  DNA bending on length scales shorter than a persistence length plays an
integral role in the translation of genetic information from DNA to cellular
function. Quantitative experimental studies of these biological systems have
led to a renewed interest in the polymer mechanics relevant for describing the
conformational free energy of DNA bending induced by protein-DNA complexes.
Recent experimental results from DNA cyclization studies have cast doubt on the
applicability of the canonical semiflexible polymer theory, the wormlike chain
(WLC) model, to DNA bending on biological length scales. This paper develops a
theory of the chain statistics of a class of generalized semiflexible polymer
models. Our focus is on the theoretical development of these models and the
calculation of experimental observables. To illustrate our methods, we focus on
a specific toy model of DNA bending. We show that the WLC model generically
describes the long-length-scale chain statistics of semiflexible polymers, as
predicted by the Renormalization Group. In particular, we show that either the
WLC or our new model adequate describes force-extension, solution scattering,
and long-contour-length cyclization experiments, regardless of the details of
DNA bend elasticity. In contrast, experiments sensitive to short-length-scale
chain behavior can in principle reveal dramatic departures from the linear
elastic behavior assumed in the WLC model. We demonstrate this explicitly by
showing that our toy model can reproduce the anomalously large
short-contour-length cyclization J factors observed by Cloutier and Widom.
Finally, we discuss the applicability of these models to DNA chain statistics
in the context of future experiments.
