Journal of Nonlinear Mathematical Physics

Volume 18, Issue Supplement 2, December 2011

Research Article

2. How the Mutational-Selection Interplay Organizes the Fitness Landscape

Franco Bagnoli, Píetro Lió
Pages: 265 - 286
Fundamental questions posed in classical genetics since early 20th century are still fundamental in today post genomic age. What has changed is the availability of huge amount of molecular genetics information on a broad spectrum of species and a more powerful and rich methodological approach, particularly...
Research Article

3. Soliton Propagation in Homogeneous and Inhomogeneous Models for DNA Torsion Dynamics

Mariano Cadoni, Roberto de Leo, Sergio Demelio
Pages: 287 - 319
The existence of solitonic excitations is a generic feature of a broad class of homogeneous models for nonlinear DNA internal torsional dynamics, but many properties of solitonic propagation depend on the actual model one is considering. In this paper we perform a detailed and comparative numerical investigation...
Research Article

4. Nonlinear Deterministic Equations in Biological Evolution

Kavita Jain, Sarada Seetharaman
Pages: 321 - 338
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in...
Research Article

5. On the Pseudo-Schrödinger Equation Approximation of the Transfer-Integral Operator for 1-Dimensional DNA Models

Marc Joyeux
Pages: 339 - 357
The Transfer-Integral (TI) operator is a powerful method to investigate the statistical physics of 1-dimensional models, like those used to describe DNA denaturation. At the cost of a certain number of approximations, the TI equation can be reduced to a Pseudo–Schrödinger Equation (PSE), according to...
Research Article

6. Some Rigorous Results on the Eigen Quasispecies Model with a Periodically Moving Sharp-Peak Landscape

Armando G. M. Neves
Pages: 359 - 379
In this paper we prove some results and detail some calculations published in a previous paper by us on the Eigen model with a periodically moving sharp-peak landscape. The model is concerned with evolution of a virus population in a time-dependent environment mimicking interaction of the viruses with...
Research Article

7. The Transfer Integral Operator Method in the Study of DNA Unzipping and Bubble Formation

Z. Rapti, K. Ø. Rasmussen, A. R. Bishop
Pages: 381 - 396
In this work we reexamine the unzipping and bubble formation of DNA in the context of the Peyrard–Bishop–Dauxois DNA model using the transfer integral operator method. After a brief overview of the method, we use it to calculate the probabilities that consecutive base-pairs are stretched beyond a threshold...
Research Article

8. Bayesian Approach to the Determination of the Kinetic Parameters of DNA Hairpins Under Tension

Marco Ribezzi-Crivellari, Mario Wagner, Felix Ritort
Pages: 397 - 410
In this paper we propose a Bayesian scheme for the determination of the unfolding and refolding kinetic rates of DNA hairpins under tension. This method is based on the hypothesis that the unfolding-refolding dynamics is well described by a Markov Chain. The results from the Bayesian method are contrasted...
Research Article

9. Phenomenological Modeling of DNA Overstretching

Ray W. Ogden, Giuseppe Saccomandi, Ivonne Sgura
Pages: 411 - 427
A phenomenological model based on the three-dimensional theory of nonlinear elasticity is developed to describe the phenomenon of overstretching in the force-extension curve for double-stranded DNA (dsDNA). By using the concept of a material with multiple reference configurations a single formula is...
Research Article

10. Bubbles, Clusters and Denaturation in Genomic DNA: Modeling, Parametrization, Efficient Computation

Nikos Theodorakopoulos
Pages: 429 - 447
The paper uses mesoscopic, nonlinear lattice dynamics based (Peyrard–Bishop–Dauxois, PBD) modeling to describe thermal properties of DNA below and near the denaturation temperature. Computationally efficient notation is introduced for the relevant statistical mechanics. Computed melting profiles of long...
Research Article

11. Biomechanics of DNA: Rotational Oscillations of Bases

L. V. Yakushevich
Pages: 449 - 461
In the present paper we investigate the rotational oscillations of the nitrous bases that form a central base pair in a short DNA fragment consisting of three base pairs. For this purpose we use a simple mechanical model of the DNA fragment where the bases are imitated by pendulums, and the interactions...
Research Article

12. Helicoidal Peyrard–Bishop Model of DNA Dynamics*

Slobodan Zdravković
Pages: 463 - 484
A nonlinear model describing DNA dynamics, called helicoidal Peyrard–Bishop model, is described. It is shown that the model can explain a local opening of a DNA helix during transcription. An impact of friction forces is also studied. It is pointed out that a role of viscosity is crucial for DNA-RNA...