Force transformation in spider strain sensors: white light interferometry

Abstract

Scanning white light interferometry and micro-force measurements were applied to analyse stimulus transformation in strain sensors in the spider exoskeleton. Two compound or 'lyriform' organs consisting of arrays of closely neighbouring, roughly parallel sensory slits of different lengths were examined. Forces applied to the exoskeleton entail strains in the cuticle, which compress and thereby stimulate the individual slits of the lyriform organs. (i) For the proprioreceptive lyriform organ HS-8 close to the distal joint of the tibia, the compression of the slits at the sensory threshold was as small as 1.4 nm and hardly more than 30 nm, depending on the slit in the array. The corresponding stimulus forces were as small as 0.01 mN. The linearity of the loading curve seems reasonable considering the sensor's relatively narrow biological intensity range of operation. The slits' mechanical sensitivity (slit compression/force) ranged from 106 down to 13 nm mN(-1), and gradually decreased with decreasing slit length. (ii) Remarkably, in the vibration-sensitive lyriform organ HS-10 on the metatarsus, the loading curve was exponential. The organ is thus adapted to the detection of a wide range of vibration amplitudes, as they are found under natural conditions. The mechanical sensitivities of the two slits examined in this organ in detail differed roughly threefold (522 and 195 nm mN(-1)) in the biologically most relevant range, again reflecting stimulus range fractionation among the slits composing the array.

Figure 1.

(a) Arrangement of the tibia–metatarsus joint for the adequate stimulation of the lyriform organ HS-8. (i) The metatarsus was kept at an angle of 50° to the fixed tibia. (ii) For stimulation under the white light interferometer, the metatarsus was deflected backwards (red arrow) and the forces resisting this deflection (blue arrow) measured at a distance of 22 mm from the pivot point. (b) Arrangement of the metatarsus–tarsus joint for adequate stimulation of the lyriform organ HS-10. The tarsus was deflected upwards (red arrow) and contacted the metatarsal pad at the mechanical threshold angle of 27°. At larger angles, the slits of organ HS-10 were compressed. The force resisting this deflection (blue arrow) was measured directly at the tarsus using the force transducer. (c) (i) Scanning electron micrograph (SEM) of the lyriform organ HS-8; (ii) SEM (courtesy of R. Müllan) of the metatarsal lyriform organ HS-10.

Figure 2.

Measurement of the forces applied to the metatarsus stimulating the tibial lyriform organ HS-8. The white light interference scans were taken 1 min after loading and the corresponding force values read out at the times marked by black bars. The three load steps shown here deflected the metatarsus by 300 µm (0.78°), 600 µm (1.56°) and 900 µm (2.34°) from the initial zero position.

Figure 3.

Loading of the exoskeleton of Cupiennius salei to stimulate two different lyriform organs: (a) HS-8 on the tibia and (b) HS-10 on the metatarsus. (a) When stimulating the proprioreceptive organ HS-8 by backward deflection of the metatarsus, the forces increased linearly (N = 6, n = 18). (b) When stimulating the vibration-sensitive metatarsal organ HS-10 by the upward deflection of the tarsus, the forces increased exponentially. Inset: x-axis starts with mechanical threshold at 27° tarsal deflection; note the exponential increase of force from this angle onward (N = 6, n = 6).

Figure 4.

(a) SEM of the posterior aspect of the tibia–metatarsus joint. The yellow line indicates the line corresponding to the surface profiles shown in (d,e). The asterisk marks the pivot point of the joint where the joint ball of the tibia contacts the joint socket on the metatarsus. (b) Simplified schematic of the deformation and stresses in the tibia cuticle in cross section at the site of lyriform organ HS-8 following a backward deflection of the metatarsus. Enlarged sections show bending beams with maximum stress and deformation at the surface. Arrows indicate compression and dilatation. (c) Change of the cross section of the tibia (cuticle surface) at the line in (a) due to differing deflections of the metatarsus. Black, unloaded state; red, backward deflection of the metatarsus by an angle of 10.2°, which effectively stimulates organ HS-8; green, forward deflection of the metatarsus by an angle of 10.2°, which stimulates organ VS-4 on the anterior side of the tibia. (d) Profiles of the posterior tibia surface as indicated in (a) in the resting position (black), and at anteriad (green) and posteriad (red) deflections of the metatarsus by 10.2°. (e) Flattening and bulging of the cuticle at the lyriform organ HS-8 perpendicular to the long axes of the slits. The profiles are superimposed and aligned at the upper right (posterior aspect of the tibia situated dorsal to the organ).

Figure 5.

White light interferograms and profiles of the slits of lyriform organ HS-8. (a) (i) Six slits of the unloaded organ. White lines drawn at a right angle to the long axes of the slits and next to the coupling cylinder with the dendrite tip mark the positions of the profiles shown in (b). (ii) Downward-shifted cuticle surface and compressed slits with the metatarsus loaded by 9.96 mN (deflection angle 7.77°). The height (z-axis) is represented by the colour coding. (b) Surface profiles of the slits used for the measurements of slit width and depth corresponding to the interferograms in (a). The inset shows an example (slit 2) of the data points used for the measurement of both slit width and depth.

Figure 6.

Width of individual slits determined interferometrically in the lyriform organ HS-8 at the site of the dendrite coupling cylinder (as indicated in the inset) relative to the unloaded state (N = 6, n = 6). The mechanical sensitivity goes down sequentially from 4.78% mN⁻¹ in slit 1 to 0.49% mN⁻¹ in slit 7 as indicated by the linear regression lines.

Figure 7.

(a) Gradual increase of the depth of three selected slits of the lyriform organ HS-8 (N = 4, n = 4). Negative values represent an increase of slit depth. (b) Correlation between depth change following stimulation and initial depth of 11 slits (N = 4).

Figure 8.

(a) Dorsal view of the metatarsus–tarsus leg joint with the metatarsal lyriform organ HS-10. At stimulation, the tarsus pushes against the pad on the metatarsus (black arrow) compressing the slits of organ HS-10 perpendicular to their long axes. The colour lines indicate the surface profiles shown in (b). (b) White light interferometric surface profiles taken along the leg's long axis as indicated in (a). The lines of the profiles are broken because of invalid data points. The straight thin red line indicates the length of organ HS-10 and of the cuticular pad in the profiles used for the measurements shown in (c). The blue and the green lines show the surface profiles taken anteriorly and posteriorly of the lyriform organ (see (a)), and clearly represent the furrow between the soft pad and the well-sclerotized cuticle of the metatarsus. (c) Width of organ HS-10 (filled circles) and of the pad (open circles) under increasing load drawn as percentage of the width (100% at 27° tarsal deflection). From an angle of 37° onward, the pad is clearly compressed more than the lyriform organ.

Figure 9.

(a) White light interferograms of the central region of the metatarsal vibration receptor HS-10 of a first left leg under increasing load (from left to right). The uppermost interferogram was taken close to the mechanical threshold corresponding to a deflection of the tarsus by 27°. Note the increasing compression of the slits. The z-axis is represented by the colour code. The white lines are drawn next to the dendrite attachment site. They indicate the positions for the measurement of the widths of slits 2 and 6. Slit 2 spans the entire curvature of the cuticular bridge structure and its dendrite attachment site is located towards the anterior aspect of the leg. Initial width 3.46 ± 0.55 µm (N = 5); length measured on SEM images in a plane 152 µm (figure 1c). Slit 6 is located more proximally and its dendrite attachment site is close to the middle of the cuticular bridge. Unloaded width 3.68 ± 0.91 µm (N = 5), slit length approximately 116 µm (figure 1c). (b) Compression of the slits in (a), compared with a reference measurement with no contact of the force transducer and the tarsus, at increasing tarsal deflection angle (N = 1, n = 1).

Figure 10.

Width of slits (a) 2 and (b) 6 of the metatarsal organ (see inset) under loading relative to the resting position (100%). The red lines connect the mean values (±s.d.) obtained from five measurements (n = 25) in five preparations (N = 5) within the biologically relevant range of forces indicated by the two dashed vertical lines. The slopes of the curves (i.e. relative slit compression per force in mN) and the regression coefficients R² are given for the same range.