Abstract
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≫N1/3) each chain has {pipe}Wr{pipe}≈N1/2, and each pair of chains has average {pipe}Ca{pipe}≈N/R3/2; alternately for sufficiently tight confinement (N1/3≫R), {pipe}Wr{pipe}≈{pipe}Ca{pipe}≈N/R3/2. Adding segment-segment avoidance modifies this result: for n chains with excluded volume interactions {pipe}Ca{pipe}≈(N/n)1/2f(φ) where f is a scaling function that depends approximately linearly on the segment concentration φ=nN/R3. 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.
Original language | English (US) |
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Pages (from-to) | 1353-1370 |
Number of pages | 18 |
Journal | Journal of Statistical Physics |
Volume | 142 |
Issue number | 6 |
DOIs | |
State | Published - Apr 2011 |
Funding
Acknowledgements This work was supported by NSF Grants DMR-0715099, PHY-0852130, DMR-0520513 and MCB-1022117, and by NIH Grant 1U54CA143869-01 (NU-PS-OC). We acknowledge staff and instrumentation support from the Center for Structural Biology at Northwestern University. Support from the R.H. Lurie Comprehensive Cancer Center of Northwestern University to the Structural Biology Facility is acknowledged.
Keywords
- Chromosome structure
- Chromosome topology
- Confined polymers
- Polymer statistics
- Polymer topology
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics