Fractal Macromolecules : Mean First-Contact Times and Self-Contact Density

Orateur : Maxim DOLGUSHEV (LPTMC, Paris)

This talk is presenting our investigations on the role of complex connectivity of fractal macromolecules for contact formation and contact density. Fractals provide typical models, e.g., for hyperbranched polymers, proteins, sol-gel branched clusters, and colloidal aggregates. We have studied the impact of the connectivity on the cyclization kinetics of macromolecules with a fractal structure [1]. We have shown that the non-Markovian effects (i.e. memory) of the tagged monomer motion in a macromolecule are reflected in the out-of-equilibrium conformations at the instant of the first contact. We have connected the multiscale monomer dynamics to the corresponding behavior of the mean-first contact times and have demonstrated that the memory effects increase with the degree of branching. In works [2,3] we have considered marginally compact fractals. These special structures use very effectively the available space by filling it densely, but at the same time they have almost all their monomers on the surface. They are of a particular interest in connection with melts of ring polymers as well as with chromatin. However, their existence has been questioned theoretically because of a logarithmic divergence of their self-contact density. We have shown that such a divergence can be removed in practice by introducing linear spacers [2] or semiflexibility constraints [3] and we have characterized the dynamics of these structures.

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