Muscle cells produce lactate and become acidic (9) during anaerobic glycogenolysis and during intense aerobic glycolysis, giving rise to net lactic acid production. The identity of the mechanisms involved and the size of their contributions to acidosis in muscle during exercise were debated extensively in 2005 (3, 7, 8, 12, 14, 15) and 2008 (2, 11) and now again. One reason for these continued disputes is the lack of quantitative analyses of the proton loads generated by biochemical reaction fluxes and proton transport fluxes that result in the observed cellular pH transients. Here we argue that our kinetic model, based on analysis of the time courses of phosphate metabolites and pH in intact muscle, provides definitive answers. All reactions produce or take up H+ as described below; only the lactate dehydrogenase reaction produces lactate−. Thus lactic acid is the result of a network of reactions advancing in an aqueous solution with all substrates and products in rapid equilibrium with free cations within the cell.
Reactions that generate lactate and H+.
Breakdown of glucose or glycogen to lactate anion through the reactions of glycolysis occurs without generating significant H+ (see Fig. 1 and discussion below). Hence other reaction(s) must generate H+ in substantial amounts to change intracellular pH in the face of high buffer capacity. Our analysis (17) demonstrates that only cellular ATP hydrolysis (ATPase) flux generates sufficient H+ to acidify the cytoplasm during anoxia. The H+ and lactate generated separately remain nearly completely dissociated with <0.1% in the form of undissociated lactic acid because its pKa ∼ 4 and cellular pH ∼ 7.
Lactate and H+ ratio from glycolysis and ATP hydrolysis in the steady state.
Gevers (5) treated biochemical reactants as multiple cation bound species and calculated that in the steady state the breakdown of glucose alone to synthesize two ATP and two lactate molecules per glucose molecule generated no proton load, but the hydrolysis of the generated ATP molecules produced one proton per ATP at physiological pH and ionic conditions. (Proton load is defined as the net number of free hydrogen ions generated.) Hochachka and Mommsen (6) showed that the net proton load generated by glycogenolysis coupled to ATPase resulted in the generation of two protons and two lactate molecules per glucose unit independent of the pH. The muscle cell pH, in turn, is determined by proton transport across the sarcolemma, proton buffering, and the net metabolic proton flux, which is given by the algebraic sum of the products of proton stoichiometry and the fluxes through biochemical reactions. During a steady state the proton stoichiometric coefficients may be added and then multiplied with the steady-state flux to obtain the metabolic proton flux. However, during metabolic transients, the proton stoichiometries of reactions may not be summed as, simply, due to dynamic changes in proton binding to biochemical reactants. To establish a causal relationship between biochemical reaction fluxes and pH transients, the time courses of biochemical reactants and the consequent metabolic proton loads could be computed by applying known enzyme kinetics and physical chemistry of multiple cation equilibria.
Computing pH time courses due to biochemical reaction and transport processes.
Vinnakota and colleagues (16, 18) computed pH time courses due to biochemical reaction fluxes by treating biochemical reactants as a sum of cation bound species in a dynamic computational model. The following equations summarize our approach for muscle cell cytoplasm assuming relatively constant free magnesium and potassium ion concentrations: (1) where β is the buffer capacity of the muscle cell cytoplasm.
The rate of change of proton concentration is given by the following differential equation: (2) where Jtransport is the total proton influx into the cytoplasm due to sarcolemmal proton transport mechanisms, ΔrNHk is the proton stoichiometry of the kth biochemical reaction, ϕrk is the flux through the kth biochemical reaction, Ci is the concentration of the ith biochemical reactant including histidine related proton buffers, and ΔN̄Hi/Δ[H+] is the partial derivative of the average proton binding N̄Hi (defined as the fraction of the biochemical reactant bound to protons) of the ith biochemical reactant. The time courses of biochemical reactant concentrations Ci are simultaneously computed by solving ordinary differential equations that describe the rate of change of each Ci as the algebraic sum of fluxes generating and consuming the total biochemical reactant.
Defining pH as −log10([H+]), we obtain: (3)
The buffer capacity due to both histidine related proton buffers and biochemical reactants is given by: (4)
Buffering by the CO2/HCO3− may be defined as an additional proton flux while accounting for the CO2 generation and hydration and the transport of CO2 and HCO3− across various physiological spaces. See Vinnakota and colleagues (16, 17) for a detailed derivation of Eq. 2 and Alberty (1) for a broad overview on multiple cation equilibria in biochemical thermodynamics.
Lactate and H+ ratio from glycolysis and ATP hydrolysis during transient anoxia.
We applied the approach summarized in Eqs. 1–4 to analyze the time courses of phosphocreatine, inorganic phosphate, and pH measured using NMR in superfused mouse extensor digitorum longus (EDL) and soleus muscles and of total lactate in the buffer outflow following transient resting anoxic perturbation of various durations (17). A detailed picture of proton consumption fluxes from our analysis in mouse EDL during anoxia in Fig. 1 (redrawn from Fig. 9 in Ref. 17) shows that 1) the net H+ production of the 13 reactions in the glycogenolytic and glycolytic pathway sums to zero; 2) ATPase is the major source of H+ production and; 3) the creatine kinase reaction is an important source of H+ uptake as PCr concentration declines during a transient metabolic stress due to anoxia. This is a key result of the analysis and simulations relevant to the question of the source(s) of proton production and uptake, which confirms the essential validity of simpler analyses (5, 6, 10). During the early phase of anoxia (∼15 min) the large magnitude of proton consumption flux through creatine kinase relative to other proton fluxes results in a net alkalinization. The inset in Fig. 1 (redrawn from Fig. 10 in Ref. 17) further shows that the lactate generation computed by integrating the flux through the lactate dehydrogenase reaction and proton load computed by integrating the total metabolic proton flux , have a ratio of 1.06 during anoxia after the first 15 min. In addition, recent work demonstrated a 1:1 relationship (within experimental error) between proton load calculated from PCr, Pi, and pH changes measured using 31P-NMR and chemical measurements of lactate during ischemia in mouse muscle in vivo (13). In summary, evidence from experimental data and theoretical studies shows that lactate and protons generated from different biochemical reactions bear a near 1:1 relationship during anaerobic glycogenolysis coupled to ATP hydrolysis. This 1:1 relationship between lactate generation and metabolic H+ generation may be disrupted when ATP hydrolysis flux is uncoupled from glycogenolysis.
What remains to be learned?
During intense muscle contractions, the transition from the initial alkalinizing state to the acidotic state can be expected to be much faster with a 1:1 relationship between lactate and proton generation during the acidotic state, but model analysis of experiments of this type have not been published yet. Additionally, the contribution of mitochondrial oxidative phosphorylation, mitochondrial transport of metabolites and transfer of reducing equivalents, glycolysis and ATPase, and sarcolemmal proton transport to the observed pH transients during aerobic muscle contractions have not been worked out. The analysis of oxidative glycolysis and the resulting pH transients during aerobic muscle contractions requires a quantitative model of the dynamics of glycolysis coupled to oxidative phosphorylation. Such models could be constructed by integrating existing validated models of glycolysis (17), mitochondrial oxidative phosphorylation and the Krebs cycle (19), and sarcolemmal proton transport mechanisms (4) with a suitable model of muscle perfusion.
- Copyright © 2011 the American Physiological Society