First published online August 31, 2007
Journal of Experimental Biology 210, 3147-3159 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.005207
Modulation of in vivo muscle power output during swimming in the African clawed frog (Xenopus laevis)
Christopher T. Richards* and
Andrew A. Biewener
Harvard University, 100 Old Causeway Road, Bedford, MA 01730,
USA
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Fig. 1. Electrode implantation and force transducer calibration. (A) Anatomy of the
plantaris longus in the X. leavis hindlimb showing implantation of
electrodes. Muscle activity and changes in muscle fascicle length were
measured by bi-polar EMG electrodes and sonomicrometry crystals, respectively.
Plantaris longus force was measured by a strain gauge force transducer (inset)
tied to the inner surface of the Achilles tendon (see text for further
details). (B) Representative tendon force transducer calibration (frog 5). The
foot was removed from the animal and the plantaris muscle was mechanically
isolated from proximal tissues (see text) allowing the muscle–tendon
unit to be mounted in-line with a calibrated load cell in a simple jig. (C)
The data record shows force from the calibrated load cell (broken line) and
the voltage output from the force transducer (solid line) for a series of
loading cycles. (D) Load cell force is plotted against force transducer output
to show the linear response of the force transducer over the cycles shown in
C.
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Fig. 2. Representative patterns of swimming velocity and acceleration for frog 6.
(A) Moderate speed swimming. Velocities (top) and accelerations (bottom) for
four consecutive stroke cycles showing increasing velocity and acceleration
digitized from the video sequence of a single trial. (B) Vigorous swimming.
Velocities (top) and accelerations (bottom) for four stroke cycles from a
contrasting trial of the same frog showing a rapid escape stroke followed by
three high velocity strokes. Numbers above each acceleration peak represent
the plantaris muscle mass-specific power output (W kg–1) for
each cycle.
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Fig. 3. (A) Representative data recordings of plantaris longus force (red),
whole-muscle length (blue), and activation (black) from a single burst
swimming trial of frog 5. Broken lines on the length and force traces
represent resting muscle length (Lrest, measured when the
animal was unmoving in the aquarium) and resting force, respectively. Vertical
dotted lines (1–5) illustrate kinematic stages defining the stroke
cycle. The ankle joint is highlighted in red. A swimming stroke begins with a
propulsive phase characterized by rapid joint extension (1–3). The
recovery phase that follows (3–5) prepares the limb for the next stroke
by returning the leg to its initial configuration. (B) Expanded view of data
record in A to show a single stroke cycle. (C) Four in vivo work
loops (representing four consecutive swimming strokes) are plotted directly
from force–length data shown in the data traces in A. The colored bars
above the length trace shown in A match the work loop colors to show how the
force–length data were partitioned to calculate work and power. Muscle
power (W kg–1 muscle) is shown for each stroke.
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Fig. 4. (A) Data recordings of plantaris longus force (red), whole-muscle length
(blue), and activation (black) from frog 4 to show the maximum differences
observed between individual animals (compare with
Fig. 3A). (B) Diagram showing
the variation in the relative timing of force–length activation events
among swimming strokes for frog 5. Note that force develops passively at the
end of the previous cycle, as the limb is being protracted and the ankle and
knee are flexed.
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Fig. 5. Box-and-whisker diagram showing the variability of muscle performance
parameters within and among individual frogs. For each performance parameter,
the coefficient of variation (CV) was found from the data for each frog. The
boxes represent 50% of the data range and the whiskers bracket the
interquartile range of observed data compared across individuals. Bold
horizontal bars represent the median CV found among frogs. High median CV
values indicate large variability within individual frogs, whereas broad boxes
signify high variability among individuals.
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Fig. 6. (A,B) Scatter plots showing the variation in plantaris power output as a
function of cycle duration (A) and work (B) for all six individuals. (C,D)
Plots for power vs cycle duration (C) and power (D) vs cycle
work for frog 5, to exemplify trends seen within individuals. Regression lines
for each individual frog were plotted using simple least-squares regression to
illustrate general trends in the data. Regression lines that are not
statistically significant (tested separately by multiple least-squares
regression) are not shown. Solid and broken regression lines (where shown)
correspond to data represented by solid circles and open circles,
respectively. Partial coefficients of determination (r2)
were calculated from partial least-squares regression and path analysis to
account for variance explained by interaction between independent variables
(see text). For clarity, regression lines are omitted from A.
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Fig. 7. A statistical model explaining the relationships of all measured muscle
performance parameters in relation to muscle power output. (A) Path diagram
summarizing the results from three separate multiple regression tests. Arrows
pointing from each independent variable to a dependent variable represent
relationships revealed by one multiple regression test. Colored arrowheads
identify the three separate tests. Test 1: cycle power vs cycle work
and cycle duration (blue); Test 2: cycle work vs peak stress and
strain amplitude (red); Test 3: peak stress vs EMG intensity and EMG
duty cycle (green). Black numbers above the arrows are path coefficients and
red numbers below the arrows are partial coefficients of determination
(r2=path coefficient x partial correlation
coefficient) describing the fractional variance explained by each covariate.
Values are mean ± s.d. for all frogs that demonstrated a significant
correlation (P 0.05). (B) Reduced path diagram summarizing data
from a single frog (frog 5) indicates that four primary performance parameters
(cycle duration, EMG intensity, EMG duty cycle and strain amplitude) explain
approximately 76% of the variance in plantaris power. Black numbers represent
path coefficients and red numbers partial coefficients of determination; these
are given for each individual frog in Table
3. Independent variables that did not significantly contribute to
the regression model (P>0.05) are not included in the average
values shown on the path diagrams.
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Fig. 8. (A,B) Scatter plots showing the variation in plantaris cycle work as a
function of strain amplitude (A) and peak stress (B) for all six individuals.
(C,D) Plots for work vs strain amplitude (C) and work vs
peak stress (D) for frog 5. Regression lines and partial coefficients of
determination (r2) were calculated in the same manner as
in Fig. 6.
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Fig. 9. (A,B) Scatter plots showing variation in peak plantaris stress as a
function of EMG duty cycle (A) and EMG intensity (B) for all six individuals.
(C,D) Plots for peak stress vs EMG duty cycle (C) and peak stress
vs EMG intensity (D) for frog 5. Regression lines and partial
coefficients of determination (r2) were calculated in the
same manner as in Fig. 6.
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Fig. 10. Diagram showing the relative timing of peak ankle extension velocity, peak
plantaris muscle stress, peak muscle shortening velocity and peak muscle
shortening. Black squares and whiskers show mean ± s.d. for frog 5
(N=45 swimming strokes).
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© The Company of Biologists Ltd 2007
