Confined Space and Effective Interactions of Multiple Self-Avoiding Chains

Abstract

We study the link between three seeming-disparate cases of self-avoiding polymers: strongly overlapping multiple chains in dilute solution, chains under spherical confinement, and the onset of semidilute solutions. Our main result is that the free energy for overlapping n chains is independent of chain length and scales as n9/4, slowly crossing over to n3, as n increases. For strongly confined polymers inside a spherical cavity, we show that rearranging the chains does not cost an additional free energy. Our results imply that, during cell cycle, global reorganization of eukaryotic chromosomes in a large cell nucleus could be readily achieved.

Time scale of entropic segregation of flexible polymers in confinement: Implications for chromosome segregation in filamentous bacteria

“…As the two chains can gain conformational entropy by demixing, they effectively repel each other. Note that the free energy cost for simultaneous overlap of n chains scales as n 9/4 in the dilute regime and then increases faster as n 3 in the more concentrated regime, independent of the chain length [15,16]. Thus, for two intermingling chains illustrated in Fig.…”

Polymer translocation through a cylindrical channel

“…These results need to be appended by a proper account of excluded volume effect in order to compare with experimental systems. Even for an isolated spherical cavity, there is a continuing debate [46][47][48] for the form of the confinement free energy. However, when the excluded volume effect is removed, our exact results must be recovered.…”

Segregation of polymers in confined spaces

“…For λ ≥ 1, the total free energy is independent of l, therefore, there is no force driving segregation and the motion of the two chains is purely diffusive [18]. For λ ≤ 1, F (l) is a monotonically increasing function of l, and this repulsive potential drives segregation [19].…”

“…For a single chain confined in a rectangular box, assuming homogeneous distribution of monomers [16,17,18], leads to…”

“…The width is chosen to be less than R g , the radius of gyration of the free polymer. A scaling theory of the free energy of confined polymers is based on the blob pictures with each blob contributing k B T to the free energy of a polymer ( Fig.1(a)) [16,17,18]. The blob size, ξ blob , is determined by the competition between confinement, excluded-volume effects, and entropy.…”