ИСТИНА

Lately there has been a renewed interest in the unentangled fractal globule state of polymers, which is primarily motivated by the conjecture that spatial organisation of chromosomes in both eucaryotic and procariotic organisms can be satisfactory described by this model. In this work we show, both theoretically and by the means of dissipation particle dynamics (DPD) computer simulations, that dynamics of self-diffusion in the fractal globule state is slower than usual Rouse dynamics but faster than reptation dynamics in entangled globules. A simple scaling theory we present suggests that the dynamic should be self-diffusive with mean-square displacement of the monomers growing as $\langle R^2(t) \rangle \sim t^{\alpha}$ with exponent $\alpha$ close to 0.4. In computer simulations we study equilibrium and fractal globules of $2^{18}=262144$ monomers in periodic boundary conditions. After some annealing of the initial states we study the motion of the monomers in the globule. Note that times accessible in the simulations are much smaller than the reptation time needed for the fractal globule to relax into equilibrium one, allowing us to study a clearly distinct metastable fractal globule state akin to the state of a long unknoted polymer ring, as well as the equilibrium globule state. On the largest accessible timescales in the equilibrium globule statewe observe a subdiffusion with exponent $\alpha \approx 0.24$ is observed which is in good agreement with reptation theory prediction $\alpha_{rept} = 1/4$, while for the fractal state we observe $\alpha \approx 0.38$. In order to distinguish results of our model from ones based on Rouse chain in subdiffusive media we discuss the two point correlations between the displacement of the monomers (chromosome loci) positioned at a given genomic distance from each other. We show that the generalized Rouse time, i.e., typical time at which motion of the two loci becomes correlated, behaves as $\tau \sim s^{5/3}$ for our model, and $\tau \sim s^{5/2}$ for the Rouse polymer in subdiffusive media, which may allow to distinguish experimentally between two competing explanations of the slow subdiffusive dynamics of chromosome loci.