Exact theory of kinkable elastic polymers

Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, USA.
Physical Review E (Impact Factor: 2.29). 03/2005; 71(2 Pt 1):021909. DOI: 10.1103/PhysRevE.71.021909
Source: PubMed


The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection angles, many rod systems exhibit a high-curvature softening. The signature behavior of these rod systems is a kinking transition in which the bending is localized. Recent DNA cyclization experiments by Cloutier and Widom have offered evidence that the linear-elastic bending theory fails to describe the high-curvature mechanics of DNA. Motivated by this recent experimental work, we develop a simple and exact theory of the statistical mechanics of linear-elastic polymer chains that can undergo a kinking transition. We characterize the kinking behavior with a single parameter and show that the resulting theory reproduces both the low-curvature linear-elastic behavior which is already well described by the worm-like chain model, as well as the high-curvature softening observed in recent cyclization experiments.

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    • "Assuming the nicks do not affect the local mechanical properties of DNA compared to B -form DNA, the above reported mechanical anomaly can be explained by breakdown of the WLC polymer model due to potential excitation of DNA structural defects when DNA is sharply bent. Indeed, it has been theoretically demonstrated that excitation of flexible mechanical defects under bending constraint through DNA melting or kinking could explain these results [17] [18] [19]. This possibility was in part supported by an experiment reporting that covalently closed 63 − 65 bp DNA minicircles without nicks could be digested by the BAL-31 nuclease [20] [21], indicating ssDNA generated in these DNA minicircles. "
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    ABSTRACT: Several recent experiments have suggested that sharply bent DNA has a surprisingly high bending flexibility, but the cause is poorly understood. It has been demonstrated that excitation of flexible defects can explain the results; while whether such defects can be excited under the level of DNA bending in those experiments has remained unclear and been debated. Interestingly, due to experimental design DNA contained pre-existing nicks in nearly all those experiments, while the potential effect of nicks have never been considered. Here, using full-atom molecular dynamics (MD) simulations, we show that nicks promote DNA basepair disruption at the nicked sites which drastically reduced DNA bending energy. In the absence of nicks, basepair disruption can also occur, but it requires a higher level of DNA bending. Overall, our results challenge the interpretations of previous sharp DNA bending experiments and highlight that the micromechanics of sharply bent DNA still remains an open question.
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    • "However, there are also other studies reporting that dsDNA strands with curvature radius of 2 − 20 nm have higher flexibility than the WLC model predicts (12,13,15). The higher flexibility was attributed to a local melting bubble (25) or kink (26) formation during sharp bending (15). The reason for the discrepancy between this study and the previous works suggesting higher flexibility is unknown. "
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    ABSTRACT: A molecular system of a nanometer-sized reel was developed from F(1)-ATPase, a rotary motor protein. By combination with magnetic tweezers and optical tweezers, single-molecule double-stranded DNA (dsDNA) was wound around the molecular reel. The bending stiffness of dsDNA was determined from the winding tension (0.9-6.0 pN) and the diameter of the wound loop (21.4-8.5 nm). Our results were in good agreement with the conventional worm-like chain model and a persistence length of 54 ± 9 nm was estimated. This molecular reel system offers a new platform for single-molecule study of micromechanics of sharply bent DNA molecules and is expected to be applicable to the elucidation of the molecular mechanism of DNA-associating proteins on sharply bent DNA strands.
    Nucleic Acids Research 07/2012; 40(19):e151. DOI:10.1093/nar/gks651 · 9.11 Impact Factor
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    • "However, there is no clear consensus on the constitutive law's functional form and how it maps from the base-pair sequence. Recent experimental observations [4] [9] indicate that linear constitutive laws are ineffective in capturing the general structural deformations of DNA molecules [35] [33]. The general form of constitutive law remains largely unknown, and the capability to determine constitutive law of DNA that governs its structure and dynamics is severely limited by the absence of a systematic approach to best leverage the limited data available. "
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    ABSTRACT: Long length-scale structural deformations of DNA play a central role in many biological processes including gene expression. The elastic rod model, which uses a continuum approximation, has emerged as a viable tool to model deformations of DNA molecules. The elastic rod model predictions are however very sensitive to the constitutive law (material properties) of the molecule, which in turn, vary along the molecules length according to its base-pair sequence. Identification of the nonlinear sequence-dependent constitutive law from experimental data and feasible molecular dynamics simulations remains a significant challenge. In this paper, we develop techniques to use elastic rod model equations in combination with limited experimental measurements or high-fidelity molecular dynamics simulation data to estimate the nonlinear constitutive law governing DNA molecules. We first cast the elastic rod model equations in state-space form and express the effect of the unknown constitutive law as an unknown input to the system. We then develop a two-step technique to estimate the unknown constitutive law. We discuss various generalizations and investigate the robustness of this technique through simulations. Comment: 13 pages, 16 figures, submitted to Automatica
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