Steady state

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Steady state


A system is in a steady state if the state variables of a dynamic system do not change over time due to exchange processes with the environment, which compensate for internal dissipative transformations — such as chemical reactions or diffusion — and thus prevent any changes of the system and externalize dissipative changes to the environment. The dynamic nature of the steady state differentiates it from the thermodynamic equilibrium state. {Quote}: Steady states can be obtained only in open systems, in which changes by internal transformations, e.g., O2 consumption, are instantaneously compensated for by external fluxes across the system boundary, e.g., O2 supply, thus preventing a change of O2 concentration in the system (Gnaiger 1993). Mitochondrial respiratory states monitored in closed systems satisfy the criteria of pseudo-steady states for limited periods of time, when changes in the system (concentrations of O2, fuel substrates, ADP, Pi, H+) do not exert significant effects on metabolic fluxes (respiration, phosphorylation). Such pseudo-steady states require respiratory media with sufficient buffering capacity and substrates maintained at kinetically-saturating concentrations, and thus depend on the kinetics of the processes under investigation. {end of quote: BEC 2020.1). Whereas fluxes may change at a steady state over time, concentrations are maintained constant. The 'respiratory steady state' (Chance and Williams 1955) is characterized by constant fluxes (O2 flux, H2O2 flux) and measured variables of state (cytochrome redox states, Q redox state, NADH redox state, mitochondrial membrane potential). High-resolution respirometry allows for the measurement of several parameters (e.g. O2 flux, H2O2 flux, mitochondrial membrane potential) at pseudo-steady states, when changes of concentrations in the closed system do not exert any control on fluxes. Combination with the Titration-Injection microPump (TIP2k) allows operation with programmable titration regimes at steady-state ADP concentration (Gnaiger 2001), oxygen concentration (oxystat mode; Gnaiger et al 2000, Harrison et al 2015) or steady-state pH (pH-stat more), yielding an expanded flexibility in experimental design by combining the technical advantages of closed and open systems approaches.

Reference: BEC 2020.1, Gnaiger 2000 Proc Natl Acad Sci U S A, Gnaiger 2001 Respir Physiol, Harrison 2015 J Appl Physiol

Communicated by Doerrier C 2020-04-20, last update by Gnaiger E 2020-06-02

Hyphenation: Steady state or steady-state?

Hyphenate if steady-state concentrations are concerned, but do not hyphenate when measurements are made at steady state. - See

DatLab oxygen flux: performance and data analysis

Oxygen fluxes should stabilize — reaching a constant value of the rate — before proceeding with the next titration in the SUIT protocol. The following DatLab traces illustrate examples of stable and unstable respiratory rates:

OXPHOS state

After addition of inhibitors


Bioblast linkReferenceYear
Chance B, Williams GR (1955) Respiratory enzymes in oxidative phosphorylation: III. The steady state. J Biol Chem 217:409-27.1955
Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002.1993
Gnaiger E (2001) Bioenergetics at low oxygen: dependence of respiration and phosphorylation on oxygen and adenosine diphosphate supply. Respir Physiol 128:277-97.2001
Gnaiger E, Méndez G, Hand SC (2000) High phosphorylation efficiency and depression of uncoupled respiration in mitochondria under hypoxia. Proc Natl Acad Sci U S A 97:11080-5.2000
Gnaiger Erich et al ― MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1. doi:10.26124/bec:2020-0001.v1.2020
Harrison DK, Fasching M, Fontana-Ayoub M, Gnaiger E (2015) Cytochrome redox states and respiratory control in mouse and beef heart mitochondria at steady-state levels of hypoxia. J Appl Physiol 119:1210-8.2015


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