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First published online August 30, 2006
Journal of Experimental Biology 209, 3610-3620 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02394
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A reaction-diffusion analysis of energetics in large muscle fibers secondarily evolved for aerobic locomotor function

Kristin M. Hardy1,*, Bruce R. Locke2, Marilia Da Silva2 and Stephen T. Kinsey1

1 Department of Biology and Marine Biology, University of North Carolina Wilmington, 601 South College Road, Wilmington, NC 28403-5915, USA
2 Department of Chemical and Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310-6046, USA


Figure 1
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  		Fig. 1. Schematic of the reaction-diffusion mathematical model. Metabolite concentrations during a contraction-recovery cycle in dark levator fibers were modeled over the length {lambda}/2, which represents half of the distance between mitochondrial clusters.

 

Figure 2
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  		Fig. 2. Representative 31P-NMR spectra collected from perchloric acid extracts of large dark levator muscle fibers that demonstrate the changes in relative concentrations of AP and Pi during a contraction-recovery cycle. Spectra were collected from crabs at rest, and after 0, 30 and 60 min of recovery from burst exercise. The same pattern of recovery was observed in the small dark fibers, except that complete AP resynthesis occurred in only 15 min. Chemical shifts are in units of parts per million.

 

Figure 3
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  		Fig. 3. Relative changes in AP (A) and Pi (B) content and absolute changes in ATP (C) and AP+Pi+ATP (D) content in small (open symbols) and large (filled symbols) dark levator fibers during a contraction-recovery cycle. In A and B, values at each time point have been normalized to the mean immediately after contraction to allow direct comparison of the recovery rate between the size classes (absolute resting values are in Table 3). Note how quickly AP and Pi levels are restored in the small fibers compared to the large fibers during recovery, as well as the relative stability in ATP and total high-energy phosphate content during contraction and recovery in both size classes. The arrow indicates when burst contractile exercise was stimulated; the asterisk indicates that values are significantly different from the resting value; and the dagger indicates that AP levels in each size class were significantly different from each other at the common 15 min recovery time point. N≥7 for every point.

 

Figure 4
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  		Fig. 4. Relative changes in glycogen content in small (open symbols) and large (filled symbols) dark levator fibers during a contraction-recovery cycle. Values at each time point have been normalized to the mean resting value to allow direct comparison between the size classes (absolute resting values are in Table 3). The arrow indicates when burst contractile exercise was stimulated. The asterisk indicates values significantly different from the resting value. N≥10 for every point.

 

Figure 5
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  		Fig. 5. Measured AP recovery (symbols) compared to the volume averaged model of AP recovery (solid line) in small (A) and large (B) dark fibers. The dotted line indicates the resting concentration. In the model, the myosin ATPase was activated long enough to cause a decrease in AP that was comparable to the measured data. (C,D) Three-dimensional graphs show the temporally and spatially resolved concentrations of AP for small (C) and large (D) dark levator fibers during a contraction-recovery cycle. This model output was generated using parameters in Table 2. Note the absence of concentration gradients.

 

Figure 6
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  		Fig. 6. The effect of increasing the rate of mitochondrial ATP production and myosin ATPase activity during steady-state contraction in small fibers on the temporal and spatial profiles of AP (A,C,E) and ATP (B,D,F). Metabolite concentrations during a typical steady-state contraction, where Vm,mito=1.00x10-14 mmol µm-2 s-1 and Vm,myo=1 mmol l-1 s-1 (A,B), during steady-state with a threefold increase in Vm,mito and Vm,myo (C,D), and during steady-state with a sevenfold increase in Vm,mito and Vm,myo (E,F).

 

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© The Company of Biologists Ltd 2006