Gnaiger 1989 Energy Transformations
Gnaiger E (1989) Mitochondrial respiratory control: energetics, kinetics and efficiency. In: Energy transformations in cells and organisms. Wieser W, Gnaiger E (eds), Thieme, Stuttgart:6-17. |
Abstract: Mitochondrial respiratory control mechanisms are central in regulating the flux of ATP turnover which mediates between catabolism and anabolism. Such control can be exerted by the catabolic driving force for ATP production or by the load on the ATP system due to the ATP demand for biosynthesis, ion pumps or muscle activities. The signals of drive and load are integrated in the energy status of the ATP/ADP system, expressed by the phosphorylation potential. Is metabolic flux regulated by energy demand or energy supply? Do ATP/ADP ratios or ADP concentrations regulate the flux of mitochondrial oxidative phosphorylation? Different answers are obtained depending on metabolic conditions, but primarily depending on the particular model of flux control. Clearly, a reconciliation of divergent traits of kinetics and nonequilibrium thermodynamics ("ergodynamics") is of great theoretical and practical importance. Such a reconciliation is proposed here on the basis of Einstein's diffusion equation. The new concept accounts for the effects exerted on flux by both the Gibbs force of reaction and the total concentration of all substrates and products. Its application to the study of chemical reactions as complex as mitochondrial oxidative phosphorylation provides new insights into the regulatory mechanisms of energy transformation, emphasizing the effect of efficiency on the control of flux.
• Keywords: Gibbs force, free activity, reaction pressure
• O2k-Network Lab: AT Innsbruck Gnaiger E
Labels: MiParea: Respiration
Organism: Rat
Tissue;cell: Liver
Preparation: Isolated mitochondria
Regulation: ADP, ATP, ATP production, Coupling efficiency;uncoupling, Flux control Coupling state: OXPHOS
Einstein's diffusion equation and Fick's law: vectors
- J_{d} = -u·c·F_{d} (Einstein 1905).
- J_{d} is the flux of diffusion of a substance per unit area of a plane, in the direction perpendicular to the plane [mol·s^{-1}·m^{-2}]
- F_{d} = dμ/dz is the force of diffusion, which is the chemical potential gradient of the diffusing substance in the z direction perpendicular to the plane [J·mol^{-1}·m^{-1}].
- μ is the chemical potential of the diffusing substance [J·mol^{-1}].
- z is the distance in the z direction perpendicular to the plane [m].
- P_{V} = J_{d}·F_{d} [W·m^{-3}]; the product of flux and force is volume-specific power.
- c is the local concentration (free activity, α) of the diffusing substance, localized across the plane at a diffusion distance at which F'd is measured [mol·dm^{-3}].
- c = n/V; concentration is amount of substance, n, divided by volume, V.
- u is the mobility, or the reciprocal value of the frictional coefficient [mol·s^{-1}·kJ^{-1}·m].
- Diffusion pressure gradient: d_{d}Π/dz = c·dμ/dz= α·F_{d} [kJ·m^{-3}·m^{-1} = kN·m^{-2}·m^{-1} = kPa·m^{-1}]
- Pressure of the ideal gas law (osmotic pressure, generalized by Van't Hoff): Π = RT·n/V = RT·c
- Einstein's diffusion equation: J_{d} = -u·d_{d}Π/dz = -u·c·dμ/dz
- Fick's first law of diffusion: J_{d} = -D·dc/dz
- Taken together: D·dc/dz = u·c·dμ/dz = u·RT·dc/dz
- c·dμ/dz = RT·dc/dz = d_{d}Π/dz; the diffusion pressure gradient is RT times the concentration gradient.
- D = u·RT; the diffusion coefficient equals the mobility times RT (Einstein 1905).
- Fick's first law of diffusion describes a linear flux-pressure relation, but not a linear flux-force relation: J_{d} = -u·RT·dc/dz = -u·d_{d}Π/dz
Compartmental description of diffusion: vectorial flux and force in a discontinuous system
Chemical reaction, force of reaction, and reaction pressure
- Gibbs force of reaction: F_{r} = RT·ln(M/K) = Σ_{B}(_{B}·μ_{B} [J·mol^{-1}]
- Reaction Gibbs energy: Δ_{r}G = F_{r}
- Equilibrium constant: K = M_{eq}; the equilibrium constant equals the mass action ratio at equilibrium.
- Mass action ratio: M = Π_{B}(a_{B}^ν_{B}) = Π_{p}(a_{p}^ν_{p})/Π_{s}(a_{s}^-ν_{s}); M is the product of the activities of all reactants, B, to the power of their stoichiometric numbers, ν_{B}. ν_{B} is positive for products, p, and negative for substrates, s.
- Activity: a_{B} = c_{B}/c°; division of concentrations by the standard concentration, c° = 1 mol.dm^{-3}), yields dimensionless quantities for activities, K, and M.
- Free activity, α = (_{p}a-_{s}a)/ln(_{p}a/_{s}a) [mol·dm^{-3}]
- _{p}a is the product activity, including all products.
- _{s}a is the substrate activity, including all substrates.
- Reaction pressure: Δ_{r}Π = α·F_{r} [J·dm^{-3} = kJ·m^{-3} = kPa]
- Reaction flux: J_{r} = -b·α·F_{r} = -b·Δ_{r}Π (Gnaiger 1989)