Botanical ratchets

Abstract

Ratcheting surfaces are a common motif in nature and appear in plant awns and grasses. They are known to proffer selective advantages for seed dispersion and burial. In two simple model experiments, we show that these anisotropically toothed surfaces naturally serve as motion rectifiers and generically move in a unidirectional manner, when subjected to temporally and spatially symmetric excitations of various origins. Using a combination of theory and experiment, we show that a linear relationship between awn length and ratchet efficiency holds under biologically relevant conditions. Grass awns can thus efficiently transform non-equilibrium environmental stresses from such sources as humidity variations into useful work and directed motion using their length as a fluctuation amplifier, yielding a selective advantage to these organelles in many plant species.

Figure 1

(a) Grass species that exhibit ratchet motility (for (i) to (iii)): (i) single spikelet of foxtail grass (H. murinum), (ii) green bristlegrass (Setaria viridis), and (iii) barley (Hordeum vulgare); scale bar, 2 cm. (b) Hordeum murinum's micro-barb surface structure is responsible for the ratcheting effect (SEM); scale bar, 50 μm. (c) A single clamped unstrained H. murinum awn (with micro-barbs pointing to the right) glides easily on the substrate moving to the right (paper cover). (d) Awn buckling and progressive micro-barb locking induced by substrate motion to the left (see movie 1 in the electronic supplementary material). (e) A barb-locked awn on the substrate also resists upward lift forces (see movie 2 in the electronic supplementary material).

Figure 2

Ratcheting in the inertial regime. (a) Foxtail grass moves unidirectionally on a harmonically oscillating horizontal shaker (see movie 3 in the electronic supplementary material). (b) The mean velocity is shown as a function of the shaker frequency, with error bars from five different foxtail specimens (circles). The best fit to a theoretical model (see text), with γ=0.4, is shown as a solid line. Inset: graphical model for ratchet motion on an oscillating substrate. The ratchet leaves the substrate frame when its inertia overcomes the frictional force at t=t₁, and it locks and moves with the substrate again when the ratchet and substrate velocities coincide again at t=t₂.

Figure 3

Ratcheting in a continuously deforming environment. (a,b) Experimental set-up: foxtail spikelets are placed inside a 4 mm inner diameter rubber tube that is periodically strained (see movie 4 in the electronic supplementary material). Spikelets move in the direction of their tips (stained black for video analysis) with an efficiency that varies with their length. The distance between marker lines on the tube is 2.54 cm. (c) An intensity line scan (kymograph) corresponding to the time dynamics in (a) shows the periodic tube motion and the average propulsion of the spikelet over the time course of 60 s (x-axis). (d) Propulsion distance per strain cycle versus maximal rubber tube strain for four spikelets of various lengths: experimental points with error bars from seven to nine measurements and best fits to ${\text{Δ}}_{\text{g}}^{II}=a{ϵ}_{\text{s}}^{\text{max}}/(1+{ϵ}_{\text{s}}^{\text{max}})$ (solid lines). Inset: the fitted effective contact length (y-axis, centimetre units) versus the measured length of the longest awn (x-axis, centimetre units) of individual spikelets. While the effective lengths show a good correlation with the measured lengths, they are slightly smaller due to occasional awn buckling and imperfect tube–awn contact.