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: 2.33). 03/2005; 71(2 Pt 1):021909. DOI: 10.1103/PhysRevE.71.021909
Source: PubMed

ABSTRACT 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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    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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    ABSTRACT: By exploring a recent model in which DNA bending elasticity, described by the wormlike chain model, is coupled to basepair denaturation, we demonstrate that small denaturation bubbles lead to anomalies in the flexibility of DNA at the nanometric scale, when confined in two dimensions (2D), as reported in atomic-force microscopy experiments. Our model yields very good fits to experimental data and quantitative predictions that can be tested experimentally. Although such anomalies exist when DNA fluctuates freely in three dimensions (3D), they are too weak to be detected. Interactions between bases in the helical double-stranded DNA are modified by electrostatic adsorption on a 2D substrate, which facilitates local denaturation. This work reconciles the apparent discrepancy between observed 2D and 3D DNA elastic properties and points out that conclusions about the 3D properties of DNA (and its companion proteins and enzymes) do not directly follow from 2D experiments by atomic-force microscopy.
    Biophysical Journal 07/2009; 96(11):4464-9. DOI:10.1016/j.bpj.2009.03.035 · 3.83 Impact Factor
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    ABSTRACT: The continuum-rod model has emerged as an efficient tool to describe the long-length-scale structural-deformations of DNA which are critical to understanding the nature of many biological processes such as gene expression. However, a significant challenge in continuum-mechanics-based modeling of DNA is to estimate its constitutive law, which follows from its interatomic bond-stiffness. Experiments and all-atom molecular dynamics (MD) simulations have suggested that the constitutive law is nonlinear and non-homogeneous (sequence-dependent) along the length of DNA. In this paper, we present an estimation method and a validation study using discrete-structure simulations. We consider a simple cantilever-rod with an artificially constructed, discrete lattice-structure which gives rise to a constitutive law. Large deformations are then simulated. An effective constitutive-law is estimated from these deformations using inverse methods. Finally, we test the estimated law by employing it in the continuum rod-model and comparing the simulation results with those of discrete-structure simulations under a different cantilever loading-conditions. Comment: Proceedings of the ASME 2009 IDETC/CIE, Aug 30-Sept 2, 2009, San Diego, CA, USA (Paper Accepted)


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