Neuromuscular control of free-flight yaw turns in the hawkmoth Manduca sexta

Animals are highly successful at navigating their environments and achieve remarkable manoeuvrability and stability using locomotor mechanisms that, in most cases, differ substantially from those of human-engineered vehicles. These abilities arise, at least in part, from the interaction of the organisms’ unique biomechanical properties and their neural control mechanisms (Dickinson et al., 2000; Nishikawa et al., 2007). For instance, investigations into terrestrial arthropod locomotion have shown that the properties of the mechanical (Full et al., 1998; Sponberg and Full, 2008) and sensory systems (Cowan et al., 2006) can simplify control of locomotion (Cowan and Fortune, 2007). In this study, we extend neuromechanical investigation of control of animal movement to flight, showing how aerodynamic damping influences neuromuscular control of turning in freely flying hawkmoths.

The importance of FCT to the control of yaw orientation is supported by recent work. Fruit flies, when subjected to unexpected rotational perturbations, use passive damping to halt rotation for both the perturbation and their active recovery. Counter-rotational damping thus allows the flies to adopt a recovery strategy where the response consists of only a rotational impulse equal and opposite to that of the perturbation (Ristroph et al., 2010).

However, the presence of damping also introduces a penalty to locomotor energy efficiency in a manner analogous to normal fluid drag. To perform a given manoeuvre, the flying animal must expend energy not only to overcome its inertia but also to counteract damping. FCT damping and its associated effects on the control of movement may thus represent a compromise between stability and potentially simplified control on the one hand and locomotor energy efficiency and manoeuvrability on the other.

To assess the degree to which the passive damping properties affect flight control and provide insight into the possible manoeuvrability/stability compromises with which flying animals contend, we correlated muscle activation patterns and task-level kinematics of freely flying hawkmoths engaged in planar yaw turns. Although we are unable to directly assess the neural control of these voluntary manoeuvres at their origin in the central nervous system, we are able to infer general characteristics of the control framework by measuring neuromuscular activation patterns and external kinematics. Hawkmoths perform voluntary yaw turns by producing asymmetric aerodynamic forces that, in turn, are the product of asymmetric activation of the insect’s flight muscles. As bilateral activation timing differences in these muscles are correlated with mechanical power output (Josephson, 1985), asymmetric flapping kinematics (e.g. Balint and Dickinson, 2004) and yaw torque production (Sponberg and Daniel, 2010), we can assess the magnitude of the hawkmoth’s turning input by acquiring neuromuscular activation data from bilateral pairs of flight muscles.

The substantial passive damping observed in hawkmoths (Hedrick and Robinson, 2010) led us to hypothesize that they exhibit a damping-dominated yaw control architecture. In this case, a model that correlates observed yaw velocity and muscle activation timing differences will best fit the observed yaw turn kinematics during individual wingbeats. Alternatively, a model correlating yaw acceleration (or wingbeat to wingbeat changes in velocity) with muscle activation will better fit the observed kinematics for a hawkmoth with inertia-dominated plant dynamics.

Specifically, we simultaneously made extracellular muscle activation recordings and acquired body kinematics of Manduca sexta (L.) during free-flight yaw turns. We used freely flying subjects, rather than those attached to rigid tethers, to preserve the full aerodynamic effects of FCT. Free-flight preparations also maintain natural sensor–motor feedback, reducing the likelihood that our results will be distorted by aberrant or exaggerated behaviours, which are sometimes observed in rigidly tethered animals (Wang et al., 2008). We correlate dorsal longitudinal muscle (DLM; wing depressor muscle) and dorsal ventral muscle (DVM; wing elevator muscle) bilateral activation phase differences with yaw velocity and yaw acceleration. Though the DLM and DVM have historically been categorized as ‘power’ muscles (Pringle, 1957), there is growing evidence (Sponberg and Daniel, 2010; Tu and Daniel, 2004; Wang et al., 2008) that flying insects with synchronous flight muscles (e.g. moths) may, like vertebrate flyers (Hedrick and Biewener, 2007b), modulate main flight muscle power output during manoeuvres.

We chose M. sexta for this study because it is a large insect with synchronous flight muscles capable of complex manoeuvres, including prolonged stable hovering. All these traits simplify collection of neuromuscular activation data from freely behaving animals. Additionally, their widespread cultivation in a laboratory setting and study by numerous researchers offer ample anatomical and physiological references. Earlier studies of neural control of flight in both tethered (e.g. Kammer, 1971) and freely flying contexts (e.g. Wang et al., 2008) provide many opportunities for comparison of our results with those of other researchers.

We gathered male and female M. sexta as pupae from a domestic colony maintained by the Duke University Department of Biology. Pupae and adult moths were housed in 30×30×30 cm mesh cages inside an environment chamber. We maintained the moths on a 22 h:2 h light:dark cycle to reduce wear on their wings. Individuals were differentiated using a small amount of enamel paint applied to the abdomen tip.

Beginning 2–3 days after eclosion, we presented moths with both natural and artificial flowers to elicit feeding behaviour. Suitable feeding behaviour consisted of sustained (longer than 10 s), stable hovering and tracking of the feeding target. Though occurring naturally in M. sexta, we reinforced this behaviour with a food reward consisting of 1:4 honey:water mixture. Moths became candidates for electrode implantation once they demonstrated consistent flight and feeding behaviour.

Prior to electrode implantation, we placed the subject in a chilled (5°C) enclosure until quiescent (typically between 4 and 10 min). Once quiescent, the moth was restrained, using padded clamps over its wings, on a chilled operating table such that the dorsal surfaces of the thorax and abdomen were accessible. We removed scales obscuring the areas of implantation using forceps and compressed air.

To ease the insertion of electrodes, we first made a circular incision, 0.25 mm in diameter, through the exposed cuticle over each muscle of interest (Fig. 2). We then inserted a 1–2 mm long, 0.1 mm diameter tungsten electrode (A-M systems, Inc., Carlsborg, WA, USA), electrically and physically bonded to a 1 m long signal wire (0.15 mm diameter, copper, enamel coated; EIS/Fay Electric Wire, Elmhurst, IL, USA), through each incision and into the muscle tissue.

We secured all electrodes to the animal at the insertion site with a combination of cyanoacrylate adhesive (Loctite Super Glue; Henkel Corp., Avon, OH, USA) and sodium bicarbonate. To limit motion artefacts created by the animal’s movement and to improve electrode longevity through reduced strain at the insertion site, we additionally secured the signal wires to the tip of the abdomen with the same adhesive technique, allowing sufficient slack between the two attachment sites to permit normal abdominal flexion and other postural movements.

We placed a single electrode in four separate flight muscles, the left DLM, left DVM, right DLM and right DVM. We connected ipsilateral electrodes (e.g. left DLM and left DVM) to a differential amplifier (gain ×100, analog filters 10 Hz to 10 kHz bandpass, 60 Hz notch; Model 1800; A-M Systems, Inc.) as shown in Fig. 3. A 14-bit data acquisition system (USB-6251; National Instruments, Austin, TX, USA), operating at 15 kHz per channel, digitized and saved all amplified electromyograms (EMGs). As the DVM and DLM are not co-activated in flight, this method essentially produces a single signal, which is a superposition of two, opposite-polarity, single-point recordings from the two muscles. The DLM and DVM signals can then be distinguished during the analysis stage by comparing recorded EMGs with corresponding video data; DLM signals precede downstroke while DVM signals precede upstroke (Kammer, 1967). Although this is an unconventional electrode configuration, it reduces the number of required implantations, the handling time and the additional mass the moth must carry (Wang et al., 2008).

Three high-speed video cameras (two Phantom v7.1 and one Phantom v5.1; Vision Research, Wayne, NJ, USA) operating at either 500 or 1000 frames s^–1 (shutter duration between 700 and 990 μs) recorded the moths. A set of eight custom-made high-intensity LED lamps provided additional near-infra-red (760 nm) illumination. The camera activity signal, recorded with the same analog-to-digital acquisition system as the electrophysiological data, provided temporal synchronization between video and EMG data.

The cameras were calibrated for 3D kinematic reconstruction via a direct linear transform and kinematics acquired using the DLTdv5 package for MATLAB (Hedrick, 2008). We reconstructed the moth’s yaw orientation for each video frame from the head and abdomen positions (Fig. 4), filtered using a smoothing spline with error tolerances provided by the 3D reconstruction error in the three-camera stereo array (Hedrick, 2008). Differentiation of the resulting spline polynomials provided yaw velocity and yaw acceleration, allowing us to extract kinematic values at specific times (e.g. yaw velocity at the beginning or end of a wingstroke, with beginning and end defined by DLM activation as described above).

Following implantation, the moths were allowed to recover for a minimum of 1 h, after which they were placed inside a 0.7×0.7×0.7 m chamber and recording commenced. We elicited flight by presenting natural and artificial flowers and/or applying gentle pressure to the moth’s abdomen. Once active, we allowed the moth to fly in a self-selected fashion while continuously acquiring video and EMG data. Moths that were unable to achieve flight performance similar to that exhibited in training, as a result of additional mass from the implant, motion constraints imposed by the signal wires, substantial handling during the implantation process or some other factor, were given a further recovery period or discarded. We saved only recordings in which the moth demonstrated a substantial yaw turn with minimal additional manoeuvring and without external interference such as physical contact between the moth’s proboscis and the flower.

The basic observational unit in this study is a time series of successive wingbeats. For each wingbeat, we considered initial and final yaw velocities along with muscle activation timing differences. Different time series of varying lengths were obtained from the same individual on different occasions (trials) as well as from different individuals. To assess the effects of initial velocity, phase differences in the DLM and phase differences in the DVM on the final velocity reached by the moth during each wingbeat, we fitted a linear mixed-effects model using the nlme package of R 2.12 (Pinheiro et al., 2009; R Development Core Team, 2011). Using these data for all individuals and trials, we fitted four mixed models: damping-dominated (predicts final velocity, ω_n,final, from only muscle activation, Δφ_n,DLM and Δφ_n,DVM), inertia-dominated (predicts ω_n,final from initial velocity, ω_n,initial, and muscle activation, Δφ_n,DLM and Δφ_n,DVM), a control–neutral, or null, model (predicts ω_n,final from ω_n,initial only), and a combined model (predicts ω_n,final from both muscle activation, Δφ_n,DLM and Δφ_n,DVM, and ω_n,initial). We then compared the predictive power and Akaike’s information criterion (AIC, see below) of each model to judge which most accurately reflected the actual control relationship. A detailed explanation of the formulation of each of these models from Eqns 1, 2, 3, 4, 5 is given in the Appendix.

To address the repeated measures within trials and to account for the unbalanced nature of the data, we used a random intercepts model in which observations coming from the same moth were assigned the same random effect (Pinheiro and Bates, 2000). Although trials were also nested in moths, we did not assign a random effect to trials because all trials tend to have a non-zero average yaw velocity, which is removed by a per-trial random factor. As non-zero average yaw velocities are consistent with both damping and inertia-dominated motion models, we left them intact by restricting random factors to moths only. The data also did not support treating additional parameters beyond the intercepts as random.

Models were fitted using maximum likelihood and the best predictor set was determined using AIC, an information-theoretic measure in which a model’s log-likelihood is penalized by the number of estimated parameters used (Burnham and Anderson, 2002). The best model among a set of candidate models is the one with the smallest AIC value. Analysis of the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the level-1 residuals of the AIC best model revealed a significant temporal autocorrelation that approximated a first-order auto-regressive AR(1) process. Consequently an AR(1) correlation structure for the residuals was added to each of the random intercepts models. In the final model, all the reported terms were judged statistically significant at α=0.05.

Using bilateral combined DLM/DVM recording techniques, we examined 5 individuals making 22 yaw turns over a total of 455 individual wingbeats. Recorded manoeuvres included stationary hovering, and both left and right yaw turns with maximum speeds distributed between 0 and 1000 deg s^–1. Fig. 5 shows representative data from a single trial.

We found statistically significant correlations in each of our candidate models (Table 1). However, the fit of each of these models to the observed kinematics varied greatly.

The damping-dominated model, which represents a case where neuromuscular input is directly proportional to yaw velocity, found that final yaw velocity was significantly associated with both DLM activation phase difference (LME, t=3.457, P=0.0006) and DVM phase (LME, t=7.363, P<0.0001, Table 1). Despite statistical significance, this model performed poorly when compared with the moth’s actual motion (Fig. 6A).

The inertia-dominated model, which represents a system where damping does not significantly influence rotational acceleration, found that DVM activation phase difference had a significant effect on final yaw velocity (LME, t=3.423, P=0.0007). In this case, however, DLM phase difference was not significantly associated with the model (LME, t=0.004, P=0.997, Table 1). Again, despite the statistical significance of the correlation, this model also weakly predicted the observed motion (Fig. 6B). Note that the inertia-dominated model includes the initial yaw velocity of each wingbeat. However, there is no coefficient associated with this term so it does not contribute to the AIC.

The control–neutral model, which uses only initial velocity to predict final velocity, disregarding muscle activation data, found that initial velocity was significantly correlated with final velocity in these data (LME, t=26.528, P<0.0001, Table 1). Although this model does not consider any input from the moth’s neuromuscular system, it fits the observed kinematics better than the previous two models (Fig. 6C).

Finally, the combined model, which includes both muscle activation timing differences and initial velocity as predictors of final velocity, found that all three predictors were significantly correlated with the final velocity for that wingbeat (LME, initial velocity: t=23.472, P<0.0001; DLM: t=2.420, P=0.016; DVM: t=6.807, P<0.0001; Table 1). The sign of the coefficients for DLM and DVM activation timing differences both indicate that asymmetric activation is associated with a turn towards the muscle that was activated first (e.g. activation of the right DVM before the left DVM is correlated with a turn to the right). This model yields the best overall fit to the moths’ observed motion (Fig. 6D) and also had the smallest (i.e. best) AIC (Table 2). Thus, among the models presented here, it best represents the relationship between the moths’ neural inputs and turning behaviour. Data from all measurements used in these models are available in supplementary material Table S1.

In this study, we correlated flight muscle activation timing differences with behavioural kinematics in freely flying moths to determine how passive damping influences the control of planar yaw turns. We tested our initial hypothesis that passive damping from FCT reduces yaw control to a damping-dominated regime where muscle torques directly prescribe final angular velocity on a wingbeat by wingbeat basis by fitting a linear model (A) associating observed yaw manoeuvring velocities with muscle activation timing differences alone. We also tested additional models that fitted manoeuvring velocities (B) from muscle activation in conjunction with initial wingbeat velocity, (C) from initial yaw velocity and a damping coefficient (a control–neutral model), and (D) from both damped initial velocity and muscle activation. The poor fit of models A and B where kinematics are associated with muscle activation alone (Table 1, Fig. 6) suggests that flapping-flight yaw turns lie in neither an extreme damping nor inertia-dominated control domain. Instead, our data best support mixed control model D where the animal produces momentary torques that lead to within-stroke accelerations but simultaneously experiences substantial damping. Inclusion of this damping in a neuromechanical model of flight control is crucial for interpreting the effect of neural outputs on manoeuvring flight. Analyses that consider only the neural data explain little of the overall behaviour (Fig. 6A,B), as much of the observed dynamics are due to damping (Fig. 6C).

Our findings are consistent with mathematical models for FCT that predict a damping half-life of 0.7 wingbeats for M. sexta (Hedrick and Robinson, 2010), matched by the values of 0.72 and 0.65 for the velocity coefficient in statistical models C and D, which include a damping term (Table 1). However, this result is somewhat surprising because the moths are neither exploiting damping forces to simplify turning control on a wingbeat to wingbeat time scale nor avoiding the potential increase in locomotor energy requirements caused by constant damping.

The importance of both damping and inertial effects in the neuromechanics of hawkmoth yaw turns has several possible explanations, including the following. (1) FCT damping is an inherent feature of flapping flight that is undesirable from a manoeuvring and efficiency standpoint, but reducing FCT is costly for other reasons. For instance, reducing damping might require changes to morphology that increase the inertial power requirements of flight (Weis-Fogh, 1973) or produce other undesirable consequences. In this case, we expect similar control relationships among flying animals regardless of flight performance requirements. (2) Alternatively, damping and inertia-dominated systems represent the two extremes of a scale where an animal trades manoeuvrability for stability. Thus, the moth’s position at the midpoint of the two extremes may represent a compromise between providing stability against external perturbations and simultaneously providing adequate manoeuvrability to fly in a cluttered environment and avoid predators. In this case, neuromechanical control relationships and their interaction with damping are likely to vary widely among species.

The degree to which animals exhibit damping or inertia-dominated neuromuscular to manoeuvring relationships also depends on the time scale of damping as compared with manoeuvring inputs. In the case of a moth, damping occurs on approximately the same time scale as a single wingbeat, the time scale at which the moth varies its neuromuscular inputs (Fig. 5). However, this ratio may vary substantially among all flying animals. Fruit flies and other insects with asynchronous flight muscle may have only limited neuromuscular control of individual wingbeats (Heide, 1983), while bats and birds may vary neuromuscular activity within a single wingbeat (Warrick et al., 1998). However, birds and bats also experience greater damping in a non-dimensional time scale than fruit flies (Hedrick et al., 2009). In general, we expect that reducing passive dynamics time scales via the introduction of damping or self-correcting mechanisms such as those due to FCT or demonstrated in simulations of rapid hexapedal locomotion (Kubow and Full, 1999) will favour damping-dominated control of locomotion, but faster neuromuscular time scales would favour inertia-dominated control. Thus, the trends in neuromuscular and body dynamics time scales in flying animals act in opposite directions, leaving open the question of whether the damped neuromuscular control relationship found here is typical of most flying animals or is particular to M. sexta.

As described above, our results demonstrate an association between DLM and DVM phase differences and turning flight. They do not, however, show that the DLM and DVM directly produce turns, although there is increasing evidence that this is the case. Wang et al. (Wang et al., 2008) found a correlation between DVM activation and changes in the stroke plane angle; Sponberg et al. (Sponberg and Daniel, 2010; Sponberg et al., 2012) directly correlated yaw torque production and DLM phase differences in tethered hawkmoths; and Bozkurt et al. (Bozkurt et al., 2009) observed yaw turn wing kinematics following direct stimulation of the DLM and DVM in tethered hawkmoths. Nevertheless, other flight muscles, most notably the third axillary, have also been correlated with changes in wing flapping kinematics in both tethered and freely flying hawkmoths (Rheuben and Kammer, 1987; Wang et al., 2008) and it is likely that information from these muscles, along with simultaneous information from the DLM and DVM, is required for a full understanding of how hawkmoths create asymmetric aerodynamic forces. For instance, DLM and DVM modulation may occur if additional muscle force is required to produce a yaw torque while simultaneously maintaining the same average lift on the left and right wings. However, even in these scenarios where a suite of muscles is co-activated to produce yaw turns, our overall finding that the relationship between neural inputs to the flight musculature remains intact as although the DLM and DVM may not be directly causal to turning, they are a necessary part of it.

This finding represents a departure from the traditional categorization of muscles as either ‘power’ or ‘steering’ in synchronous fliers such as Lepidoptera. The traditional categorization may, however, still be appropriate for asynchronous fliers (e.g. dipterans, hymenoptera) as their wingbeat frequency exceeds the maximum rate of neurogenic activation, making direct associations between DLM or DVM timing and manoeuvres unlikely.

It remains to be shown how advancing the activation of indirect flight muscles can produce asymmetric aerodynamic forces in free flight. An investigation, conducted while the moth is engaged in stationary hovering, where the natural activation of the DVM is overwritten with an artificial signal (e.g. Sponberg et al., 2011) would permit correlation of within-wingbeat body and wing kinematics with muscle activation phase. By stimulating only the indirect flight muscles, we may be able to isolate their effects from those of the typically co-activated direct flight muscles. Similar investigations, conducted on a wide range of flight muscles, may reveal the extent to which each muscle contributes to a variety of behaviours.

Here, we present a description of the mathematical models underlying the different yaw turning relationships examined via statistical analysis of observed hawkmoth flight kinematics and neuromuscular activity in this study.

As is shown in Eqn A2, the duration of application of the torque clearly influences our predictions. However, from a practical standpoint, the measured neural inputs of the moth change from flap to flap, but the flap duration was similar throughout the experiment and for all moths (36.7±1.9 ms, n=483, mean ± s.d.). Thus, from this point forward we assume that duration does not vary, i.e. t is constant.

As noted in the Materials and methods, we use the AIC to identify the model that best describes the relationship between the moth’s angular velocity at the end of the flapping cycle, its initial angular velocity, and the activation phase differences between the left and right DLM and DVM pairs. Because the models do not all incorporate the same number of free parameters, it is possible for a model to better fit the final velocity from its inputs but have a worse AIC.

Finally, while the different statistical models do provide grounds for moth-level random effects, i.e. differences among moths, they do not support the use of trial-level random effects as outputs from the underlying physical parameters that may give rise to differences among individuals are not expected to vary among trials from the same individual.

 
• ACF

  autocorrelation function

 
• b_ω

  constant coefficient

 
• DLM

  dorsal longitudinal muscle

 
• DVM

  dorsal ventral muscle

 
• EMG

  electromyogram

 
• FCT

  flapping counter-torque

 
• I

  moment of inertia

 
• n

  nth wingbeat

 
• PACF

  partial autocorrelation function

 
• t

  time

 
• T

  wingbeat period

 
• ΔφDLM

  DLM phase difference

 
• ΔφDVM

  DVM phase difference

 
• θ

  yaw

 
• τ

  torque

 
• ω

  rotational velocity

 
• ωi

  initial velocity

 
• ω_n,final

  final velocity

 
• ω_n,initial

  initial velocity

 
• ωs

  saturation velocity

 
• ω˙

  rotational acceleration

We wish to thank M. Ellis Driver for assistance with figures, Laura Pianowski for assistance in the experiments and video analysis, Jack Weiss for assistance with statistical analyses, and Monica Daley for valuable discussion. Two anonymous referees contributed insightful comments that greatly improved the manuscript. Hawkmoths were provided courtesy of F. Nijhout at Duke University.