The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a unique metastable fractal globule state. We show monomer motion in this state to be subdiffusive described by ⟨X(2)(t)⟩∼t(αF) with αF close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics, which makes an additional argument in support of the fractal globule model of chromatin packing.

In this article, we investigate the effect of hydrocarbon addition on the rheological properties and structure of wormlike micellar solutions of potassium oleate. We show that a viscoelastic solution of entangled micellar chains is extremely responsive to hydrocarbons-the addition of only 0.5 wt % n-dodecane results in a drastic drop in viscosity by up to 5 orders of magnitude, which is due to the complete disruption of micelles and the formation of microemulsion droplets. We study the whole range of the transition of wormlike micelles into microemulsion droplets and discover that it can be divided into three regions: (i) in the first region, the solutions retain a high viscosity (∼10-350 Pa·s), the micelles are entangled but their length is reduced by the solubilization of hydrocarbons; (ii) in the second region, the system transitions to the unentangled regime and the viscosity sharply decreases as a result of further micelle shortening and the appearance of microemulsion droplets; (iii) in the third region, the viscosity is low (∼0.001 Pa·s) and only microemulsion droplets remain in the solution. The experimental studies were accompanied by theoretical considerations, which allowed us to reveal for the first time that (i) one of the leading mechanisms of micelle shortening is the preferential accumulation of the solubilized hydrocarbon in the spherical end caps of wormlike micelles, which makes the end caps thermodynamically more favorable; (ii) the onset of the sharp drop in viscosity is correlated with the crossover from the entangled to unentangled regime of the wormlike micellar solution taking place upon the shortening of micellar chains; and (iii) in the unentangled regime short cylindrical micelles coexist with microemulsion droplets.

We analyze the mean time t(app) that a randomly moving particle spends in a bounded domain (sphere) before it escapes through a small window in the domain's boundary. A particle is assumed to diffuse freely in the bulk until it approaches the surface of the domain where it becomes weakly adsorbed, and then wanders diffusively along the boundary for a random time until it desorbs back to the bulk, etc. Using a mean-field approximation, we define t(app) analytically as a function of the bulk and surface diffusion coefficients, the mean time it spends in the bulk between two consecutive arrivals to the surface and the mean time it wanders on the surface within a single round of the surface diffusion.