Model analysis of the relationship between intracellular PO2 and energy demand in skeletal muscle

Abstract

On the basis of experimental studies, the intracellular O(2) (iPo(2))-work rate (WR) relationship in skeletal muscle is not unique. One study found that iPo(2) reached a plateau at 60% of maximal WR, while another found that iPo(2) decreased linearly at higher WR, inferring capillary permeability-surface area (PS) and blood-tissue O(2) gradient, respectively, as alternative dominant factors for determining O(2) diffusion changes during exercise. This relationship is affected by several factors, including O(2) delivery and oxidative and glycolytic capacities of the muscle. In this study, these factors are examined using a mechanistic, mathematical model to analyze experimental data from contracting skeletal muscle and predict the effects of muscle contraction on O(2) transport, glycogenolysis, and iPo(2). The model describes convection, O(2) diffusion, and cellular metabolism, including anaerobic glycogenolysis. Consequently, the model simulates iPo(2) in response to muscle contraction under a variety of experimental conditions. The model was validated by comparison of simulations of O(2) uptake with corresponding experimental responses of electrically stimulated canine muscle under different O(2) content, blood flow, and contraction intensities. The model allows hypothetical variation of PS, glycogenolytic capacity, and blood flow and predictions of the distinctive effects of these factors on the iPo(2)-contraction intensity relationship in canine muscle. Although PS is the main factor regulating O(2) diffusion rate, model simulations indicate that PS and O(2) gradient have essential roles, depending on the specific conditions. Furthermore, the model predicts that different convection and diffusion patterns and metabolic factors may be responsible for different iPo(2)-WR relationships in humans.

Fig. 1.

Schematic representation of substrate transport and metabolism in skeletal muscle. See Glossary for abbreviations.

Fig. 2.

Blood flow (Q̇), arteriovenous O₂ difference (C_A-V^T), and O₂ uptake (V̇o₂) for pump-perfused (PP) canine gastrocnemius muscle stimulated at 60% of peak V̇o₂ (V̇o_2peak) under hyperoxia with RSR-13. Experimental data are from Ref. . Vertical line denotes transition between rest and contraction.

Fig. 3.

Q̇, arteriovenous O₂ concentration difference, and V̇o₂ for self-perfused (SP) and PP canine gastrocnemius muscle stimulated at 60% of V̇o_2peak under normoxia. Experimental data are from Ref. . Vertical line denotes transition between rest and contraction.

Fig. 4.

Q̇, arteriovenous O₂ difference, and V̇o₂ for PP canine gastrocnemius muscle stimulated at 60% of V̇o_2peak under normoxia and hyperoxia. Experimental data are from Refs. and 24. Vertical line denotes transition between rest and contraction. Note that hyperoxia had no effect on these responses at this submaximal metabolic rate.

Fig. 5.

Q̇, arteriovenous O₂ difference, and V̇o₂ for SP and PP canine gastrocnemius muscle stimulated at 100% of V̇o_2peak under normoxia. Experimental data are from Ref. . Vertical line denotes transition between rest and contraction. Note that elevated Q̇ (Q̇_m) at the onset of contractions at this higher metabolic rate resulted in faster V̇o₂ on-kinetics (bottom).

Fig. 6.

Effect of glycolytic capacity (α_gly) on steady-state relationships of intracellular Po₂ 〈iPo₂〉, V̇o₂, O₂ gradient [extracellular Po₂ 〈ePo₂〉-〈iPo₂〉], and averaged concentration of ATP 〈C_ATP) with work rate (k_ATPase). Solid, dashed, and dotted lines represent simulations obtained for α_gly = 0.2, 0.4, and 0.6, respectively.

Fig. 7.

Effect of capillary permeability-surface area (PS) on steady-state relationships of 〈iPo₂〉, V̇o₂, O₂ gradient, and 〈C_ATP〉 with work rate (k_ATPase). Solid, dashed, and dotted lines represent simulations obtained for PS = 200, 100, and 80 l·l⁻¹·min⁻¹, respectively. Note that higher values result in higher 〈iPo₂〉, V̇o₂, and 〈C_ATP〉, along with lower O₂ gradient.

Fig. 8.

A: V̇o₂-Q̇ relationship for physiological (spontaneous) and elevated PP Q̇. Solid line represents spontaneous Q̇, calculated from an empirical linear V̇o₂-Q̇ relationship based on experimental data for SP muscle (–25, 28, 31, 39, 66). Dashed-dotted line represents elevated Q̇, constant at 101 ml·100 g⁻¹·min⁻¹. B: effect of different Q̇ on steady-state iPo₂-work rate (k_ATPase) relationship with PS^max set to 200 l·l⁻¹·min⁻¹. Solid line represents spontaneous Q̇ varying with work rate; dashed-dotted line represents elevated Q̇ at rest and through the transition at contraction onset.

Fig. 9.

Effect of PS on steady-state iPo₂-percent maximal work rate (WR_max) relationship when Q̇ is at spontaneous, physiologically normal level. Solid, dashed, and dotted lines represent simulations obtained for PS = 200, 100, and 80 l·l⁻¹·min⁻¹, respectively. ●, Experimental data of Molé et al. (49); ○, experimental data of Richardson et al. (57); ◇, resting iPo₂ (58). Note the strong effect of PS^max on the iPo₂ response; also note that results of Molé et al. and Richardson et al. may actually be consistent rather than contradictory.