Simple combined model for nonlinear excitations in DNA

Ideas and methods of nonlinear mathematics and theoretical physics in DNA science: the McLaughlin-Scott equation and its application to study the DNA open state dynamics

The review is devoted to a new and rapidly developing area related to the application of ideas and methods of nonlinear mathematics and theoretical physics to study the internal dynamics of DNA and, in particular, the behavior of the open states of DNA. There are two main competing approaches to this research. The first approach is based on the molecular dynamics method, which takes into account the motions of all structural elements of the DNA molecule and all interactions between them. The second approach is based on prior selection of the main (dominant) motions and their mathematical description using a small number of model equations. This review describes the results of the study of the open states of DNA performed within the framework of the second approach using the McLaughlin-Scott equation. We present the results obtained both in the case of homogeneous sequences: poly (A), poly (T), poly (G) and poly (C), and in the inhomogeneous case when the McLaughlin-Scott equation has been used for studying the dynamics of open states activated in the promoters A1, A2 and A3 of the bacteriophage T7 genome, in the genes IFNA17, ADRB2, NOS1 and IL-5, in the pBR322 and pTTQ18 plasmids. Particular attention is paid to the results concerning the effect of various external fields on the behavior of open states. In the concluding part of the review, new possibilities and prospects for the development of the considered approach and especially of the McLaughlin-Scott equation are discussed.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s12551-021-00801-0.

A review on nonlinear DNA physics

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.

High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA

By means of the semidiscrete multiple-scale method, we study the existence and properties of high-order envelope solitons and discrete breathers in a homogeneous DNA chain model that is based on pairing enthalpies and site-dependent finite stacking. We obtain the analytical solutions for an envelope soliton, and find that at the Brillouin zone center, discrete breather solutions can appear below the bottom of the phonon band. The behavior of two solitons in collisions and the stability of discrete breathers are confirmed by numerical simulations of the exact equations of the system.

Modeling the electrical conduction in DNA nanowires: charge transfer and lattice fluctuation theories

An analytical approach is proposed for the investigation of the conductivity properties of DNA. The charge mobility of DNA is studied based on an extended Peyrard-Bishop-Holstein model when the charge carrier is also subjected to an external electrical field. We have obtained the values of some of the system parameters, such as the electron-lattice coupling constant, by using the mean Lyapunov exponent method. On the other hand, the electrical current operator is calculated directly from the lattice operators. Also, we have studied Landauer resistance behavior with respect to the external field, which could serve as the interface between chaos theory tools and electronic concepts. We have examined the effect of two types of electrical fields (dc and ac) and variation of the field frequency on the current flowing through DNA. A study of the current-voltage (I-V) characteristic diagram reveals regions with a (quasi-)Ohmic property and other regions with negative differential resistance (NDR). NDR is a phenomenon that has been observed experimentally in DNA at room temperature. We have tried to study the affected agents in charge transfer phenomena in DNA to better design nanostructures.

Multifractal analysis of thermal denaturation based on the Peyrard-Bishop-Dauxois model

The theory of DNA dynamics is exceedingly complex and not easily explained. In the past two decades, by adapting methods of statistical physics, the dynamics of DNA in contact with a thermal bath is widely studied. In this paper, the thermal denaturation of DNA in the framework of the Peyrard-Bishop-Dauxois (PBD) model through the Rényi dimension is investigated. As a result, the Rényi dimension spectrum of the melting transition process reveals the multifractal nature of the dynamics of the Peyrard-Bishop-Dauxois model. Also, it can be concluded that the Rényi dimension (D(q)) at negative values of q is the characteristic signature of pre-melting and thermal denaturation of DNA. Furthermore, this approach is in excellent agreement with previous experimental studies.