the following anecdotes, which are recorded by the writer on
“Wordsworth,” (Chamber’s Tracts) as a good joke, or I will hope, as a
picture of the folly of the time.
“A writer in Blackwood for November, 1829, gives an amusing sketch of
a party where the ‘Intimations of Immortality,’ revered by the initiated as
the ‘Revelation,’ was read aloud by a true disciple, in a kind of
unimaginable chant then peculiar to the sect. There were one or two
believers present, with a few neophytes, and one or two absolute and
wicked sceptics! No sooner had the recitation fairly commenced, than one
of the sceptics, of laughing propensities, crammed his handkerchief half-
way down his throat; the others looked keen and composed: the disciples
groaned, and the neophytes shook their heads in deep conviction.’ The
reciter proceeded with deeper unction, till on being asked by a neophyte to
give an explanation, which he was unable to give, he got angry, and
‘roundly declared, that things so out of the common way, so sublime, and so
abstruse, could be conveyed in no language but their own. When the reciter
came to the words, ‘Callings from us,’ the neophyte again timidly requested
an explanation, and was informed by one of the sceptics, that they meant
the child’s transitory gleams of a glorious pre-existence, that fall away and
vanish almost as soon as they appear. The obstinate neophyte only replied,
in a tone of melancholy, ‘When I think of my childhood, I have only visions
of traps and balls, and whippings. I never remember being “haunted by the
eternal mind.” To be sure I did ask a great many questions, and was
tolerably obstinate, but I fear these are not the “obstinate questionings” of
which Mr. Wordsworth speaks.’ This is but a small sample of the
Wordsworthian scenes and disputations then of every-day occurrence. In
1816 a kind of shadow of Horace Smith again took the field. It seems that
Hogg intended to publish an anthology of the living British bards, and had
written to some of them for specimens. A wag, who had heard of the
project, immediately issued an anthology, purporting to be this, but
containing merely the coinage of his own brain. As may be imagined,
Wordsworth occupied a prominent corner; and indeed some of the
imitations—for most were imitations rather than parodies—did him no
discredit. ‘The Flying Tailor,’ however, was not an infelicitous burlesque of
the poet’s blank verse:—
“Ere he was put
By his mother into breeches, Nature strung
The muscular part of his anatomy
To an unusual strength; and he could leap,
All unimpeded by his petticoats,
Over the stool on which his mother sat,
More than six inches—o’er the astonished stool!”
Enough, however, has been said about these critics, for the present, at
least. Wordsworth’s was a struggle to get for poetry, once more, a true
utterance; to annihilate the old dead, mechanical form which it had for the
most part assumed, from the time of Pope downwards to him; for although
Burns and Cowper had sounded the first trumpet in this morning of the
resurrection, it was reserved for Wordsworth to awake the dead, and infuse
into them a new and living soul.
During the residence of the poet at Grasmere, his sister kept a diary of
the proceedings of their little household, which, with Wordsworth’s letters,
are the chief biographical records of this period, respecting the poet himself.
The following extracts will give some idea of the calm and beautiful life
which they led together:—
“As we were going along, we were stopped at once, at the distance,
perhaps of fifty yards from our favourite birch-tree; it was yielding to the
gust of wind, with all its tender twigs; the sun shone upon it, and it glanced
in the wind like a flying sunshiny shower; it was a tree in shape, with a stem
and branches, but it was like a spirit of water....
When we were in the woods before Gowbarrow Park, we saw a few
daffodils close to the water-side.... As we went along there were more, and
yet more; and at last, under the boughs of the trees, we saw there was a long
belt of them along the shore. I never saw daffodils so beautiful. They grew
among the mossy stones about them; some rested their heads on these
stones, as on a pillow; the rest tossed, and reeled, and danced, and seemed
as if they verily laughed with the wind, they looked so gay and glancing.”
The poet was frequently indebted to this beautiful sister for the material
of his poems; and many of the minor pieces are a musical transformation of
her descriptions of natural scenery, and the feelings with which she beheld
it. The poem of “The Beggars” is an instance of this; and if the reader will
peruse “The Daffodils,” and compare it with Miss Wordsworth’s description
of these fair flowers, as quoted above, he will perhaps discover how much
the poet is indebted to her, in this instance also. Here is the poem.
“I wandered lonely as a cloud

That floats on high o’er vales and hills,
When all at once I saw a crowd,
A host, of golden daffodils,
Beside the lake, beneath the trees,
Fluttering and dancing in the breeze.
Continuous as the stars that shine

And twinkle on the milky way,
They stretch’d in never ending line
Along the margin of a bay:
Ten thousand saw I at a glance,
Tossing their heads in sprightly dance.
The waves beside them danced; but they

Outdid the sparkling waves in glee:
A poet could not but feel gay,
In such a jocund company:
I gazed—and gazed—but little thought
What wealth the show to me had brought.
For oft, when on my couch I lie

In vacant, or in passive mood,
They flash upon that inward eye
Which is the bliss of solitude;
And then my heart with pleasure fills,
And dances with the daffodils.”
In writing to his friends the Wranghams, November 4, 1802,

Wordsworth, after thanking them for their good opinion of this poem,
alludes to “Butler, Montague’s friend,” as having said of it (the poem,)
“Aye, a fine morsel this for the reviewers,”—and adds, “When this was told
me (for I was not present) I observed that there were two lines in that little
poem, which, if thoroughly felt, would annihilate nine-tenths of the reviews
of the kingdom, as they would find no readers. The lines I alluded to were
these—
‘They flash upon that inward eye,
Which is the bliss of solitude.’ ”
And, now, I will make a few quotations from Miss Wordsworth’s

journal:—
“1802. Wednesday, April 28.—Copied the ‘Prioress’ Tale.’ W. in the
orchard tired. I happened to say, that when a child, I would not have pulled
a strawberry blossom; left him, and wrote out the ‘Manciples’ Tale.’ At
dinner he came in with the poem on children gathering flowers [the poem
entitled ‘Foresight’].
“April 20.—We went into the orchard after breakfast, and sat there. The
lake calm; sky cloudy. W. began poem on the “Celandine.”
“May 1.—Sowed flower seeds; W. helped me. We sat in the orchard. W.
wrote the ‘Celandine.’ Planned an arbour,—the sun too hot for us.
“May 7.—W. wrote ‘The Leech Gatherer.’
“May 21.—W. wrote two sonnets, ‘On Buonaparte,’ after I had read
Milton’s sonnets to him.
“May 29.—W. wrote his poem “On going to M. H.” I wrote it out.
“June 8.—W. wrote the poem ‘The sun has long been set.’
“June 17.—W. added to the ‘Ode’ he is writing [‘On the Immortality of
the Soul’].
“June 19.—Read Churchill’s ‘Rosciad.’
“July 9.—W. and I set forth to Keswick, on our road to Gallow Hill (to
the Hutchinsons’, near Malton, York). On Monday, the 11th, went to
Eusemere (the Clarksons’). 13th, walked to Emont Bridge, thence by Greta
Bridge. The sun shone cheerfully, and a glorious ride we had over the
moors; every building bathed in golden light; we saw round us miles
beyond miles, Darlington spire, &c. Thence to Thirsk; on foot to the
Hamilton Hills—Rivaux. I went down to look at the ruins; thrushes singing,
cattle feeding amongst the ruins of the abbey; green hillocks about the ruins
—these hillocks scattered over with grovelets of wild roses, and covered
with wild flowers: could have staid in this green quiet spot till evening,
without a thought of moving, but W. was waiting for me....
July 30.—Left London between five and six o’clock of the morning,
outside the Dover coach. A beautiful morning. The city, St. Paul’s, with the
river—a multitude of little boats—made a beautiful sight, as we crossed
Westminster Bridge [Wordsworth’s sonnet “On Westminster Bridge” was
written on the roof of the Dover coach]; the houses, not overhung by their
clouds of smoke, were spread out endlessly; yet the sun shone so brightly,
with such a pure light, that there was something like the purity of one of
Nature’s own grand spectacles.... Arrived at Calais at four in the morning of
July 31st.
Delightful walks in the evening; seeing far off in the west the coast of
England, like a cloud, crested with Dover Castle, the evening star, and the
glory of the sky: the reflections in the water were more beautiful than the
sky itself; purple waves, brighter than precious stones, for ever melting
away on the sands.
August 29.—Left Calais, at twelve o’clock in the morning, for Dover ...
bathed, and sat on the Dover Cliffs, and looked upon France; we could see
the shores almost as plain as if it were but an English lake. Mounted the
coach at half-past four; arrived in London at six, August 30. Stayed in
London till 22nd September: arrived at Gallow Hill on Friday, September
24th.
On Monday, October 4th, 1802, W. was married, at Brompton church, to
Mary Hutchinson.... We arrived at Grasmere, at six in the evening, on
October 6th, 1802.”
And that the reader may hereafter have a clear perception of the persons
of the poetic household at Grasmere, I will now go to De Quincy, who has
drawn portraits of them, which, in the absence of any similar literary
venture, are invaluable. Speaking of Mrs. Wordsworth, he says,—she was a
tall young woman, with the most winning expression of benignity upon her
features that he had ever beheld; her manner frank, and unembarrassed.
“She was neither handsome or comely, according to the rigour of criticism,
and was generally pronounced plain-looking, but the absence of the
practical power and fascination which lie in beauty, were compensated by
sweetness all but angelic, simplicity the most entire, womanly self-respect,
and purity of heart, speaking through all her looks, acts, and movements.
She rarely spoke; so that Mr. Slave-trade Clarkson used to say of her, that
she could only say God bless you. Certainly her intellect was not of an
active order; but in a quiescent, reposing, meditative way, she appeared
always to have a social enjoyment from her own thoughts; and it would
have been strange indeed, if she, who enjoyed such eminent advantages of
training, from the daily society of her husband and his sister; not only
hearing the best parts of English literature daily read, or quoted by short
fragments, but also hearing them very often critically discussed in a style of
great originality and truth, and by the light of strong poetic feeling,—
strange would it have been had any person, dull as the weeds of Lethe in the
native constitution of mind, failed to acquire the power of judging for
herself, and putting forth some functions of activity. But undoubtedly that
was not her element: to feel and to enjoy a luxurious repose of mind—there
was her forte and her peculiar privilege; and how much better this was
adapted to her husband’s taste, how much more suited to uphold the
comfort of his daily life, than a blue-stocking loquacity, or even a legitimate
talent for discussion and analytic skill may be inferred from his celebrated
verses, beginning:
‘She was a phantom of delight

When first she gleamed upon my sight;’
and ending with this matchless winding up of
‘A perfect woman, nobly planned

To warn, to comfort, to command;
And yet——’
going back to a previous thought, and resuming a leading impression of the

whole character—
‘And yet a spirit too, and bright

With something of an angel light.’ ”
“From these verses,” continues De Quincy, “it may be inferred what

were the qualities which won Wordsworth’s admiration in a wife; for these
verses were written upon Mary Hutchinson, his own cousin, and his wife;
and not written as Coleridge’s memorable verses upon “Sara,” for some
forgotten original Sara, and consequently transferred to every other Sara
who came across his path. Once for all, these exquisite lines were dedicated
to Mrs. Wordsworth; were understood to describe her—to have been
prompted by the feminine graces of her character; hers they are and will
remain for ever.” To these, therefore, De Quincy refers the reader for an
idea infinitely more powerful and vivid, he says, than any he could give, of
what was most important in the partner and second self of the poet. And to
this abstract of her moral portrait he adds the following remarks upon her
physical appearance. “She was tall, as already stated; her figure was good—
except that for my taste it was rather too slender, and so it always
continued. In complexion she was fair; and there was something peculiarly
pleasing even in this accident of the skin, for it was accompanied by an
animated expression of health, a blessing which in fact she possessed
uninterruptedly, very pleasing in itself, and also a powerful auxiliary of that
smiling benignity which constituted the greatest attraction of her person.
Her eyes—the reader may already know—her eyes
‘Like stars of twilight fair;

Like twilight, too, her dark brown hair;
But all things else about her drawn
From May time and the cheerful dawn.’
But strange it is to tell, that in these eyes of vesper gentleness, there was
a considerable obliquity of vision; and much beyond that slight obliquity
which is often supposed to be an attractive foible of the countenance; and
yet though it ought to have been displeasing or repulsive, in fact it was not.
Indeed, all faults, had they been ten times and greater, would have been
swallowed up or neutralised by that supreme expression of her features, to
the intense unity of which every lineament in the fixed parts, and every
undulation in the moving parts or play of her countenance, concurred, viz.,
a sunny benignity—a radiant perception—such as in this world De Quincy
says he never saw equalled or approached.”
Such, then, is the portrait of Mrs. Wordsworth; and now for that of
sweet, musical, romantic, true and generous Dorothy. She was much
shorter, much slighter, and perhaps in other respects as different from Mrs.
Wordsworth in personal characteristics as could have been wished for the
most effective contrast. “Her face was of Egyptian brown: rarely in a
woman of English birth had a more determined gipsy tan been seen. Her
eyes were not soft, as Mrs. Wordsworth’s, nor were they fierce or bold; but
they were wild and startling, and hurried in their motion. Her manner was
warm, and even ardent; her sensibility seemed constitutionally deep; and
some subtle fire of impassioned intellect apparently burned within her,
which, being alternately pushed forward into a conspicuous expression by
the irrepressible instinct of her temperament, and then immediately checked
in obedience to the decorum of her sex and age, and her maidenly condition
(for she had rejected all offers of marriage, out of pure sisterly regard to her
brother, and subsequently to her sister’s children) gave to her whole
demeanour and to her conversation, an air of embarrassment and even of
self conflict, that was sometimes distressing to witness. Even her very
utterance, and enunciation often, or rather generally, suffered in point of
clearness and steadiness, from the agitation of her excessive organic
sensibility, and perhaps from some morbid irritability of the nerves. At
times the self-contracting and self-baffling of her feelings, caused her even
to stammer, and so determinedly to stammer, that a stranger who should
have seen her, and quitted her in that state of feeling, would have certainly
set her down for one plagued with that infirmity of speech, as distressingly
as Charles Lamb himself.... The greatest deductions from Miss
Wordsworth’s attractions, and from the exceeding interest which
surrounded her in right of her character, her history, and the relation which
she fulfilled towards her brother, was the glancing quickness of her
motions, and other circumstances in her deportment—such as her stooping
attitude when walking, which gave an ungraceful, and even an unsexual
character to her appearance when out of doors. She did not cultivate the
graces which preside over the person and its carriage. But on the other hand
she was a person of very remarkable endowments intellectually; and in
addition to the other great services which she rendered to her brother, this
may be mentioned as greater than all the rest, and it was one which equally
operated to the benefit of every casual companion in a walk—viz., the
extending sympathy, always ready, and always profound, by which she
made all that one could tell her, all that one could describe, all that one
could quote from a foreign author, reverberate as it were a plusieurs
reprises to one’s own feelings, by the manifest pleasure it made upon her....
Her knowledge of literature was irregular, and not systematically built up.
She was content to be ignorant of many things; but what she knew and had
really mastered, lay where it could not be disturbed—in the temple of her
own most fervid heart.”... At the time this sketch was written, both the
ladies were about twenty-eight years old. “Miss Wordsworth,” continues De
Quincy, “had seen most of life, and even of good company; for she had
lived, when quite a girl, under the protection of a near relation at Windsor,
who was a personal favourite of the royal family, and consequently of
George the Third.” Nevertheless, De Quincy thinks that “Mrs. Wordsworth
was the more ladylike person of the two.”
The last figure, and the greatest, in this little group of portraits, is
Wordsworth’s, and it is certainly hit off, like the others, with a free and
discriminating hand.
“Wordsworth was, upon the whole, not a well-made man. His legs were
positively condemned by all the female connoisseurs in legs that De Quincy
ever heard lecture on that topic; not that they were bad in any way that
would force itself upon your notice—there was no absolute deformity about
them; and undoubtedly they had been serviceable legs, beyond the average
standard of human requisition; for with these identical legs Wordsworth
must have travelled a distance of one hundred and seventy-five to one
hundred and eighty thousand English miles,—a mode of exertion which to
him stood in the stead of wine, spirits, and all other stimulants whatever to
the animal spirits; to which he has been indebted for a life of unclouded
happiness, and even for much of what is most excellent in his writings. But
useful as they have proved themselves, the Wordsworthian legs were
certainly not ornamental; it was really a pity that he had not another pair for
evening dress parties, when no boots lend their friendly aid to mask our
imperfections from the eyes of female rigourists—the elegantes formarum
spectatrices.... But the worst part of Wordsworth’s person was the bust;
there was a narrowness and a stoop about the shoulders, which became
striking, and had an effect of meanness, when brought into close
juxtaposition with a figure of a most statuesque “order.” ... Further on, De
Quincy relates how he was walking out with Miss Wordsworth, the poet
being before them, deeply engaged in conversation with a person of fine
proportions, and towering figure,—when the contrast was so marked, and
even painful to the poet’s sister, that she could not help exclaiming: “Is it
possible? Can that be William? How very mean he looks!” “And yet,”
continues De Quincy, “Wordsworth was of a good height, just five feet ten,
and not a slender man; on the contrary, by the side of Southey, his limbs
looked thick, almost in a disproportionate degree. But the total effect of
Wordsworth’s person was always worst in a state of motion; for, according
to the remark I have heard from the county people, ‘he walked like a cade;’
a cade being a kind of insect which advances by an oblique motion. This
was not always perceptible, and in part depended (I believe) upon the
position of his arms; when either of these happened (as was very
customary) to be inserted into the unbuttoned waistcoat, his walk had a wry
or twisted appearance; and not appearance only,—for I have known it by
slow degrees gradually to edge off his companion, from the middle to the
side of the high road.’ Meantime his face—that was one which would have
made amends for greater defects of figure; it was certainly the noblest for
intellectual effect, that, De Quincy says, he ever saw. Haydon, the eminent
painter, in his great picture of Christ’s Entry into Jerusalem, has introduced
Wordsworth in the character of a disciple attending his Divine Master....
“Wordsworth’s face was of the long order, often classed as oval, ... and if
not absolutely the indigenous face of the lake district, at any rate a variety
of that face,—a modification of the original type. The head was well filled
out.... The forehead was not remarkably lofty ... but it was, perhaps,
remarkable for its breadth and expansive development. Neither were the
eyes large, ... on the contrary, they were rather small; but that did not
interfere with their effect, which at times was fine, and suitable to his
intellectual character.... The mouth and the region of the mouth—the whole
circumference of the mouth, were about the strongest feature in
Wordsworth’s face. There was nothing especially to be noticed in the mere
outline of the lips, but the swell and protrusion of the parts above and
around the mouth are noticeable.” And then De Quincy tells us why. He had
read that Milton’s surviving daughter, when she saw the crayon drawing
representing the likeness of her father, in Richardson the painter’s thick
octavo volume of Milton, burst out in a rapture of passionate admiration,
exclaiming—“This is my father! this is my dear father!” And when De
Quincy had procured this book, he saw in this likeness of Milton a perfect
portrait of Wordsworth. All the peculiarities, he says, were retained—“A
drooping appearance about the eyelids—that remarkable swell that I have
noticed about the mouth,—the way in which the hair lay upon the forehead.
In two points only there was a deviation from the rigorous truth of
Wordsworth’s features—the face was a little too short and too broad, and
the eyes were too large.—There was also a wreath of laurel about the head,
which, (as Wordsworth remarked,) disturbed the natural expression of the
whole picture; else, and with these few allowances, he also admitted that
the resemblance was, for that period of his life (but let not that restriction be
forgotten;) perfect, or, as nearly so as art could accomplish. This period was
about the year 1807.
Here, then, thanks to De Quincy, who, for these “Lake Reminiscences”
alone, is well worthy of a pension, which, had I been Prime Minister, he
should have had long ago; for no living man is more deserving of this
distinction for the service he has rendered to our literature:—here, I say, we
have portraits of the inmates of the white cottage at Grasmere; and beautiful
portraits they are. One could have wished that Dr. Wordsworth had given a
little more vitality to his biography of these inmates—that he had used his
pallet and brushes a little more freely (for he can paint, if he likes, as the
description of Rydal Mount shows); but instead of vitality, we have dry
facts—which are the mere bones of biography—and these are often strung
together with very indifferent tendons. We have no picture, for example, of
the poet’s wedded life at this time—we cannot get behind the scenes; all we
know is, that a wedding had taken place, and the good doctor tells us, that
the twain were afterwards very happy all the days of their life, just as fairy
tales wind up. There seems to be a good deal of needless reserve about this
matter; and I, for one, do not thank the greedy poet when he says, touching
his private life, that “a stranger intermeddleth not with his joy.” No one
wishes to meddle with it; but to sympathise with it, and to know how this
joy manifested itself in the little household, appear to be legitimate
demands of the curious lovers of Wordsworth, and, indeed of all curious
men, whether lovers of Wordsworth or not. But the doctor has nothing to
say on these points; and all we can gather respecting them is to be found in
the “Prelude,” and one or two other poems. Here is the extract from the
“Prelude,” expressing the poet’s feelings as he left the cottage with his sister
before his marriage:—
“Fareweil! thou little nook of mountain-ground,

Farewell! we leave thee to Heaven’s peaceful care,
Thee, and the cottage, which thou dost surround.
We go for one to whom ye will be dear;
And she will prize this bower, this Indian shed,
Our own contrivance—building without peer;
A gentle maid....
Will come to you, to you herself will wed,
And love the blessed life that we lead here.”
And in this place it will be well to give De Quincy’s sketch of the cottage
itself, where this blessed life was lived, and to share which the poet went to
fetch his bride from her father’s house:—“A little semi-vestibule between
two doors, prefaced the entrance into what might be considered the
principal room of the cottage. It was an oblong square, not above eight and
a half feet high, sixteen feet long, and twelve broad; very prettily
wainscotted, from the floor to the ceiling, with dark polished oak, slightly
embellished with carving. One window there was—a perfect and
unpretending cottage window—with little diamond panes, embowered, at
almost every season of the year, with roses; and in the summer and autumn,
with jessamine and other fragrant shrubs. From the exuberant luxuriance of
the vegetation around it, and from the dark hue of the wainscotting, this
window, though tolerably large, did not furnish a very powerful light to one
who entered from the open air.... I was ushered up a little flight of stairs—
fourteen in all—to a little dingy room, or whatever the reader chooses to
call it. Wordsworth himself has described the fire-place of this, his—
‘Half kitchen and half parlour fire.’
It was not fully seven feet six inches high, and in other respects of pretty
nearly the same dimensions as the rustic hall below. There was however, in
a small recess, a library of perhaps three hundred volumes, which seemed to
consecrate the nook as the poet’s study, and composing room; and so
occasionally it was.”
So far then, De Quincy; and the following poem, already alluded to, will
give an idea of the poet’s feelings respecting the bride he brought with him
to share the cottage blessedness of Grasmere.
“She was a phantom of delight,
When first she gleamed upon my sight;
A lovely apparition, sent
To be a moment’s ornament.
Her eyes as stars of twilight fair;
Like twilight too her dusky hair;
But all things else about her drawn
From May time and the cheerful dawn;
A dancing shape, an image gay,
To haunt, to startle, and waylay.
I saw her upon nearer view,

A spirit, yet a woman too!
Her household motions light and free,
And steps of virgin liberty;
A countenance in which did meet
Sweet records, promises as sweet;
A creature not too bright or good
For human nature’s daily food;
For transient sorrows, simple wiles,
Praise, blame, love, kisses, tears, and smiles.
And now I see with eye serene

The very pulse of the machine;
A being breathing thoughtful breath,
A traveller between life and death;
The reason firm, the temperate will,
Endurance, foresight, strength and skill;
A perfect woman, nobly planned,
To warn, to comfort, to command;
And yet a spirit still, and bright,
With something of angelic light.”
This beautiful poem, so full of calm affection, and intellectual homage,

is a fair sample of Wordsworth’s love poems, as well as a charming tribute
to his wife’s loveliness and virtue. In early life, it is thought by De Quincy
and others, that the poet had experienced a tragical termination to an early
love, and that the poems of which “Lucy” is the theme, were addressed to
the object of this love; but Wordsworth always maintained a mysterious
silence about the whole affair, and would never resolve the riddle of this
attachment. The “Lucy” poems, however, beautiful as they are, are chiefly

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A Metaheuristic Approach to Protein

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1 Backgrounds on Protein Structure Prediction and Metaheuristics . . 1

2.6 Protein Structure Prediction Using Metaheuristics: A Road

4.5 Performance Analysis of the Metaheuristic Algorithms . . . . . . . . . 124

7 Hybrid Metaheuristic Approach for Protein Structure

Fig. 1.1 Basic structure of an amino acid . . . . . . . . . . . . . . . . . . . . . . . .. 3

Fig. 4.10 Correlograms for artiﬁcial protein sequences in 2D AB

Fig. 4.27 Convergence curve of algorithms for RSs in 3D AB off-lattice

Table 1.1 Summary of the most representative metaheuristic

Table 4.1 Encoding and class labels of a landscape path with

Table 5.2 Results of the LdDE and other compared algorithms

Algorithm 1 Differential Evolution (DE) . . . . . . . . . . . . . . . . . . . . . . . . . 18

Abstract This chapter provides a comprehensive overview of the protein structure

© Springer International Publishing AG 2018 1

“This spot of orchard ground is ours;

“On Nature’s invitation do I come,

“I wandered lonely as a cloud

Continuous as the stars that shine

The waves beside them danced; but they

For oft, when on my couch I lie

In writing to his friends the Wranghams, November 4, 1802,

And, now, I will make a few quotations from Miss Wordsworth’s

‘She was a phantom of delight

and ending with this matchless winding up of

‘A perfect woman, nobly planned

going back to a previous thought, and resuming a leading impression of the

‘And yet a spirit too, and bright

“From these verses,” continues De Quincy, “it may be inferred what

‘Like stars of twilight fair;

“Fareweil! thou little nook of mountain-ground,

‘Half kitchen and half parlour fire.’

I saw her upon nearer view,

And now I see with eye serene

This beautiful poem, so full of calm affection, and intellectual homage,

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