Tensioning the helix: a mechanism for force generation in twining plants

Abstract

Twining plants use their helical stems to clasp supports and to generate a squeezing force, providing stability against gravity. To elucidate the mechanism that allows force generation, we measured the squeezing forces exerted by the twiner Dioscorea bulbifera while following its growth using time-lapse photography. We show that the development of the squeezing force is accompanied by stiffening of the stem and the expansion of stipules at the leaf base. We use a simple thin rod model to show that despite their small size and sparse distribution, stipules impose a stem deformation sufficient to account for the measured squeezing force. We further demonstrate that tensioning of the stem helix, although counter-intuitive, is the most effective mechanism for generating large squeezing forces in twining plants. Our observations and model point to a general mechanism for the generation of the twining force: a modest radial stem expansion during primary growth, or the growth of lateral structures such as leaf bases, causes a delayed stem tensioning that creates the squeezing forces necessary for twining plants to ascend their supports. Our study thus provides the long-sought answer to the question of how twining plants ascend smooth supports without the use of adhesive or hook-like structures.

Figure 1

Three modes of deformation of a helical structure. A ring is shown for clarity, but the same is true for any helix. (a) Relaxed state. (b) The stem can be bent, (c) stretched, or (d) twisted to squeeze the support. Deformations are exaggerated for illustration.

Figure 2

Characterization of helical geometry. The relationship among helix parameters a, c, d can be pictured by wrapping a right triangle of width 2πa and height 2πc around a cylinder of radius a. The hypotenuse of the triangle, with length 2πd, forms a single gyre. The helix has radius a, pitch c, and arc length per radian d; it has curvature a/d² and torsion c/d² (Silk & Hubbard 1991). From the geometry of the triangle, d²=a²+c²; the angle of ascent β of the helix is given by cos β=a/d.

Figure 3

Development of twining shoot and increase in squeezing force for four stems. (a–d) Stem twining around the force plate (half-pole held in place by two load cells). (e–h) Development of the squeezing force (running average of 12 values, or 2 hours interval) as a function of time and arc length from the shoot apex to the lower edge of the sensing region. Force was proportional to the total output of two load cells holding the force plate. (e) An arrow indicates the position corresponding to the time of each picture (a–d) for the first plant. The positions where gyres are completed are shown by grey vertical lines (±1 standard deviation; standard deviation increases because error accumulates with gyre number).

Figure 4

(a) Stipule (S) developing at the petiole base in D. bulbifera. (b) The growth of the stipule pushes the stem away from the support.

Figure 5

Stipule growth, stem radius, the Young modulus and growth strain remaining along the stem of D. bulbifera. (a) Stipule expansion and stem radius along three twining stems. Stipule size is measured as the distance from the stem to the edge of the stipule (filled circles, stipule; open diamonds, stem radius). (b) Stem Young's modulus versus distance from shoot apex for five stems. (c) Growth strain remaining (see §2) versus distance from apex for 10 circumnutating plants.

Figure 6

Model for development of tension in stem of D. bulbifera. (a) Strain (ϵ, equation (2.5)) and stretching stiffness (S, equation (2.1)) based on data, and predicted tension (T, equation (2.6)) along the axis of a vine on a rigid cylinder. Because the tension is an integral of the stretching stiffness with the derivative of the strain, it evolves further along the axis than either the strain or the stiffness (dot-dashed line, strain; dashed line, stretching stiffness; solid line, tension). (b) Average force recorded from four plants on mechanical poles (figure 2e–h), and force predicted (solid line) by the model taking into account the compliance of the load cells and assuming the average growth rate of 2.25 mm h⁻¹.

Figure 7

Principle of squeezing by tension in a twining vine. (a) The most apical portion of the vine moves freely and contacts the support only periodically (image is average of 100 frames of a time-lapse video). Further from the apex, the position of the vine on the support becomes fixed, and a small force is applied by twist in the vine. Finally, this small force starts a frictional interaction that allows the accumulation of axial tension along the vine axis during development. (b) Gently uncoiled twining stem of D. bulbifera still held in place by its most apical gyre. Frictional interactions provide stability under tension. The gravitational load of the uncoiled stem acts similar to the tension in a twining stem.