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First published online March 2, 2007
Journal of Experimental Biology 210, 1092-1108 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02729
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The extensor tibiae muscle of the stick insect: biomechanical properties of an insect walking leg muscle

Christoph Guschlbauer, Hans Scharstein and Ansgar Büschges*

Zoological Institute, University of Cologne, Weyertal 119, 50923 Cologne, Germany


Figure 1
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  		Fig. 1. Schematic representation of the geometrical arrangement of the femur–tibia joint in the stick insect middle leg. For details see text.

 

Figure 2
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  		Fig. 2. Isometric forces induced in the middle leg extensor tibiae muscle by electrical stimulation of nerve nl3 with different current amplitudes. In all panels the top trace is a stimulus monitor (note pulse height changes as stimulus amplitude was increased), the second trace is an extracellular recording of nerve nl3, and the third trace is muscle force. (Ai–Aiii) Sequential recruitment of FETi (Ai), FETi and SETi (Aii) and FETi, SETi and CI1 (Aiii) recorded in extensor leg nerve F2 in response to single stimuli. (Aiv) An enlarged version of the recordings, showing the sequential addition of new units (asterisks). 1 T=0.0023 mA. (Bi–Biv) F2-recordings and forces in response to a 50 Hz pulse train. (Bi) 75% of the pulses excited FETi and 25% FETi and SETi. (Bii) 50% of the stimuli elicited FETi and 50% FETi, SETi and CI1. (Biii) Recruitment of all three motor units with every pulse. Doubling the current amplitude (Biv) induced no further increase in force. In this experiment the SETi spikes were of larger amplitude than FETi spikes. This is uncommon and likely because nerve F2 was recorded very distally in the femur. In all panels the electrical disturbance in the nerve recording that coincides with the stimulus is a stimulus artifact, not an action potential (arrow in Ai). T, threshold.

 

Figure 3
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  		Fig. 3. (A) Relationship between muscle resting length and femur length in front leg (F; squares), middle leg (M; circles) and hind leg (H; triangles). Filled symbols, extensor tibiae; open symbols, flexor tibiae. The dotted lines give the linear fit under the assumption of pure proportionality between muscle length and femur length. The solid line indicates the 1:1 proportion, for comparison. Values are shown in Table 1. (B) Relation between middle leg muscle resting length and fibre length. Extensor muscle fibre length depends on resting muscle length (P<0.03), whereas no such dependence is present in the flexor muscle (dotted regression lines). Open, fibres in muscle medial regions; filled circles, fibres in muscle proximal regions. Values are means ± s.d. from nine experiments.

 

Figure 4
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  		Fig. 4. Normalised muscle length change as a function of femur–tibia (FT)-joint angle. Extensor data are shown compared with +cos({alpha}), flexor data are compared with –cos({alpha}) (solid lines).

 

Figure 5
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  		Fig. 5. Relation between femur–tibia joint moment arm and femur length. Note that moment arm does not depend on femur length. Closed symbols, data from extensor muscles from two front legs (F; squares), two hind legs (H; triangles), and three middle legs (M; circles); open symbols, data for flexor tibiae muscles from five middle legs (circles) and two front legs (triangles).

 

Figure 6
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  		Fig. 6. Passive forces of the unstimulated, denervated middle leg extensor tibiae. (A) Time course of passive force induced by a ramp stretch of 0.5 mm amplitude in 1 s. Note the dynamic nature of the force change and its subsequent relaxation to a nearly constant value with maintained stretch. (B) Tonic resting force versus muscle length. Data from N=10 experiments (see text for details). Please note that the number for individual means can differ (6≤N≤10).

 

Figure 7
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  		Fig. 7. (A) Average time course of a single twitch of the extensor tibiae (n=43). (B) Force development generated upon repetitive stimulation with differing stimulation frequencies between 30 Hz and 200 Hz (see values in Table 2). Broken line, resting force level.

 

Figure 8
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  		Fig. 8. Isometric force (mN, left ordinate) as a function of muscle stretch (mm, lower abscissa) and relative fibre length (top abscissa) in the middle leg extensor tibiae of nine individuals. Values for (A) single twitch (N=8), (B) 50 Hz (N=9) and (C) 200 Hz (N=9), see maximum values in Table 3. For comparison with other muscles, the right ordinate shows stress (N cm–2). The working range from 180° (fully stretched joint angle) to 30° (maximally flexed joint angle) is marked. Please note that the number for individual means can differ; for single twitch measurements 3≤N≤9, for 50 Hz and 200 Hz measurements 5≤N≤9.

 

Figure 9
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  		Fig. 9. Two extreme examples of extensor tibiae muscle single twitch and tetanical forces as a function of muscle stretch. With increasing stimulation frequency, the maximum force in A moves markedly towards lower values of fibre length while the shift in B is much less prominent. Axes as in Fig. 8.

 

Figure 10
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  		Fig. 10. The loaded release experiment. (A) Response of a tetanically activated muscle to a switch from isometric to isotonic conditions with counterforces less than the force the muscle had developed during its isometric contraction (see different `Force' traces). (B) The muscle shows an abrupt length change (bracket `a') followed by a smooth, initially linear contraction (b; see text for details).

 

Figure 11
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  		Fig. 11. (A) Variability of the force–velocity characteristic (Hill hyperbola, see Materials and methods for details) of the extensor muscle (see values in Table 4). Different symbols represent different animals. (B) Deviation of the force–velocity curve from hyperbolic shape in the region of P/P0 between 0.6 and 1 for one typical experiment (open circles). In the region P/P0>1, force–velocity measurements are shown under stretch (filled circles, data from six experiments) to demonstrate the sigmoid zero crossing of the Hill hyperbola. The force axis was normalised to the maximum isometric contraction force P0. See text for details.

 

Figure 12
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  		Fig. 12. Length dependence of maximum contraction velocity V0 in two experiments. One experiment (filled symbols) was done at 200 Hz and at 50 Hz stimulation frequency. The other experiment (open symbols) was done only at 200 Hz (see text for details).

 

Figure 13
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  		Fig. 13. Hill curves at different stimulation frequencies from one animal (see values in Table 5).

 

Figure 14
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  		Fig. 14. Dependence of the parameters of the Hill curve on stimulation frequency. (A) Dependence of the isometric force P0 on stimulation frequency (N=11). (B) Dependence of maximum contraction velocity V0 on stimulation frequency (N=5). In both A and B the data from each experiment were fitted by an exponential saturation function leading to the same mean `frequency-constant' of about 60 Hz for both dependencies. The dotted lines show the shallowest and steepest fits and the bold lines show mean ± s.d. Please note that the number for individual means can differ (in A, 6≤N≤9; in B, 4≤N≤5). (C) Coupling of maximum contraction velocity V0 with isometric force P0 under variation of stimulation frequencies (N=5). The values of each set of experiments are marked by connecting straight lines. For all individual experiments the data showed a significant correlation (P<0.03). Note that the maximum values V0 and P0 at 200 Hz for each experiment roughly determine the overall slopes of the diagrams. See text for details.

 

Figure 15
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  		Fig. 15. Nonlinear spring-characteristic of the series elasticity. (A) Fast length change in the loaded release experiment starting from different tetanical force levels; change in force over the resultant change in length. (B) Common parabola fit for all shifted curves in A. The respective starting values are marked by circles. See text for details.

 

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© The Company of Biologists Ltd 2007