Medium compensation in a spring-actuated system

Diverse biological systems, including locusts and mantis shrimp, use latch-mediated, spring-actuated systems to generate movements with incredibly high speeds and mechanical power (Gronenberg, 1996; Ilton et al., 2018; Patek et al., 2011; Rosario and Patek, 2015). The speeds of these systems are often so fast that neural feedback is insufficient to change the behavior once the loaded spring is released. The 1–2 ms timeframe of these movements necessitates use of open-loop neural control to set the speed and direction of the behavior prior to de-latching the spring (Burrows, 2006; Kagaya and Patek, 2016; Patek et al., 2006). Mantis shrimp (stomatopods), in particular are known for their ability to propel a specialized pair of spring-actuated maxillipeds (raptorial appendages) at speeds of up to 30.6 m s⁻¹ (Cox et al., 2014). The strike is used for multiple behaviors including predation, agonistic combat and defense, and its output force can be tuned according to these different tasks (Green et al., 2019). Like other spring-actuated biological systems, in mantis shrimp the movement is preceded by first latching the raptorial appendages in place before co-contracting large muscles that store potential energy in spring-like, cuticular structures (Rosario and Patek, 2015). When the latch disengages, the spring releases, converting the stored energy into rotational movement of the striking appendages (Fig. 1). In other systems with spring-actuated movements (such as locusts, froghoppers and fleas), elastic energy is completely transmitted to kinetic energy (Bennet-Clark, 1975). Given that mantis shrimp use similar mechanics to other spring-actuated systems, we hypothesized that the same amount of energy would be stored prior to strikes deployed for a single behavioral task. A fundamental difference between mantis shrimp strikes and other systems, however, is that mantis shrimp strike in water rather than in air. By measuring the speed of strikes in air and in water, our hypothesis predicts that strikes in air (not slowed down by viscous water drag) will be faster than those in water. Unexpectedly, the exact opposite was observed.

Live, healthy mantis shrimp of the species Squilla mantis (Linnaeus 1758) were purchased from local fishermen in Andalucia, Spain in January 2018. Animals were captured using traditional fishing methods and maintained in a large bucket of seawater until purchase, then transported to Málaga, Spain and housed in filtered seawater aquaria. All experiments were conducted within 1–2 days of collection on six females and one male, all from the same collection.

Lightly restrained mantis shrimp were held in a fixed position and mechanically stimulated to strike in air, then in water (or the reverse) by adjusting the water level in the aquarium. Neither animal nor camera were moved between treatments. High-speed video (HSV) cameras (5000 frames s⁻¹, 1024×640 pixel resolution, Photron SA2 model 86K-M4, San Diego, CA, USA) were positioned lateral to the animal to record strikes. Approximately 2.5 cm of space lay between the animal and the aquarium glass, minimizing magnification effects of the image from the addition of water. Videos were captured and saved using Photron FastCam Visualization software (v.3.6.9.0) run on a PC laptop (Gigabyte P34 Geforce GTX 1050). Only strikes generated by the appendage ipsilateral to the camera were analyzed. The order by which each animal experienced different media was randomized among the seven individuals tested. A minimum of five strikes were recorded per animal in each medium condition (water or air), although only strikes that exhibited the initial sliding motion of the carpus (Fig. S1) – indicating release of the latch mechanism – were analyzed (Patek et al., 2007). One animal was tested in water, then air, then back to water because of its robust participation in the experiment. This was also the only male tested.

Each individual was mounted on a gimballed platform (Nootle, Grifiti LLC, Sausalito, CA, USA), ventral surface up (supine position). A partial restraint was developed to control for variation in body posture between strikes induced in different media (air and water). In a restrained prone position, the raptorial appendages passively open under gravity. Supine restraint allowed the raptorial appendages to remain in a consistent, folded position. Padded, plastic-coated wire restraints were used to fix the animal to the gimballed platform at two points: the first pair of walking legs and the telson. This restraint only restricted movement in the posterior abdomen, leaving the thoracic carapace and maxillapeds free. The restraints were also placed outside the range of the pleopods, so fanning and respiration could occur. The gimballed platform was adjusted to ∼45 deg angle to allow the pleopods to remain submerged. The mounted animal was placed in a small (∼20 liter) aquarium containing enough seawater to cover the abdomen and gills (air treatment) or completely submerge the animal (water treatment). Strikes were elicited by mechanical stimulation to the abdomen with a 4-mm-diameter fiberglass stick, eliciting reproducible, defensive-type strike responses. All animals were in good health upon completing the experiment.

Strike videos were saved in Tiff stack format and opened in ImageJ (Fiji; Schindelin et al., 2012). Using the ImageJ plugin MTrackJ (Meijering et al., 2012), two points on the propodus and two points on the merus were manually tracked using natural landmarks and/or a small piece of black nylon glued to the appendage. The change in angle between the two lines described by points 1–2 and 3–4 (Fig. 1) was used to calculate the angular velocity of the rotating appendage during each strike using R code modified from the literature (Kagaya and Patek, 2016; McHenry et al., 2016). A polynomial function of 10 was fit to the resulting angular rotation data over time. Angular velocity was calculated as the first derivative of the smoothed rotation curve. Angular acceleration was calculated as the second derivative of angular rotation as a function of time. Movement of the carpus during a strike was measured as a function of linear distance over time between two points digitized on the merus and carpus (Fig. S1A–D). Start times for both carpus slide and propodus rotation were quantified as time of peak acceleration for each movement. The difference between the start time of propodus rotation and carpus slide was then calculated as a metric (C_T) to quantify carpus sliding (Fig. SA–C).

As animals survived beyond the experiment, the exact masses of each segment of the raptorial appendage could not be measured. Instead, masses of the merus, propodus and dactyl were estimated from mass and dimensional data compiled from additional S. mantis specimens. Morphometric measurements of limb features and the total wet mass of each measured limb segment were collected from 12 individuals additional to those recorded in the strike experiment. Each limb segment mass was plotted vs the dimensional measurements and fit to a linear regression (R²>8.3; Fig. S1). The morphometric dimensions were selected based on their lateral visibility in video recordings of mantis shrimp strikes. The raptorial limb dimensions of individuals used in the strike experiment were then measured using calibrated still frames from the high-speed video data. These measurements were used to estimate mass via the linear regression equations (reported in Fig. S1). Due to differences in merus size, a metric of meral width multiplied by meral saddle width was used to evaluate mass.

Power was calculated by dividing the peak kinetic energy during the strike by the time between the initial movement of the propodus and the time of peak angular rotation (the acceleration time). The time between the initial motion and the moment that the propodus reached its highest angular velocity is thus the ‘launch’ time for this latch-mediated spring-actuated system (Longo et al., 2019). Paired t-test statistical analyses were performed in R to assess the mean differences in strikes performed in air vs water (n=7).

A total of 31 strikes in air and 36 strikes in water were recorded and analyzed from seven animals, with individual energetic parameters being estimated by generating a mean for each individual animal, and then the means of the seven animals calculated here. The number of air and water strikes measured by individual and their associated kinematics are reported in Table S1. The majority of the specimens were female (six) with only one male represented, owing to random collection of specimens.

When striking in air, S. mantis propels its limb with a mean peak angular velocity of 8250±1980 deg s⁻¹ (tip velocity 5.0±1.1 m s⁻¹; Table 1, Fig. 2B). When striking in water, the rotating limb is propelled almost twice as quickly 14,140±3750 deg s⁻¹ (tip velocity 8.7±1.3 m s⁻¹; Table 1, Fig. 2C). Water strikes therefore have three times more kinetic energy than air strikes (15.5±8.6 mJ vs 5.0±2.4 mJ in water vs air) and almost five times the power (2.0±1.2 W vs 0.42±0.28 W in water vs air) (Table 1, Fig. 2D–G). No evidence of fatigue effect (such as decreased strike velocity) was observed among sequential strikes performed by any individual (Fig. 2A). Paired t-tests revealed significant differences between air and water strike velocity (P=1.1e−04) and acceleration (P=1.5e−07). Significant differences in power were observed during the strike launch (initiation of movement to the moment of peak velocity, corresponding to spring actuation; P=2.2e−02). Although takeoff power (time from peak velocity to the end of the strike, corresponding to movement not actuated by the spring) presents a similar trend to launch power, the difference was not significant in this dataset (P=7.9e−02; Fig. 2H).

The power per muscle mass of water strikes (1144±604 W kg⁻¹, N=7; range=364–1936) indicated that S. mantis use an elastic storage system since these values exceed the power output limit of high power muscle (∼400 W kg⁻¹, Askew and Marsh, 2002). Air strikes, however, yielded significantly less power, suggesting that an elastic storage system may not be used during these strikes. However, we cannot rule out the use of elastic storage during air strikes for several reasons. First, two of the animals had air strikes with power outputs higher than 400 W kg⁻¹ (485 and 414 W kg⁻¹), indicating that elastic storage was utilized at least twice. Second, our method of evaluating elastic storage overestimated extensor muscle mass (used total limb segment mass) and ignored energy losses to the medium (i.e. underestimated the energy, and thus power density during movement). Third, unlike the very ‘fast’ muscles used to define the 400 W kg⁻¹ limit, the extensor muscles in the merus are not particularly ‘fast’ and can take as long as 700 ms to reach maximum tension (Burrows and Hoyle, 1972; Patek, 2019). This means that the power threshold for S. mantis muscles alone is likely to be much less than 400 W kg⁻¹. Finally, carpus sliding prior to strike rotation is an accepted metric for reporting deployment of an elastic mechanism (Patek et al., 2007). Our quantification of the carpus slide revealed that 100% of strikes analyzed present a carpus movement initiated prior to strike (7.6±5.1 ms). The carpus sliding movement occurs significantly faster during the fastest strikes (>15,000 deg s⁻¹) than the slowest strikes (<8000 deg s⁻¹; P=3.1e−04; Fig. S1C).

If we assume that S. mantis utilized a latch-mediated spring-actuated strike in both air and water strikes, these results can be explained by two possible mechanisms. Either, the force of the mechanical strike system does not transfer as efficiently in air as it does in water, or mantis shrimp modulate the speed of their strike based on the surrounding medium. Given recent findings related to strike modulation in different behavioral contexts (Green et al., 2019), and the current hypothesis as to how this system functions (Rosario and Patek, 2015), it is unclear to us how a difference in medium would change the transmission of energy from elastic structures in the appendage into kinetic energy. Consequently, the latter hypothesis, that the strike speed is modulated, is a much more likely explanation of our findings.

A second result of our experiment is an observed coincidence between the amount of energy S. mantis air strikes produced and the grasshopper latch-mediated spring-actuated jump system. When striking in air, the mantis shrimp accelerates a 1.2±0.21 g limb with a mechanical power output of 0.42±0.28 W, despite the fact that the S. mantis is mechanically capable of generating up to almost 4 W of power (Table 1). The power output of the mantis shrimp, (0.42±0.28 W) is similar to the power output of the similarly sized jumping adult grasshopper, which accelerates 1.5–2.0 g of mass with 0.3–0.8 W of mechanical energy (Bennet-Clark, 1975). Likewise, the kinetic energy output of the mantis shrimp (5.0±2.4 mJ; Table 1) is also similar to that of a single locust leg (4.5–5.5 mJ, (Bennet-Clark, 1975). The similar performances of these evolutionarily divergent systems suggests that there may be a maximum kinetic energy capacity limit for 1–2 g airborne latch-mediated, spring-actuated biological systems. That the mantis shrimp performs strikes at this limit in air, even though it is mechanically able to strike much faster, suggests a hypothesis that faster movements, without media to dissipate excess kinetic energy, may damage the system. Evaluation of other similarly sized latch-mediated spring-actuated systems need to be analyzed to differentiate between this hypothesis or the alternative – that this is just a coincidence.

One of the most remarkable features of biological spring-actuated systems is their ability to load, release and dissipate large amounts of energy such that the system can be used again and again without incurring damage. The huge amount of energy released from a recoiling spring system creates the need for systems to help control the limb and absorb excess kinetic energy. An appropriate limb ‘set up’ minimizes possible errors and prevents damage to the system prior to the initiation of the behavior. In the previously discussed locust leg system, use of the shock-absorbing material resilin serves to spill off any unused kinetic energy when the joint reaches its maximum angle (Bayley et al., 2012). Although mantis shrimp produce one of the fastest spring-actuated movements, the braking mechanism is not currently known. Studies of drag for species with similarly sized raptorial appendages (Lysiosquillina maculata), estimate that the water can absorb 10–20 mJ of energy during a strike (McHenry et al., 2016), predicting that the medium absorbs most of the kinetic energy during a strike in water. Since a shock absorbing mechanism analogous to the locust limb is not known in mantis shrimp raptorial appendages, it is possible that, in air, mantis shrimp may prevent damage to the joint by simply striking more slowly. The similar energetics of stomatopod and locust spring-actuated movements in air provide a good paradigm for investigating properties of the mantis shrimp limb that dissipate residual energy in the absence of both resilin and viscous drag.

In conclusion, we show that the surrounding medium affects output forces generated during mantis shrimp strikes. Our findings contribute to growing evidence that mantis shrimp precisely control strike output behaviors, despite their ‘feed forward’ control. To control such behaviors, an assembly of information from both the external environment and internal muscular state must be processed to predict the consequences of a strike prior to execution. In both the air and water strikes, the animals struck at open space in response to posterior prodding. Defensive strikes executed from freely moving S. mantis individuals perturbed anteriorly with a stick, might be even faster than defensive water strikes from restrained individuals. Mantis shrimp may engage faster, more powerful strikes when they receive sensory feedback that describes both sufficient medium viscosity and an impact target to absorb excess strike energy. We subsequently propose the hypothesis that the surrounding medium and strike target work together as external shock absorbers for mantis shrimp strikes. As research moves forward to characterize the mechanisms underlying strike brakes and power output modulations, the properties of the surrounding medium should also be considered.

We thank Margarita Paloma Bellido Martin and Enrique Gonzalez Silva for their generous help in the field; Jacob Harrison for answering questions pertaining to analysis; as well as Sheila Patek and Malcolm Burrows for feedback and discussion.