Diffusion of bio-polymers

The classical diffusion theory by Einstein-Langeven-Smolukhovski gives the description of the motion of the solid sphere of the small mass $m$ and radius $r$ under action of the random collusions with the molecules of the fluid environment (physical Brownian motion). The diffusion coefficient here is proportional to the absolute temperature $T$. The diffusion of the bio-polymers, typically in the salt solution, has several new features:
1. the existence of the phase transition from the globular (folded) form to the diffusive (unfolded) form.
2. The globule has non-spherical shape and fluctuations in time.
3. The experimental data demonstrate the decreasing of the diffusion coefficient as the function of $T$ (in complete contrast to the classical case).
4. The interaction between bio-polymer molecules especially near the threshold value $T_{cr}$ of temperature suppresses (and even eliminates) the diffusion, due to percolation effects.
The talk will contain the review of the theoretical models as well as the experimental results in the actual for biochemical and biotechnological application area. The list of the open mathematical problems also will be presented.