Passiflora edulis, like other climbing plants, possesses long, tender, soft, curly and flexible organs called tendrils whose circumnutation allows the plant to find support. Tendrils curl into spirals or twist into a helix, often of one handedness over half of its length and of the opposite handedness over the other half, the two halves being connected by a short straight section - a perversion, depending on whether they are supported at just one end or supported at both ends, respectively. This is a consequence of an intrinsic curvature of the tendrils. We report on liquid crystalline cellulosic fibers and jets, which mimic the shapes of helical tendril structures. Liquid crystalline and isotropic cellulosic precursor solutions of curved and straight fibers are examined using nuclear magnetic resonance imaging (MRI) and polarizing optical microscopy (POM) techniques to determine morphological and structural features contributing to fiber curvature. We study the subtle physical mechanisms responsible for self-winding behavior as a result of the intrinsic curvature due to the non-uniform deformation of filaments. In the case of liquid-crystalline cellulosic fibers, this is due to a core of disclination forming off-axis along the filament. We also highlight the critical dependence of the helical structures on temperature, which offers a potential for direct fabrication of biocompatible tunable high-surface area membranes with mechanical adaptability.