A Stochastic Mechanism for DNA Melting
Page: 1-15 (15)
Author: Sencer Taneri*
DOI: 10.2174/9789815179965123010004
PDF Price: $15
Abstract
In Chapter 1, we have DNA as a kind of nucleic acid consisting of two strands which
are made up of two Watson-Crick base pairs: adenine-thymine (AT) and guanine-cytosine
(GC). There are three components of the total energy. These are the inharmonic stacking
interaction, hydrogen bond interaction and kinetic energy. Morse potential is used to mimic
the hydrogen bond interaction between bases on the opposite strands for the overlapping π electrons, when two neighboring bases move out of the stack. The AT pair has 2 hydrogen
bonds and the GC pair has 3 of them. The π electrons obey Bose - Einstein (BE) statistics,
and the overlapping of them results in quantum fluctuation. It will be shown that this can be
simplified into < Δy(t)Δy(t) >= 2DqΔt type fluctuation between the base pairs. Thus, a
metropolis algorithm can be developed for the total potential energy by superposing two
potential energy terms as well as including the quantum fluctuation in terms of random
displacement of the π electrons. So, one can calculate the melting temperature of base pairs.
A Theoretical Analysis of a Percolation Model
Page: 16-25 (10)
Author: Sencer Taneri*
DOI: 10.2174/9789815179965123010005
PDF Price: $15
Abstract
In Chapter 2, we demonstrate an analytical analysis of a previously published
research for a percolation simulation. In that research the effect of mutations on adaptability
was investigated in a bit-string model of invading species in a random environment. However,
analytical analysis was missing which will be the topic here. The Hausdorff dimensions are
calculated for the fractals and the conditions on invasion are analyzed analytically by
manipulation of partial differential equations. Thus, various conclusions may be reached
without having to run long simulations.
A Monte Carlo Assisted Simulation of Stochastic Molecular Dynamics for Folding of the Protein Crambin in a Viscous Environment
Page: 26-45 (20)
Author: Sencer Taneri*
DOI: 10.2174/9789815179965123010006
PDF Price: $15
Abstract
In Chapter 3, we investigate the folding dynamics of the plant-seed protein Crambin
in a liquid environment, that usually happens to be water with some certain viscosity. To take
into account the viscosity, necessitates a stochastic approach. This can be summarized by a 2D-Langevin equation, even though the simulation is still carried out in 3D. Solution of the
Langevin equation will be the basic task in order to proceed with a Molecular Dynamics
simulation, which will accompany a delicate Monte Carlo technique. The potential wells, used
to engineer the energy space assuming the interaction of monomers constituting the protein-chain, are simply modeled by a combination of two parabola. This combination will
approximate the real physical interactions, that are given by the well known Lennard-Jones
potential. Contributions to the total potential from torsion, bending and distance dependent
potentials are good to the fourth nearest neighbor. The final image is in very good geometric
agreement with the real shape of the protein chain, which can be obtained from the protein data
bank. The quantitative measure of this agreement is the similarity parameter with the native
structure, which is found to be 0.91 < 1 for the best sample. The folding time can be
determined from Debye-relaxation process. We apply two regimes and calculate the folding
time, corresponding to the elastic domain mode, which yields 5.2ps for the same sample.
Continuum Space Model for Folding of the Protein Crambin
Page: 46-55 (10)
Author: Sencer Taneri*
DOI: 10.2174/9789815179965123010007
PDF Price: $15
Abstract
In Chapter 4, we have studied the chain length dependence of folding time for
proteins by implementing a novel Monte Carlo (MC) method. The physical parameters in our
model are derived from the statistics for bending and torsion angles and distances between the
centers of the monomers up to the fourth neighborhood. By assigning potential wells to each
of the physical parameters, we are able to use a modified Metropolis algorithm to efficiently
trace the later conformations of the proteins as time evolves. Our prescription for microscopic
dynamics for the protein "Crambin" results in an increase in folding times with increasing chain
length. The folding times are determined via Debye relaxation process.
A Stochastic Mechanism for DNA Vitrification
Page: 56-64 (9)
Author: Sencer Taneri*
DOI: 10.2174/9789815179965123010008
PDF Price: $15
Abstract
In Chapter 5, DNA is a kind of nucleic acid consisting of two strands which are
made up of two Watson-Crick base pairs: adenine-thymine (AT) and guanine-cytosine (GC). Vitrification (from Latin vitreum, "glass") on the other hand is the transformation of a
substance into a glass. DNA vitrification is achieved by rapidly cooling DNA in a liquid state
through the glass transition. The quantum fluctuation in terms of random displacement and
specific heat capacity of the π electrons in hydrogen bonds was studied earlier to calculate the
DNA melting temperature. Same principles along with the inclusion of longitudinal
phonon vibrations will be used here in order to calculate the vitrification temperature (glass
transition temperature) of base pairs. This has an important application in cryonics and
cryopreservation.
A Theoretical Investigation on 10-12 Potential of Hydrogen-Hydrogen Covalent Bond
Page: 65-73 (9)
Author: Sencer Taneri*
DOI: 10.2174/9789815179965123010009
PDF Price: $15
Abstract
In Appendix, we have an analytical investigation of the well-known 10-12 potential
of hydrogen-hydrogen covalent bond. In this research, we will make an elaboration of the well-known 6-12 Lennard-Jones potential in case of this type of bond. Though the results are
illustrated in many text books and literature, an analytical analysis of these potentials is missing
almost everywhere. The power laws are valid for small radial distances, which are calculated
to some extent. The internuclear separation as well as the binding energy of the hydrogen
molecule are evaluated with success.
Introduction
This monograph research presents research in applied biomathematics carried out by the author at the beginning of this millennium. Monte Carlo simulations have been widely used by computational biologists to understand stochastics of living systems in biological matter. This work demonstrates how Monte Carlo simulations can help us to understand the nucleic acid structure, biophysics and chemistry. The author presents research on methods to understand aspects of the molecular dynamics of nucleic acids, DNA melting, evolutionary genetics, protein folding of Crambin and DNA vitrification. The book consists of five chapters and an appendix on the theoretical investigation on 10-12 potential of Hydrogen-Hydrogen covalent bond. Some of the previous research published in İnternational Journal of Modern Physics C and Modern Physics Letters B is extended for additional insight. Readers will find simple computer algorithms for hard mathematical physics problems such as mesoscopic, fractals, percolation, Metropolis algorithm and Langevin dynamics – many of which are also crucial to understanding experimental results of computer-aided drug discovery and cryopreservation. The author has taken care to explain calculations in a clear manner. All simulations have been conducted using Fortran (f77).