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First published online June 15, 2006
Journal of Experimental Biology 209, 2535-2553 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02276
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Storage and recovery of elastic potential energy powers ballistic prey capture in toads

A. Kristopher Lappin*, Jenna A. Monroy, Jason Q. Pilarski, Eric D. Zepnewski, David J. Pierotti and Kiisa C. Nishikawa*,{dagger}

Department of Biological Sciences, Northern Arizona University, Flagstaff, AZ 86011-5640, USA


Figure 1
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  		Fig. 1. (A) Force-lever setup and (B) in situ jaw–joint preparation for measurement of contractile and elastic properties of the depressor mandibulae muscles.

 

Figure 2
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  		Fig. 2. Cranium and lower jaw of Bufo showing the mouth-opening muscle (depressor mandibulae=DM) and the largest of the mouth-closing muscles (levator mandibulae posterior longus=LM). The jaw joint is indicated by a white circle, and the in- and out-levers are indicated by white bars. Contraction of the depressor mandibulae (upward arrow) produces rotation of the lower jaw about the joint (downward arrow).

 

Figure 3
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  		Fig. 3. Change in length of a depressor mandibulae muscle vs time during a load-clamp experiment. When the load is reduced (t=0), the muscle exhibits a fast phase of shortening and a slow phase of shortening with oscillations during the transition. To define the fast to slow phase transition (red circle), a line representing shortening during the slow phase, and bisecting the oscillations, was extrapolated back to its initial intersection with the length trace. Fast phase displacement is defined as the change in length that occurs from the initial position (t=0) to this point of intersection. This trace corresponds to Ba 1 ({Delta}F=2.82) in Fig. 8B.

 

Figure 4
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  		Fig. 4. Elastic recoil model of the toad cranium. The model includes the pair of depressor mandibulae muscles, which originate on the cranium (ground) and insert on the retroarticular processes of the lower jaw. Each muscle (red) was modeled as a force generator (i.e. cross bridges) and a spring (i.e. series elastic component) arranged in series. On each side of the cranium, the depressor mandibulae muscle is arranged in series with an extra-muscular spring element (blue) that represents the sum of all extra-muscular structures that are strained by contraction of the depressor mandibulae prior to movement (i.e. cranium and retroarticular process). The effective mass (meff) is suspended from these springs. Effective damping (beff) of the mass-spring system is depicted in purple.

 

Figure 5
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  		Fig. 5. (A) Fit between observed and predicted displacement (xt) vs time. Displacements from two trials (high effort and low effort) are shown for two toads. Colors represent different individuals. For each toad (N=4), effective mass (meff) was estimated from anatomical data. For each feeding trial (N=71), total displacement (xt) vs time was estimated from digital images. The time solution for the general equation of motion (Eqn 3) was solved to find the values of the spring constant (kt) and damping coefficient (beff) that provided the best fit (dotted black lines) to the observed kinematic data. (B) Maximum instantaneous in vivo power output of the depressor mandibulae muscles and series connective tissues during ballistic mouth opening. Colors represent different individuals.

 

Figure 6
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  		Fig. 6. (A) Gape profile during prey capture (black line) synchronized with EMG activity of the depressor mandibulae (DM, red) and levator mandibulae posterior longus (LM, blue). The ballistic phase of mouth opening is completed during the first 20 ms and is followed by slower mouth opening as the prey item is transported into the oral cavity. The depressor mandibulae exhibits a large burst of activity that precedes the onset of movement by up to 250 ms, and a smaller burst that accompanies the increase in gape angle during prey transport. The levator mandibulae shows low-level activity before movement, followed by a large-amplitude burst during mouth closing. Neither muscle is active during ballistic mouth opening. (B) Examples of depressor mandibulae activity during a trial with a smaller total displacement (xt=2.8 mm, 0.16 ML, above) vs a trial with a larger total displacement (xt=3.3 mm, 0.19 ML, below). Both trials are from the same toad (Ba 2). During the trial with the larger total displacement, the depressor mandibulae exhibits greater amplitude and a longer duration of activity prior to movement than during the trial with the smaller total displacement. Vertical lines delineate the ballistic phase of mouth opening. (C) Relationship between total integrated area of depressor mandibulae activity (mVs) preceding movement and total displacement (mm) during ballistic mouth opening (N=2). (D) Relationship between distance to prey (cm) and duration of depressor mandibulae activity prior to movement (N=4). Colors represent different individuals.

 

Figure 7
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  		Fig. 7. (A) Length–tension curves for the depressor mandibulae muscle (N=3). At resting length (arrow), the muscle is at its optimum length (L0), and a small amount of passive tension (~0.1 N) is present. Below resting length, active and passive tension decline rapidly. Colors represent different individuals (lines are best least-squares fit to third-order polynomials). Black dotted line represents mean for all individuals combined. (B) Force–velocity curves for the depressor mandibulae muscle (N=3). For the three individuals, Vmax was 3.74, 3.62, and 3.48 ML s–1. P=observed force, P0=maximum isometric force, V=observed velocity, Vmax=maximum shortening velocity. Colors represent different individuals (lines are best least-squares fit to Eqn 7). Black dotted line represents mean for all individuals combined.

 

Figure 8
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  		Fig. 8. Original data from 200 ms load-clamp experiments. (A) Change in length, force and stimulation (black line) vs time for load-clamp trials at a high clamp force (2.60 N, blue lines) and a low clamp force (0.31 N, red lines). The depressor mandibulae muscles were stimulated isometrically for 200 ms before the load was reduced. (B) Original records of force (left) and change in length (right) vs time from load-clamp experiments (N=3 toads). Numbers to the right of the force traces indicate change in load ({Delta}F). Note that length traces (right) begin 200 ms after the onset of muscle stimulation.

 

Figure 9
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  		Fig. 9. Elastic properties of the depressor mandibulae muscles. Red lines: 200 ms muscle stimulation prior to load clamp (N=3). Blue lines: 50 ms muscle stimulation prior to load clamp (N=2). Purple line: 100 ms muscle stimulation prior to load clamp (N=1). (A) Change in force ({Delta}F) vs displacement (xm) of the depressor mandibulae during load-clamp experiments. (B) Spring constant (km) as a function of the change in force ({Delta}F) during load-clamp experiments. (C) Linear regressions between coefficients c1 (N) and c2 (kg s–2) and muscle force (N). The coefficients describe the shape of the exponential function relating xm to {Delta}F (Eqn 9). Dotted lines show 95% confidence intervals for the regression slopes.

 

Figure 10
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  		Fig. 10. Elastic properties of extra-muscular connective tissues. (A) Time course of depressor mandibulae shortening, which equals total stretch of extra-muscular connective tissues at the origin and insertion, measured using digital imaging during in situ muscle stimulation. (B) Depressor mandibulae force vs depressor mandibulae shortening. The slope is equal to the spring constant of the extra-muscular connective tissues (ke), which averaged 1300 N m–1. (C) Relative depressor mandibulae shortening (L/L0) as a function of relative muscle force (P/P0). Colors represent different individuals (N=3). Black dotted lines in B and C represent mean for all individuals combined.

 

Figure 11
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  		Fig. 11. Transmission electron micrograph of depressor mandibulae sarcomeres at resting (= optimal) length. The sarcomeres are short (~1.5 µm) compared to those of typical vertebrate skeletal muscles. The A-band (double-headed arrow) is also proportionately shorter (~1.0 µm) so that the relative overlap of thick and thin filaments is similar to that of a typical vertebrate skeletal muscle at L0. Scale bar, 1 µm.

 

Figure 12
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  		Fig. 12. (A) Displacement (xm, xe, xt) predicted by the elastic recoil model as a function of the force developed by the depressor mandibulae muscles prior to movement. At all but the lowest forces (>0.25 N), the depressor mandibulae muscles (xm) contribute more to total displacement (xt) than the extra-muscular connective tissues (xe). (B) Load-dependence of the relationship between depressor mandibulae force prior to movement (Fbefore) and total stiffness (kt). The loads illustrated include 10 times the in vivo load (0.89 N, blue line), 5 times the in vivo load (0.45 N, brown line), twice the in vivo load (0.18 N, yellow line) and the observed in vivo load (0.09 N, black line), half the in vivo load (0.045 N, green line), and one tenth the in vivo load (0.009 N, red line). (C) Observed vs predicted relationship between the depressor mandibulae force prior to movement (Fbefore) and total stiffness (kt). The solid line shows the total stiffness predicted by the elastic recoil model at the in vivo load. Dotted lines represent the 95% confidence interval. Colored symbols show the observed relationship between depressor mandibulae force prior to movement (Fbefore) and total stiffness (kt) for each individual toad (mean ± s.e.m.) estimated by fitting the observed kinematic data to Eqn 3.

 

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© The Company of Biologists Ltd 2006