The Rouse Model of Viscoelasticity and Diffusion Behavior of Chromatin
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Rouse Model of Viscoelasticity and Diffusion Behavior of Chromatin V. A. Stepanyana, A. A. Hayrapetyana, and E. Sh. Mamasakhlisova, * a
Yerevan State University, Yerevan, Armenia *e-mail: [email protected]
Received April 9, 2020; revised April 28, 2020; accepted May 3, 2020
Abstract—A dynamic model of a polymer chain is presented, in which the effects of viscoelasticity in the framework of the standard model of the linear body is taken into account. The general solution for the motion equation of the Fourier–Laplace components of the coordinates of the monomers of the polymer chain is obtained. The diffusion behavior of the center of mass of the polymer chain is analyzed for the relaxation dynamics of the system. Keywords: polymer dynamics, viscoelasticity, chromatin DOI: 10.3103/S1068337220030123
1. INTRODUCTION The nucleus of eukaryotic cell is an active medium in which the ATP-driven molecular machines act in combination with ordinary thermal fluctuations, creating specific structures that demonstrate nontrivial dynamic properties [1], which are the subject of many works [2–10]. Moreover, the dynamics of nuclear material is important for the cell functioning, because the chromosomal DNA is completely rearranged during the cell passage through the various phases of its life cycle. In addition, in each of these phases, the dynamic rearrangement of chromosomes apparently contributes to the occurrence of biological processes such as transcription, replication, recombination, and segregation. Tracking the movement of chromosomal loci provides relevant information on the physical processes that cause the movement of the DNA in complex with various associated proteins and the RNA in a condensed environment of a nuclear cell [11–13]. It has been experimentally shown that the genomic loci do not diffuse freely, but instead perform a subdiffusive motion, which differs from that predicted by simple models of polymer dynamics [11]. In addition to the observed subdiffusion of the trajectories of individual loci, the collective movements of chromatin are coherent outside the chromosomes, which suggests that there is some kind of mechanical connection between the loci that are distant from each other along the polymer chain, or even belonging to two different polymer chains [13, 14]. The medium surrounding the chromosomes is also considered as viscoelastic, which follows from the measurement of the autocorrelation function of fluorescently labeled loci [12]. In this article, we propose a model of the Rouse model type, which includes the viscoelastic effects. This model is a rough model of the polymer chain, which includes the effects of local internal friction and hydrodynamic friction against the solvent. We believe that this model is promising for describing experiments on chromatin dynamics. 2. THE ROUSE MODEL, CONSISTING OF ELEMENTS OF A STANDARD LINEAR BODY From a microscopic point of view, the internal friction in a flexible chain polymer arises because of the processes of jump through the internal rotation barrie
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