Virtual Screening and Computer-aided Drug Design in Molecular
Docking via Lyapunov Function
Shih- Ching Ou 1 Chun- Yen Chung* 2 Wen-Tsai Sung 2
Chia - Chih Tsai 2 Chin - Chih Chien 2 Da -Yu Su 2
Department of Information Communication, Leader University ,Taiwan 1
Bioinformatics Lab, Department of Electrical Engineering, National Central University ,Taiwan
2
Abstract: - Virtual screening of compound librarieshas become a component of many preclinical
discovery programs. Large pharmaceutical companies and also many smaller chemistry-oriented
businesses support substantial efforts in this area, the hope being that in silico screening and analysis
will significantly aid in the identification of small molecular inhibitors and antagonists. In a number of
cases, the potential of these efforts has already been demonstrated and interesting new molecules have
been identified. In this paper, the authors have demonstration some examples in protein folding
kinetics and drug docking computations, and this work succeeds in citing Lyapunov equation and
molecular dynamics to support this theme.
Key-words: -Virtual screening, Drug, docking, Lyapunov Function
1 Introduction
The idea of screening compound databases on
the computer is certainly not new. Virtual
screening, as we understand it today, has its
roots in pioneering efforts in the 1970s
introducing compound database
searches using 2D structural fragments or 3D
queries, and the subsequent automated docking
of ligands into protein binding sites. In addition
to protein-ligand docking, structure-based
capable of analyzing screening datasets and
deriving predictive models of biological activity.
approaches include the development of
pharmacophores from active or binding site
features. On the other hand, methods that start
from hits or leads range from pharmacophore or
multi-dimensional QSAR models and binary
fingerprints to compound clustering or
partitioning methods and statistical techniques
clique-search approach. This is done by
matching features in the ligand to features in the
receptor. Another approach in rigid docking is
geometric hashing. Geometric hashing has its
origins in computer vision. These rigid models
worked well for some examples and not so well
in other examples. In reality molecules are not
rigid and are often quite flexible.
2 Drug Docking
In the 1970s people began molecular dynamics
simulation. In 1982 Kuntz et al. published the
DOCK algorithm. It was the first docking
program to approach the problem from a
non-simulation approach. It instead used a
orientation of the previous pieces. FlexX is one
of the more popular incremental approach
programs. A third approach in flexible ligand
docking is genetic algorithms and evolutionary
programming. This approach mimics biological
evolution, where the individuals are different
configurations of the molecules. A fitness
function determines whether or not different
configurations are used in the next generation of
configurations. One of the first programs
developed using this approach was GOLD based
Fig.1 : Hypothetical ligand and receptor
molecules in undocked ( upper ) and
docked ( lower ) configurations. Both
on the ideas of Jones et al. There are various
other techniques for flexible docking. A program
that we used was AutoDock, which uses
geometry and forces determine whether
and how molecules will dock. In the
docked image, hydrophobic areas,
interacting through van der Waals
forces, as well as oppositely charged
areas, interacting electrostatically, come
together.
simulated annealing to find the docked
conformation. Later a genetic algorithm
approach was added to AutoDock. There is other
less used approaches and approaches that
combine the previously mentioned to round out
the work done on flexible-ligand docking. Many
good results have come from introducing ligand
The ligand was the first part to become flexible.
The ligand is usually a small molecule with few
degrees of freedom. The first approach was to
find all or most of the conformations the flexible
ligand would take on and feed those
conformations into a rigid docking program. The
Flexibase/FLOG docking programs were based
on this conformation ensemble approach.
Another popular approach is fragmentation. In
flexibility. However, the problem becomes much
more difficult when trying to add in protein
flexibility. A ligand is usually a small molecule
with from 10 to 100 atoms. However, a protein
has thousands of atoms, and thus has many more
degrees of freedom. This makes the problem
difficult, and solving this problem is what we've
been working on. Our approach uses various
search and dimensionality reduction techniques
this case the ligand is broken up in some way
and then placed piece by piece into the receptor.
There are two major subsets of this approach.
One is “place and join” where all of the
fragments are placed independently and then the
program tries to connect them together. The
other is an incremental approach, where the
fragments are placed one by one according to the
to solve the problem.
3 Virtual libraries
What are the sources of compounds for in silico
screening? Two types of collection are generally
used: ‘truly’ virtual libraries, produced by
computational design; and libraries assembled
from
commercial
sources
or
company
important method and tool in the field of
inventories. True virtual libraries are generally
designed to populate theoretical ‘chemistry
spaces ’, and can contain billions of molecules.
The basic idea behind these predictions is of
course not to synthesize all compounds (as in
combinatorial library design, for example) but to
select only preferred molecules. Other libraries
focus on compounds that already exist. It is
possible to extract several million compounds
from catalogs of combinatorial or medicinal
innovative drug research and development.
CADD come into the circulation of innovative
drug research could shorten the cycle and cost of
research and development and enhance the
success rate of screening. The great majority
company adopts variety methods, including
parallel protein simulation method, structurebased parallel docking program, drug-like
prediction methods and QSAR analysis methods,
to carry out the CADD. Therefore, we proposed
chemistry vendors and organize these in a virtual
library. In most pharmaceutical companies,
computational groups also generate such
some VHTS concepts and solution for this study
via survey interrelated literatures.
compound
collections
when developing
acquisition strategies. Experience has shown that
up to half of the collected compounds are not
available for purchase for one reason or another,
but the information content of these libraries is
valuable. Unavailable molecules can usually be
resynthesized, which is not the case in some
truly virtual libraries, where the synthetic
feasibility is frequently questioned by chemists.
4 Lead Discovery on CADD and VHTS
The process of innovative drug discovery and
development is time-consuming and expensive,
while the rate for success is low. Generally, only
one of 10,000 compounds synthesized by
Fig.2 : Integration of high-throughput and virtual
screening.
After a library subset has been screened
experimentally and a few initial hits have been
chemist can reach the market. According to
recent survey on current drugs on the market, on
average it costs the pharmaceutical industry
300-500 million US dollars to bring a new
chemical entity molecule to the marketplace, and
the process from discovery to market usually
takes 10-15 years. According to the overhead
mentions, CADD has become a new and
obtained, HTS data can be used to calculate
predictive models of activity. These models are
subsets for testing. The higher the information
content the more successful data mining will be
Smart. HTS screening will then have a greater
value to the company.
Fig.3 : The similarity paradox. A fingerprint
search for damnacanthal, a potent
inhibitor of tyrosine kinase p561ck,
minor modifications (red) of this
scaffold render compounds either
active or inactive. In virtual screening
calculatioms, both of these closely
related analogs are considered similar
to the template.
5 Inside Rational Drug Design
Rational drug design (RDD) methods accelerate
the discovery process for pharmaceutical
research organizations. RDD involves the design
and optimization of small, organic therapeutics
from the ideal case, where a protein structure is
available, to the other extreme where only a
small collection of 'hits' from high throughput
screening can be utilized. The breadth of
innovative techniques for structure-based,
analog, and combinatorial library design allows
you to efficiently use information from all
possible sources on your therapeutic target.
4 situations can arise in rational drug design:
Fig. 4 : Four Situations for Drug Discovery
6 Molecular Mechanics and
Dynamics (MM and MD)
The mechanical molecular model was developed
out of a need to describe molecular structures
and properties in as practical a manner as
possible. The range of applicability of molecular
mechanics (MM) includes:
Molecules containing thousands of atoms
Organics, oligonucleotides, peptides, and
saccharides Vacuum, implicit, or explicit
solvent environments. Ground state only
Therm od ynam i c and ki net i c properti es
The object of MM is to predict the energy
associated with a given conformation of a
molecule. However, MM energies have no
meaning as absolute quantities. Only differences
in energy between two or more conformations
have meaning. A simple MM energy equation is
given by:
Energy (E) = E Stretch + EBending +
ETorsion + E Non-bonded Interactions (1)
These equations together with the data
(parameters) required to describe the behavior of
different kinds of atoms and bonds, is called a
force-field. Many different kinds of force-fields
have been developed over the years. Some
include additional energy terms that describe
other kinds of deformations. Some force-fields
account for coupling between bending and
stretching in adjacent bonds in order to improve
the accuracy of the mechanical model. All of the
potential energy functions are illustrated in the
graph below:
Fig.6:
Energy Lyapunov Functions
Molecular Dynamic System
for
8 Conclusion
Fig.5 :potential energy function
7 Energy Lyapunov Functions for
Molecular Dynamic System
A Lyapunov functi on is som e kind of
mathematical quantity that is maximized by
a particular dynamical system as it changes
according to whatever rules it works by.
A general methodology in the stability analysis
of equilibrium of a nonlinear dynamical system
is to find a suitable Lyapunov function. This
is in general a very difficult task, but
for nonlinear molecular dynamic systems
there often is a natural candidate Lyapunov
fun ct i on, nam el y t h e ene r g y fun ct i on.
Lyapunov developed a general theory of
dynamic stability applicable to both linear and
nonlinear systems.
On the most elementary level, bu ilding
a 3D representation of a small molecule
that can be easily rotated and conformationally
analyzed enables a thought process almost
impossible to achieve from a 2D drawing.
DRUG was founded to demonstrate that high
performance computing computer assisted drug
design not only dramatically improves the
process of discovering new drugs, but also is an
affordable tool for CADD industries.
This study proposed a novel minimum energy
scheme for drug docking applications. The
proposed scheme preserves the important
advantages inherent in a protein folding process
and ligand become locked key. In final,
authors cited Lyapunov Equation to prove the
stability of drug docking.
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