Regulatory, Integrative and Comparative Physiology

Lactate metabolism during exercise: analysis by an integrative systems model

Marco E. Cabrera, Gerald M. Saidel, Satish C. Kalhan


To provide a framework for quantitative analysis of metabolic and transport processes associated with ATP production during exercise, we adapted a recently developed model that links cellular metabolism and its control to whole body responses at rest. The enhanced model is based on dynamic mass balances for glycogen, glucose, pyruvate (PY), lactate (LA), O2, and CO2 and is solved numerically to simulate responses to acute (<20 min), moderate exercise (i.e., below the LA threshold, less than ∼60% maximal rate of O2 uptake). Simulations of responses to a step change in muscle ATP turnover predict substrate changes in muscle, splanchnic, and other tissues compartments, as well as changes in other metabolites (e.g., NADH, ADP) whose reactions are coupled to the main reactions. Even a significant (64%) decrease in muscle O2concentration ( Cm,O2 ) did not affect muscle O2 consumption. Model simulations of moderate exercise show that1) muscle oxygenation is sufficient ( Cm,O2 >2 mM) even during the transient state; 2) transient increases in concentration of muscle LA and arterial concentration of LA are associated with increases in glycolysis from increases in ADP/ATP and in LA production associated with a rise in NADH/NAD; 3) muscle ADP/ATP reaches a higher steady state that stimulates glycolysis, glycogenolysis, and oxidative phosphorylation to match the ATP demand; and4) muscle NADH/NAD reaches a lower steady state that stimulates LA oxidation. It is suggested that the continuous stimulation of ATP synthesis processes during moderate exercise is mainly due to a higher ADP/ATP, not to a higher NADH/NAD. Critical measurements needed to quantify metabolic control mechanisms are identified.

  • metabolic control
  • energy metabolism
  • lactate threshold
  • muscle hypoxia
  • biochemical regulation

a crucial metabolic pathway contributing to muscle ATP regulation is glycolysis. The endpoint of glycolysis is pyruvate (PY), which represents a crossroad metabolite that can be reduced to form lactate (LA) or oxidized to CO2 and H2O, depending on the level of energy demand and conditions of the cell. Because glycolysis serves to produce cytosolic ATP and to support mitochondrial ATP production, its control and coordination with the rest of the energetic pathways is a key issue to investigate for ATP homeostasis.

The relative contribution of the glycolytic pathway to the overall rate of ATP regeneration in muscle has been typically studied using measurements of blood LA concentration ([LA]). However, the blood LA pool mainly represents the balance between the rates of LA release (by skeletal muscle and the gut) and utilization by several tissues/organs (e.g., liver, cardiac muscle, nonworking skeletal muscle, other tissues). In addition, the blood LA response to exercise seems to have a triphasic nature (4, 25). During mild or moderate exercise [typically <60% maximal rate of O2 consumption (V˙o 2 max)], the rate of glycolysis increases severalfold but does not lead to a sustained LA accumulation in blood. During heavy exercise (∼60–80%V˙o 2 max), the rate of blood LA appearance initially exceeds its rate of uptake so that muscle and blood LA reach higher steady-state levels than at rest. When the maximum limits of exercise (>80%V˙o 2 max) are approached, anaerobic glycolysis supplements the energy derived from aerobic ATP production and causes a progressive accumulation of LA in muscle and blood until fatigue ensues.

The control mechanisms leading to an increase in muscle and blood [LA] are not well understood. Many factors in addition to the metabolic condition of working muscle may be responsible for the observed increase in [LA]. Because other tissues/organs that produce and/or consume LA contribute to the blood LA pool, interpretation of blood [LA] changes is difficult (3, 6,9). Nevertheless, the blood LA response to exercise has been used for exercise prescription, predicting endurance performance, and designing training programs. Furthermore, mathematical models of LA kinetics and bioenergetic processes have been developed to guide training or predict performance more accurately (7, 21, 32, 39). However, no comprehensive model has been developed that quantitatively accounts for the behavior of glycolysis, its integration to other pathways through control metabolites, and its regulation during exercise (8).

To provide a framework for the analysis of the processes involved in ATP regulation during exercise, we present an adaptation of a recently developed mathematical model of the human bioenergetic system at rest (5) to permit quantitative evaluation of the responses to exercise. Model parameters are derived from in vivo physiological measurements in human tissues and blood. The enhanced model enables us to simulate the responses at the cellular, tissue/organ, and whole body levels to a stimulus representing a step change from rest to exercise of moderate intensity. Specifically, it permits analysis of the dynamics of LA in various tissue compartments and blood, which allows testing of hypotheses in the context of a system model.

In this study we examine the metabolic pathways affecting LA production and its control. We hypothesize that LA is continuously being produced in skeletal muscle, even at rest. Furthermore, the muscle's rate of LA production is 1) directly controlled by [PY], NADH/NAD, or both, and2) indirectly controlled by ADP/ATP or by the cellular [O2]. The basis for the latter control assumes that [O2] affects the rate of cellular respiration and, consequently, the rate of NADH oxidation in the mitochondria and the redox state (NADH/NAD) in the cytosol (38).

At the tissue/organ level, we quantitatively evaluate the muscle rates of LA formation and utilization, as well as the rates of LA uptake and release in muscle, splanchnic, and other tissues. We hypothesize that skeletal muscle can be a simultaneous producer and consumer of LA. Although LA production is larger than LA utilization at rest, a continuous net LA release occurs without muscle LA accumulation. During moderate exercise, the relative rates of production and utilization of muscle LA may depend on the muscle's metabolic rate, the amount of PY and LA present in the muscle, and the oxygenation and redox states of the myocites.

At the whole body level, we investigate and quantify the effects of other tissues on blood [LA]. We hypothesize that blood [LA] is determined by various factors and, in general, does not represent the metabolic state of skeletal muscle during moderate exercise.

The following sections describe our model, including biochemical pathways, regional blood flows, and rates of O2 consumption, which are necessary to simulate the metabolic responses to moderate exercise. The sensitivity of processes affecting LA metabolism to changes in relevant model parameters is assessed. Model simulations of responses to a step increase in metabolic rate are compared with those of experimental data. Then the results are analyzed in terms of cellular mechanisms of metabolic regulation in skeletal muscle and interaction of systemic tissues. Finally, critical measurements needed to quantify metabolic control mechanisms are identified. These measurements can facilitate model validation and improve our understanding of metabolic regulation during exercise.


Arterial concentration of species j
Ci, j
Concentration of substrate j in tissue i
Mixed venous concentration of species j
Cvi, j
Concentration of species j in venous blood drainingtissue i
Michaelis-Menten parameter for O2consumption by muscle
Total adenylates concentration in muscle
Total nicotinamide nucleotides concentration in muscle
Total creatine concentration in muscle
Metabolic rate in tissue i; total metabolic rate = MR = ΣMRi
Pi, j
Endogenous rate of production of substrate j in tissue i
Cardiac output
Regional blood flow
Respiratory exchange ratio,V˙co2/V˙o2
Respiratory quotient in tissue i = Pi,CO2 / Ui,O2 , i.e., CO2 production/O2 consumption
Time delay in function representingV˙o2 and V˙co2 in terms of work rate
Ui, j
Endogenous rate of utilization of substrate j intissue i
Alveolar ventilation
Effective volume of substrate j in tissue i
Rate of O2 uptake by lungs
Rate of CO2 output or elimination by lungs
Work rate
Conversion factor relating ATP hydrolysis to metabolic rate
Conversion factor relating O2 uptake to WR
Conversion factor relating ATP hydrolysis to WR
Conversion factor relating rate of alanine formation to WR
Conversion factor relating rate of glycerol utilization to WR
Conversion factor relating cardiac output to O2 uptake
Conversion factor relating regional blood flow to O2 uptake
Efficiency fraction of mechanical coupling of muscle during contraction
Parameters in Michaelis-Menten functions modulating conversion ofj to k
λi, j→k
Rate of utilization of substrate j for formation kthrough process p in tissue i
ςi, j
Blood-tissue partition coefficient for substrate j intissue i = Cvi, j/Ci, j
φpi, j→k
Rate of utilization of substrate j for formation k through process p in tissue i
Rate of O2 utilization to form H2O or rate of O2
consumption by tissue i
τO2 , τCO2
Response times in functions representingV˙o2 orV˙co2 as a function of WR


The structure and general form of the human bioenergetic system model (Fig. 1) and its overall biochemical reaction processes were presented previously (4). In the model, the concentrations of key substrates in perfectly mixed tissues/organ compartments are described by dynamic mass balances and chemical kinetic relations ( ). Metabolite transport here is considered as a phenomenological process occurring between cells and tissues/organs. The variable regulated by each tissue/organ is [ATP]. A step change in ATP turnover is the model input. We assume that only skeletal muscle can adapt its rates of ATP production and O2consumption to the work rate level. The alveolar space serves simply as a gas exchanger.

Fig. 1.

Schematic structure of 4-compartment model of human bioenergetic system, with inspired O2concentration ( Embedded Image ) and work rate (WR) as its inputs and alveolar O2 and CO2 concentrations ( Embedded Image , Embedded Image ), heat, and water as its outputs. Tissues compartments include1) skeletal muscle (m), representing working muscles in the lower extremities;2) splanchnic (s), representing splanchnic region (liver and viscera);3) other tissues (o), which include brain, heart, adipose tissue, and the rest of the tissues; and4) alveolar (A), which includes lungs as a gas exchanger and heart as a pump. In each compartment, main substrate pools are labeled with arrows indicating direction of conversion processes. Most reactions between 2 substrates [glycogen (GY), glucose (GL), fatty acids (FA), glycerol (GR), pyruvate (PY), lactate (LA), alanine (AL), CO2, O2, and H2O] are coupled to formation of NAD or NADH, and/or formation of ATP or ADP. SeeGlossary for additional abbreviations.

At rest, ATP homeostasis is maintained by matching ATP synthesis to the equivalent of the resting metabolic rate. During exercise, a work rate (WR) input induces parallel adaptive changes in O2 uptake, blood flow, and enzyme levels to supply exercising muscles the required fuels to maintain muscle [ATP] constant. Regulation occurs when a system maintains a variable (e.g., [ATP]) within narrow bounds over time despite fluctuations in external conditions (e.g., WR input). Control refers to adjusting the output of a system with time to match a specified signal or to obtain a desired response.

Energy Conversions and Energetic Estimates

The total metabolic rate (MR) is the sum of metabolic rates of individual tissue compartments. On the assumption that 6 mol of ATP are formed for each mole of O2consumed and that most energy at rest is derived aerobically, then if the body consumes 250 ml O2/min at rest (11.2 mmol O2/min), the resting ATP turnover rate would be 67 mmol ATP/min.

Regardless of substrate, the portion of the energy released from substrate oxidation that is conserved in the ATP molecule (i.e., phosphorylative coupling efficiency, ζ) is ∼40% under standard conditions (1 atm, 25°C, pH 7.0). The remaining 60% free energy is released as heat. Thus the standard free energy (ΔGo) of ATP hydrolysis is approximately −30 kJ/mol (37). Under most physiological conditions, however, ζ ranges from 40 to 60%, with the higher values occurring under in vivo conditions. At rest and under physiological conditions (34–38°C, pH 7.0), the ΔG of ATP hydrolysis ranges between −50 and −67 kJ/mol ATP (37). We assume ΔG(rest) = −67 kJ/mol, which results in an energy expenditure of ∼75 W. Thus, on the assumption of a caloric equivalent of 403 kJ/mol O2, a heat production of 1,550 kcal/day (75 W) results from consuming 250 ml O2/min. Typically, this resting MR varies between 1,200 and 2,400 kcal/day for a 70-kg male.

During exercise, the proportion of ΔG available from ATP hydrolysis decreases with increasing ATP turnover and temperature and with decreasing intracellular pH. Furthermore, the muscle's ability to transform chemical bond energy of ATP into muscular work (i.e., mechanical-coupling efficiency, η) is ∼50% (37). Therefore, the amount of energy effective for external work during exercise depends not only on the efficiencies ζ and η, but also on the muscle conditions (temperature, pH) during contraction (37). Thus, during muscular contraction and under physiological conditions (temperature = 37°C, pH < 7.0), the free energy of ATP hydrolysis, ΔG(exercise), is approximately −46 kJ/mol, which is 33% lower than ΔG(rest). On the assumption that η = 0.5 and ζ = 0.6, that is, an overall muscular contraction efficiency of ∼30% (37), the amount of external mechanical work that can be performed for a given rate of O2consumption is reduced by a factor of two compared with the resting state. During cycle exercise at a WR of 25 W, the body consumes 750 ml O2/min, which includes the O2 cost of rest (250 ml O2/min), unloaded pedaling (250 ml O2/min), and external mechanical work (250 ml O2/min).

We assume that in any tissue the only energy source for work is derived from hydrolysis of ATP to ADPφi,ATPADP=α0MRi Equation 1 where MRi is the MR (watts) of theith organ/tissue and α0 a conversion factor (mmol ATP ⋅ min−1 ⋅ W−1). The rate of ATP utilization required to perform exercise at a specific WR, i.e., φm,ATP→ADP(WR), can be expressed asφm,ATPADP(WR)=φm,ATPADP(rest) +φm,ATPADP(unloaded)+αmWR Equation 2where φm,ATP→ADP(rest) is the muscle's rate of ATP utilization at rest, φm,ATP→ADP(unloaded) is its rate of ATP utilization above rest during unloaded cycling, approximately the same as φm,ATP→ADP (rest), and αm is a conversion factor.

During exercise, we assume that changes inV˙o 2 are mainly due to changes in the muscle's rate of O2consumption (i.e., O2 consumption by the splanchnic and other tissues remains constant). The steady-stateV˙o 2 requirement [V˙o 2(WR)] during exercise of moderate intensity on a cycle ergometer depends on the WR and can be expressed asV˙O2(WR)=V˙O2(rest)+V˙O2(unloaded)+αWR Equation 3 whereV˙o 2(rest) is the O2 uptake at rest,V˙o 2(unloaded) is the O2 uptake increase above rest during unloaded cycling, approximately the same asV˙o 2(rest), and α is a conversion factor representing the ratio ΔV˙o 2/ΔWR in the moderate intensity range above unloaded pedaling.

The V˙o 2 andV˙co 2 response to a step WR input can be expressed empirically (27, 51, 52) asΔV˙O2(t,WR)=ΔV˙O2(WR){1exp[(ttd)/τO2]} Equation 4 ΔV˙CO2(t,WR) =ΔV˙CO2(WR){1exp[(ttd)/τCO2]} Equation 5where t d is the time delay for the appearance of changes inV˙o 2 andV˙co 2 from the time at which the step change in the input WR was applied. Ast increases, the O2 uptake and CO2 output reach steady-state values [V˙o 2(WR),V˙co 2(WR)]. The time taken to reach steady state is determined by the assigned time constants, i.e., τO2 , τCO2 . The resting rates of V˙o 2 andV˙co 2 can be expressed as functions of PO2 and PCO2 in the inspired and alveolar air and the alveolar ventilation (V˙A). Alveolar ventilation can be related to arterial PO2 and PCO2 (5, 36).

Cardiac output (Q) is linearly related toV˙o 2 over a wide range of WRs in normal subjectsQ(t,WR)=Q(rest)+β[V˙O2(t,WR)V˙O2(rest)] Equation 6 where β is the slope ΔQ/ΔV˙o 2conversion factor, Q(rest) is the resting cardiac output, and V˙o 2(rest) is the resting rate ofV˙o 2. We assume that Q changes with a time course identical to that forV˙o 2. Splanchnic blood flow decreases linearly with increases in the rate of O2 uptake by the muscleQs(t,WR)=Qs(rest)γ[V˙O2(t,WR)V˙O2(rest)] Equation 7 whereas blood flow to other tissues Qoincreases by the same amount that Qs decreasesQo(t,WR)=Qo(rest)+γ[V˙O2(t,WR)V˙O2(rest)] Equation 8 where γ is the slope ΔQo/ΔV˙o 2. Thus muscle blood flow changes by the same amount as QQm(t,WR)=Q(t,WR)[Qs(rest)+Q0(rest)] Equation 9 To link processes of ATP synthesis to ATP hydrolysis during exercise, we define a relative MRRMR={(1/η) [WR+WR(unloaded)]+MR(rest)}/MR(rest) Equation 10 where WR(unloaded) is the WR equivalent of unloaded cycling, η is the efficiency fraction of the mechanical coupling of the muscle during contraction, and MR(rest) is the resting MR. In the absence of any external work RMR = 1.

Biochemical Conversion Rates (φijk) and Control Coefficients (λijk)

In our model, the set of biochemical reactions in a pathway is represented by one summarizing reaction, the rate of which is controlled by a nonlinear function (“rate coefficient,” λijk) of metabolic modulators [e.g., ADP, ATP, NADH, NAD, phosphocreatine (PC), creatine (CR)]. Modulators enhance or inhibit enzyme activity, thus controlling reaction rates (e.g., ATP inhibits enzymatic activity, whereas ADP and Pistimulate it). In this application, the reactions associated with the metabolic processes are represented as first-order or zero-order reactions with nonlinear functions of the modulators as control coefficients.

Because of the high affinity of oxidative phosphorylation for O2, the rate of O2 utilization by the tissues will not be limited by [O2] until this becomes very low (<20 μM), causing the rate to decrease. In this enhanced model, the reaction representing the cellular rate of O2 utilization is assumed to follow Michaelis-Menten kinetics (5) and is modulated by ADP/ATP and/or NADH/NAD (38). This modulation is quantified by a double Michaelis-Menten factor (ping-pong kinetics), which has been previously applied to model substrate utilization (22)φm,O2H2O=φm,O2H2Omax(1+Km,O2/Cm,O2) Cm,ADP/Cm,ATPKO2H2OA+(Cm,ADP/Cm,ATP) Equation 11 +Cm,NADH/Cm,NADKO2H2ON+Cm,NADH/Cm,NAD where Km,O2 ,K A O2 → H2 O, andK N O2H2O are parameters and φm,O2 → H2 O maxis given byφm,O2H2O(max)=φm,O2H2O(rest) +φm,O2H2O(unloaded) +αWR[1exp(t/τO2)] Equation 12Because O2 utilization is coupled to NADH oxidation and ATP formation in the mitochondria, the dynamics of NADH and ADP are affected by a reduced cellular [O2]. Therefore, a limited O2 supply to the myocites may not necessarily cause a reduction in O2 utilization, because compensatory changes in ADP/ATP and NADH/NAD could keep O2 utilization unaltered (38). However, these compensatory changes will in turn affect cellular metabolism (e.g., ADP/ATP changes modulate glycolysis, and NADH/NAD changes modulate LA metabolism). Consequently, LA metabolism and glycolysis will be regulated by cellular [O2]1) indirectly, at levels that do not affect the cellular rate of O2consumption, through compensatory changes in ADP/ATP and NADH/NAD;2) directly, at concentrations that reduce the cellular rate of O2consumption, through changes in ADP/ATP and NADH/NAD leading to enhanced anaerobic ATP production (13, 14). In a similar manner, other metabolic processes coupled to reactions involving ADP, NADH, or PC are modulated in a coordinated way through the control coefficients.

Other conversion processes considered as sources or sinks of energy substrates are expressed as a function of the WR. The rate of PY utilization to form alanine (AL) in the muscle is expressed asφm,PYAL=φm,PYAL(rest)+αpWR Equation 13The contribution of glycerol (GR) to gluconeogenesis in the splanchnic region is also assumed to be linearly related to the WRφs,GRGL=φs,GRGL(rest)+αrWR Equation 14The rate coefficients of the reactions in the splanchnic region and the other tissues compartments are assumed constant.

We assume that the muscle produces 70% and the other tissues 30% of the total AL consumed by the splanchnic region (1, 2, 34). Also, the rate of AL uptake by the splanchnic region and the rate of AL production by the other tissues are proportional to the AL production rate in muscleφs,ALPY=1.43φm,PYAL,φo,PYAL=0.43φm,PYAL Equation 15


We simulated the system responses to a step change in ATP turnover rate induced by performing mechanical work of moderate intensity for 10 min. These responses were obtained by solving the model equations using commercially available software, Scientist (MicroMath Scientific Software). The algorithm implemented in Scientist's differential equation solver is a well-tested integration program for stiff dynamic systems (EPISODE) developed at the Lawrence Livermore Laboratory (11). For these simulations, values of basal substrate concentrations and estimation of model parameters are needed.

Initial Values and Parameters Estimation

Values for in vivo substrate concentrations in tissues and arterial blood in human studies were obtained from many sources (1, 2, 13, 33), as presented previously (5). The rate coefficients at rest were estimated by fitting the basal steady-state equations to the published experimental data (tissue concentrations, blood flows, and a-v differences). In vivo muscle concentrations of modulators were obtained from studies in which biopsies were taken from the quadriceps femoris of normal men (26). The parameters representing the total pools of high energy phosphates and nicotinamide nucleotides were computed under the assumptions that the amount of muscle AMP is very small (<3%) relative to muscle ADP and ATP concentrations and that these metabolites are not synthesized de novo during the period of exercise.

In our simulations, the metabolite concentrations represent the total tissue contents and not the concentrations in free forms. We chose to use these values because published human studies from the same lab provided consistent physiological measurements useful for simulations. The nuclear magnetic resonance (NMR) values of free ADP in skeletal muscle are determined by the assumption of equilibrium of the creatine kinase reaction (20). Consequently, the values obtained from biochemical assays and NMR could differ (26), in particular, the ADP concentration in skeletal muscle (20, 26).

Parameters characterizing the dynamics of pulmonary gas exchange or the WR relationships are listed in Table 1, whereas the parameters in Michaelis-Menten functions that modulate the MRs are listed in Table 2.

View this table:
Table 1.

Parameters related to gas exchange or work rate

View this table:
Table 2.

Parameters in Michaelis-Menten functions that modulate metabolic rates

Dynamic Responses to Moderate Exercise

To examine the effect of a step increase in MR on a cycle ergometer, we performed simulations of system behavior when the WR was increased from 0 to 65 W, representing an intensity ≤40%V˙o 2 max, for 10 min. These responses are not well defined experimentally in humans, especially in the transient state because of methodological limitations, particularly when acquiring in vivo tissue metabolites. Cardiac output increased from 5.5 to 10.3 l/min, with an associated increase in the blood perfusing the muscle compartment from 0.9 to 5.7 l/min. Because V˙o 2 andV˙co 2 increased from 0.25 to 1.04 l/min and from 0.2 to 0.8 l/min, respectively, RER decreased from 0.8 to 0.77 (Fig.2 A).

Fig. 2.

Dynamic responses of A: oxygen uptake (V˙o 2), carbon dioxide output (V˙co 2), cardiac output (Q), and muscle blood flow (Qm); andB: muscle rate of O2 consumption ( Embedded Image ), as well as muscle ( Embedded Image ), arterial ( Embedded Image ) and mixed venous ( Embedded Image ) concentrations of O2 to a step increase in work rate (65 W) from resting state.

Muscle O2 utilization rose from 2.5 to 36 mM/min. Muscle [O2] decreased sharply first and then slowly from 6.0 to 2.1 mM. Arterial [O2] increased slightly from 8.8 mM at exercise onset and then decreased linearly to 8.5 mM. Mixed venous [O2] followed a pattern similar to muscle [O2] (Fig.2 B). Muscle CO2 production increased from 1.8 to 27 mM/min. Muscle, arterial, and mixed venous [CO2] increased quickly at exercise onset and then decreased slowly toward their steady-state values.

At the start of exercise, the rate of LA production increased very rapidly to a value much higher than its resting value and then decreased to its new steady-state value. The rate of LA utilization, on the other hand, increased significantly and almost immediately reached its steady-state value. Muscle LA concentration increased abruptly from 1.6 to 1.8 mM at exercise onset and then decreased slowly toward its steady-state value (1.6 mM). Arterial LA, however, rose slowly toward its steady-state value (0.7 to 0.8 mM; Fig.3 A). The rates of arterial LA input (Ia,LA) and output (Oa,LA) increased abruptly with exercise initiation and then decreased, reaching their steady-state values after 3 min. However, Ia,LArose above Oa,LA at the beginning of exercise (Fig. 3 B). The net rate of LA release by the muscle (NRm,LA) increased from 0.16 to 0.41 mM/min, whereas the splanchnic net rate of LA uptake (NUs,LA) went from 0.24 to 0.27 mM/min. The other tissues switched from releasing LA at a rate of 0.08 mM/min to taking up LA at a rate of 0.14 mM/min (Fig.4 A).

Fig. 3.

Dynamic responses of A: rate of muscle lactate production (Pm,LA), rate of lactate utilization (Um,LA), muscle lactate concentration (Cm,LA), and arterial lactate concentration (Ca,LA) andB: rate of lactate input into (Ia,LA) and output from arterial blood (Oa,LA) compared with response in arterial LA concentration (Ca,LA) to a step increase in work rate (65 W) from resting state.

Fig. 4.

Dynamic responses of A: rates of net LA release by muscle (NRm,LA), net uptake by splanchnic region (NUs,LA), and uptake/release by other tissues (URo,LA) and B: metabolic modulators in skeletal muscle, i.e., Cm,NADH/Cm,NAD, Cm,ADP/Cm,ATP, and Cm,PC/Cm,CR compared with dynamic changes in concentration of oxygen in muscle to a step increase in work rate (65 W) from resting state.

Muscle glycogen concentration decreased linearly from 85 to 82 mM, whereas arterial and muscle [GL] did not change (<1%). Muscle glucose uptake increased from 0.16 to 1.4 mM/min, whereas splanchnic glucose release increased from 0.8 to 2.0 mM/min. The rates of PY production and utilization followed a similar pattern of rapid initial increase with exercise initiation and a subsequent gradual rise toward new steady-state values. Both muscle and arterial [PY] rose rapidly toward their steady-state values, with small net increases in their concentrations (0.13–0.15 and 0.07–0.09 mM, respectively). The net rate of PY release by the muscle increased threefold, whereas the rate of PY uptake by the splanchnic region increased only 3% and in the other tissues the rate of PY release decreased by 28%.

The rates of production and utilization of NAD rose steeply toward their steady-state values, increasing from 5.7 to 75 mM/min, resulting in a drop in the NADH concentration from 0.2 to 0.11 mM. The rates of production and utilization of ADP rose sharply from 17 to 228 mM/min. The difference in their pattern of change during the transient period caused a 2% decrease in the initial [ATP] of 25.2 mM. The rate of production of PC increased quickly toward its steady-state (7.5 mM/min), but the utilization rate was slightly higher by 0.02 mM/min. This resulted in a decrease in [PC] from 80 to 75 mM. The ratios of control metabolites all reached steady state after 3 min, whereas muscle [O2] reached its steady state after 8 min (Fig.4 B).

Sensitivity Analysis

To evaluate the effect of changes in relevant parameters on model outputs directly related to LA metabolism, we include explicit sensitivity equations to the model. Model outputs of interest are the rates of LA production and utilization by the muscle; the rates of LA uptake or release by the muscle, splanchnic, and other tissues compartments; the [PY] in muscle; and the [LA] in muscle, splanchnic, and other tissues. A set of relevant parameters (θ =K N PY→LA, λPY→LAmax,K N LA→PY, λLA→PYmax) modulating the rates of interconversion between PY and LA was considered to investigate the explicit sensitivity of muscle LA concentration (Cm,LA) to changes in the parameters θi as represented by ξ = ∂Cm,LA/∂θ. Changes in the parameters modulating the rates of interconversion between PY and LA did not affect Cm,ADP, Cm,ATP, or any of the processes modulated by these metabolites. Under these circumstances, the rate of LA formation is entirely controlled by NADH/NAD. This allows us to examine the effect of NADH/NAD on LA production independently from PY changes induced by changes in ADP/ATP and enhanced glycolysis.

Examination of changes in the sensitivity coefficients, ξi, and selected model outputs to changes in model parameters, θi, showed that Cm,LA is most sensitive to changes inK N PY→LA(Fig. 5). A tenfold decrease inK N PY→LAresults in a five- to sixfold increase in ∂Cm,LA/∂K N PY→LA, which mainly affects the rates of LA production (31%) and release (37%) by muscle. Changes in Ca,LA(21%) paralleled changes in Cm,LA(22%), resulting in increases in the rates of LA uptake by the splanchnic (24%) and other tissues (61%) and increases in their LA concentrations (20%). Because the rate of PY reduction increased, muscle PY concentration decreased (−5%).

Fig. 5.

Relative changes (%) in model outputs of interest related to lactate metabolism to parameters variations from those selected to perform computer simulations during moderate exercise (A:K N PY→LA= 0.11; B:K N LA→PY= 9). From 4 parameters (K N PY→LA, λPY→LAmax,K N LA→PY, λLA→PYmax) affecting 2 control coefficients (λPY→LA; λLA→ PY) relating muscle NADH/NAD to reaction fluxes between pyruvate and lactate (φm,PY→LA, φm,LA→PY), sensitivity analysis showed that muscle lactate concentration, Cm,LA, was most sensitive to changes inK N PY→LA(see ,Control Coefficients for Muscle Compartment). Changes in parameter values of several orders of magnitude did not affect stability of solutions or affect significantly outcome of simulations.

Muscle [LA] was less sensitive to changes inK N LA→PY.A tenfold increase inK N LA→PYresults in a four- to fivefold increase in ∂Cm,LA/∂K N LA→PY, which mainly affects LA utilization (21%) and release (−22%) by muscle. Changes in Ca,LA(−11%) paralleled changes in Cm,LA (−12%), resulting in decreases in the rates of LA uptake by the splanchnic (−12%) and other tissues (−41%) and a 10% decrease in their [LA]. Because the rate of LA oxidation increased, muscle [PY] increased (2%).

We conclude that the parameter values selection for the processes regulating muscle LA metabolism are appropriate and sensitive enough to modulate LA production and utilization. Changes in parameter values of several orders of magnitude did not affect the stability of the solutions or affect significantly the outcome of the simulations. However, it provided the appropriate feedback to stimulate or inhibit the rates of the reaction processes within a physiological range.


Experimentally, the in vivo dynamics of muscle LA production and utilization have not been measured in humans during exercise. Moreover, none of the metabolic modulators of the pathways of ATP regeneration (ADP, NADH) have been studied in vivo and dynamically during exercise. On the assumption that measurement of the dynamics of these metabolites and fluxes can be accomplished in humans in vivo in the future, the relationships among them are still rather complex and require a framework for their analysis. We adapted a recently developed mathematical model of human bioenergetics at rest to permit quantitative evaluation of exercise responses (5). In particular, we analyzed hypotheses about LA metabolism and its regulation during moderate exercise. Through computer simulations, we can follow the dynamics of muscle LA production, utilization, uptake, and release as well as the dynamics of muscle NADH and ADP when a stimulus (step change in WR) is applied to the bioenergetic system. Because muscle PO2 decreases as WR increases, we simulated the in vivo mechanisms controlling the glycolytic pathway and PY reduction to evaluate the link between muscle PO2 and LA production. These simulations quantify the extent of the relationship between the rates of LA production, accumulation, and release and1) the phosphorylation state (ADP/ATP), 2) the redox state (NADH/NAD), and 3) the concentration of O2 in the contracting muscle during moderate exercise.

LA Metabolism During Exercise

Compared with exercise under normoxic conditions, submaximal exercise of short duration (≤20 min) under hypoxic conditions leads to increased [LA] in blood and muscle (16). Although these responses suggest that LA formation is dependent on O2 availability to the exercising muscles (14), the mechanistic dependency of LA formation on [O2] during submaximal exercise has not been shown quantitatively and thus remains controversial (3, 6, 9, 15, 29). The classical explanation has been that the contracting muscle during exercise is limited by the O2 availability and requires supplemental energy from anaerobic pathways producing ATP as well as LA (10). Wasserman and Koike (35) and Katz and Sahlin (14) have performed many experiments showing that perturbations leading to a decrease in O2 delivery to the muscle result in LA production and, consequently, in elevated muscle and blood LA concentration.

According to Katz and Sahlin (14), LA metabolism can be affected by low [O2] long before the rate of cellular respiration is reduced. Even under conditions of low [O2], they suggest that this rate can be maintained by increases in ADP and NADH that stimulate oxidative phosphorylation, glycolysis, and the LDH reaction, leading to increased LA production. Stainsby and Brooks (29), however, recognize hypoxia as only one possible cause of elevated muscle LA production and blood [LA]. They suggest that the underlying mechanism of increased LA production is β-adrenergic stimulation of muscle glycogenolysis.

Jöbsis and Stainsby (12) investigated whether muscle LA production is caused by a reduction in O2 supply to the mitochondria and concluded that LA production results instead from a transient imbalance between PY production by glycolysis and PY oxidation by the tricarboxylic acid cycle and oxidative phosphorylation. Other studies have observed increases in LA production by fully oxygenated contracting muscle even near maximal stimulation, concluding that LA production is not necessarily caused only by muscle hypoxia (6, 28).

Inferences about LA metabolism and oxygenation state of a particular tissue have generally been derived from measurements of [LA] in arterial blood and muscle. These concentrations change little (or not at all) after constant load, moderate intensity exercise of short duration (i.e., <20 min) (34). The typical time profile of arterial [LA] during the exercising period shows either no increase or an abrupt increase early in exercise and then a gradual return to its resting value (25). Dynamic changes in muscle [LA], on the other hand, are difficult to obtain because they require a muscle biopsy every few seconds. Even if possible to obtain, they would still give incomplete information on muscle LA metabolism. A significant improvement in the understanding of LA exchange occurred with the use of isotopic tracer techniques (31). The rates of appearance and disappearance of LA in the blood and their relationship to arterial [LA] and MR provided a different view of the role of LA in energy metabolism (31). However, neither the dynamics of the rates of LA production, utilization, and release by the muscle nor the rates of LA uptake by the splanchnic region and uptake or release by other tissues have been studied in vivo due to technical limitations. Similar limitations prevent simultaneous measurement in humans of the muscle ATP, PC, NADH concentrations and their fluxes (production, utilization).

Because the blood LA response to exercise is the net result of all exchange and transport processes between blood and the various tissues/organs producing and/or oxidizing LA (LA shuttle hypothesis), interpretation of blood LA measurements can be difficult. In addition, the mechanistic relationship between LA production by a specific tissue (e.g., active muscle), its oxygenation level, and blood [LA] during exercise is not well understood.

A key issue is why muscle and blood [LA] increase at a particular submaximal WR intensity (9). Do muscle and blood [LA] increase because there are sites of inadequate O2 supply within submaximally exercising muscle (traditional hypothesis)? Alternatively, the glycolytic rate may increase by 1) activation of key regulatory enzymes in the glycolytic pathway causing an imbalance between the fluxes that produce PY, reduce PY to LA, oxidize PY to CO2, or transport PY and NADH into the mitochondria; 2) an increase in circulating epinephrine;3) recruitment of fast twitch fibers; 4) vasoconstriction from sympathoadrenal activity resulting in decreased blood flow to liver and inactive muscle and thus decreased LA uptake and oxidation (multifactorial hypothesis).

A unifying hypothesis (near-equilibrium steady-state hypothesis) has also been proposed that addresses the regulatory mechanisms that may occur at the cellular level to compensate for the expected decline in muscle PO2 as WR increases. Under this hypothesis, as PO2 decreases, the mitochondrial oxidative phosphorylation rate and the rate of O2 consumption can be maintained through an increase in either the cytosolic ADP Pi/ATP, the intramitochondrial NADH/NAD, or a combination of both. Thus the near-equilibrium steady-state hypothesis suggests that LA formation is dependent on O2 levels through compensatory mechanisms that maintain the phosphorylation rate and the rate of O2 consumption constant. Alternatively, the traditional hypothesis suggests that LA formation results from an increase in NADH/NAD caused by a reduced rate of oxidative phosphorylation from inadequate O2 levels, whereas the multifactorial hypothesis attributes the increase in LA formation to factors other than inadequate O2levels (9).

In a recent study, Richardson et al. (23) showed the decoupling between arterial [LA] and intracellular PO2 . They observed an increase in arterial [LA] with incremental one-leg exercise, whereas the intracellular PO2 (from magnetic resonance spectroscopy) remained fairly constant at a low value. On the basis of a simple transport model, they computed an increase in the diffusional conductance (Do 2) as the major regulator of O2 flux and not intracellular PO2 . If Do 2increases during exercise due to an increase in effective surface area available for diffusion, then the flux would increase even if intracellular PO2 were constant. The experimental maximal rate of consumption by the exercising muscle, however, is dependent on its O2supply (23). This dependence of the rate of O2 demand on WR is quantitatively expressed in our model (equation 12). In addition, the actual rate of oxygen consumption varies with Cm,O2 and is modulated by the redox and phosphorylation states (equation 11).

Another important consideration is whether enzyme activities, metabolite concentrations, kinetic coefficients, and mechanisms determined in vitro are applicable in vivo. In cellular extracts and tissue preparations, the cellular organization and interaction with other organs is disregarded. By contrast, in whole organisms the relationships between organ systems and the control of physiological processes are integrated.

Model Analysis of Moderate Exercise

Typically, our model simulations provided good predictions of the changes in the main substrates and control metabolites induced by a step change in MR (Table 3). Simulations show a continuous decrease in muscle glycogen. If exercise were to be continued for a longer period of time (>4 min), the phosphorylation state had to increase and remain above its resting value to stimulate a continuous supply of carbohydrates within the muscle. As a consequence, ATP would be slightly reduced from its initial value. The net rate of GL utilization and uptake by the muscle increased by the same amount from 0.16 to 1.3 mM/min. These results are consistent with the report that the rates of GL utilization and uptake by the muscle are identical up to at least 50%V˙o 2 max, because until this point GL does not accumulate in the muscle (33).

View this table:
Table 3.

Comparison of simulated and experimental data

By model simulations, we quantify changes in metabolites regulating cellular energy metabolism and link these changes and their mechanism of regulation to observed changes in key substrates in various tissues and blood. In particular, we quantified mechanisms affecting muscle LA metabolism during moderate exercise by examining redox state (NADH/NAD), phosphorylation state (ADP/ATP), and oxygenation and their effects on the rates of LA production and utilization in skeletal muscle. Changes in ADP/ATP affect primarily glycogenolysis, glycolysis, PY oxidation, and tricarboxylic acid cycle. Changes in the redox state affect a partially different set of processes: glycolysis, LA oxidation, PY oxidation, and tricarboxylic acid cycle. A marked drop in muscle [O2] affects only oxidative phosphorylation, but may cause adaptive changes in redox state, phosphorylation state, or both.

Immediately after the onset of the exercise stimulus, the muscle's rate of LA production rose fivefold and LA utilization decreased ∼12%, mainly due to a 36% increase in redox state and a 14% increase in [PY]. The increase in [PY] was due to a threefold transient increase in ADP/ATP, which remained 20% above resting levels during steady state and stimulated the rates of glycogenolysis and glycolysis. In the phase after exercise stimulus, the redox state dropped exponentially to half its resting value, which stimulated glycolysis, LA oxidation, the tricarboxylic acid cycle, and fatty acid oxidation and inhibited LA formation and oxidative phosphorylation.

The dynamics of NADH/NAD and ADP/ATP followed a similar pattern of abrupt transient increase and then an exponential decrease toward their steady-state values. However, whereas NADH/NAD increased initially by 35% and then decreased toward 50% its resting value, ADP/ATP increased threefold and then decreased toward a value 20% above its resting value. Muscle [O2], on the other hand, decreased monotonically to 30% its resting value, which still is two orders of magnitude larger than the critical concentration that would reduce the rate of O2consumption by half. This level of O2 in the muscle (∼2 mM) would have caused a negligible change in the redox state (<0.1%). Thus the drop in muscle O2 concentration induced by exercise of moderate intensity was not large enough to significantly affect muscle redox state and, consequently, LA formation. If [O2] had significantly reduced the rate of O2 consumption below that required for the metabolic demand, then the redox state would most likely have remained above its resting value in the steady state (toward reduction) to stimulate cellular respiration and consequently LA formation. Except for 15 s after exercise initiation, the redox state did not remain above its initial value during the exercising period and allowed LA utilization. In contrast, the phosphorylation state (ADP/ATP) increased markedly immediately after WR input and then remained at a higher steady state. This rise in ADP/ATP stimulated glycogenolysis, glycolysis, and cellular respiration, resulting in an abrupt increase in PY. During exercise of moderate intensity, the O2 in the tissue is adequate even during the transient state. Furthermore, increases in muscle and arterial blood [LA] are mainly due to the sudden increase in the glycolytic rate and LA production stimulated at exercise initiation by abrupt changes in phosphorylation state and redox state, respectively.

LA Production Hypothesis

Our model simulations are compatible with the hypothesis that LA production can occur in fully oxygenated contracting muscles. These simulations show that LA is produced at rest and its rate of production increases during exercise when the muscles are fully oxygenated ( Cm,O2 ∼2 mM). Simulations are also compatible with the hypothesis that LA production results from a transient imbalance between PY production by glycolysis and PY oxidation by the tricarboxylic acid cycle and oxidative phosphorylation. Thus LA production is not necessarily caused only by muscle hypoxia. In fact, LA production can be increased by low [O2] long before the rate of cellular respiration is significantly reduced (14). Model simulations of respiratory hypoxia show that a small reduction in the cellular rate of respiration induced by low muscle [O2] (but above the critical O2 value) can cause a large increase in muscle LA production through changes in the redox state (5).

Feedforward and feedback control mechanisms interact to maintain muscle ATP homeostasis in the presence of an exercise stimulus. Feedforward control (represented by relative MR parameters) provides immediate metabolic coarse regulation and leads to overshoot in some metabolites. The feedback control (represented by metabolic modulator ratios: ADP/ATP, NADH/NAD, PC/CR) provides the steady-state metabolic regulation. These change redox and phosphorylation states to maintain stimulation of the appropriate metabolic pathways to keep [ATP] fairly constant at the MR for sustained exercise.

The total rate of LA input into the blood increased from 0.24 mM/min at rest to 0.41 mM/min at 65 W. The difference between the rates of muscle LA production and utilization increase with exercise, resulting in a larger net rate of LA production and release (0.41 mM/min). LA release by the muscle represents the only source of LA release into the circulation during steady-state moderate exercise. The largest changes in muscle and arterial [LA] occur during the transient state because of the large initial change in the rates of muscle LA production and input into the blood. Even though muscle [LA] was the same at steady-state exercise as at rest, the rates of muscle LA production and utilization increase and remain at a higher level than at rest. Similarly, blood [LA] remains almost the same during exercise as at rest. However, the rates of LA input into the blood (appearance) and output from the blood (disappearance) increase with exercise. Although these rates converge to the same value, the difference between the rates of muscle LA production and utilization widens with exercise and increases the rate of muscle LA release. In the other tissues compartment, LA is produced and released at rest, but taken up and utilized during exercise. This emphasizes the need for additional information (e.g., arterial/venous samples across various tissues, fluxes using tracers) when judging tissue LA metabolism. It cannot be based solely on arterial LA concentration measurements. Our model simulations show quantitatively that LA metabolism and exchange are important for distributing carbohydrate energy sources during exercise, i.e., the LA shuttle hypothesis (3).

Comparison of Simulated and Experimental Responses

We compared results from the model simulations for 10 min of exercise to data obtained under similar conditions with a group of healthy adults (33). The physiological data consist of measurements in the resting state and during upright exercise for 10 min on a cycle ergometer at a WR of 65 W (Table 3). Simulations and experimental data show a fourfold increase inV˙o 2. Carbon dioxide output showed a tendency to overshoot during the transient and reached a slightly lower steady state than experimentally observed data. The tendency to overshoot is most likely a normal response, which was not sustained due to a drop in CO2production at the cellular level.

The RER increased a few percent in the experiment (0.77 ± 0.01 to 0.79 ± 0.02), but dropped a few percent in the simulation (0.80 to 0.77). Several factors may contribute to this small simulated decrease of the RER response: 1) fatty acid oxidation is represented as a source (flux) of reducing equivalents and CO2 and not as a dynamic metabolic variable; 2) acetyl CoA is not considered as a separate substrate, because the present study emphasizes control of glycolysis and LA formation;3) the flux representing the rate of fatty acid utilization to form CO2is not controlled by NADH/NAD. These factors can affect the rates of carbohydrate and fatty acid oxidation, the production of CO2, and consequently the RER. The current model does not provide a mechanism to gradually increase reliance on carbohydrate rather than on fatty acid oxidation with increasing exercise intensity. This limitation is not expected to affect our conclusions because the experimental increase in RER is only 2%. Greater reliance on carbohydrate metabolism might, however, increase the turnover rates for glycogen, glucose, PY, and LA and enhance simulated responses. For simulations of higher WRs, a mechanism for a gradual shift in substrate oxidation should be included (24).

The arterial concentrations of GL, PY, and LA showed an increase in both experiment and simulation. For glucose and LA, the simulated change was smaller than the experimental change. This underestimation may be associated with a lower simulated rate of glycogen utilization, which in part may be due to the equal stimulation of glycogen breakdown and fatty acid oxidation assumed in the model.

Simulated metabolite concentrations were compared with corresponding experimental data (45) from bicycle exercise for 10 min at 40%V˙o 2 max (115 W). Because our simulations are for a WR of 65 W (25–30%V˙o 2 max), the experimental data would be expected to show larger changes in some metabolite concentrations. Muscle content of NADH changes in a similar way in both experimental and simulated data. The ATP content decreased from 25 mM by 3% in both the simulated and experimental data. The muscle PC concentration decreased 6% from 80 mM in the model simulation and decreased 11% from 79 mM in the experimental data (Table 3). Larger decreases in PC concentration have been observed experimentally. Mole et al. (20) used NMR spectroscopy to evaluate dynamic changes in human forearm muscle pH, [ATP], [PC], and [Pi] during the transition from rest to steady-state exercise. The exercise consisted of repeatedly squeezing the bulb of a pneumatic handgrip ergometer at a rate of 30 contractions/min against 200 mmHg. A transient increase in ATP (first 25 s) and then a decay toward a lower steady state was observed. The initial drop in PC was larger than the increase in Pi, accounting for the transient increase in ATP and thus the biphasic nature of its dynamics. The increase in [ATP] observed in this study is very intriguing, because previous experiments performed on cycle ergometers and using muscle biopsies have showed [ATP] to remain unchanged or to fall slightly. However, the experimental conditions are quite different. Supine forearm exercise in a magnet does not increase oxygen uptake at levels comparable to upright cycle ergometer exercise at 65–115 W.

Model of Bioenergetics

To our knowledge, no other dynamic model exists that quantitatively describes the human bioenergetic processes and links cellular metabolism and its control to whole body responses. Mathematical models of LA kinetics and bioenergetic processes have been developed to explain the observed blood LA changes during or after exercise (7, 21,32, 39). Stegmann et al. (32) developed a compartmental model in which diffusion from the muscle into the blood compartment and elimination from the muscle compartment are considered. That model permits estimation of parameters characterizing LA kinetics during and after exercise and emphasizes the need for individual assessment of the LA threshold at the point where the maximal rate of elimination is in equilibrium with the rate of diffusion. This equilibrium point was labeled “individual anaerobic threshold” by Stegmann et al. Zouloumian and Freund (39) developed a two-compartment model of LA kinetics to analyze blood [LA] collected at short time intervals (10–30 s) after exercise on a cycle ergometer (8, 39). The postexercise rate of LA production in both compartments was considered constant, whereas the rates of LA utilization and release were assumed to be proportional to the LA contents of these compartments. These models, however, cannot simulate transient responses during submaximal exercise because the rates of LA production and/or utilization are absent or assumed constant.

The first theoretical model of human bioenergetics during exercise was proposed by Margaria (18) and was later generalized and implemented mathematically by Morton (21). This model includes the three sources of energy of the body and is tested withV˙o 2 responses to a step (submaximal) input in WR. Morton's dynamic model (21) represents the energy flows (V˙o 2, LA production, and PC breakdown) during exercise and recovery but does not include the dynamics of control metabolites. Control metabolites (e.g., AMP, ADP, PC) are included in the model of Mader and Heck (17) to describe the metabolic pattern of muscle LA in the working muscle or the whole body at a submaximal WR. Although this metabolic model helps to understand the origin of the “anaerobic threshold” during incremental exercise, it cannot describe dynamic responses to disturbances. Furthermore, previous models are not general enough to take into account tissues with distinct metabolic characteristics (e.g., liver, active muscle, heart), other substrates (e.g., glycogen, glucose, fatty acids, amino acids) for energy production, or other physiological conditions (e.g., hypoxia, glucose infusion).

The model presented here predicts, in muscle and blood, the transient responses of the concentrations and fluxes of LA and other substrates involved in energy metabolism and provides an integrated systems approach to facilitate metabolic regulation analysis during exercise. Dynamic mass balances and mechanistic kinetics describe processes in muscle, splanchnic, and other body tissues for many substrates and modulators through coupled reaction processes. Although our dynamic model includes various body tissues and many substrates, it still represents only a gross approximation to the actual physiological system. Neural or hormonal control of glucose and other metabolites are not taken into account. The brain, heart, and adipose tissue are lumped in a single compartment. The assumption of homogeneous compartments is a major limitation of the model, which restricts the spectrum of its applications (e.g., localized ischemia, muscle fibers with different metabolic characteristics). Many sequential biochemical reactions are described in an overall lumped form. Using a top-down approach to modeling metabolic processes, we do not attempt to incorporate a fully detailed model of all behavior at the cellular level. Nevertheless, the model represents a reasonable approximation of the human bioenergetic system. From comparisons of model predictions with experimental data, we believe that our model provides a good basis for quantitative representation of the regulatory, metabolic, and transport processes involved in ATP homeostasis at cellular, tissue/organ, and whole body levels.

Critical Experiments

According to the objectives of this study, the most important coefficients are those directly affecting the muscle rates of production and utilization of LA, i.e., λPY→LA and λLA→PY. These depend on the parametersK N PY→LA, λPY→LAmax,K N LA→PY, λLA→PYmax, and Cm,NADH/Cm,NAD. Sensitivity analysis shows that these parameters are key for regulating muscle LA metabolism and sensitive enough to modulate LA production and utilization. Although it is important to distinguish production and utilization in skeletal muscle, in vivo human studies have measured only the net rates of uptake or release of LA. In cardiac muscle, however, Stanley (30) demonstrated with tracer studies that the rate of LA utilization was smaller than the rate of myocardial LA uptake due to dilution from unlabeled LA produced by the heart. A similar method could be used to distinguish between the rates of LA production and release by contracting skeletal muscle. We would expect at rest and during exercise that the rate of LA production is larger than the rate of LA release due to simultaneous LA utilization by the muscle. This information is crucial to quantitatively understanding the control of muscle LA metabolism, particularly at high exercise intensity and increased rate of glycolysis. At the same net flux from PY to LA, when the cycling rate between PY and LA is greater, the sensitivity in control of this reversible pathway is greater and the change in muscle NADH/NAD concentration ratio required to produce high rates of LA production is smaller.

Further validation of our model and its quantitative predictions requires measurements of the dynamic responses of1) regional blood flows and2) substrate fluxes (production, utilization) to step changes in MR (e.g., exercise), especially of substrates participating in branching pathways (e.g., PY) or in futile cycles (glycogen, glucose). Determining the perfusion patterns of the tissues/organs at various exercise intensities is essential in the calculation of the substrate input and output fluxes, for example, in determining oxygen delivery at the onset of exercise. Evaluating the forward and reverse reaction fluxes in futile cycles such as glycogenolysis and glycolysis will quantitatively determine the control sensitivity. High sensitivity needed to control these key pathways requires a high rate of cycling (production or utilization) compared with the net flux through the pathway (production minus utilization). In this manner, small changes in key modulators (e.g., ADP/ATP) can produce a large response in reaction processes with futile cycles (e.g., glycogenolysis and glycolysis) through enormous increases in the activity of the enzymes catalyzing them.

To understand the control processes involved in the regulation of [ATP] during exercise it is critical to measure the ATP turnover rate and the mitochondrial respiratory rate in vivo, as well as [ATP], [ADP], and Pi changes; [PC]; intracellular pH; and mitochondrial redox state in contracting muscle after the onset of exercise. However, because [ATP] is highly regulated, a time resolution of 1 s in the measurements would be needed to describe the dynamics of metabolic modulators during the transition from rest to exercise.

In conclusion, our model provides a framework for analyzing disparate experimental information given in the literature and for examining the validity of several types of mechanisms during moderate exercise. At the macroscopic level, the model allows us to quantify the contributions of various tissues/organs to the dynamics of blood [LA]. At the microscopic level, the model allows us to quantify the effects of metabolic modulators (e.g., ADP/ATP, NADH/NAD) in the integrative control of glycolysis and LA formation.

Model simulations provide quantitative insight into the mechanisms affecting LA production and its control (in humans performing exercise in the upright position on a cycle ergometer) at intensities that do not induce a sustained elevation in blood or muscle [LA]. Experimentally, these adaptations to a rest-work transition have not been observed because the interval between biopsies or blood samples is too large (>30 s). New experimental studies are needed to test this theory.


We are grateful for the helpful discussions and input provided by Dr. Brian J. Whipp, Dr. Linda S. Lamont, Dr. Richard J. Connett, Dr. Thomas J. Barstow, and Dr. William C. Stanley.


  • Address for reprint requests and other correspondence: M. E. Cabrera, Pediatric Cardiology, RBC-380N, Rainbow Babies and Children's Hospital, 11100 Euclid Ave., Cleveland, OH 44106-6011 (E-mail:mec6{at}

  • This work was supported in part by a National Institutes of General Medical Sciences Predoctoral Fellowship GM-14863.

  • The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.


Muscle Compartment

  Vm(dCm,GY/dt) = φm,GL → GY − φm,GY → GLVm(dCm,GL/dt) = φm,GY → GL + 0.5 φm,PY → GL − φm,GL → GY −  φm,GL → PY + Qm(Ca,GL − ςm,GLCm,GL) Vm(dCm,PY/dt) = 2φm,GL → PY + φm,LA → PY − φm,PY → AL − φm,PY → LA −  φm,PY → CO2 + Qm(Ca,PY − ςm,PYCm,PY) Vm(dCm,LA/dt) = φm,PY → LA − φm,LA → PY + Qm(Ca,LA − ςm,LACm,LA) Vm(dCm,O2/dt) = −φm,O2 → H2 O+ Qm(Ca,O2 − ςm,O2Cm,O2) Vm(dCm,CO2/dt) = 3φm,PY → CO2 + 16φm,FA → CO2 + φm,HCO3 → CO2 +  Qm(Ca,CO2 − ςm,CO2Cm,CO2) Vm(dCm,NAD/dt) = φm,PY → GL + φm,PY → LA + 2φm,O2 → H2 O −  2φm,GL → PY − φm,LA → PY − 5φm,PY → CO2 − 43φm,FA → CO2Vm(dCm,ADP/dt) = 2φm,PY → GL + φm,GL → GY + φm,CR → PC +  φm,ATP → ADP − 2φm,GL → PY − φm,GY → GL − φm,PC → CRVm(dCm,PC/dt) = φm,CR → PC − φm,PC → CR Cm,NAD + Cm,NADH = Cm,TN Cm,ATP + Cm,ADP = Cm,TA Cm,PC + Cm,CR = Cm,TC

Splanchnic Compartment

  Vs(dCs,GY/dt) = φs,GL → GY − φs,GY → GLVs(dCs,GL/dt) = φs,GY → GL + φs,GR → GL + 0.5 φs,PY → GL − φs,GL → GY+  Qs(Ca,GL − ςs,GLCs,GL) Vs(dCs,PY/dt) = 2φs,GL → PY + φs,AL → PY + φs,LA → PY − φs,PY → GL+  Qs(Ca,PY − ςs,PYCs,PY) Vs(dCs,LA/dt) = −φs,LA → PY + Qs(Ca,LA − ςs,LACs,LA) Vs(dCs,O2/dt) = −φs,O2 → H2 O+ Qs(Ca,O2 − ςs,O2Cs,O2) Vs(dCs,CO2/dt) = 16φs,FA → CO2 + Qs(Ca,CO2 − ςs,CO2Cs,CO2)

Other Tissues Compartment

  Vo(dCo,GL/dt) = 0.5φo,PY → GL − φo,GL → PY + Qo(Ca,GL − ςo,GLCo,GL) Vo(dCo,PY/dt) = 2φo,GL → PY + φo,LA → PY − φo,PY → AL − φo,PY → LA −  φo,PY → CO2 + Qo(Ca,PY − ςo,PYCo,PY) Vo(dCo,LA/dt) = φo,PY → LA − φo,LA → PY + Qo(Ca,LA − ςo,LACo,LA) Vo(dCo,O2/dt) = −φo,O2 → H2 O+ Qo(Ca,O2 − ςo,O2Co,O2) Vo(dCo,CO2/dt) = 3φm,PY → CO2 + 16φo,FA → CO2 + Qo(Ca,CO2 −  ςo,CO2Co,CO2)

Alveolar Compartment

  VA(dCA,GL/dt) = Q(Cv,GL − Ca,GL) VA(dCA,PY/dt) = Q(Cv,PY − Ca,PY) VA(dCA,LA/dt) = Q(Cv,LA − Ca,LA) VA(dCA,O2/dt) =M˙A,O2 + Q(Cv,O2− Ca,O2) VA(dCA,CO2/dt) =M˙A,CO2 + Q(Cv,CO2− Ca,CO2)

Control Coefficients for Muscle Compartment



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