Locomotor resilience through load-dependent modulation of muscle co-contraction

Navigating complex environments requires flexible control of the interaction between limbs and substrate. A key aspect of this interaction is the load distribution among the legs with ground contact. It requires sustained, steady-state adjustment to a given substrate, e.g. as load distribution changes with substrate slope (insects: Full and Tullis, 1990; Seidl and Wehner, 2008; Weihmann and Blickhan, 2009; Mendes et al., 2014; Dallmann et al., 2019; mammals: Gregor et al., 2006; Lay et al., 2007), but also transient adjustments on a step-by-step basis, as each foot lift-off causes load transfer among legs (Zill et al., 2009; Dallmann et al., 2017) and may affect stability (Szczecinski et al., 2018). Here, we tested whether the same mechanism may explain resilience to both sustained and transient changes in load distribution. If so, we would expect to find the same change in muscle activity during the transition from one steady state to another and in response to transient disturbances.

Theoretical and engineering studies suggest that load transfer among neighboring legs is sufficient to entrain coordinated stepping even without neural coupling (Ekeberg and Pearson, 2005; Owaki et al., 2013, 2017). Further, experimental studies show that touch-down events induce load transfer between ipsilateral leg pairs (Zill et al., 2009) in a manner that can support temporal coordination in walking (Dallmann et al., 2017). There is strong evidence that walking insects continuously monitor the load on each leg by strain-sensitive campaniform sensilla (CS; Ridgel et al., 1999, 2000; Zill et al., 2004) and that CS afferent activity changes with substrate slope (Noah et al., 2001). Thus, it could be possible that neuromuscular activity downstream of CS afferents responds similarly to transient load transfer among legs and sustained changes in load distribution as a function of body pitch relative to gravity.

In a previous study, we showed that stick insects experience substantial changes in joint torques when walking on upward or downward slopes, with little or no difference in walking speed and body posture (Dallmann et al., 2019). As the observed change in joint torques correlated with a sustained change in the activity ratio of two antagonistic muscles, we concluded that persistent changes in load distribution were compensated for by regulation of antagonist muscle co-activity. This was supported by preliminary single-trial results that suggested a gradual change of antagonist co-activity rather than interspersed distinct transition strides. The latter have been proposed for some mammals prior to stepping onto a slope (Gottschall and Nichols, 2011). Accordingly, our first objective was to build on our preliminary data and to identify parameters that vary as a continuous function of body pitch when insects transition between two steady states. Second, we related the principle underlying slope-dependent changes in motor activity to transient changes due to load transfer during horizontal walking and to other gait-related changes in motor activity.

We did so by combining recordings of antagonistic hindleg muscle activity with 3D motion capture of freely walking Carausius morosus in response to a step-change in walkway slope by ±45 deg, both upward and downward. Owing to their size, stick insects permit a detailed analysis of whole-body kinematics (Theunissen and Dürr, 2013) and muscle activity (Dallmann et al., 2017) during unrestrained locomotion. Muscle activity was recorded from the antagonistic muscle pair that governs forward/backward movement of the leg: retractor and protractor coxae. We focused on the hindlegs, as they attach closely to the center of mass and are important for propulsion and posture control (Cruse, 1976; Dallmann et al., 2016). Apart from monitoring muscle activity time courses, we applied an activation dynamics model for insect muscle (Harischandra et al., 2019) to estimate the time course of co-activation of the antagonist muscle pair during free walking. Assuming that hindleg kinematics change very little as stick insects walk on different slopes (Dallmann et al., 2019), we reasoned that any slope-dependent change in muscle co-activation should reflect a slope-dependent change in co-contraction. With this rationale, we used muscle co-activation as a proxy for thorax–coxa joint stiffness, i.e. the ability of the joint to resist passive deflection.

We show that muscle activity changes continuously with increasing/decreasing body pitch, with a graded decrease in co-contraction throughout the traversal. As the exact same change in co-contraction occurs during transient responses to load transfer due to lift-off events or during crawling, we conclude that resilience to both transient and sustained changes in load distribution is achieved by the same mechanism of load-dependent regulation of joint stiffness.

To evaluate the load-dependent adjustments of freely walking female stick insects (Carausius morosus, de Sinéty 1901; Fig. 1) in response to a step-change in slope (either +45 deg upwards or −45 deg downwards), recordings of muscle activity were combined with 3D motion capture. During the transition from level to slope walking, the effects on kinematic parameters and muscle activity of the right hindleg were examined on a step-by-step basis. Nine adult, female stick insects (body mass: 0.93±0.19 g; hindleg femur length: 14.30±0.51 mm; mean±s.d.) were tested. Animals were reared under constant conditions in a laboratory colony with a 12 h:12 h light:dark cycle. Experiments were conducted under constant conditions with a mean (±s.d.) temperature of 26.9±1.4°C and humidity of 37±3%.

Unrestrained animals walked along a wooden walkway that allowed the transition from steady-state level walking to steady-state walking on a slope (Fig. 1). By careful examination of complementary digital videos, lift-off and touch-down timings for all six legs were annotated manually. Based on the movements of individual legs, steps of the right hindleg were categorized as either steady-state steps or transition steps. Steady-state steps were defined as hindleg step cycles during which all legs were stepping on the same part of the setup, either the horizontal part or the slope. All other steps were defined as transition steps and further categorized based on which leg of the right side was next to swing toward the inclined part of the setup. Hindleg step cycles during which only the ipsilateral front leg swung toward the inclined part were defined as ‘first transition’ steps. Accordingly, hindleg step cycles during which the ipsilateral middle leg swung toward the incline were defined as ‘second transition’ steps. Finally, hindleg step cycles during which the hindleg itself swung to the incline were defined as ‘third transition’ steps. This resulted in five possible step categories for both slope conditions: steady-state level walking, steady-state slope walking, and three transition steps separating the two steady states. Step cycles during which searching movements of one of the six legs or ground contact of the thorax occurred were excluded from the analysis (except for analysis of crawling behavior; see below). Moreover, only those trials that comprised at least one valid step during steady-state level walking and at least one step of another category were considered. According to these criteria, muscle activities (see below) of each category could be related directly to level walking on a trial-by-trial basis, thus accounting for possible differences between recordings.

Movements of the whole body were recorded by tracking the 3D positions of 18 light-weight, retro-reflective markers (mass: 4 mg; diameter: 1.5 mm) with a commercial high-speed motion capture system comprising eight cameras, sampling at 200 frames s⁻¹ (Vicon MX10 with T10 cameras; Nexus 1.8.5; Vicon, Oxford, UK). Spatial accuracy of 3D marker localization was approximately 0.1 mm. Markers were attached to the body and leg segments of the animal (Fig. 1A): three markers were attached to the metathorax (T3), and one to the mesothorax (T2), prothorax (T1), head (Hd), each femur and each tibia. Marker coordinates were post-processed in Matlab (version 2018a, The MathWorks, Natick, MA, USA). Leg kinematics were calculated by adopting a 3D rigid link model (Dallmann et al., 2016). Additionally, a digital video camera (A602fc, Basler, Ahrensburg, Germany) was used to record a complementary, synchronized side-view video at 100 frames s⁻¹ for visual validation and movement annotation.

Hindleg joint angle time courses were divided into swing and stance movements based on careful manual annotation of all trials. The resulting intervals were resampled to the average duration (swing: 160 ms; stance: 730 ms; sampling rate: 200 Hz) of the respective movement, using shape-preserving, piecewise cubic interpolation.

Simultaneously with whole-body kinematics, electromyograms (EMGs) of the retractor and protractor muscles of the right hindleg were recorded. For each muscle, a pair of steel electrodes (50 μm diameter, insulated except for the tip) was implanted through small holes in the metathoracic cuticle (Fig. 1B). Correct electrode placement was verified by testing resistance reflex responses to imposed movements of the thorax–coxa (ThC) joint. Dental glue (Protemp II, 3 mol l⁻¹ ESPE, St Paul, MN, USA) held the electrodes in place. To ensure unrestrained walking, a light-weight EMG backpack (aluminium hook; mass: ∼50 mg; see Dallmann et al., 2017) was used to direct the wires to the amplifiers (Fig. 1A,B). The backpack was positioned close to the mean center of mass (CoM) of the walking animal, just behind the hindleg coxae, and fixed with beeswax. A custom-built amplifier (MA102, Electronics Workshop, Zoological Institute, Cologne, Germany) was used to amplify (3000-fold) and filter EMG signals (50 Hz notch, 250 Hz high-pass, 7.5 kHz low-pass) which, subsequently, were A/D converted (Power 1401 mk II; Cambridge Electronic Design, Cambridge, UK) and recorded with Vicon Nexus (version 1.8.5, Vicon, Oxford, UK) at a sampling rate of 6 kHz.

For the later analysis, raw EMG signals were first corrected for a possible baseline shift. Subsequently, signals were rectified and then smoothed with a temporal first-order low-pass filter (τ=25 ms). Next, the recordings were divided into swing and stance movements and resampled to the respective average duration as described for joint angle time courses above. Finally, rectified and smoothed signals of steps in each category were normalized to level walking. For this, signals were set in relation to the average magnitude from the corresponding step(s) during level walking of the respective trial.

To estimate muscle co-contraction and its load-dependent modulation during walking on inclines, we applied a computational model of muscle activation dynamics. As steady-state limb kinematics was found to differ little between level walking and walking on inclines of ±45 deg (Dallmann et al., 2019), we neglected length dependence of muscle activation and contraction dynamics and opted for the Hatze–Zakotnik model (Zakotnik et al., 2006) that takes account of non-linear force potentiation for low to medium spike frequencies (Harischandra et al., 2019). To this end, we applied the IMADSim toolbox for Matlab (Harischandra et al., 2019) with the parameter set of Zakotnik et al. (2006) to transform spike trains from measured EMG traces into a continuous function of muscle activation over time, for both the retractor and protractor muscle. The binary input signal was generated by detecting peaks in raw EMGs according to an amplitude threshold and representing each of these events by a unit pulse of 1 ms width. The modeled time courses of muscle activation were processed in the same manner as the filtered EMG data, i.e. by resampling to standardized swing and stance duration and subsequent normalization to the average magnitude during level walking (see above).

The term joint stiffness will be used qualitatively as the ability to counteract passive deflection. Owing to the non-linear force–length curves of muscle, and the fact that muscle activation increases the slope of the force–length curve, co-activation of antagonist muscles leads to an increase in joint stiffness without affecting the equilibrium position of the joint (Bührmann and Di Paolo, 2006). Accordingly, we used the estimate of antagonist co-activation as a proxy for joint stiffness.

All analyses were calculated in Matlab. If not stated otherwise, averages represent grand means (means of animal means) with error bars and shaded areas indicating bootstrapped 95% confidence intervals with B=5000 samples. Violin plots show probability density estimates based on the bootstrap samples. The range of the violins was bounded to the observed minimum and maximum values, respectively. Horizontal lines superimposed on the violins indicate means.

The data supporting this study's findings are available on Dryad (doi:10.5061/dryad.mw6m9060g).

To gain insight into adaptive motor control, unrestrained walking stick insects were recorded as they encountered a step-change in walkway slope (±45 deg), causing a change in load distribution among the legs. In total, n=990 steps from N=9 animals were collected across all step categories (see Table 1 for numbers for each category). In the following sections, we first analyze how the change in load distribution affects hindleg muscle activity and kinematics. In particular, we analyze how this relates to load-dependent regulation of joint stiffness by estimating the co-activation of antagonistic muscles. Finally, we connect our findings on the transition between two steady states to transient modulation of muscle activity in response to destabilizing lift-off events of neighboring legs or overall unloading of legs during crawling.

Muscle activity showed substantial inclination-dependent changes during the transition from level to slope walking. Differences between step categories were visible in raw EMG traces (Fig. 2A,B; Movies 1 and 2). During swing movements, the motoneuronal drive to the retractor was independent of the step category (P=0.24, s=2; ranked consistency randomization test; Fig. 2Ci). However, during stance movements the motoneuronal drive was modulated by the step category (P=10⁻⁸, s=26; ranked consistency randomization test), with activity increasing with increasing inclination (Fig. 2Cii). Effects between consecutive step categories were on average small (d=0.2), indicating gradual changes. Yet, they added up to a very large effect when comparing steady-state downwards with upwards walking (d=1.2, P=0.007, s=7; two-sample two-tailed randomization test). At the same time, the protractor received strong motoneuronal drive during swing movements (Fig. 2Di), reflecting the forward movement of the leg. The spike rate was modulated by the step category (P=10⁻⁸, s=26; ranked consistency randomization test) with, on average, minor effects between consecutive step categories (d=0.4) that add up to a large effect (d=1.4) when comparing steady-state downwards with upwards walking (P=6.8×10⁻⁴, s=10; two-sample two-tailed randomization test). For stance movements, the drive to the protractor was also modulated by the step category (P=10⁻⁸, s=26; ranked consistency randomization test) with activity decreasing with increasing inclination (Fig. 2Dii). Again, this modulation changed gradually (mean d=0.6) and eventually added up to a substantial effect (d=1.8) when comparing the two categories of steady-state slope walking (P=6.2×10⁻⁶, s=17; two-sample two-tailed randomization test). Altogether, the activity of both muscles, retractor and protractor, was modulated gradually as the animal experienced a transition in load distribution in conjunction with a step-change in slope.

To further illustrate this load-dependent modulation of muscle activity throughout the step cycle, we used rectified and smoothed EMG traces normalized to the mean duration of swing and stance phases (Fig. 3A). For the transition from level to upslope walking, retractor muscle activity during stance increased gradually with each subsequent leg on the incline, whereas it gradually decreased during the transition from level to downslope walking (Fig. 3Ai). Along with a change in magnitude, the time of the maximum activity gradually shifted to an earlier part of the stance movement during an upslope transition and to a later part during a downslope transition. This was different for the protractor. There, muscle activity during stance was strongest during steady-state downward walking, intermediate for level walking and diminished during upward walking (Fig. 3Aii). During swing movements, i.e. when the hindleg was not mechanically coupled to its neighboring legs through the ground, protractor activity still showed inclination-dependent modulation. With each leg stepping onto a downward slope, the magnitude of protractor activity decreased gradually, whereas it increased gradually as the animal stepped onto the upward slope.

As a proxy for joint stiffness at the ThC joint, we estimated the degree of co-contraction of the two antagonist muscles. In a first step to do so, we calculated the time course of muscle activation of both muscles using the non-linear Hatze–Zakotnik model of insect muscle activation dynamics (Zakotnik et al., 2006; Harischandra et al., 2019). This model takes account of the long time constants of single twitches in insect muscle and non-linear force potentiation for spike frequencies between 10 and 30 Hz. The mean and 95% confidence bands of the estimated muscle activation time courses are shown in Fig. 3B,C. Muscle activation of the retractor (Fig. 3Bi) showed essentially the same inclination-dependent modulation as found for retractor muscle activity (Fig. 3Ai). Yet, the curves of Fig. 3B were generally not as steep as their counterparts in Fig. 3A. This can be attributed to the long time constants of insect muscle activation dynamics. During stance, maximum retractor activation increased gradually during the upslope transition, whereas it decreased gradually during the downslope transition. In contrast, protractor activation during stance was highest for steady-state downward walking, intermediate for level walking and diminished in the second half of stance during upward walking (Fig. 3Bii). Again, time courses of transition steps of either walking condition resembled intermediates of the steady states between which they occurred.

Taken together, these results suggest that muscle activation of the two antagonists that protract/retract the hindleg about the ThC joint is subject to strong, inclination-dependent modulation.

As both retractor and protractor muscles were active during level walking, and the slope-dependent changes in the activity of the two muscles were similar, though with opposing sign, both neural co-activity and muscular co-activation of antagonists appeared to be important parameters in this paradigm. The most salient slope-dependent changes in muscle activity occurred during the first half of the stance movement (Fig. 3), reflecting previous reports on the biphasic nature of stick insect stance movements with an early support part (Graham, 1983). Therefore, only the first half of the step cycle was evaluated further. To do so, protractor activity was subtracted from retractor activity. The corresponding average time courses are shown in Fig. 4Ai. The difference in muscle activity depended strongly on step category (P=10⁻⁸, s=26; ranked consistency randomization test). The first transition step, i.e. with only the front leg on the incline, was clearly distinguishable from level walking. The difference in muscle activity strongly changed in favor of the retractor during the upward transition, and in favor of the protractor during the downward transition (p_up1=0.053, s_up1=4, d_up1=0.9, p_dwn1=0.011, s_dwn1=6, d_dwn1=1.1; two-sample two-tailed randomization test). With each subsequent leg on the slope, the difference between the two muscles increased gradually in the respective direction. The graded change in the pattern of muscle activity throughout the traversal was strongly correlated with a change in body pitch relative to gravity (r²=0.97, logistic regression; Fig. 4Aii). With regard to our proxy for joint stiffness, we found a similarly strong correlation between the difference in muscle activation and a change in body pitch relative to gravity (P=10⁻⁸, s=26; ranked consistency randomization test; Fig. 4Bii). Although the effect size of the step towards the slope was smaller (d_up1=0.9; d_dwn1=0.5), the eventual steady-state difference was of a similar magnitude.

Hindleg kinematics were recorded in synchrony with antagonistic muscle activity. To evaluate potential kinematic adjustments in response to a step-change in walkway slope and the resulting change in mechanical demand, we compared kinematic parameters during level walking with those during steady-state slope walking and the transition strides in between.

With walking speeds ranging from 13.6 to 81.3 mm s⁻¹ (38.2±10.6 mm s⁻¹; mean±s.d.), animals readily transitioned from level to slope walking (Fig. 5A). As in previous studies (for review, see Dürr et al., 2018), hindleg stance duration decreased hyperbolically with increasing speed, irrespective of step category (Fig. 5Bi). At the same time, the duration of swing movements remained nearly unaffected (Fig. 5Bii).

As in our previous study (Dallmann et al., 2019), joint angle time courses were very similar across steady-state conditions (Fig. 5Ci,ii). The hindleg was flexed, levated, supinated and protracted during swing movements, whereas it was extended, depressed, pronated and retracted during stance movements. The only joint that changed movement direction before the swing-to-stance transition was the coxa–trochanter joint. In all three steady-state conditions, the switch from levation to depression occurred before the onset of stance because depression must precede touch-down, which, in turn, must precede the onset of stance. When comparing step categories during the transition to slope walking, it was this depression in late swing that differed most noticeably from level walking, along with the subsequent depression in early stance. During the transition, the coxa–trochanter joint angle depressed more strongly during the upward transition (Fig. 5Ci) and depressed less strongly during the downward transition (Fig. 5Cii). Fig. 5Ciii illustrates these changes of the mean differences in coxa–trochanter angle compared with level walking at 25% of the step cycle (dotted lines in Fig. 5Ci,ii). The difference from level walking was strongest for the third transition step during the upward transition (P=6.3×10⁻⁴, s=10, d=1.75; one-sample two-tailed randomization test) and for the second transition step during the downward transition (P=0.002, s=9, d=1.66; one-sample two-tailed randomization test). Afterwards, the deviation decreased and approached the value during level walking. The slope-dependent differences in other joint angle time courses were not nearly as strong as those in levation of the coxa–trochanter joint. As described in our preceding paper (Dallmann et al., 2019), the hindleg tended to be flexed less and protracted more in early stance during the upward transition and pronated more strongly throughout the entire stance movement. During the downward transition, extension and supination joint angles were mainly within the 95% confidence intervals for level walking. An exception was the protraction of the ThC joint during early stance movement, which tended to be smaller. The mentioned change in protraction joint angle around the time of the swing–stance transition was consistent with a change in the anterior–posterior touch-down position (P=10⁻⁸, s=26; ranked consistency randomization test; Fig. 5D).

Taken together, these results suggest that kinematic parameters were affected little by a step-change in walkway slope and the corresponding shift in load distribution.

During walking, the stepping rhythm of each leg implies rhythmic load transfer among legs. That is, in addition to the change in load as a result of the change in inclination, each lift-off event of a leg induces mechanical load transfer to its neighboring legs. This is why we analyzed how muscle activity in the right hindleg (R3) was modulated in response to lift-off of its nearest neighbors: the ipsilateral right middle leg (R2) and the contralateral left hindleg (L3). To do so, we considered all lift-off events that occurred while R3 was in stance and, therefore, mechanically coupled with all other legs that had ground contact.

During level walking, retractor activity of R3 decreased within ∼100 ms after the ipsilateral middle leg R2 had lifted off (black area in Fig. 6Ai). For the protractor, the opposite was true, with an immediate increase of activity (black area in Fig. 6Aii). Note that this transient response follows the same pattern observed for the downward transition (Figs 3A and 4A, blue traces), i.e. shifting the difference between protractor and retractor activity in favor of the protractor. During steady-state walking on either slope, neither muscle showed consistent, event-related activity changes upon lift-off of R2 (magenta and blue shaded areas in Fig. 6A). Muscle activity during transition steps was intermediate between these steady-state response types and gradually approached the steady-state situation on the slope with each subsequent leg on the incline.

In contrast, lift-off events of the contralateral hindleg L3 had the opposite effect on retractor and protractor activity of R3 during level walking (Fig. 6B). Upon lift-off of L3, protractor activity of R3 declined rapidly, whereas retractor activity increased (black areas in Fig. 6B). Note that this response to lift-off events follows the same pattern observed for the upward transition (Figs 3A and 4A, magenta traces), i.e. shifting the difference between protractor and retractor activity in favor of the retractor. As for lift-off of R2, lift-off of L3 was followed by no pronounced, transient change in activity of either muscle during steady-state slope walking. Muscle activity during transition steps (magenta and blue lines in Fig. 6B) was intermediate between the steady states.

In summary, both retractor and protractor muscle activity revealed transient, event-related changes to destabilizing lift-off events of neighboring legs and an associated change in load distribution during level walking. Both kinds of transient destabilizations were consistently followed by a transient reduction of co-activation of antagonistic muscles. This hints at a common principle underlying transient and persistent changes in muscle activity patterns, regardless of whether the disturbance in load distribution was caused by a change in pitch relative to gravity or by a destabilizing lift-off event of a neighboring leg.

Yet another change in load distribution occurs whenever the legs do not suspend the body above the ground, such that the animal is effectively crawling rather than walking. In all analyses presented so far, steps were excluded if the thorax was in contact with – and sliding along – the ground. In the following, we will use the term crawling for this type of locomotion (as opposed to walking, where only the feet are in contact with the ground). Crawling occurred occasionally and was typically attributed to fatigue at the end of a long recording session. In the case of one animal, we were able to conduct a systematic within-session comparison between crawling as opposed to regular walking. This animal crawled for several trials in the middle of the recording session, with regular walking trials before and after this crawling episode. Thus, we could compare regular level walking steps before (n=7) and after (n=8) thoracic ground contact with those when the animal crawled (n=4) (Fig. 7). Representative side-view images (Fig. 7Ai,iii) and corresponding average joint angle time courses (Fig. 7B, black solid and dotted lines) show that the regular walking posture was maintained before and after the crawling episode. Also, raw EMG recordings and time courses of the relative retractor and protractor activity before and after crawling were broadly similar (Fig. 7C,D, solid and dotted black lines). In contrast, they differed markedly during crawling (Fig. 7C,D, green lines).

Crawling affected joint angle time courses and antagonistic muscle activity of the right hindleg substantially. Compared with regular walking steps, the leg was persistently more levated, flexed and protracted throughout the step. Solely the supination of the leg plane stayed nearly unaffected. The examples of raw EMG traces during crawling (Fig. 7Cii) were similar to those observed during steady-state upward walking (Fig. 2A), with protractor activity restricted to the swing movement. Relative muscle activity profiles (Fig. 7D) further revealed that protractor activity during swing movements was decreased, while retractor activity during stance movements was slightly increased during crawling.

Furthermore, the successful recovery of body posture and muscle activity after crawling revealed that co-activation of antagonistic muscles re-occurred only as the hindleg contributed to carrying the load of the body again, but not while the body was ‘supported’ by the ground. This suggests that co-contraction of retractor and protractor muscles may act to counter gravity-induced collapse, i.e. the effort of the animal to maintain balance with the body suspended above the ground.

Here, we provide 3-fold evidence for a fast and flexible mechanism to achieve resilience to both transient and sustained changes in load distribution that is based on continuous regulation of antagonist muscle co-activation in unrestrained moving stick insects. In a previous study, we showed that persistent changes in load distribution – as caused by a change in body orientation relative to gravity – led to substantial changes in joint torques and muscle activity, with very little change in limb kinematics (Dallmann et al., 2019). First, we replicate numerous of these findings. We show that the transition between two steady states that differ in load distribution is characterized by a gradual change in muscle activity (Fig. 2) and muscle activation (Fig. 3), with antagonist muscle co-activation following a monotonous function of body orientation relative to gravity (Fig. 4), and small, primarily transient changes in limb kinematics (Fig. 5). Second, we demonstrate that the same changes in antagonist co-activation occur in response to highly transient changes in load distribution after de-stabilizing lift-off events of neighboring legs (Fig. 6). Third, we show that a state-dependent change in load distribution during crawling (as opposed to walking) reversibly abolishes antagonist muscle co-activity (Fig. 7). Given the consistency of these three load-induced adjustments of antagonist muscle co-activity, we argue that stick insects respond to both transient and sustained changes in load distribution by continuous regulation of antagonist muscle co-activation and, therefore, regulation of muscle co-contraction and joint stiffness.

The significance of joint stiffness as a control variable in mammals has been established for a long time in sensorimotor physiology (e.g. Houk, 1979), biomechanics (e.g. Günther and Blickhan, 2002; Blickhan et al., 2007) and computational motor control (e.g. Franklin and Wolpert, 2011). Indeed, the regulation of stiffness in limb movement control must have evolved independently in all three remaining taxa of limbed animals (Arthropoda, Cephalopoda, Tetrapoda) as their last common ancestors did not have limbs. Representative examples include load compensation in targeted movements in an arthropod limb (locust: Matheson and Dürr, 2003; Zakotnik et al., 2006; Page et al., 2008), the temporary formation of quasi-rigid links in goal-directed movements of a cephalopod limb (octopus: Sumbre et al., 2006; Yekutieli et al., 2007), and the control of grasping precision in a tetrapod limb (human: De Serres and Milner, 1991; Gribble et al., 2003). Similarly, variable stiffness control has gained much attention in robotics (for review, see Wolf et al., 2016).

Owing to the non-linear properties of muscle contraction dynamics, a pair of antagonistic muscles allows for independent control of joint position and stiffness, with antagonist co-activation being key for controlling joint stiffness (Bührmann and Di Paolo, 2006). Because of the long activation and deactivation time constants of insect muscles (Bässler and Stein, 1996; Hooper et al., 2007), our finding of load-dependent adjustment of antagonist co-activity implies that stick insects regulate a variable related to muscle co-activation. As muscle activation determines isometric contraction force (e.g. Harischandra et al., 2019), muscle co-activation translates into isometric co-contraction and, therefore, the resistance of the actuated joint against deflection, i.e. joint stiffness. Comparing the estimated characteristic of antagonist co-activation on body pitch (Fig. 4Bii) with that of co-activity (Fig. 4Aii), muscle activation dynamics prove to have a linearizing effect. For level walking, when both the retractor and protractor were active throughout the stance movement (Fig. 3), ThC joint stiffness was the largest. Yet, in the case of body pitch changing in either direction relative to gravity, ThC joint stiffness decreased through an increasing bias towards activation of one ThC joint muscle only.

Note that we did not measure muscle co-contraction or joint stiffness directly, but inferred it from estimates of muscle co-activation, i.e. the degree of ‘neural drive’ to both muscles actuating the ThC joint. This indirect estimate neglects any differences between retractor and protractor muscles and lever arms. As we found very little slope-dependent change in joint kinematics, but strong slope-dependent change in muscle co-activation, our conclusion of slope-dependent change in co-contraction and joint stiffness is justified qualitatively. Nevertheless, further research will be necessary to provide a quantitative estimate of joint stiffness, as this requires knowledge of the underlying muscle and joint geometries.

Our finding reflects the persistent changes in load distribution and altered mechanical demand at the ThC joint for propulsion (upward walking), stability of body posture (level walking) or braking (downward walking). Co-contraction of coxal muscles has also been reported for freely walking locusts (Duch and Pflüger, 1995), which alter their muscular activity patterns to cope with different conditions, such as vertical climbing or upside-down walking. Adjustments of muscle co-contraction as a result of changing mechanical demand, e.g. a change in load, were further evaluated by Zakotnik et al. (2006) on locust hindleg extensor and flexor tibiae muscles. By expanding on the dynamic range of joint torques, they found that net joint torques can be increased substantially by rather small changes in muscle force, provided that the normal movement involved sufficient co-contraction.

In line with several earlier studies, we observed the most salient changes in the first half of the stance movement, corroborating the concept of a biphasic stance movement with an early support and a later propulsive part (cockroach: Krauthamer and Fourtner, 1978; Larsen et al., 1995; stick insect: Graham, 1983). Similarly, our results on protractor activity agree with previous experiments revealing braking activity during the early part of this movement (Graham and Wendler, 1981). The phasic nature of load-dependent effects on stance muscle activation supports the view of a reflexive control of limb posture, resulting in relatively small changes in spatial and temporal kinematic parameters (Fig. 5). Similarly, seed-harvesting ants do not employ different locomotor behaviors when carrying loads but use their hindlegs to cling to the ground (Merienne et al., 2020). We conclude that insects from different orders regulate limb posture by adjusting muscle activation in response to changes in load distribution.

Compared with such persistent changes in load distribution, transient load transfer to the hindleg after lift-off of the anterior or contralateral neighbor leg increases the mechanical demand at the ThC joint to stabilize posture. Owing to its vicinity to the CoM, the ThC joint of the hindleg needs to be stabilized with opposite sign, depending on whether the ipsilateral middle leg (anterior to the CoM) or contralateral hindleg (posterior to the CoM) lifts off. The reflexive nature of this response is typically attributed to sensory feedback from CS, which are known for their important role in postural control and walking (reviewed by Zill et al., 2004; Tuthill and Wilson, 2016). The discharges of CS depend upon their location (e.g. Haberkorn et al., 2019), the orientation of their long axis (Spinola and Chapman, 1975) and the vectoral direction of the imposed or self-generated forces (e.g. Zill et al., 2012). This implies that a change in body orientation relative to gravity will affect the overall distribution of CS activity. In the case of muscle activity at the ThC joint, as investigated here, trochanteral CS are known to be part of feedback loops that minimize imposed strains in the leg during standing and walking (Schmitz, 1993; Schmitz and Stein, 2000). CS ablations revealed that load-dependent activation of retractor and protractor muscles of the ThC joint are mainly driven by trochanteral CS, although CS from more distal leg parts may modulate retractor activity (Haberkorn et al., 2019). Furthermore, the neural processing of trochanteral CS depends on walking direction and is sufficient to trigger the transition from stance to swing in both forward and backward walking animals (Akay et al., 2004, 2007).

This body of evidence strongly suggests that the three kinds of changes in load distribution tested here must have affected load encoding of trochanteral CS and, as a consequence, retractor and protractor motoneuron activity. Yet, we cannot rule out additional effects of other CS groups (e.g. femoral CS group 5; see Haberkorn et al., 2019), indirect contributions and/or interaction of CS activity from legs other than the hindleg recorded, or the influence of other sensory signals (e.g. contact information). Given the complexity of CS effects in stationary animals with highly controlled stimuli (Haberkorn et al., 2019) and the encoding of loading and unloading (Ridgel et al., 1999), a systematic investigation of CS effects on muscle co-contraction in freely walking animals is clearly beyond the scope of the present study. Future research will need to address both the interplay of several CS groups and the up- and down-regulation of antagonistic muscle activity in freely walking insects.

As a neuromuscular strategy, co-contraction of antagonistic muscles has also been identified for mammals that transition between slopes (Gottschall and Nichols, 2011). Here, changes in muscle activity were reported to correspond mostly with modifications of head pitch. The integration of vestibular information with information from neck proprioceptors could be used to estimate body orientation with respect to gravity. Notably, humans adjust muscle activity and head pitch in anticipation of the slope, but only if the upcoming disturbance has not been camouflaged (Müller et al., 2015). This could be explained by the fast speed of humans and the fact that bipedal locomotion demands distinct anticipation and transition steps (Gottschall and Nichols, 2011). We did not observe distinct transition steps in our study, and potentially a six-legged walker with low speed and low inertia does not need to anticipate disturbances. In principle, stick insects could use their long antennae to perceive relative changes in the direction of the gravity vector (Wendler, 1965; Bässler, 1971), although walking C. morosus only rarely touch the ground with their antennae. Future work may address the contribution of antennal graviception to the observed changes in leg muscle co-contraction.

Last but not least, our third example addressed state-dependent changes in load distribution during crawling, where antagonist muscle activity was strictly alternating without co-activity (Fig. 7C,D). We argue that the transfer of load from the legs to the main body implies that the legs need no longer counteract gravity-induced collapse through increased joint stiffness, making costly co-contraction of antagonistic muscles dispensable.

Our results on state-dependent protractor–retractor co-contraction during level walking and crawling are in line with studies using three different experimental contexts. Whereas the maintained antagonist co-activity during walking (Fig. 7Ci,iii,D,E) replicates our previous findings (Dallmann et al., 2019), our results on crawling are the same as those obtained from supported walking animals in that antagonist muscle activity was strictly reciprocal (treadmill: Akay et al., 2004; slippery surface: Rosenbaum et al., 2010). Supported-walking paradigms (treadmill; slippery surface) and crawling have in common that the animal does not support its body weight and, therefore, does not need to stabilize the body against gravity-induced collapse. We conclude that our results in Fig. 7 could resolve an apparent discrepancy in the literature by highlighting the significance of the acting load distribution on the generation of rhythmic motor patterns. While this conclusion is consistent with current knowledge about sensorimotor effects of changes in load (see the previous section), future research on the sensory modulation of muscle co-contraction will need to test for potential effects of body contact as it occurs during crawling and supported-walking paradigms.

Resilience to sudden changes in substrate properties is crucial for terrestrial locomotion when navigating through variable environments. Our study provides 3-fold evidence on adjustments of antagonist muscle activity in response to a change in load distribution. We conclude that both persistent (though graded) and transient adjustments of antagonist muscle co-contraction follow the same load-dependent and continuous pattern during the first half of the stance phase. While further research will need to address how local pre-motor and motor networks integrate local load feedback to up- or down-regulate activity of both antagonistic muscles, our results clearly suggest a common mechanism underlying both transient and persistent regulation of antagonist co-contraction and, thus, joint stiffness.

We thank Chris J. Dallmann for introducing Y.G. to the setup and for valuable support along the way, Thierry Hoinville for helpful comments on data analysis, and Brigitta Otte-Eustergerling for maintaining our stick insect colony.