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Conformational properties of complex polymers: rosette versus star-like structures

Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyze the size and shape characteristics of complex polymer structures, containing in general $f_1$ loops (petals) and $f_2$ linear chains (branches). Within the frames of continuous model of Gaussian macromolecule, we apply the path integration method and obtain the estimates for gyration radius $R_g$ and asphericity $\hat{A}$ of typical conformation as functions of parameters $f_1$, $f_2$. In particular, our results qualitatively reveal the extent of anisotropy of star-like topologies as compared to the rosette structures of the same total molecular weight.