We have numerically investigated the effects of helicity and inhomogeneities on DNA base pairs op... more We have numerically investigated the effects of helicity and inhomogeneities on DNA base pairs opening. The inhomogeneities are due to the site-dependent stacking and hydrogen bonding energies in DNA and protein molecules. We have considered a situation in which the active site of the RNA-polymerase molecule binds onto the promoter site of the spin-like model of the DNA molecule at the physiological temperature and creates a bubble. During the study, we have found that the helical coupling has to be very weak compared to intra-strand coupling in the real DNA molecule. Results show that inhomogeneities do not affect the general pattern of base pair opening, even as the periodic inhomogeneity introduces a train of periodic oscillations on the tail of the bubble; while the height of the bubble is an increasing function of the helical coupling parameter. The basic properties of breather-like modes, obtained here by taking into account helical structure and inhomogeneities, are essential for DNA functioning since such breathing-like modes are considered to be much better candidates for the nonlinear modes responsible for a locally open state where biological functioning takes place.
Physica Scripta. 89 085003
Issue 8 (August 2014)
Received 19 April 2013, accepted for publication 29 May 2014
Published 26 June 2014
doi:10.1088/0031-8949/89/8/085003
http://iopscience.iop.org/1402-4896/89/8/085003/
Using a mathematical spin-like model of DNA molecule, we have studied its dynamics, by taking int... more Using a mathematical spin-like model of DNA molecule, we have studied its dynamics, by taking into account forces due to the surrounding medium. Thus, we have shown the robustness of bubble-like solitons, by mathematically modeling the nonlinear interaction between the DNA and an enzyme at the physiological temperature. Noise, damping, and driving forces are added to get a set of deterministic discrete motion equations. Numerical results show that the bubble-like soliton is initially stable but after a long time the system becomes more disordered due to the noises and the soliton would be covered up by these noises. While viscosity makes amplitude to damp out, driving force put energy on it, and both simultaneous effects offset each other.
Reference: CNSNS3428
Journal title: Communications in Nonlinear Science and Numerical Simulation
Corresponding author: Mr. Mirabeau Saha
First author: Mr. Mirabeau Saha
Final version published online: 14-FEB-2015
Full bibliographic details: Communications in Nonlinear Science and Numerical Simulation 23 (2015), pp. 1-9
DOI information: 10.1016/j.cnsns.2014.12.001
The influence of power-low long-range interactions (LRI) and helicoidal coupling (HC) on the prop... more The influence of power-low long-range interactions (LRI) and helicoidal coupling (HC) on the properties of localized solitons in a DNA molecule when a ribonucleic acid polymerase (RNAP) binds to it at the physiological temperature is analytically and numerically investigated in this paper. We have made an analogy with the Heisenberg model Hamiltonian of an anisotropic spin ladder with ferromagnetic legs and anti-ferromagnetic rung coupling. When we limit ourselves to the second-order terms in the Taylor expansion, the DNA dynamics is found to be governed by a completely integrable nonlinear Schrödinger (NLS) equation. In this case, results show that increasing the value of HC force or LRI parameter enhances the bubble height and reduces the number of base pairs which form the bubble. For the fourth-order terms in a Taylor expansion, results are closely resembling those of second-order terms, and are confirmed by numerical investigation. These results match with some experimental data and thus provide a better representation of the base pairs opening in DNA which is essential for the transcription process.
""In this paper, the comparison between power-law long-range interaction and Kac–Baker long-range... more ""In this paper, the comparison between power-law long-range interaction and Kac–Baker long-range interaction in the DNA molecule is investigated. This is done by employing an extended version of spin-like model of the DNA molecule with long-range interaction between intra-strand nucleotides and helicoidal coupling between inter-strand nucleotides when an RNA-polymerase binds to the DNA at biological temperature. Results show that LRIs have an undeniable effect on the DNA dynamics and that one is free to use either PLLRI or KBLRI to study DNA behaviors.
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0217979213501439""
The effects of long-range interactions between peptides on the protein–DNA dynamics in the long-wa... more The effects of long-range interactions between peptides on the protein–DNA dynamics in the long-wave limit are studied. The investigation, done at the physiological temperature, is based on a coupled spin system of DNA molecule which includes the helicoidal geometry of DNA molecule and the Kac–Baker long-range interaction between the peptides of the protein molecule. By using the Holstein–Primakoff bosonic representation of the spin operators, we show that the original discrete equations for the protein–DNA interaction dynamics can be reduced to the nonlinear Schr¨odinger (NLS) equation of which the dispersive and the nonlinear coefficients depend among other things on the protein long-range interaction parameter and on the helicoidal coupling coefficient. Furthermore, we find that the amplitude and the width of the resulting breather solution, in the form of the bubble moving along the DNA molecule, are strongly influenced by the long-range and helicoidal interactions. This result shows a relevant length scale for real protein–DNA interaction.
Abstract:
When an inhomogeneous RNA-polymerase (RNAP) binds to an inhomogeneous DNA at the physi... more Abstract:
When an inhomogeneous RNA-polymerase (RNAP) binds to an inhomogeneous DNA at the physiological temperature, we propose a spin-like model of DNA nonlinear dynamics with long-range interactions (LRI) between adjacent and distant base pairs to study RNAP-DNA dynamics. Using Holstein-Primakoff’s representation and Glauber’s coherent state representation, we show that the model equation is a completely integrable nonlinear Schrödinger equation whose dispersive coefficient depends on LRI’s parameter. Inhomogeneities have introduced perturbation terms in the equation of motion of RNAP-DNA dynamics. Considering the homogeneous part of that equation, a detailed study of the solution shows that the number of base pairs which form the bubble, the height, and the width of that bubble depend on the long-range parameter. The results of the perturbation analysis show that the inhomogeneities due to the DNA and RNAP structures do not alter the velocity and amplitude of the soliton, but introduce some fluctuations in the localized region of the soliton. The events that happen in the present study may represent binding of an RNAP to a promoter site in the DNA during the transcription process.
Lead Paragraph:
It is well known that a DNA macromolecule is a most important complex biological system for the simple reason that it is the repertory of the genetic codes of a descent. Thus, the behavioral study of its functioning is the center of interest of several researchers. For instance, understanding the mechanisms of transcription and replication in the DNA double-helix are some of essential problems of DNA physics and molecular biology. Complete solution of the problem has not been attained because of insufficient knowledge of the DNA helix transformation mechanisms and the complex structure of the macromolecule. It had been found that due to the presence of phosphate groups along the DNA’s strands, the long-range interactions (LRI) exists in that macromolecule and allows to take into account the screening of the interactions or an indirect coupling between base pairs via water filaments. Furthermore, the DNA and RNAP are constituted by specific sites such as promoter, coding, or terminator, which has a specific sequence of bases and peptides, and this makes the strands site dependent or inhomogeneous. Many qualitative discrepancies have been discovered and shared by theoretical findings so that the real long-range force to be adopted for DNA dynamics remains unclear. To contribute to these behavioral analysis of the DNA’s molecule while studying the influence of LRI on its dynamics, we have considered spin model of that molecule (a form of modeling among several DNA’s models which exist because of enormous degrees of freedom in dynamics of a DNA macromolecule) in which we introduce the intra-strand LRI when an inhomogeneous RNAP molecule comes to bind on an inhomogeneous DNA molecule at the biological temperature. It comes out from our results that the breather-like solitons, solitary waves which govern the transport of bubbles during the transcription, are deeply influenced by the LRI. Indeed, we find that the energy of the bubble (or bubble height) decreases with the decreasing of the LRI’s parameter (the dimensionless inverse radius of interaction) and if a base pair interacts with many other pairs which form the bubble (the width of bubble increases while its height decreases). The results also show that inhomogeneities introduce some fluctuations in the localized region of the breather. This dynamical behavior may act as energetic activators of the enzyme transport during the process of transcription in DNA and reinforces the efficiency and sturdiness of energy localization within transcription phenomenon.
We have numerically investigated the effects of helicity and inhomogeneities on DNA base pairs op... more We have numerically investigated the effects of helicity and inhomogeneities on DNA base pairs opening. The inhomogeneities are due to the site-dependent stacking and hydrogen bonding energies in DNA and protein molecules. We have considered a situation in which the active site of the RNA-polymerase molecule binds onto the promoter site of the spin-like model of the DNA molecule at the physiological temperature and creates a bubble. During the study, we have found that the helical coupling has to be very weak compared to intra-strand coupling in the real DNA molecule. Results show that inhomogeneities do not affect the general pattern of base pair opening, even as the periodic inhomogeneity introduces a train of periodic oscillations on the tail of the bubble; while the height of the bubble is an increasing function of the helical coupling parameter. The basic properties of breather-like modes, obtained here by taking into account helical structure and inhomogeneities, are essential for DNA functioning since such breathing-like modes are considered to be much better candidates for the nonlinear modes responsible for a locally open state where biological functioning takes place.
Physica Scripta. 89 085003
Issue 8 (August 2014)
Received 19 April 2013, accepted for publication 29 May 2014
Published 26 June 2014
doi:10.1088/0031-8949/89/8/085003
http://iopscience.iop.org/1402-4896/89/8/085003/
Using a mathematical spin-like model of DNA molecule, we have studied its dynamics, by taking int... more Using a mathematical spin-like model of DNA molecule, we have studied its dynamics, by taking into account forces due to the surrounding medium. Thus, we have shown the robustness of bubble-like solitons, by mathematically modeling the nonlinear interaction between the DNA and an enzyme at the physiological temperature. Noise, damping, and driving forces are added to get a set of deterministic discrete motion equations. Numerical results show that the bubble-like soliton is initially stable but after a long time the system becomes more disordered due to the noises and the soliton would be covered up by these noises. While viscosity makes amplitude to damp out, driving force put energy on it, and both simultaneous effects offset each other.
Reference: CNSNS3428
Journal title: Communications in Nonlinear Science and Numerical Simulation
Corresponding author: Mr. Mirabeau Saha
First author: Mr. Mirabeau Saha
Final version published online: 14-FEB-2015
Full bibliographic details: Communications in Nonlinear Science and Numerical Simulation 23 (2015), pp. 1-9
DOI information: 10.1016/j.cnsns.2014.12.001
The influence of power-low long-range interactions (LRI) and helicoidal coupling (HC) on the prop... more The influence of power-low long-range interactions (LRI) and helicoidal coupling (HC) on the properties of localized solitons in a DNA molecule when a ribonucleic acid polymerase (RNAP) binds to it at the physiological temperature is analytically and numerically investigated in this paper. We have made an analogy with the Heisenberg model Hamiltonian of an anisotropic spin ladder with ferromagnetic legs and anti-ferromagnetic rung coupling. When we limit ourselves to the second-order terms in the Taylor expansion, the DNA dynamics is found to be governed by a completely integrable nonlinear Schrödinger (NLS) equation. In this case, results show that increasing the value of HC force or LRI parameter enhances the bubble height and reduces the number of base pairs which form the bubble. For the fourth-order terms in a Taylor expansion, results are closely resembling those of second-order terms, and are confirmed by numerical investigation. These results match with some experimental data and thus provide a better representation of the base pairs opening in DNA which is essential for the transcription process.
""In this paper, the comparison between power-law long-range interaction and Kac–Baker long-range... more ""In this paper, the comparison between power-law long-range interaction and Kac–Baker long-range interaction in the DNA molecule is investigated. This is done by employing an extended version of spin-like model of the DNA molecule with long-range interaction between intra-strand nucleotides and helicoidal coupling between inter-strand nucleotides when an RNA-polymerase binds to the DNA at biological temperature. Results show that LRIs have an undeniable effect on the DNA dynamics and that one is free to use either PLLRI or KBLRI to study DNA behaviors.
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0217979213501439""
The effects of long-range interactions between peptides on the protein–DNA dynamics in the long-wa... more The effects of long-range interactions between peptides on the protein–DNA dynamics in the long-wave limit are studied. The investigation, done at the physiological temperature, is based on a coupled spin system of DNA molecule which includes the helicoidal geometry of DNA molecule and the Kac–Baker long-range interaction between the peptides of the protein molecule. By using the Holstein–Primakoff bosonic representation of the spin operators, we show that the original discrete equations for the protein–DNA interaction dynamics can be reduced to the nonlinear Schr¨odinger (NLS) equation of which the dispersive and the nonlinear coefficients depend among other things on the protein long-range interaction parameter and on the helicoidal coupling coefficient. Furthermore, we find that the amplitude and the width of the resulting breather solution, in the form of the bubble moving along the DNA molecule, are strongly influenced by the long-range and helicoidal interactions. This result shows a relevant length scale for real protein–DNA interaction.
Abstract:
When an inhomogeneous RNA-polymerase (RNAP) binds to an inhomogeneous DNA at the physi... more Abstract:
When an inhomogeneous RNA-polymerase (RNAP) binds to an inhomogeneous DNA at the physiological temperature, we propose a spin-like model of DNA nonlinear dynamics with long-range interactions (LRI) between adjacent and distant base pairs to study RNAP-DNA dynamics. Using Holstein-Primakoff’s representation and Glauber’s coherent state representation, we show that the model equation is a completely integrable nonlinear Schrödinger equation whose dispersive coefficient depends on LRI’s parameter. Inhomogeneities have introduced perturbation terms in the equation of motion of RNAP-DNA dynamics. Considering the homogeneous part of that equation, a detailed study of the solution shows that the number of base pairs which form the bubble, the height, and the width of that bubble depend on the long-range parameter. The results of the perturbation analysis show that the inhomogeneities due to the DNA and RNAP structures do not alter the velocity and amplitude of the soliton, but introduce some fluctuations in the localized region of the soliton. The events that happen in the present study may represent binding of an RNAP to a promoter site in the DNA during the transcription process.
Lead Paragraph:
It is well known that a DNA macromolecule is a most important complex biological system for the simple reason that it is the repertory of the genetic codes of a descent. Thus, the behavioral study of its functioning is the center of interest of several researchers. For instance, understanding the mechanisms of transcription and replication in the DNA double-helix are some of essential problems of DNA physics and molecular biology. Complete solution of the problem has not been attained because of insufficient knowledge of the DNA helix transformation mechanisms and the complex structure of the macromolecule. It had been found that due to the presence of phosphate groups along the DNA’s strands, the long-range interactions (LRI) exists in that macromolecule and allows to take into account the screening of the interactions or an indirect coupling between base pairs via water filaments. Furthermore, the DNA and RNAP are constituted by specific sites such as promoter, coding, or terminator, which has a specific sequence of bases and peptides, and this makes the strands site dependent or inhomogeneous. Many qualitative discrepancies have been discovered and shared by theoretical findings so that the real long-range force to be adopted for DNA dynamics remains unclear. To contribute to these behavioral analysis of the DNA’s molecule while studying the influence of LRI on its dynamics, we have considered spin model of that molecule (a form of modeling among several DNA’s models which exist because of enormous degrees of freedom in dynamics of a DNA macromolecule) in which we introduce the intra-strand LRI when an inhomogeneous RNAP molecule comes to bind on an inhomogeneous DNA molecule at the biological temperature. It comes out from our results that the breather-like solitons, solitary waves which govern the transport of bubbles during the transcription, are deeply influenced by the LRI. Indeed, we find that the energy of the bubble (or bubble height) decreases with the decreasing of the LRI’s parameter (the dimensionless inverse radius of interaction) and if a base pair interacts with many other pairs which form the bubble (the width of bubble increases while its height decreases). The results also show that inhomogeneities introduce some fluctuations in the localized region of the breather. This dynamical behavior may act as energetic activators of the enzyme transport during the process of transcription in DNA and reinforces the efficiency and sturdiness of energy localization within transcription phenomenon.
Uploads
Papers by Mirabeau Saha
Physica Scripta. 89 085003
Issue 8 (August 2014)
Received 19 April 2013, accepted for publication 29 May 2014
Published 26 June 2014
doi:10.1088/0031-8949/89/8/085003
http://iopscience.iop.org/1402-4896/89/8/085003/
Reference: CNSNS3428
Journal title: Communications in Nonlinear Science and Numerical Simulation
Corresponding author: Mr. Mirabeau Saha
First author: Mr. Mirabeau Saha
Final version published online: 14-FEB-2015
Full bibliographic details: Communications in Nonlinear Science and Numerical Simulation 23 (2015), pp. 1-9
DOI information: 10.1016/j.cnsns.2014.12.001
Download for free until April 5, 2015:
http://authors.elsevier.com/a/1QXqJ3b654dErq
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0217979213501439""
When an inhomogeneous RNA-polymerase (RNAP) binds to an inhomogeneous DNA at the physiological temperature, we propose a spin-like model of DNA nonlinear dynamics with long-range interactions (LRI) between adjacent and distant base pairs to study RNAP-DNA dynamics. Using Holstein-Primakoff’s representation and Glauber’s coherent state representation, we show that the model equation is a completely integrable nonlinear Schrödinger equation whose dispersive coefficient depends on LRI’s parameter. Inhomogeneities have introduced perturbation terms in the equation of motion of RNAP-DNA dynamics. Considering the homogeneous part of that equation, a detailed study of the solution shows that the number of base pairs which form the bubble, the height, and the width of that bubble depend on the long-range parameter. The results of the perturbation analysis show that the inhomogeneities due to the DNA and RNAP structures do not alter the velocity and amplitude of the soliton, but introduce some fluctuations in the localized region of the soliton. The events that happen in the present study may represent binding of an RNAP to a promoter site in the DNA during the transcription process.
Lead Paragraph:
It is well known that a DNA macromolecule is a most important complex biological system for the simple reason that it is the repertory of the genetic codes of a descent. Thus, the behavioral study of its functioning is the center of interest of several researchers. For instance, understanding the mechanisms of transcription and replication in the DNA double-helix are some of essential problems of DNA physics and molecular biology. Complete solution of the problem has not been attained because of insufficient knowledge of the DNA helix transformation mechanisms and the complex structure of the macromolecule. It had been found that due to the presence of phosphate groups along the DNA’s strands, the long-range interactions (LRI) exists in that macromolecule and allows to take into account the screening of the interactions or an indirect coupling between base pairs via water filaments. Furthermore, the DNA and RNAP are constituted by specific sites such as promoter, coding, or terminator, which has a specific sequence of bases and peptides, and this makes the strands site dependent or inhomogeneous. Many qualitative discrepancies have been discovered and shared by theoretical findings so that the real long-range force to be adopted for DNA dynamics remains unclear. To contribute to these behavioral analysis of the DNA’s molecule while studying the influence of LRI on its dynamics, we have considered spin model of that molecule (a form of modeling among several DNA’s models which exist because of enormous degrees of freedom in dynamics of a DNA macromolecule) in which we introduce the intra-strand LRI when an inhomogeneous RNAP molecule comes to bind on an inhomogeneous DNA molecule at the biological temperature. It comes out from our results that the breather-like solitons, solitary waves which govern the transport of bubbles during the transcription, are deeply influenced by the LRI. Indeed, we find that the energy of the bubble (or bubble height) decreases with the decreasing of the LRI’s parameter (the dimensionless inverse radius of interaction) and if a base pair interacts with many other pairs which form the bubble (the width of bubble increases while its height decreases). The results also show that inhomogeneities introduce some fluctuations in the localized region of the breather. This dynamical behavior may act as energetic activators of the enzyme transport during the process of transcription in DNA and reinforces the efficiency and sturdiness of energy localization within transcription phenomenon.
© 2012 American Institute of Physics
http://link.aip.org/link/doi/10.1063/1.3683430
Physica Scripta. 89 085003
Issue 8 (August 2014)
Received 19 April 2013, accepted for publication 29 May 2014
Published 26 June 2014
doi:10.1088/0031-8949/89/8/085003
http://iopscience.iop.org/1402-4896/89/8/085003/
Reference: CNSNS3428
Journal title: Communications in Nonlinear Science and Numerical Simulation
Corresponding author: Mr. Mirabeau Saha
First author: Mr. Mirabeau Saha
Final version published online: 14-FEB-2015
Full bibliographic details: Communications in Nonlinear Science and Numerical Simulation 23 (2015), pp. 1-9
DOI information: 10.1016/j.cnsns.2014.12.001
Download for free until April 5, 2015:
http://authors.elsevier.com/a/1QXqJ3b654dErq
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0217979213501439""
When an inhomogeneous RNA-polymerase (RNAP) binds to an inhomogeneous DNA at the physiological temperature, we propose a spin-like model of DNA nonlinear dynamics with long-range interactions (LRI) between adjacent and distant base pairs to study RNAP-DNA dynamics. Using Holstein-Primakoff’s representation and Glauber’s coherent state representation, we show that the model equation is a completely integrable nonlinear Schrödinger equation whose dispersive coefficient depends on LRI’s parameter. Inhomogeneities have introduced perturbation terms in the equation of motion of RNAP-DNA dynamics. Considering the homogeneous part of that equation, a detailed study of the solution shows that the number of base pairs which form the bubble, the height, and the width of that bubble depend on the long-range parameter. The results of the perturbation analysis show that the inhomogeneities due to the DNA and RNAP structures do not alter the velocity and amplitude of the soliton, but introduce some fluctuations in the localized region of the soliton. The events that happen in the present study may represent binding of an RNAP to a promoter site in the DNA during the transcription process.
Lead Paragraph:
It is well known that a DNA macromolecule is a most important complex biological system for the simple reason that it is the repertory of the genetic codes of a descent. Thus, the behavioral study of its functioning is the center of interest of several researchers. For instance, understanding the mechanisms of transcription and replication in the DNA double-helix are some of essential problems of DNA physics and molecular biology. Complete solution of the problem has not been attained because of insufficient knowledge of the DNA helix transformation mechanisms and the complex structure of the macromolecule. It had been found that due to the presence of phosphate groups along the DNA’s strands, the long-range interactions (LRI) exists in that macromolecule and allows to take into account the screening of the interactions or an indirect coupling between base pairs via water filaments. Furthermore, the DNA and RNAP are constituted by specific sites such as promoter, coding, or terminator, which has a specific sequence of bases and peptides, and this makes the strands site dependent or inhomogeneous. Many qualitative discrepancies have been discovered and shared by theoretical findings so that the real long-range force to be adopted for DNA dynamics remains unclear. To contribute to these behavioral analysis of the DNA’s molecule while studying the influence of LRI on its dynamics, we have considered spin model of that molecule (a form of modeling among several DNA’s models which exist because of enormous degrees of freedom in dynamics of a DNA macromolecule) in which we introduce the intra-strand LRI when an inhomogeneous RNAP molecule comes to bind on an inhomogeneous DNA molecule at the biological temperature. It comes out from our results that the breather-like solitons, solitary waves which govern the transport of bubbles during the transcription, are deeply influenced by the LRI. Indeed, we find that the energy of the bubble (or bubble height) decreases with the decreasing of the LRI’s parameter (the dimensionless inverse radius of interaction) and if a base pair interacts with many other pairs which form the bubble (the width of bubble increases while its height decreases). The results also show that inhomogeneities introduce some fluctuations in the localized region of the breather. This dynamical behavior may act as energetic activators of the enzyme transport during the process of transcription in DNA and reinforces the efficiency and sturdiness of energy localization within transcription phenomenon.
© 2012 American Institute of Physics
http://link.aip.org/link/doi/10.1063/1.3683430