Dynamics of topological solitons describing open states in the DNA double helix are studied in the frameworks of the model which takes into account asymmetry of the helix. It is shown that three types of topological solitons can occur in the DNA double chain. Interaction between the solitons, their interactions with the chain inhomogeneities and stability of the solitons with respect to thermal oscillations are investigated.
We investigate solitons in Peyrard-Bishop model of DNA molecule using Renormalization group methods which provide a systematic way for perturbation analysis. Small amplitude expansion is carried out in both the continuous and discrete limits. We review exact solution for the continuous model. Further, we discuss reliability of the solitonic solutions and argue that the envelope should propagate with a group velocity contrary to previous proposals.
We investigate the nonlinear dynamics of the Peyrard-Bishop DNA model taking into account site dependent inhomogeneities. By means of the multiple-scale expansion in the semi-discrete approximation, the dynamics is governed by the perturbed nonlinear Schrodinger equation. We carry out a multiple-scale soliton perturbation analysis to find the effects of the variety of nonlinear inhomogeneities on the breatherlike soliton solution. During the crossing of the inhomogeneities, the coherent structure of the soliton is found stable. The global shape of the inhomogeneous molecule is merged with the …
A couple of models are explained. Helicoidal PB model is studied in more details. It is shown that semi-discrete approximation yields to breather-type soliton moving along the chain. The model can explain local opening as a resonance mode. Also, DNA-RNA transcription is explained through a standing solitary mode.
Nonlinear dynamics of two biomolecules is studied. These are a microtubule and DNA molecule. Two mathematical procedures are explained, yielding to three kinds of solitary waves moving through the systems. These waves are kinks, modulated solitary waves called breathers and bell-type solitons.
Bacterial genomes have been shown to be partitioned into several kilobases long chromosomal domains that are topologically independent from each other, meaning that change of DNA superhelicity in one domain does not propagate to neighbors. Both in vivo and in vitro experiments have been performed to question the nature of the topological barriers at play, leading to several predictions on possible molecular actors. Here, we address the question of topological barriers using polymer models of supercoiled DNA chains. More specifically, we determine under which conditions DNA-bridging proteins ma…
Understanding and controlling the rheology of polymeric complex fluids that are pushed out-of-equilibrium is a fundamental problem in both industry and biology. For example, to package, repair, and replicate DNA, cells use enzymes to constantly manipulate DNA topology, length, and structure. Inspired by this, here we engineer and study DNA-based complex fluids that undergo enzymatically-driven topological and architectural alterations via restriction endonuclease (RE) reactions. We show that these systems display time-dependent rheological properties that depend on the concentrations and prope…
Knots are fascinating topological structures that have been observed in various contexts, ranging from micro-worlds to macro-systems, and are conjectured to play a fundamental role in their respective fields. In order to characterize their physical properties, some topological invariants have been introduced, such as unknotting number, bridge number, Jones Polynomial and so on. While these invariants have been proven to theoretically describe the topological properties of knots, they have remained unexplored experimentally because of the difficulty associated with control. Herein, we report th…
We showed in our previous studies that just $3\%$ cross-links, at special points along the contour of the bacterial DNA help the DNA-polymer to get organized at micron length scales \cite{jpcm,epl}. In this work, we investigate how does the release of topological constraints help in the organization of the DNA-polymer. Furthermore, we show that the chain compaction induced by the crowded environment in the bacterial cytoplasm contributes to the organization of the DNA-polymer. We model the DNA chain as a flexible bead-spring ring polymer, where each bead represents $1000$ base pairs. The speci…
