Journal of Nonlinear Mathematical Physics
Volume 18, Issue Supplement 2, December 2011
Pages: v - xii
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...
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...
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...
5. On the Pseudo-Schrödinger Equation Approximation of the Transfer-Integral Operator for 1-Dimensional DNA Models
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...
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...
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...
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...
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...
10. Bubbles, Clusters and Denaturation in Genomic DNA: Modeling, Parametrization, Efficient Computation
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...
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...
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...