Walking on smooth or rough ground: passive control of pretarsal attachment in ants

Abstract

The hymenopteran tarsus is equipped with claws and a movable adhesive pad (arolium). Even though both organs are specialised for substrates of different roughness, they are moved by the same muscle, the claw flexor. Here we show that despite this seemingly unfavourable design, the use of arolium and claws can be adjusted according to surface roughness by mechanical control. Tendon pull experiments in ants (Oecophylla smaragdina) revealed that the claw flexor elicits rotary movements around several (pre-) tarsal joints. However, maximum angular change of claws, arolium and fifth tarsomere occurred at different pulling amplitudes, with arolium extension always being the last movement. This effect indicates that arolium use is regulated non-neuronally. Arolium unfolding can be suppressed on rough surfaces, when claw tips interlock and inhibit further contraction of the claw flexor or prevent legs from sliding towards the body. To test whether this hypothesised passive control operates in walking ants, we manipulated ants by clipping claw tips. Consistent with the proposed control mechanism, claw pruning resulted in stronger arolium extension on rough but not on smooth substrates. The control of attachment by the insect claw flexor system demonstrates how mechanical systems in the body periphery can simplify centralised, neuro-muscular feedback control.

Appendix

We model the pretarsus as a system of limbs connected with joints containing torsion springs (Figs. 3c, 6). The torsion springs are located (1) at the unguifer, where the manubrium is hinged, (2) at the distal end of the manubrium, around which the arcus rotates; and (3) at the flexible connection between unguitractor plate and planta.

Fig. 6

Spring model of arolium unfolding, see Fig. 3c. The lengths and angles used for the calculation of F* are shown in the lower panel. See Fig. 3 for explanation of abbreviations

Direction of force relative to tarsus axis

The claw flexor muscle produces a force F along its tendon, which acts to move the unguitractor plate proximally into the last tarsal segment. This force can be divided into a translational and a rotational component:

$$ F_{{\text{trans}}} = F\cos \theta \quad{\text{and}}\quad F_{{\text{rot}}} = F\sin \theta $$

We model the anterior ventral margin of the last tarsomere as a frictionless pivot so that the combination of F _rot and F _trans gives rise to a force F* which deflects torsion spring (3) at the flexible connection between unguitractor plate and planta and pushes upward (dorsally) at the end of the planta, where the arcus is hinged. The lever arm l* on the distal side of the pivot is l* and its angle to the other side of the pivot is ω₁.

The ratio between the lever arms on both sides of the pivot is ${l_{1} } \mathord{\left/ {\vphantom {{l_{1} } {l*}}} \right. \kern-\nulldelimiterspace} {l^*}.$ The magnitude of F* can be obtained by adding $F_{{\text{rot}}} \cdot {l_{1} } \mathord{\left/ {\vphantom {{l_{1} } {l^*}}} \right. \kern-\nulldelimiterspace} {l^*}$ and F _trans vectorially:

$$ \begin{aligned}{} \overline{{F^*}} & = {\sqrt {{\left( {F_{{\text{rot}}} \cdot {l_{1} } \mathord{\left/ {\vphantom {{l_{1} } {l^*}}} \right. \kern-\nulldelimiterspace} {l^*}} \right)}^{2} + F^{2}_{{\text{trans}}} - 2{\left( {F_{{\text{rot}}} \cdot {l_{1} } \mathord{\left/ {\vphantom {{l_{1} } {l^*}}} \right. \kern-\nulldelimiterspace} {l^*}} \right)}F_{{\text{trans}}} \cos {\left( {90^\circ - \omega _{1} } \right)}} } \\ &= F \cdot {\sqrt {{\left( {\sin \theta \cdot {l_{1} } \mathord{\left/ {\vphantom {{l_{1} } {l^*}}} \right. \kern-\nulldelimiterspace} {l^*}} \right)}^{2} + \cos ^{2} \theta - 2{\left( {\sin \theta \cdot {l_{1} } \mathord{\left/ {\vphantom {{l_{1} } {l^*}}} \right. \kern-\nulldelimiterspace} {l^*}} \right)}\cos \theta \sin \omega _{1} } } \\ \end{aligned} $$

To find the direction of ${\overrightarrow{{F^*}}}$ relative to the tarsus, the angle β₂ is calculated from:

$$ \cos \omega _{2} = \frac{{F\sin \theta \cdot {l_{1} } \mathord{\left/ {\vphantom {{l_{1} } {l^*}}} \right. \kern-\nulldelimiterspace} {l^*} - F\cos \theta \sin \omega _{1} }} {{\overline{{F^*}} }} = \frac{{\tan \theta \cdot {l_{1} } \mathord{\left/ {\vphantom {{l_{1} } {l^*}}} \right. \kern-\nulldelimiterspace} {l^*} - \sin \omega _{1} }} {{{\sqrt {{\left( {\tan \theta \cdot {l_{1} } \mathord{\left/ {\vphantom {{l_{1} } {l^*}}} \right. \kern-\nulldelimiterspace} {l^*}} \right)}^{2} + 1 - 2{l_{1} } \mathord{\left/ {\vphantom {{l_{1} } {l^*}}} \right. \kern-\nulldelimiterspace} {l^*}\tan \theta \sin \omega _{1} } }}} $$

and the angle γ from:

$$ \psi = 90^\circ - \theta - \omega _{1} + \omega _{2} $$

Effective lever arm

The force F* elicits both a proximal rotation of the manubrium (joint 1) and an extension of the arolium (joint 2). We determined the lever arms H ₁ and H ₂ around both joints (i.e. the distance of vector ${\overrightarrow{{F^*}}}$ to the unguifer and the arcus base, respectively). The “effective lever arms” of the arolium and manubrium joints can be calculated as the torsional moment $F^{*} \cdot H_{\text{i}}$ divided by the tendon force F.

Insufficiency of the model

Our simple model does not correctly predict the rotation of the manubrium. During the claw flexor contraction, the predicted force vector ${\overrightarrow{{F^*}}}$ did not consistently point in the proximal direction but it was sometimes oriented distally (i.e. H ₁ was negative), suggesting that the manubrium undergoes proximal and distal movements while the claw flexor is contracting. However, our observations show that the manubrium only moves proximally when the claw flexor contracts. We assume that this behaviour is due to a spring-like connection between the unguitractor plate and the manubrium (indicated by the dotted spring in Figs. 3c and 6). Morphologically, this spring represents the elastic cuticle connection of the unguitractor plate via the claws to the claws and the unguifer. This spring may also be responsible for the fact that at the beginning of the claw flexor contraction (when the unguitractor plate is still not in contact with the anterior ventral margin of the fifth tarsomere), the plate rotates away from the direction of the tendon pull.