Sensory signals of unloading in insects are tuned to distinguish leg slipping from load variations in gait: experimental and modeling studies

Abstract

In control of walking, sensory signals of decreasing forces are used to regulate leg lifting in initiation of swing and to detect loss of substrate grip (leg slipping). We used extracellular recordings in two insect species to characterize and model responses to force decrements of tibial campaniform sensilla, receptors that detect forces as cuticular strains. Discharges to decreasing forces did not occur upon direct stimulation of the sites of mechanotransduction (cuticular caps) but were readily elicited by bending forces applied to the leg. Responses to bending force decreases were phasic but had rate sensitivities similar to discharges elicited by force increases in the opposite direction. Application of stimuli of equivalent amplitude at different offset levels showed that discharges were strongly dependent upon the tonic level of loading: firing was maximal to complete unloading of the leg but substantially decreased or eliminated by sustained loads. The contribution of cuticle properties to sensory responses was also evaluated: discharges to force increases showed decreased adaptation when mechanical stress relaxation was minimized; firing to force decreases could be related to viscoelastic "creep" in the cuticle. Discharges to force decrements apparently occur due to cuticle viscoelasticity that generates transient strains similar to bending in the opposite direction. Tuning of sensory responses through cuticular and membrane properties effectively distinguishes loss of substrate grip/complete unloading from force variations due to gait in walking. We have successfully reproduced these properties in a mathematical model of the receptors. Sensors with similar tuning could fulfil these functions in legs of walking machines.NEW & NOTEWORTHY Decreases in loading of legs are important in the regulation of posture and walking in both vertebrates and invertebrates. Recordings of activities of tibial campaniform sensilla, which encode forces in insects, showed that their responses are specifically tuned to detect force decreases at the end of the stance phase of walking or when a leg slips. These results have been reproduced in a mathematical model of the receptors and also have potential applications in robotics.

Keywords: posture; sensory encoding; unloading; walking.

Graphical abstract

Figure 1.

Preparations for recording discharges of tibial campaniform sensilla and responses to cap indentation vs. leg bending. A and B: recording preparations—activities of tibial campaniform sensilla were recorded through a pair of wires (placed adjacent to a nerve containing the receptor axons. In most experiments, forces were applied to the end of the tibia with a probe (containing strain gauges that was driven by a motor (A). In studies in stick insects, forces were also applied with an Aurora puller (B), which permitted independent control of force or displacement. C: structure of campaniform sensilla—(left): a campaniform sensillum consists of a sensory neuron whose dendrite inserts into a cuticular cap at the surface of the exoskeleton. Detailed drawing of cuticular cap [middle, after Gnatzy et al. (26)]. The cap of the campaniform sensillum is linked to the cuticle via a collar. Confocal fluorescence micrograph of cockroach tibial sensilla (right): the collars appear as bright rings of elastic cuticle surround the darkened (sclerotized) caps. D: indentation of cuticular caps—indenting the caps of individual stick insect tibial campaniform sensilla with a fine probe (time indicated by indent cap) produced discharges to force increases in 6B (left) and 6A (right) receptors but no firing to decreases in indentation force. E: brief application of bending forces (forced extension of the tibia) elicited firing of 6B sensilla to force increases and action potentials in 6A receptors to force decreases. F: application of bending forces at different rates of rise and decline produced more prolonged firing of 6A receptors that reflected the rate of force decrease (left). Plots of sensory firing frequencies vs. rate of force application show that similar rate sensitivities are found to decreasing forces and to increasing forces in the opposite direction (6A: n = 28, N = 2; 6B: n = 40, N = 4).

Figure 2.

Responses of sensilla to bending forces applied as “staircase” functions at progressively increasing and decreasing levels. A and B: bending forces were applied to the tibia in the direction of extension (movement resisted) as step increases and decreases (STIM, stimulus) in a stick insect (A) and cockroach (B). In stick insects, 6B receptors discharged to force increases while 6A receptors respond to the step decreases. In cockroaches, a similar pattern of firing to force increases and decreases was obtained from proximal and distal tibial campaniform sensilla. In both animals, firing was phasic to step decreases but more prolonged when applied forces declined to their initial values. C and D: plots of sensilla discharges to force decreases in response to stair case functions (gray dots indicate maximum and minimum values). In both stick insects and cockroaches, discharges of receptors to force decreases were maximal as force levels approached zero. The range of responses was broader in stick insects than in cockroaches (C: n = 137; N = 3; D: n = 56, N = 3).

Figure 3.

Sensory responses to forces applied as ramp and hold functions at different offset levels. A and B: responses of tibial sensilla of a stick insect (A) and a cockroach (B) to application of forces as the same ramp and hold functions (direction of joint extension) at different offset levels. Discharges of stick insect 6B sensilla and cockroach proximal receptors increased at higher offset levels. Firing to force decreases was strongly dependent upon the level of load: discharges were minimal/did not occur after large load offsets but were intense and prolonged when at loads were decreased to the initial offset value. C and D: plots of mean discharges to force decreases (gray dots indicate maximum and minimum values; see text for discussion) (C: n = 336, N = 4; D: n = 506; N = 3). STIM, mechanical stimulus.

Figure 4.

Effects of offset on force encoding in tibial sensilla campaniform sensilla (CS). A: line plot of mean discharge frequencies of stick insect large amplitude tibial campaniform sensilla (6B, blue and 6A, red) to forces applied to the tibia using ramp and hold waveforms at different offset levels (Offset = 1—0 mN, 2—2.9 mN, 3—5.4 mN) in a single preparation. Responses to force increases (6B receptors) rapidly adapted but were more sustained at higher offset levels. Sensillum discharges (6A sensilla) were highest at zero offset and decreased substantially at increasing offset levels. B: plot of discharges of all 6B sensilla. Firing is sustained during the hold phase when 6B smaller sensilla are included but only phasic in 6A receptors. C: plot of mean sensory firing during the period of decreasing forces in stick insect 6A receptors. D: line plot of mean discharges of cockroach tibial campaniform (proximal receptors, blue and distal sensilla, red) to forces applied to the tibia using ramp and hold waveforms at different offset levels (mean amplitude = 0.85 mN ± 0.42; Offset = 1—0 mN, 2—0.92 mN, 3—1.84 mN). Proximal sensilla fired vigorous and sustained discharges that reflected the magnitude of tonic offsets. Distal receptors showed intense phasic firing to force decreases and the firing frequency decreased and then ceased when progressively larger offsets were applied. E: plot of mean sensory firing during the period of decreasing forces in stick insect 6A receptors. F: plot of relative gain of sensory discharges (calculated as the ratio of firing frequencies to minimal offset) in both species. In cockroaches, the slope of the decline is greater than in stick insects, which may be correlated with differences in cuticle properties (same data set as Fig. 3).

Figure 5.

Force encoding and cuticle viscoelasticity. A: the Aurora system allows for independent control of force and displacement. In response to maintained displacement (left), viscoelastic materials exhibit “stress relaxation” and resisting forces decline gradually. When forces are held constant (right), “creep” occurs and displacement gradually increases. B: bending forces applied as constant displacements to the stick insect tibia elicited discharges of the 6B sensilla that declined rapidly after the onset of the hold phase due to stress relaxation. C: stimuli applied as constant forces produced firing large 6B receptors that was prolonged at low force levels. At moderate force levels, discharges were sustained during the entire hold phase. Measurements of displacement showed gradual creep in these tests. D: pooled data on effects of force increases—application of forces as constant displacements (left) produced a brief cessation of discharge at the start of the hold phase due to stress relaxation that did not occur when forces were applied as constant forces (right) (D: constant displacement: n = 137, N = 5; constant force: n = 119, N = 5; note the stimulus channel indicates the waveform applied to the motor so no absolute scale is included.). STIM, mechanical stimulus.

Figure 6.

Responses to decreased forces and mechanical “creep.” A: recording of stick insect tibial sensilla to forces applied (in constant force feedback mode) to ramp and hold functions applied at the same force levels but with increasing durations of the hold phase. Forces are held at constant levels but displacements reflect viscoelasticity in the cuticle. Firing of 6B sensilla are sustained reflects at all durations of the hold phase but discharges of 6A receptors to force decreases increased following longer hold phases. B: diagram of effect of increasing duration on mechanical “creep”—creep (increase in displacement) gradually increases but reaches higher levels in longer displacements. C: plot of mean “creep” vs. duration in three preparations. D: plot of mean firing frequencies of 6A receptors to force decrease vs. duration of the preceding hold phase in three preparations (experiments 1, 2, and 3). The discharges frequencies of all receptors show similar duration dependent increases. E: discharges of 6A receptors vs. “creep”—the sensory firing frequency reflects the effects of cuticle viscoelasticity. (C: n = 42; N = 4; D: each test at 10 durations: experiment 1: n =14; experiment 2: n = 10; experiment 3: n = 12; total 36 tests; E: n = 46 test at 10 durations, N = 4). STIM, mechanical stimulus.

Figure 7.

Simulation of experimental results on effects of offset loads in a mathematical model of the receptors. A: the model, tuned based on previous stick insect results, produces 6B responses that are relatively insensitive to the offset force but produces 6A responses that are relatively sensitive to the offset force. This results from the interplay between the adaptive function and tonic function in the model. Compare these results from experimental results in Fig. 4B. B: the model’s discharge during offsets is inversely proportional to the offset force, as seen in the experimental results in Fig. 4C. C: the model, tuned based on previous cockroach results, produces proximal campaniform sensilla (CS) responses that are relatively insensitive to the offset force but produces distal responses that are relatively sensitive to the offset force. Compare these results from experimental results in Fig. 4D. D: the model’s discharge during offsets is inversely proportional to the offset force, as seen in the experimental results in Fig. 4E.

Figure 8.

Simulation of experimental results on effects of stimulus duration/viscoelastic properties in a mathematical model of the receptors. A: the model campaniform sensilla (CS) responses to unloading (top) exhibit discharge amplitude that is proportional to the duration of the hold phase of the stimulus (cyan asterisks). Plotting the model’s dynamic threshold variable x (middle) in response to the stimulus force u (bottom) shows that x exhibits “creep” like that measured in the animal’s cuticle. The amount of “creep” in response to the first stimulus is indicated by the dotted horizontal line. The maximum creep is indicated by cyan asterisks. B: the maximum value of x’s “creep” depends on the duration of the hold phase of the stimulus (compare to Fig. 6C). C: the sensory discharge in response to force decrements is proportional to the amount of “creep” that x undergoes.

Figure 9.

Predictive use of model: effects of force offset at higher resolution. A: model simulation of discharge of 6A sensilla to force decrements that would occur at offsets forces applied at five levels. B: experimental test of model—recording of stick insect tibial campaniform sensilla (CS) to forces applied as in the simulation. C: plot of discharges of 6A sensilla to offset forces applied as small steps. Sensory encoding is progressively decreased by increasing offset forces in both the model and experimental data (C: n = 1,500 tests, N = 3 animals).

Figure 10.

Summary: mechanisms underlying responses to decreasing forces. A: forces and strains—force are applied as a step displacement, hold and decrease on the end of the tibia. Discharges of campaniform sensilla (CS) indicate that the strains increase then decline during the hold phase. Force decreases produce strains similar to force increases in the opposite direction. B: graphical model—force increases initially produce compressive strains that activate the proximal (6B) sensilla. During the hold phase, viscoelasticity in the cuticle generates “creep” and transiently acts to create a new “neutral” position. Decrease in forces produces strains similar to force increases in the opposite direction transiently activating the distal (6A) receptors.