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Issue 31, 2018
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Effective Hamiltonian of topologically stabilized polymer states

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Topologically stabilized polymer conformations in melts of nonconcatenated polymer rings and crumpled globules are considered to be a good candidate for the description of the spatial structure of mitotic chromosomes. Despite significant efforts, the microscopic Hamiltonian capable of describing such systems still remains unknown. We describe a polymer conformation by a Gaussian network – a system with a Hamiltonian quadratic in all coordinates – and show that by tuning interaction constants, one can obtain equilibrium conformations with any fractal dimension between 2 (an ideal polymer chain) and 3 (a crumpled globule). Monomer-to-monomer distances in topologically stabilized states, according to available numerical data, fit very well the Gaussian distribution, giving an additional argument in support of the quadratic Hamiltonian model. Mathematically, the polymer conformations are mapped onto the trajectories of a subdiffusive fractal Brownian particle. Moreover, we explicitly show that the quadratic Hamiltonian with a hierarchical set of coupling constants provides the microscopic background for the description of the path integral of the fractional Brownian motion with an algebraically decaying kernel.

Graphical abstract: Effective Hamiltonian of topologically stabilized polymer states

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Publication details

The article was received on 16 Apr 2018, accepted on 18 Jul 2018 and first published on 27 Jul 2018

Article type: Paper
DOI: 10.1039/C8SM00785C
Citation: Soft Matter, 2018,14, 6561-6570
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    Effective Hamiltonian of topologically stabilized polymer states

    K. Polovnikov, S. Nechaev and M. V. Tamm, Soft Matter, 2018, 14, 6561
    DOI: 10.1039/C8SM00785C

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