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First published online October 5, 2007
Journal of Experimental Biology 210, 3505-3512 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.000331

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The long and winding road: influences of intracellular metabolite diffusion on cellular organization and metabolism in skeletal muscle

Stephen T. Kinsey^1,*, Kristin M. Hardy¹ and Bruce R. Locke²

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, Florida State University, Tallahassee, FL 32310-6046, USA

View larger version (46K): [in this window] [in a new window]   Fig. 1. A schematic of a muscle fiber in cross section shows the influence of mitochondrial distribution on diffusion distance. While mitochondrial distribution can be complex, shown here are two idealized patterns where mitochondria may be distributed throughout the fiber, leading to short diffusion distances (A; intermyofibrillar mitochondria), or clustered exclusively at the sarcolemmal membrane, leading to longer diffusion distances (B; subsarcolemmal mitochondria). More commonly, a combination of both subsarcolemmal and intermyofibrillar mitochondria are observed. ATP must be transported via diffusion (black arrows) from sites of production in the mitochondria (colored green) to cellular ATPases throughout the cytoplasm. Likewise, ADP must be transported back to the mitochondria (not shown). In some fibers the mitochondrial distribution changes during fiber growth from primarily intermyofibrillar to primarily subsarcolemmal, meaning the diffusion distance between mitochondria may change dramatically as muscle fibers increase in size (see text).

View larger version (9K): [in this window] [in a new window]   Fig. 2. Phosphagen kinases (AK or CK) mediate most diffusive flux of ATP in muscle. The red arrows indicate enzymatic catalysis and the black arrows net diffusive flux. The relatively thick black arrows for phosphagen kinase mediated diffusion indicates that the vast majority of net high-energy phosphate diffusion occurs in the form of phosphagen (AP or PCr), rather than directly as ATP (thin black arrows).

View larger version (61K): [in this window] [in a new window]   Fig. 3. The diffusion coefficient (D) is time- and orientation-dependent in muscle. (A) A 3-dimensional schematic of a muscle fiber shows the major barriers to diffusion, where radial diffusion (red arrow) is hindered both by the sarcoplasmic reticulum (blue shading), which is a partial membrane that surrounds myofibrils (small cylinders), and by the thick and thin filament lattice (thin black lines). In contrast, there are comparatively few barriers to axial diffusion (blue arrow), and elements that potentially limit axial diffusion, such as Z-disks (not shown), have little effect on D. Green spheroids represent mitochondria. (B) D of PCr in white muscle of goldfish is reduced from the value in solution (D of PCr in solution is shown at a diffusion time of zero) (Ellington and Kinsey, 1998), and declines to a steady state value that is lower for radial diffusion, due to the presence of intracellular barriers such as the sarcoplasmic reticulum [data from Kinsey et al. (Kinsey et al., 1999) ©1999, John Wiley and Sons, Ltd, reproduced with permission]. (C) Hindered radial diffusion in muscle (red line) increases the time required for PCr to diffuse a given distance compared to diffusion in water (broken black line). RMS is root mean square displacement and reflects the average movement of a molecule. (D) There is a large percent change in the radial diffusion time over the short intracellular diffusion distances that characterize most cells. Therefore, below a threshold diffusion distance of about 8 µm (time-dependent range), shorter diffusion distances can support higher metabolic rates without diffusion limitation.

View larger version (10K): [in this window] [in a new window]   Fig. 4. Examples of fiber size diversity in crustaceans and fishes in anaerobic (white symbols) and aerobic muscle (red symbols). In some cases, body mass was estimated from length measurements using species-specific regression analysis. Data are from the published literature (Jahromi and Atwood, 1971; Johnston and Lucking, 1978; Weatherley et al., 1979; Silverman and Charlton, 1980; Weatherley and Gill, 1987; Johnston, 1982; Jones and Sidell, 1982; Tse et al., 1983; Hoyle et al., 1986; Hoyle, 1987; Egginton and Sidell, 1989; Londraville and Sidell, 1990; Archer and Johnston, 1991; Stokes and Josephson, 1992; Egginton et al., 2000; Boyle et al., 2003; Johnston et al., 2003a; Johnston et al., 2003b; Johnston et al., 2004; Nyack et al., 2007) and personal observations (S.T.K., unpublished results).

View larger version (70K): [in this window] [in a new window]   Fig. 5. The interaction of ATP turnover rate, diffusion distance and the effectiveness factor (), which is the ratio of the reaction rate in the presence of diffusion to the rate if diffusion were not limiting. The surface was generated from a Loess fit to output from a simplified reaction–diffusion model with linear expressions for ATP production (mitochondria), ATP consumption (ATPases) and diffusion (see text for additional details). The symbols represent the positions on the surface of a variety of anaerobic (white) and aerobic (red) muscle fibers from insects (bee flight muscle) (diamonds), crustaceans (circles), fishes (squares), amphibians (frog lumbrical muscle) (inverted triangle), reptiles (including rattlesnake tailshaker muscle) (crosses), bird (hummingbird flight muscle) (triangle), and mammals (pentagons). The white lines are developmental trajectories from individual species for white muscle fibers that grow hypertrophically (muscles are, in order from low to high ATP turnover rate: blue crab light levator, black sea bass white epaxial muscle, pink shrimp abdominal flexor and grass shrimp abdominal flexor). The black arrow indicates the impact of subdividing the large aerobic fibers of blue crabs, which greatly reduces the intracellular diffusion distances and alleviates diffusion limitation associated with the hypothetical, non-subdivided case (value with a low ) (see text for additional details). Diffusion distances were taken from direct measurements or calculated as in Tyler and Sidell (Tyler and Sidell, 1984) from the mitochondrial volume density and mitochondrial surface density [the latter was calculated assuming a mitochondrial surface area to volume ratio of 6 if not directly measured (Tyler and Sidell, 1984)]. ATP turnover rates per volume of muscle fiber were determined from direct measurements of O2 consumption in tissue, isolated fibers, or isolated mitochondria assuming 22.4 l O2 mol–1 O2, an ATP/O2 ratio of 6, and an intracellular water content that was 70% of wet mass. For cases where measurements of O2 consumption were unavailable, ATP turnover rate was estimated from mitochondrial volume density assuming a sustainable rate of O2 consumption of 3 ml min–1 cm–3 of mitochondrial volume [(Schwerzmann et al., 1989); this value was not applied to mitochondria with known high cristae surface densities]. Data are from the published literature (Tyler and Sidell, 1984; Andersen and Saltin, 1985; Egginton and Sidell, 1989; Schwerzmann et al., 1989; Stokes and Josephson, 1992; Curtin et al., 1997; Conley and Lindstedt, 1998; Johnston et al., 1998; Suarez, 1998; Egginton et al., 2000; Vicini and Kushmerick, 2000; Kanatous et al., 2002; Boyle et al., 2003; Kindig et al., 2003; Johnson et al., 2004; Stary et al., 2004; Kinsey et al., 2005; Hardy et al., 2006; Nyack et al., 2007) and personal observations (S.T.K., unpublished results). In studies of ectotherms from different temperature regimes, only data from the warm acclimated or adapted groups were included.