title: Relationships between the winding angle, the characteristic radius, and the torque for a long polymer chain wound around a cylinder: implications for RNA winding around DNA during transcription.
abstract: Long polymer chains are ubiquitous in biological systems and their mechanical properties have significant impact upon biological processes. Of particular interest is the situation in which polymer chains are wound around each other or around other objects. We have analyzed the parameters of a long Gaussian polymer chain wound around a cylinder as a function of the torque applied to the ends of the chain. We have shown that for sufficiently long polymer chains, an average winding angle and a characteristic radius of the chain can be determined from a modified Bessel function of purely imaginary order, in which the value of the order is equivalent to the applied torque, normalized to the product of the absolute temperature and the Boltzmann constant. The obtained results are consistent with a simplified interpretation in terms of "torsional blobs," and this could be extended to nonideal chains with excluded volumes. We have also extended our results to the case of a polymer chain rotating in viscous medium. Our results could be used to estimate the mechanical strains that appear in DNA and RNA during transcription, as these might initiate formation of unusual DNA structures, invasion of RNA into the DNA duplex (R-loop formation), and modulation of the interactions of DNA and RNA with proteins.
authors.affiliation: Department of Biology, Stanford University, 371 Serra Mall, Herrin Labs, Stanford, California 94305-5020, USA.
authors.forename: Boris P
authors.initials: BP
authors.lastname: Belotserkovskii
mesh_terms: D001665:Binding Sites; D003198:Computer Simulation; D004247:DNA / Q000737:chemistry* / Q000235:genetics / Q000648:ultrastructure*; D004058:Diffusion; D055119:Elastic Modulus; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical; D009690:Nucleic Acid Conformation; D011108:Polymers / Q000737:chemistry; D012313:RNA / Q000737:chemistry* / Q000235:genetics / Q000648:ultrastructure*; D013314:Stress, Mechanical; D019415:Torque; D014158:Transcription, Genetic / Q000235:genetics
chemical_list: D011108:Polymers; D012313:RNA; D004247:DNA