7.2 Beyond kinking
7.3.5 General models for stiff polymers
Regardless of the outcome of the currently confusing experimental situation, these experiments have motivated a critical re-examination of the mechanics of DNA in tightly-bent conformations. The next chapter is a paper in preparation which quantitatively examines our central claim in this chapter:
although the mechanics of DNA may be significantly different from an elastic rod on the short length scales most relevant for the description of biological processes, the Wormlike Chain model describes the chain statistics of DNA as measured in most polymer physics experiments.
Chapter 8 develops a near-exact theory of the chain statistics of a class of generalized stiff polymer models. These models have a bending energy density which is an arbitrary function of curvature. For explicit computations, we use the SEC model, proposed in Sect.7.2.1. As described in Sect.7.2.1, we show that a long contour length, the chain statistics of these generalized models is generically described by the WLC model. In particular, we show that the WLC model is sufficient to describe force-extension, solution scattering, and long-contour-length cyclization experiments. The short-contour-length statistics are model dependent. We explicitly show that the SEC model can reproduce the short-contour-length J factor measured by Cloutier and Widom [1]. Although the muddled experimental picture prevents us from drawing any firm conclusion about the short-length- scale statistics of DNA, these calculations explicitly demonstrate the importance of of performing experiments, like short-contour-length cyclization, that are sensitive to the high-curvature DNA mechanics most relevant for biological systems.
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Chapter 8
A generalized theory of stiff polymers
DNA bending on length scales shorter than a persistence length plays an integral role in the trans- lation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer statistics relevant for describ- ing the conformational free energy of DNA bending induced by protein-DNA complexes. The recent DNA cyclization studies of Cloutier and Widom have questioned the applicability of the canonical stiff polymer theory, the wormlike chain (WLC) model, to DNA bending on biological length scales.
In this paper, we develop a near-exact theory of the chain statistics of a class of generalized stiff polymer models. Our focus is on the theoretical development of these models and the computation of experimental observables. To perform explicit calculations, we also introduce a toy model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics of stiff polymers, as predicted by the Renormalization Group. In particular, we show that the WLC model is sufficient to describe force-extension, solution scattering, and long-contour- length cyclization experiments. In contrast, in experiments sensitive to the short-length-scale chain statistics, the WLC model can fail dramatically. We demonstrate this explicitly by showing that our toy model can reproduce the anomalously large short-contour-length cyclizationJ factor measured by Cloutier and Widom. Finally, we discuss the applicability of these models to DNA chain statistics in the context of new experimental data.