Am J Physiol Cell Physiol AJP: Cell Physiology
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Am J Physiol Cell Physiol 295: C844-C846, 2008; doi:10.1152/ajpcell.00264.2008
0363-6143/08 $8.00
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Web of Science (2)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Kemp, G.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Kemp, G.

LETTERS TO THE EDITOR

Physiological implications of linear kinetics of mitochondrial respiration in vitro

TO THE EDITOR: Glancy et al. (4) measure the rate of oxygen consumption (Jo) by mitochondria incubated with an ATP-consuming system in the presence of creatine kinase (CK), and they show that this in vitro model of aerobically exercising skeletal muscle conforms to Meyer's electrical analog of muscle oxidative phosphorylation in vivo (23). I want to suggest that the interpretation of these experiments is enhanced by distinguishing the specific features of this model from general properties of feedback control (see 1–8 below), and making explicit its relationship (see Fig. 1) to alternative models (2, 7, 10, 16, 20, 27–30).


Figure 1
View larger version (10K):
[in this window]
[in a new window]

  		Fig. 1. Relationships between different rate equations describing oxidative ATP synthesis (JP). Relative JP (i.e., JP/JP,MAX, here called {varphi}, where JP,MAX is maximum flux) as a function of [PCr] (A), [ADP] (B), and free energy of ATP hydrolysis ({Delta}GATP) (C) [inset in C illustrates linear approximation as used in Meyer's model (23)]. D: kinetics of (logarithmic) fractional approach to steady state after step increase {Delta}JD in ATP demand (straight line means monoexponential kinetics with slope = rate constant). Cell pH is assumed constant. Scales are omitted for clarity. The JP-[ADP] relationship in B is taken as causally primary, according to {varphi} = 1/[1 + ([ADP]1/2/[ADP])n], where [ADP]1/2 is [ADP] for half-maximal flux, with Hill coefficient n = 1 (hyperbolic, Michaelis-Menten kinetics, solid lines) or n = 2 [cooperative, sigmoid, "second-order" (10) kinetics, dashed lines]. Defining the midpoint slope of Jp-X as (d{varphi}/dX)1/2, for JP-[ADP] in B, this is (n/4)/[ADP]1/2. Defining {kappa} as [ADP]1/2 relative to the [ADP] (~50 µM in human muscle) at which creatine is half-phosphorylated ({theta} = 1/2), the general midpoint slope for JP-[PCr] in A is –n(JP,MAX/[TCr])(1 + {kappa})2/(4{kappa}): for thick lines ({kappa} = n = 1), this is –JP,MAX/[TCr], a constant (12, 14); for thin lines, {kappa} > 1 and < 1. Thus, given "linear" kinetics ({kappa} = n = 1), JP,MAX is proportional to k (24) and can be estimated by extrapolating to complete PCr depletion (21), JP,MAX {approx} k[PCr]resting {approx} k[TCr] (i.e., approximately the y-intercept in A). Analogously, for the ADP-control model, JP,MAX is the inferred (17) asymptote in B. The general midpoint slope (i.e., 1/Rm) for JP-{Delta}GATP in C is n[JP,MAX/(6RT)](3/2)(1 + {kappa})/(2 + {kappa}), so for "linear" kinetics ({kappa} = n = 1: inset to C), Rm {approx} 6RT/JP,MAX, approximately constant (12, 14). A general JP-{Delta}GATP fit based on nonequilibrium thermodynamics (NET) is {varphi} = (eβ{Delta}µ – 1)/[eβ{Delta}µ + (1/{alpha})], where {Delta}µ is the difference between {Delta}GATP and {Delta}GATP* (the "static head" potential at which JP = 0), {alpha} is the (small) ratio of maximum reverse to maximum forward flux, and β = 1/(RT) for a simple substrate-to-product reaction (26) but could take other values. The midpoint flux of {varphi} = (1 – {alpha})/2 is at {Delta}µ = –(1/β)ln({alpha}), where slope is (β/4)(1 + {alpha}), which yields a linear approximation (26). The NET model entails small negative JP at very negative {Delta}GATP (unattainable in vivo or in physiological models in vitro), which could, pragmatically, be absorbed in the estimated JP,BASAL added to the suprabasal {Delta}JP measured by 31P magnetic resonance spectroscopy PCr-kinetic methods (7, 9, 16), or removed by adding {alpha} and rescaling to give {varphi} = 1/(1 + RTβeβ{Delta}{nu}), where {Delta}{nu} is the negative difference between {Delta}GATP and ({Delta}GATP)1/2, the {Delta}GATP for half-maximal flux; set β = n(1 + {kappa})/(2 + {kappa}) for a good fit, with correct midpoint slope, to the JP-{Delta}GATP in C entailed by the hypothetically causal JP-[ADP] in B. An alternative is a highly sigmoid quasi-kinetic fit (9, 10) {varphi} = 1/{1 + [({Delta}GATP)1/2/{Delta}GATP]m}; for correct midpoint slope set m = n[(1 + {kappa})/(2 + {kappa})][({Delta}GATP)1/2/(RT)] and ({Delta}GATP)1/2 – {Delta}GATP0 = RTln{[(1 + {kappa})/{kappa}2]/[TCr]}, where {Delta}GATP0 is standard free energy.

 
All approaches start from the temporal buffering of ATP (3) by CK. Since CK is near-equilibrium, d[ATP]/d[PCr] {approx} (1/{theta})([ADP]/[Cr]), where {theta} is [PCr]/[TCr], the phosphorylated fraction of the total creatine pool (TCr = PCr + Cr) (12, 14). Steady-state [ADP] is kept very low [i.e., ~15 µM in resting human muscle (15)] by feedback mechanisms described below, and the high equilibrium constant1 (4) of CK permits {theta}, nevertheless, to be near 1 [~0.8 at rest (15)]; so d[ATP]/d[PCr] {approx} 0, and [ATP] is buffered at the expense of [PCr] (3). Thus d[Pi]/d[PCr] {approx} –1, and since it happens (12) that [Pi] {approx} [Cr] at rest, this remains true during exercise (2). Thus when oxidative ATP synthesis JP (= {rho}Jo, where {rho} = P:O2 ratio) responds to a step increase from basal (resting) in ATP demand (say {Delta}JD), the kinetics of [PCr] and the increase in suprabasal JP ({Delta}JP) are given by {Delta}JP – d[PCr]/dt = {Delta}JD, and the (negative) change in [PCr] from rest is the time-integrated mismatch between ATP supply and use, –{Delta}[PCr] = {int} ({Delta}JD – {Delta}JP)dt (12, 14). The mathematical implications are that if {Delta}JP and [PCr] follow exponential kinetics (4) (with rate constant k, say, and time constant {tau} = 1/k), the relationship between JP and [PCr] must be linear, {Delta}JP = – k{Delta}[PCr]; and, conversely, from such linearity (thick line, Fig. 1A), observed or postulated, exponential kinetics follow (12, 14, 20) (thick line, Fig. 1D). The metabolic control implication is that any causal relationship between JP and [PCr] or its near-correlates, which include [ADP] (2), [Cr], [Cr]/[PCr], [Pi] (27, 28), and {Delta}GATP (7, 23) (i.e., any to which, in the terminology of metabolic control analysis, JP shows appreciable elasticity), could serve as a negative feedback signal matching ATP supply to demand (2); in engineering terms, this is a form of integral feedback, which precludes steady-state error (12). The link between these implications is that exponential kinetics (and the required linearity of JP and [PCr]) can emerge from feedback mechanisms involving [ADP] (2) or {Delta}GATP (7, 23, 29) as the key signal, as well as more complicated models (30).

For argument's sake, assume the relationship of flux to [ADP] (Fig. 1B) is causally prior: something like the hyperbolic (Michaelis-Menten) JP-[ADP] curve seen with incubated mitochondria [no doubt also in Glancy et al. (4)] can be observed in exercising muscle in vivo (2, 16) (Fig. 1B), whether this reflects mainly the ADP dependence of the adenine nucleotide translocase (10) or summarizes several such interactions of correlated metabolites (30). If JP is some function f([ADP]), then for given ATP demand, steady-state [ADP] = f–1(JD). Given an appropriate f [for example, a hyperbolic function with micromolar [ADP]1/2 (2, 16)] this will, for submaximal JP, keep steady-state [ADP] very low, as ATP-buffering requires (see above). Furthermore, in the case where [ADP]1/2 {approx} 50 µM (see Fig. 1), this hyperbolic JP-[ADP] relationship implies (at constant pH) a linear JP-[PCr] (12, 14) and therefore monoexponential kinetics (thick lines, Fig. 1, A–D), as seen in aerobic exercise (23) as well as in vitro in Glancy et al. (4). If [ADP]1/2 is higher (lower) than 50 µM, JP-[PCr] will be concave upward (downward), with probably relatively little effect on kinetics (thin lines in Fig. 1, A–D). Making JP-[ADP] sigmoid (dashed line in Fig. 1B) makes JP-[PCr] sigmoid also (dashed line, Fig. 1A) and increases the midpoint slope (Fig. 1), yielding faster but less strictly monoexponential kinetics (dashed line, Fig. 1D): the relevance is, first, that modest sigmoidicity (Hill coefficient n {approx} 2) (10) may explain the dynamic range in muscle in vivo without recourse to feed-forward (parallel activation) mechanisms (18), and second, that a small degree of sigmoidicity (1 < n < 2) could (11, 13) result from effects of [PCr]/[Cr] on [ADP]1/2 demonstrated in vitro (28).

Meyer's electrical analog (23) is a linear model in which JP (in vivo, mmol·l–1·s–1 or equivalent units) is analogous to current and {Delta}GATP (J/mmol) is analogous to voltage, their product being power (kJ·s–1·l–1); changes in [PCr] (mmol/l) are analogous to charge. Capacitance is defined as C = d[PCr]/d{Delta}GATP (mmol2·J–1·l–1), and mitochondrial resistance is defined as Rm = d{Delta}GATP/dJP (J·l–1·s–1·mmol–2), and if both are constant, exponential kinetics follow with {tau} = RmC (23). The CK equilibrium indeed constrains C to be approximately constant (23): over a midrange ({theta} {approx} 0.2 – 0.7), C {approx} [TCr]/(6RT) where R is the gas constant and T is temperature2 (23). Constancy of Rm is a midrange linear approximation to a sigmoid JP-{Delta}GATP (5, 24) (inset, Fig. 1C). This could be seen as an epiphenomenon of a causal [ADP] dependence (Fig. 1B): for hyperbolic JP-[ADP] (n = 1; solid line, Fig. 1C), Rm {approx} 6RT/JP,MAX (12, 14); more generally, 1/Rm, the actual midpoint slope of JP-{Delta}GATP, increases with n (Fig. 1), which accelerates the kinetics (dashed line, Fig. 1D). Alternative approaches using nonequilibrium thermodynamic formalism (7) or an empirical kinetic fit (9, 10) also describe a sigmoid JP – {Delta}GATP approximated by the linear relationship on which the electrical model is based (inset, Fig. 1C). Figure 1 summarizes how the JP-{Delta}GATP fit parameters relate to the (hypothetically) causal parameters of JP-[ADP], but if JP-{Delta}GATP were taken as causally prior, the relationships to [PCr] and [ADP] (Fig. 1, A and B) would be epiphenomena: the literature contains both perspectives, which cannot be distinguished at present.

Against this background, we can see that some of the results of Glancy et al. (4) are general properties of all CK-mediated feedback-controlled supply-demand mechanisms:

1) Fixed mitochondrial capacity. That measures of mitochondrial capacity (like 1/Rm) are unaffected by [TCr] but proportional to mitochondrial content (4) [as in vivo (24)] follows from, and justifies, the conceptual separation of the mitochondrion from the cytosolic CK system. The role of mitochondrial CK in this is heavily debated (14) but is probably small (11, 13).

2) Demand-drive. The low elasticity of the ATP-consumer toward CK-related signals [as in vivo, where ATP turnover is largely demand-driven (8)] explains why Jo is unaffected by changes in JP,MAX and [TCr] (4).

3) Changes in "feedback signals." Increasing demand {Delta}JD tends to increase the (let us assume stimulatory) signal X. Furthermore, increasing mitochondrial capacity JP,MAX increases open-loop gain (12), the absolute sensitivity of output to the error signal dJP/dX, which decreases the {Delta}X for given {Delta}JD. Whatever X really is, this explains why increasing Jo increases, and increasing JP,MAX decreases (4), changes in CK-correlated metabolites (3).

4) Constancy of "feedback signals." Attempts to perturb a feedback signal X must fail, at steady state, unless demand is also changed. In principle this could distinguish the causal role of an X from near-correlates: for example, that acute respiratory acidosis in vivo increases [ADP] but leaves {Delta}GATP unchanged (25) is evidence for Meyer's model and against ADP-control [although the effects of acidosis are complicated (5)]. Meyer's model also explains why {Delta}GATP, is, for a given Jo, unaffected by changing [TCr] (4) [also in vivo (1)], although a richer data set, covering a range of pH allowing dissociation between, e.g., [Cr] and [Pi] (3), would be needed to exclude independent effects of its near-correlates [and developments in detailed mitochondrial modeling (30) perhaps make this whole approach too simple].

Other findings (4) are particular, although not exclusive, properties of the subset of "linear" models:

5) Linear relationships. That some metabolite changes ({Delta}GATP and [PCr]) are linear with Jo (4) [also in vivo (24)] is likely a midrange approximation (22), compatible (algebraically and causally) with some nonlinear JP-[ADP] relationships (Fig. 1B).

6) Monoexponential kinetics. That {tau} and 1/Rm are independent of ATP turnover (4) [also in vivo (24)] follows from the linearity of JP-[PCr], when this is obtained (Fig. 1A).

7) Kinetics and [TCr]. The time constant {tau} is proportional to [TCr] in vitro (4) [also in vivo (22)] because, in Meyer's model, increasing [TCr] increases C, increasing the charge ({Delta}[PCr]) required to reach the required voltage ({Delta}GATP) (22); in ADP-control models, equivalently, it takes a bigger {Delta}[PCr] to reach the required [ADP].

8) Kinetics and mitochondrial capacity. The validity of 1/Rm and (given the approximate constancy of C) of k as measures of mitochondrial capacity, i.e., proportional to JP,MAX (4) [as also in vivo (24)]3 , rests on the validity of the linear-model assumptions in the absence of pH change (5). That {tau} is similar in vivo and in vitro when the ratio of mitochondrial volume to [TCr] is matched (4) makes sense in Meyer's model (4) and also in typical ADP-control models, where {tau} {approx} [TCr]/JP,MAX (Fig. 1).

In summary, that in a simple system "the robust energetic forces and flows maintained by the isolated mitochondria are similar to those observed in vivo" does indeed "reveal important features of mitochondrial function" (4), notably, that it is likely a demand-driven CK-mediated feedback mechanism not obviously in need of parallel activation mechanisms (18) to explain responses typical of aerobic exercise, but the data also make sense in several other perspectives than Meyer's elegant electrical analog model (23).

FOOTNOTES


Address for reprint requests and other correspondence: G. Kemp, School of Clinical Sciences, University of Liverpool, Liverpool L69 3GA, United Kingdom (e-mail: gkemp{at}liv.ac.uk)

1 At this point, Glancy et al. also cite the near-linearity of [PCr] with {Delta}GATP (23), but this is a consequence, not a cause, of ATP buffering; also "the kinetics of PCr breakdown and Jo rise are virtually identical at the onset of exercise" (4) because of ATP buffering, not "because of a relatively constant phosphorylation ratio" (4), which is not obtained. Back

2 2 Glancy et al. (4) calculate C both this way and as C = {tau}/Rm = {tau}{rho}(dJo/d{Delta}GATP), and they take the agreement as confirming their assumed {rho} (4); this is equivalent to estimating {rho} = (d[PCr]/dJo)/{tau}, as Meyer did (23). Back

3 How well estimates of actual JP,MAX (9, 17) perform is not established, although they largely avoid (19) the "artifactual" pH dependence of k (6). If causal primacy is conceded to ADP feedback (Fig 1B), 1/Rm increases with n, responding to the shape as well as the maximum of JP-[ADP], appropriately reflecting faster kinetics (Fig 1D). Back

REFERENCES

1. Brault JJ, Towse TF, Slade JM, Meyer RA. Parallel increases in phosphocreatine and total creatine in human vastus lateralis muscle during creatine supplementation. Int J Sport Nutr Exer Metab 17: 624–634, 2007.

2. Chance B, Leigh JS Jr, Clark BJ, Maris J, Kent J, Nioka S, Smith D. Control of oxidative metabolism and oxygen delivery in human skeletal muscle: a steady-state analysis of the work/energy cost transfer function. Proc Natl Acad Sci USA 82: 8384–8388, 1985.[Abstract/Free Full Text]

3. Connett RJ. Analysis of metabolic control: new insights using scaled creatine kinase model. Am J Physiol Regul Integr Comp Physiol 254: R949–R959, 1988.[Abstract/Free Full Text]

4. Glancy B, Barstow T, Willis WT. Linear relation between time constant of oxygen uptake kinetics, total creatine, and mitochondrial content in vitro. Am J Physiol Cell Physiol 294: C79–C87, 2008.[Abstract/Free Full Text]

5. Harkema SJ, Meyer RA. Effect of acidosis on control of respiration in skeletal muscle. Am J Physiol Cell Physiol 272: C491–C500, 1997.[Abstract/Free Full Text]

6. Iotti S, Lodi R, Frassineti C, Zaniol P, Barbiroli B. In vivo assessment of mitochondrial functionality in human gastrocnemius muscle by 31P MRS. The role of pH in the evaluation of phosphocreatine and inorganic phosphate recoveries from exercise. NMR Biomed 6: 248–253, 1993.[Web of Science][Medline]

7. Jeneson JA, Westerhoff HV, Brown TR, Van Echteld CJ, Berger R. Quasi-linear relationship between Gibbs free energy of ATP hydrolysis and power output in human forearm muscle. Am J Physiol Cell Physiol 268: C1474–C1484, 1995.[Abstract/Free Full Text]

8. Jeneson JA, Westerhoff HV, Kushmerick MJ. A metabolic control analysis of kinetic controls in ATP free energy metabolism in contracting skeletal muscle. Am J Physiol Cell Physiol 279: C813–C832, 2000.[Abstract/Free Full Text]

9. Jeneson JA, Wiseman RW, Kushmerick MJ. Non-invasive quantitative 31P MRS assay of mitochondrial function in skeletal muscle in situ. Mol Cell Biochem 174: 17–22, 1997.[CrossRef][Web of Science][Medline]

10. Jeneson JA, Wiseman RW, Westerhoff HV, Kushmerick MJ. The signal transduction function for oxidative phosphorylation is at least second order in ADP. J Biol Chem 271: 27995–27998, 1996.[Abstract/Free Full Text]

11. Kemp GJ. Altered creatine dependence of muscle mitochondrial respiration in vitro: what are the likely effects in vivo? J Appl Physiol 101: 1814–1815, 2006.[Free Full Text]

12. Kemp GJ. Interactions of mitochondrial ATP synthesis and the creatine kinase equilibrium in skeletal muscle. J Theor Biol 170: 239–246, 1994.[CrossRef][Web of Science][Medline]

13. Kemp GJ. Mitochondrial respiration in creatine-loaded muscle: is there 31P-MRS evidence of direct effects of phosphocreatine and creatine in vivo? J Appl Physiol 100: 1428–1429, 2006.[Abstract/Free Full Text]

14. Kemp GJ, Manners DN, Clark JF, Bastin ME, Radda GK. Theoretical modelling of some spatial and temporal aspects of the mitochondrion/creatine kinase/myofibril system in muscle. Mol Cell Biochem 184: 249–289, 1998.[CrossRef][Web of Science][Medline]

15. Kemp GJ, Meyerspeer M, Moser E. Absolute quantification of phosphorus metabolite concentrations in human muscle in vivo by 31P MRS: a quantitative review. NMR Biomed 20: 555–565, 2007.[CrossRef][Web of Science][Medline]

16. Kemp GJ, Taylor DJ, Radda GK. Control of phosphocreatine resynthesis during recovery from exercise in human skeletal muscle. NMR Biomed 6: 66–72, 1993.[Web of Science][Medline]

17. Kemp GJ, Taylor DJ, Thompson CH, Hands LJ, Rajagopalan B, Styles P, Radda GK. Quantitative analysis by 31P magnetic resonance spectroscopy of abnormal mitochondrial oxidation in skeletal muscle during recovery from exercise. NMR Biomed 6: 302–310, 1993.[Web of Science][Medline]

18. Korzeniewski B. Regulation of oxidative phosphorylation through parallel activation. Biophys Chem 129: 93–110, 2007.[CrossRef][Web of Science][Medline]

19. Lodi R, Kemp GJ, Iotti S, Radda GK, Barbiroli B. Influence of cytosolic pH on in vivo assessment of human muscle mitochondrial respiration by phosphorus magnetic resonance spectroscopy. Magma 5: 165–171, 1997.[CrossRef][Medline]

20. Mahler M. First-order kinetics of muscle oxygen consumption, and an equivalent proportionality between QO2 and phosphorylcreatine level. Implications for the control of respiration. J Gen Physiol 86: 135–165, 1985.[Abstract/Free Full Text]

21. McCully KK, Smith S, Rajaei S, Leigh JS Jr, Natelson BH. Muscle metabolism with blood flow restriction in chronic fatigue syndrome. J Appl Physiol 96: 871–878, 2004.[Abstract/Free Full Text]

22. Meyer RA. Linear dependence of muscle phosphocreatine kinetics on total creatine content. Am J Physiol Cell Physiol 257: C1149–C1157, 1989.[Abstract/Free Full Text]

23. Meyer RA. A linear model of muscle respiration explains monoexponential phosphocreatine changes. Am J Physiol Cell Physiol 254: C548–C553, 1988.[Abstract/Free Full Text]

24. Paganini AT, Foley JM, Meyer RA. Linear dependence of muscle phosphocreatine kinetics on oxidative capacity. Am J Physiol Cell Physiol 272: C501–C510, 1997.[Abstract/Free Full Text]

25. Thompson CH, Kemp GJ, Radda GK. Changes in high-energy phosphates in rat skeletal muscle during acute respiratory acidosis. Acta Physiol Scand 146: 15–19, 1992.[Web of Science][Medline]

26. Van der Meer R, Westerhoff HV, Van Dam K. Linear relation between rate and thermodynamic force in enzyme-catalyzed reactions. Biochim Biophys Acta 591: 488–493, 1980.[Medline]

27. Walsh B, Tiivel T, Tonkonogi M, Sahlin K. Increased concentrations of Pi and lactic acid reduce creatine-stimulated respiration in muscle fibers. J Appl Physiol 92: 2273–2276, 2002.[Abstract/Free Full Text]

28. Walsh B, Tonkonogi M, Soderlund K, Hultman E, Saks V, Sahlin K. The role of phosphorylcreatine and creatine in the regulation of mitochondrial respiration in human skeletal muscle. J Physiol 537: 971–978, 2001.[Abstract/Free Full Text]

29. Westerhoff HV, van Echteld CJ, Jeneson JA. On the expected relationship between Gibbs energy of ATP hydrolysis and muscle performance. Biophys Chem 54: 137–142, 1995.[CrossRef][Web of Science][Medline]

30. Wu F, Jeneson JA, Beard DA. Oxidative ATP synthesis in skeletal muscle is controlled by substrate feedback. Am J Physiol Cell Physiol 292: C115–C124, 2007.[Abstract/Free Full Text]


Graham Kemp
 School of Clinical Sciences
University of Liverpool
Liverpool
United Kingdom




This article has been cited by other articles:


Home page
 J. Appl. Physiol.Home page
G. Kemp
Interpreting the phosphocreatine time constant in aerobically exercising skeletal muscle
J Appl Physiol, January 1, 2009; 106(1): 350 - 350.
[Full Text] [PDF]

This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Web of Science (2)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Kemp, G.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Kemp, G.

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
Visit Other APS Journals Online
Copyright © 2008 by the American Physiological Society.