Helicoidal Peyrard–Bishop Model of DNA Dynamics*

Zdravković, Slobodan

doi:10.1142/s1402925111001635

Cited by 44 publications

(29 citation statements)

References 75 publications

(106 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…About Mathematical Modeling of DNA, three eminent mathematical models have been proposed for describing DNA. The most famous model presented is the PBD (Peyrard-Bishop-Dauxois) model 13 , although this model has been updated by various researchers [14][15][16][17][18] , the models presented in these studies usually have at least three significant weaknesses such as being discrete, not being outside the plane, not being spiral, and not considering the position of nucleobases. Examples of the PBD model are displayed in Fig.…”

mentioning

confidence: 99%

RETRACTED ARTICLE: A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

Marvi

Ghadiri

2020

Sci Rep

View full text Add to dashboard Cite

the DnA molecule is the most evolved and most complex molecule created by nature. the primary role of DnA in medicine is long-term storage of genetic information. Genetic modifying is one of the most critical challenges that scientists face. On the other hand, it is said that under the influence of acoustic, electromagnetic, and scalar waves, the genetic code of DnA can be read or rewritten. in this article, the most accurate and comprehensive dynamic model will be presented for DnA. each of the two strands is modeled with an out of plane curved beam and then by doubling this two strands with springs, consider the hydrogen bond strength between this two strands. Beams are traditionally descriptions of mechanical engineering structural elements or building. However, any structure such as automotive automobile frames, aircraft components, machine frames, and other mechanical or structural systems contain beam structures that are designed to carry lateral loads are analyzed similarly. Also, in this model, the mass of the nucleobases in the DNA structure, the effects of the fluid surrounding the DNA (nucleoplasm) and the effects of temperature changes are also considered. finally, by deriving governing equations from Hamilton's principle method and solving these equations with the generalized differential quadrature method (GDQM), the frequency and mode shape of the DNA is obtained for the first time. In the end, validation of the obtained results from solving the governing equations of mathematical model compared to the obtained results from the coMSoL software is confirmed. By the help of these results, a conceptual idea for controlling cancer with using the DnA resonance frequency is presented. this idea will be presented to stop the cancerous cell's protein synthesis and modifying DnA sequence and genetic manipulation of the cell. on the other hand, by the presented DnA model and by obtaining DnA frequency, experimental studies of the effects of waves on DNA such as phantom effect or DNA teleportation can also be studied scientifically and precisely.

show abstract

mentioning

confidence: 99%

RETRACTED ARTICLE: A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

Marvi

Ghadiri

2020

Sci Rep

View full text Add to dashboard Cite

show abstract

“…The latter is also the framework in which Theodorakopoulos [88] discusses several phenomena in genomic DNA, and how parameters can be chosen, and computation performed efficiently. The work by Zdravkovic [100], which also contains a large Bibliography, considers a version of the Peyrard-Bishop model, first considered by Dauxois [18], which takes into account the peculiar helicoidal geometry of DNA. Finally, the remaining two papers both consider inhomogeneous DNA models.…”

Section: Nonlinear Dynamics Of Macromoleculesmentioning

confidence: 99%

Biology, Physics and Nonlinear Science

Gaeta¹

2021

JNMP

View full text Add to dashboard Cite

“…As the helix (B-DNA) has a helical pitch of about 10 bp per turn [55], one can assume h = 5. The complete mathematical analysis including a lot of mathematical details can be found in [56]. We review it very briefly here.…”

Section: Helicoidal Peyrard-bishop Model For Nonlinear Dna Dynamicsmentioning

confidence: 99%

A review on nonlinear DNA physics

et al. 2020

Self Cite

View full text Add to dashboard Cite

The study and the investigation of structural and dynamical properties of complex systems have attracted considerable interest among scientists in general and physicists and biologists in particular. The present review paper represents a broad overview of the research performed over the nonlinear dynamics of DNA, devoted to some different aspects of DNA physics and including analytical, quantum and computational tools to understand nonlinear DNA physics. We review in detail the semi-discrete approximation within helicoidal Peyrard–Bishop model and show that localized modulated solitary waves, usually called breathers, can emerge and move along the DNA. Since living processes occur at submolecular level, we then discuss a quantum treatment to address the problem of how charge and energy are transported on DNA and how they may play an important role for the functioning of living cells. While this problem has attracted the attention of researchers for a long time, it is still poorly understood how charge and energy transport can occur at distances comparable to the size of macromolecules. Here, we review a theory based on the mechanism of ‘self-trapping’ of electrons due to their interaction with mechanical (thermal) oscillation of the DNA structure. We also describe recent computational models that have been developed to capture nonlinear mechanics of DNA in vitro and in vivo , possibly under topological constraints. Finally, we provide some conjectures on potential future directions for this field.

show abstract

Helicoidal Peyrard–Bishop Model of DNA Dynamics*

Cited by 44 publications

References 75 publications

RETRACTED ARTICLE: A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

RETRACTED ARTICLE: A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

Biology, Physics and Nonlinear Science

A review on nonlinear DNA physics

Contact Info

Product

Resources

About