ИСТИНА

It has been known for some time that apart from traditional equilibrium states of polymer systems, such as swollen polymer coils and melts of linear polymer chains, which have been studied by classical polymer physics, there exist a class of states whose properties are mostly controlled by the topological interactions of the chains. The archetypical system where topological interactions play such a crucial role is a melt of non-concatenated polymer rings, but it became more and more clear in recent years that such states can be observed, at least as metastable ones, in various other contexts including, for example, rapid collapse of a linear chain under external force (in this context they are often called crumpled or fractal globules), and conformation-dependent polymerization. Most importantly, such states seem to be a good candidate for the description of chromosome packing in living cells. Naturally, the study of polymer dynamics in this novel class of states is of substantial interest. In my talk I will present our recent advances in scaling and semi-analytical generalizations of the classical Rouse model of polymer dynamics, which allow us to describe the relaxation times, selfdiffusion and dynamical correlation functions in the fractal globule and similar polymer states. I will also discuss the generalization of the theory for the dynamics of a polymer surrounded by a viscoelastic environment subject to the generalized Langevin equation with scale-free memory. In conclusion, I will briefly talk about alternative theories of the fractal globule dynamics, based on the generalization of the reptation theory, and discuss possible applicability limits of different theories.