The distribution of end-to-end distances of the weakly bending rod model

• Published in: BIOPOLYM 2000-12, Vol.54 (7), p.561-571
• Main Authors: Schurr, J. Michael, Fujimoto, Bryant S.
• Format: Article
• Language: English
• Subjects: Approximation theory; Computer Simulation; contour length; end-to-end distances; Mathematical models; Method of moments; Models, Chemical; Models, Molecular; Molecular dynamics; Molecular structure; Monte Carlo Method; Monte Carlo methods; persistence length; Pliability; Polymers - chemistry; Thermodynamics; weakly bending rod model; wormlike chain
• ISSN: 0006-3525; 1097-0282
• DOI: 10.1002/1097-0282(200012)54:7<561::AID-BIP80>3.0.CO;2-M

The weakly bending rod model is an approximation to a wormlike chain in the limit where the ratio L0/P of the contour length L0 to the persistence length P is not too large. The range of validity of the weakly bending rod model is investigated by deriving analytical expressions for its distribution of end‐to‐end distances P(L) and its moments 〈Lm 〉 and numerically comparing the results with corresponding values for the wormlike chain model. No general, closed form analytical expression for either P(L) or the average length 〈L〉 of a wormlike chain exists, so those quantities are obtained by Monte Carlo simulations. Exact analytical expressions for 〈L2〉 and 〈L4〉 for the wormlike chain are employed in the comparison of the computed moments. Moments calculated for the approximate distributions of Daniels and Yamakawa and Stockmayer are also compared with the others. In addition, P(L) and its moments for the alternative model of Winkler et al. are compared with the others. The weakly bending rod model gives a reasonably good account of both P(L) and 〈Lm 〉, m = 1,2,4, over the range L0/P ≤ 0.6, but deviates significantly for L0/P ≥ 1.0. In contrast, the alternative model of Winkler et al. yields rather poor results in the rodlike domain. © 2000 John Wiley & Sons, Inc. Biopoly 54: 561–571, 2000