Transient kinetics of thermodynamic buffering

Metabolic systems maintain stable non-equilibrium via thermodynamic buffering

Here, we analyze how the set of nucleotides in the cell is equilibrated and how this generates simple rules that help the cell to organize itself via maintenance of a stable non-equilibrium state. A major mechanism operating to achieve this state is thermodynamic buffering via high activities of equilibrating enzymes such as adenylate kinase. Under stable non-equilibrium, the ratios of free and Mg-bound adenylates, Mg(2+) and membrane potentials are interdependent and can be computed. The adenylate status is balanced with the levels of reduced and oxidized pyridine nucleotides through regulated uncoupling of the pyridine nucleotide pool from ATP production in mitochondria, and through oxidation of substrates non-coupled to NAD(+) reduction in peroxisomes. The set of adenylates and pyridine nucleotides constitutes a generalized cell energy status and determines rates of major metabolic fluxes. As the result, fluxes of energy and information become organized spatially and temporally, providing conditions for self-maintenance of metabolism.

Thermodynamics and bioenergetics

Bioenergetics is concerned with the energy conservation and conversion processes in a living cell, particularly in the inner membrane of the mitochondrion. This review summarizes the role of thermodynamics in understanding the coupling between the chemical reactions and the transport of substances in bioenergetics. Thermodynamics has the advantages of identifying possible pathways, providing a measure of the efficiency of energy conversion, and of the coupling between various processes without requiring a detailed knowledge of the underlying mechanisms. In the last five decades, various new approaches in thermodynamics, non-equilibrium thermodynamics and network thermodynamics have been developed to understand the transport and rate processes in physical and biological systems. For systems not far from equilibrium the theory of linear non-equilibrium thermodynamics is used, while extended non-equilibrium thermodynamics is used for systems far away from equilibrium. All these approaches are based on the irreversible character of flows and forces of an open system. Here, linear non-equilibrium thermodynamics is mostly discussed as it is the most advanced. We also review attempts to incorporate the mechanisms of a process into some formulations of non-equilibrium thermodynamics. The formulation of linear non-equilibrium thermodynamics for facilitated transport and active transport, which represent the key processes of coupled phenomena of transport and chemical reactions, is also presented. The purpose of this review is to present an overview of the application of non-equilibrium thermodynamics to bioenergetics, and introduce the basic methods and equations that are used. However, the reader will have to consult the literature reference to see the details of the specific applications.

Photomodulation of oxidative metabolism and electron chain enzymes in rat liver mitochondria

Low-level laser irradiation has been applied in a variety of laboratory studies and clinical trials for photobiostimulation over the last three decades. Considerable skepticism exists regarding the concept of photostimulation within the medical community. One of the major difficulties with photoirradiation research is that it lacks experimentally supportable mechanisms for the alleged photobiostimulatory effects. This study was undertaken to determine whether oxidative metabolism and electron chain enzymes in rat liver mitochondria can be modulated by photoirradiation. Oxygen consumption, phosphate potential, and energy charge of rat liver mitochondria were determined following photoirradiation. Activities of mitochondrial enzymes were analyzed to assess the specific enzymes that are directly involved with the photostimulatory process. An argon-dye laser at a wave-length of 660 nm and at a power density of 10 mW/cm2 was used as a photon source. Photoirradiation significantly increased oxygen consumption (0.6 J/cm2 and 1.2 J/cm2, P < 0.05), phosphate potential, and the energy charge (1.8 J/cm2 and 2.4 J/cm2, P < 0.05) of rat liver mitochondria and enhanced the activities of NADH: ubiquinone oxidoreductase, ubiquinol: ferricytochrome C oxidoreductase and ferrocytochrome C: oxygen oxidoreductase (0.6 J/cm2, 1.2 J/cm2, 2.4 J/cm2 and 4.8 J/cm2, P < 0.05). The activities of succinate ubiquinone oxidoreductase, ATPase, and lactate dehydrogenase were not affected by photoirradiation.

Alterations in mitochondrial function and morphology in chronic liver disease: pathogenesis and potential for therapeutic intervention

Studies assessing mitochondrial function and structure in livers from humans or experimental animals with chronic liver disease, including liver cirrhosis, revealed a variety of alterations in comparison with normal subjects or control animals. Depending on the etiology of chronic liver disease, the function of the electron transport chain and/or ATP synthesis was found to be impaired, leading to decreased oxidative metabolism of various substrates and to impaired recovery of the hepatic energy state after a metabolic insult. Changes in mitochondrial structure include megamitochondria with reduced cristae, dilatation of mitochondrial cristae and crystalloid inclusions in the mitochondrial matrix. The most important strategies to maintain an adequate mitochondrial function per liver are mitochondrial proliferation and increases in the activity of critical enzymes or in the content of cofactors per mitochondrion. Possibilities to assess hepatic mitochondrial function and to treat mitochondrial dysfunction in patients with chronic liver disease are discussed.

Reduced activity of the electron transport chain in liver mitochondria isolated from rats with secondary biliary cirrhosis

Mitochondrial metabolism was studied in liver mitochondria isolated from rats with secondary biliary cirrhosis induced by bile duct ligation for 5 wk. State 3 oxidation rates were decreased in mitochondrial preparations from bile duct-ligated rats as compared with sham-operated control rats by 63% and 42% using beta-hydroxybutyrate and succinate as substrates, respectively. In contrast, when the substrate was ascorbate/N,N,N',N'-tetramethyl-p-phenylenediamine state 3 oxidation rates were not affected by bile duct ligation. Oxidation rates after uncoupling with dinitrophenol were decreased for both beta-hydroxybutyrate and succinate as substrates in mitochondria from bile duct-ligated rats. The phosphate potential was reduced in mitochondria from bile duct-ligated rats (12.5 +/- 0.5 vs. 13.6 +/- 0.2 kcal in control and bile duct-ligated rats, respectively; p less than 0.05). The inner mitochondrial membrane of liver mitochondria from rats with secondary biliary cirrhosis contained three times more cholesterol as compared with control rats, whereas the phospholipid composition was essentially unchanged. Mitochondrial protein content expressed per liver (calculated on the basis of activities of mitochondrial enzymes determined in liver homogenate and in isolated mitochondria) was increased by 50% in bile duct-ligated rats as compared with control rats. In conclusion, the function of the electron transport chain in liver mitochondria isolated from rats with secondary biliary cirrhosis is impaired. This decrease could be related to altered lipid composition of the inner mitochondrial membrane.

Adaptation of mitochondrial metabolism in liver cirrhosis. Different strategies to maintain a vital function

Mitochondrial function and structure in cirrhotic livers from humans or rats show a variety of changes as compared to control livers. Mitochondrial ATP production is reduced in rats with CCl4- or thioacetamide-induced liver cirrhosis and in rats with secondary biliary cirrhosis. Activity of the electron transport chain is decreased in rats with secondary biliary cirrhosis. In rats with CCl4-induced cirrhosis, the mitochondrial content of certain constituents of the respiratory chain (cytochrome a + a3, cytochrome b and ubiquinone) is increased and activities of cytochrome c oxidase and ATPase are elevated. Similarly, in humans with liver cirrhosis, mitochondrial cytochrome a + a3 content is elevated and has been used to assess the risk for hepatectomy. In rats with secondary biliary cirrhosis, compensatory strategies include increased mitochondrial volume per hepatocyte and possibly increased extramitochondrial ATP production (increased glycolysis). Thus, a variety of adaptive mechanisms are used to maintain mitochondrial function in cirrhotic livers.

Non-equilibrium thermodynamic sensitivity of oxidative phosphorylation

A new method was developed to analyse the dynamic properties of oxidative phosphorylation, in particular the sensitivity of the phosphate potential with respect to fluctuating cellular ATP utilization. This treatment is based on the eigenvalue sensitivity analysis of an experimentally supported non-equilibrium thermodynamic model of oxidative phosphorylation. Such an analysis allows direct access to the kinetic information, while circumventing the awkward conventional numerical integration of a set of nonlinear differential equations. This procedure revealed, for the parameters characteristic for liver of starved rats in vivo, that the sensitivity of oxidative phosphorylation to a fluctuating ATP utilization is minimal at a degree of coupling q = 0.95. This means that the phosphate potential is highly buffered with respect to fluctuating energy demands at the degree of coupling. This value of q agrees well with the degree of coupling qeef, at which net ATP production of oxidative phosphorylation--at optimal efficiency--occurs in the most economic way. This simultaneous maximization of kinetic stability and economic thermodynamic efficiency at the same degree of coupling appears to be a coincidence.

Mitochondrial function in carbon tetrachloride-induced cirrhosis in the rat. Qualitative and quantitative defects

Mitochondrial function is impaired in patients and experimental animals with liver cirrhosis. The relationship between mitochondrial impairment and severity of cirrhosis is unknown, however. We therefore characterized the severity of cirrhosis in rats with phenobarbital/CCl4-induced cirrhosis by the aminopyrine breath test, a microsomal function test reflecting hepatocellular mass. Mitochondrial function was evaluated by measuring oxygen consumption, enzyme activities and ATP production in mitochondria isolated from cirrhotic (N = 8) and control livers (N = 4). Oxygen consumption and mitochondrial enzyme activities calculated per liver were significantly reduced in the presence of cirrhosis. This decrease corresponded to the loss of hepatocytes calculated from the reduction in aminopyrine breath test. The effect of atractylate, oligomycin and dinitrophenol on state 3 respiration was equal between the two groups. The respiratory control ratio was significantly reduced in mitochondria from cirrhotic livers with beta-hydroxybutyrate (4.01 +/- 0.94 vs 5.45 +/- 0.40), but not with succinate as substrate. The rate of ATP production was significantly decreased in mitochondria from cirrhotic rats for both substrates. In contrast, the static head (state 4) phosphate potential was fully developed after 10 min and was equal between the two groups. We conclude that cirrhosis of the liver leads to a loss of hepatocytes which is paralleled by reduced oxygen uptake and reduced mitochondrial enzyme activities.

The adenylate kinase reaction acts as a frequency filter towards fluctuations of ATP utilization in the cell

The buffering ability of the adenylate kinase reaction with respect to the phosphate potential and efficiency of oxidative phosphorylation in the presence of a fluctuating load conductance were studied by computer simulations. Fluctuations of the load conductance, i.e., of the irreversible ATP-utilizing reactions in the cell, were generated by integrating an Ornstein-Uhlenbeck diffusion process. This real or colored noise was then injected into the set of differential equations describing the rate laws for the changes of the adenine nucleotide concentrations based on a simple nonequilibrium thermodynamic model of oxidative phosphorylation. Numerical integration of this system of stochastic differential equations allowed us to investigate the influence of different parameters on the performance of this energy converter. Probability density estimates revealed that the variance of the efficiency about its optimal value was significantly reduced by the adenylate kinase reaction. It was found that the buffering ability of this enzyme is restricted to a specific frequency domain of the fluctuations of the load conductance. This frequency filtering was confirmed by substituting the random fluctuations of the load conductance by simple sinusoidal perturbations. All these studies revealed that for each domain of frequencies of the load perturbations there exists an optimal activity of the adenylate kinase which minimizes deviations from optimal efficiency of oxidative phosphorylation.

Regulation of the degree of coupling of oxidative phosphorylation in intact rat liver

The degree of coupling of oxidative phopshorylation q was determined in isolated perfused livers and in livers in vivo from fed and fasted rats. This determination of q was based on a simple nonequilibrium-thermodynamic representation of the major reactions of cytosolic adenine nucleotides, and made use of the measured cytosolic concentrations of adenine nucleotides, phosphate, and lactate/pyruvate ratios in extracted livers. The deviations of the measured values from the theoretically predicted ones at different mass action ratios of the adenylate kinase reaction showed that the basic assumptions of the model, including linearity between flows and thermodynamic forces, were fulfilled in intact liver within the experimental error. The degree of coupling was higher in livers from fed rats than in livers from fasted rats. In particular, the determined values of q were close to the theoretical degrees of coupling qecp and qecf which allow maximization of output power and output flow of oxidative phosphorylation for fed and fasted states, respectively, at optimal efficiency and minimal energy costs. This finding indicates that conductance matching between the load and phosphorylation is fulfilled in vivo. Moreover, it was found that fatty acids lower the degree of coupling in a concentration-dependent manner. This suggested that in livers in the fasted state q is decreased due to elevated fatty-acid levels. Thus fatty acids could act as metabolic regulators of the degree of coupling, enabling the cell to optimize efficiency of oxidative phosphorylation under different metabolic regimes.