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LETTER TO THE EDITOR

Altered creatine dependence of muscle mitochondrial respiration in vitro: what are the likely effects in vivo?

On the simplest model, respiration rate (V) is a hyperbolic (Michaelis-Menten) function of ADP concentration ([ADP]) (call this A; Ref. 1; Fig. 1A, control case). If mitochondrial capacity increases, e.g., with training (5), then the slope dV/dA increases throughout, and [ADP] for given V is less, so relative ADP sensitivity (S = dlnV/dlnA, formally an elasticity) increases (Fig. 1C); if training also increases K_m (5) then V/A and dV/dA could increase or decrease. The V-A relationship in vivo is better described by cooperative (sigmoid) kinetics (Hill coefficient n > 1; Ref. 2), which permits higher ADP sensitivity S (Fig. 1C, see legend). Somewhat similar kinetics result if K_m for ADP decreases with respiration rate (3). This could arise from Cr-stimulated respiration (4; Fig. 2, A and B), but as phosphocreatine (PCr) has anopposite effect, the relevant variable in vivo is Cr/PCr (6), which at constant pH is linear with [ADP]. If K_m for ADP decreases with Cr/PCr (6; Fig. 2C), in vivo it must decrease with [ADP] (Fig. 1B). This yields a sigmoid V-A curve (3), especially in HCR (Fig. 1A), substantially decreasing [ADP] and increasing ADP sensitivity, usefully characterized by the apparent Hill coefficient (Fig. 1C). However, only with greater Cr sensitivity than observed in vitro (4, 6) does this approach values observed in vivo (2; Fig. 1C, see legend). Lastly, whether increased Cr sensitivity in HCR represents a physiological shift toward creatine shuttling from simple ADP signaling (4), this can be quantified as the fraction of total respiration change due to Michaelis-Menten ADP-dependence; this is lower in HCR (Fig. 1C, see legend) because of the steeper relation of K_m to [ADP].

View larger version (19K): [in this window] [in a new window]   Fig. 1. The ADP dependence of respiration modeled in vivo. A: respiration relative to maximal: v = 1/(1+K/A) with variable K for low- and high-capacity running (LCR and HCR, respectively; Ref. 4) and extreme Cr sensitivity (see Fig. 2C) and constant K for control (= hyperbolic kinetics, no Cr stimulation). Straight dashed lines, half-maximal respiration. B: formal ADP dependence of Km for ADP follows from causal dependence on Cr/PCr (Ref. 5; in human muscle at pH 7, [ADP] 50 x Cr/PCr). Assume K = Ko/(1+A/), where Ko is a maximum at zero Cr/PCr and is [ADP] at half-maximal K (see Fig. 2C). The [ADP] at half-maximal respiration (Am) is the intersection with the line of identity, here Am = (/2)(–1) where 2 = 1+4Ko/. For LCR, based on Ref. 5, Ko = 300 µM and = 160 µM (corresponding to Cr/PCr = 3) so = 3; to model 3-fold greater Cr sensitivity in HCR (Fig. 2C), = 50 µM (Cr/PCr = 1) so = 5; for hypothetical extreme Cr sensitivity = 5 µM (Cr/PCr = 0.1) so = 16. The fraction of respiration change due to Michaelis-Menten ADP dependence, rather than creatine sensitivity, is F = 1/(1–dlnK/dlnA) = (A+)/(2A+); at half-maximal respiration F = (1/2)(1+1/), which is 0.7, 0.6, and 0.5 for LCR, HCR, and extreme cases, respectively. C: relative ADP sensitivity. For hyperbolic kinetics S = 1/(1+A/K) = 1–v. For classical cooperative kinetics v = 1/[1+(K/A)n] and S = n/[1+(A/K)n]; at given v, S is n times the "hyperbolic" control value. With Cr sensitivity, S = (1–v)(1–dlnK/dlnA), higher than control by a factor (= 1/F, above) here equal to 22/(+1), where is 1+4[v/(1–v)]Ko/. For example, S at half-maximal respiration is Sm = /(+1), compared to 1/2 for the hyperbolic case. [Thus both reported effects of aerobic training (5), increased Ko and decreased , tend to increase S). Define an apparent Hill coefficient napp = 2Sm, which is 1.5, 1.7, and 1.9 for LCR, HCR, and the extreme case, respectively; for comparison, observed n 2 in vivo (2). Abbreviations: Cr, creatine; PCr, phosphocreatine; [ADP], ADP concentration.

View larger version (14K): [in this window] [in a new window]   Fig. 2. Parametizing published creatine dependence of respiration in vitro. A: respiration above basal (i.e., at 0 ADP) with and without creatine but in the absence of CK, in permeabilized muscle fibers from HCR and LCR rats, against incubation [ADP] (from Fig. 1 in Ref. 4); solid lines are hyperbolic fits, for which (B) shows inferred Km for ADP against incubation [Cr]; solid lines are inverse hyperbolic fits (assuming 0 asymptote) showing 3-fold higher Cr affinity in HCR; brackets denote concentration. C: inferred Km for ADP in permeabilized human muscle fibers against incubation Cr/PCr in the absence of CK (from Table 1 in Ref. 5); the notional fits correspond to the human data in Ref. 5 (used here to model LCR in Fig. 1), to 3-fold higher Cr affinity (for HCR), and to hypothetical 30-fold higher Cr affinity. Straight dashed lines represent half-maximal data.

REFERENCES

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