Marko John F
Department of Physics and Astronomy and Department of Molecular Biosciences, Northwestern University, Evanston, IL 60208, USA.
J Stat Phys. 2011 Apr;142(6):1353-1370. doi: 10.1007/s10955-011-0172-4.
Scaling laws for Gauss linking number Ca and writhing number Wr for spherically confined flexible polymers with thermally fluctuating topology are analyzed. For ideal (phantom) polymers each of N segments of length unity confined to a spherical pore of radius R there are two scaling regimes: for sufficiently weak confinement (R ⪢ N(1/3)) each chain has |Wr| ≈ N(1/2), and each pair of chains has average |Ca| ≈ N/R(3/2); alternately for sufficiently tight confinement (N(1/3) ⪢ R), |Wr| ≈ |CA| ≈ N/R(3/2). Adding segment-segment avoidance modifies this result: for n chains with excluded volume interactions |Ca| ≈ (N/n)(1/2)f(ϕ) where f is a scaling function that depends approximately linearly on the segment concentration ϕ = nN/R(3). Scaling results for writhe are used to estimate the maximum writhe of a polymer; this is demonstrated to be realizable through a writhing instability that occurs for a polymer which is able to change knotting topology and which is subject to an applied torque. Finally, scaling results for linking are used to estimate bounds on the entanglement complexity of long chromosomal DNA molecules inside cells, and to show how "lengthwise" chromosome condensation can suppress DNA entanglement.
分析了具有热涨落拓扑结构的球形受限柔性聚合物的高斯链环数(Ca)和扭曲数(Wr)的标度律。对于理想（虚设）聚合物，长度为单位长度的(N)个链段中的每一个都被限制在半径为(R)的球形孔中，存在两种标度区域：对于足够弱的限制（(R\gg N^{1/3})），每个链的(\vert Wr\vert\approx N^{1/2})，并且每对链的平均(\vert Ca\vert\approx N/R^{3/2})；相反，对于足够强的限制（(N^{1/3}\gg R)），(\vert Wr\vert\approx\vert CA\vert\approx N/R^{3/2})。添加链段-链段排斥会改变这个结果：对于具有排除体积相互作用的(n)条链，(\vert Ca\vert\approx (N/n)^{1/2}f(\phi))，其中(f)是一个标度函数，它大致线性地依赖于链段浓度(\phi = nN/R^{3})。扭曲的标度结果用于估计聚合物的最大扭曲；这被证明可以通过一种扭曲不稳定性来实现，这种不稳定性发生在能够改变打结拓扑结构并且受到外加扭矩的聚合物中。最后，链环的标度结果用于估计细胞内长染色体DNA分子的缠结复杂度的界限，并展示“纵向”染色体凝聚如何抑制DNA缠结。
