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Difference between revisions of "Flux / Slope"

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|description='''Flux / Slope''' is the pull-down menu in [[DatLab]] for (1) [[normalization of flux]] (chamber volume-specific flux, sample-specific flux or flow, or flux control ratios), (2) [[flux baseline correction]], (3) [[background correction]], and (4) [[flux smoothing]], selection of the [[scaling factor]], and stoichiometric normalization using a [[stoichiometric coefficient]].
|description='''Flux / Slope''' is the pull-down menu in [[DatLab]] for (1) [[normalization of flux]] (chamber volume-specific flux, sample-specific flux or flow, or flux control ratios), (2) [[flux baseline correction]], (3) [[background correction]], and (4) [[flux smoothing]], selection of the [[scaling factor]], and stoichiometric normalization using a [[stoichiometric coefficient]].


For each signal [[channel]], the signal for the measured substance X is typically calibrated as an amount of substance [[concentration]], ''c''<sub>X</sub> [µM = nmol/ml]. The signal of the potentiometric channel, however, is primarily expressed logarithmically as pX=-log''c<sub>X</sub>'' and then transformed to ''c<sub>X</sub>''. The slope is calculated as the change of concentration over time, d''c<sub>X</sub>''/d''t'' [nmol/(s · ml)]. In a chemical reaction, the change of substance X is stoichiometrically related to the changes of all other substrates and products involved in the reaction. If the stoichiometry of the reaction is normalized for substance X, then its stoichiometric coefficient is unity and ''ν''<sub>X</sub> equals 1 if the substance is a product formed in the reaction, but ''ν''<sub>X</sub> equals -1 if the substance is a substrate consumed in the reaction. Oxygen is formed in photosynthesis and ''ν''<sub>X</sub>=1 when expressing photosynthesis as oxygen flux. Oxyygen is consumed in aerobic respiration and ''ν''<sub>X</sub>=-1 when expressing respiration as oxygen flux.
For each [[O2k signals and output|signal channel]], the signal for the measured substance X is typically calibrated as an amount of substance [[concentration]], ''c''<sub>X</sub> [µM = nmol/ml]. The signal of the potentiometric channel, however, is primarily expressed logarithmically as pX=-log''c<sub>X</sub>'' and then transformed to ''c<sub>X</sub>''. The slope is calculated as the change of concentration over time, d''c<sub>X</sub>''/d''t'' [nmol/(s · ml)]. In a chemical reaction, the change of substance X is stoichiometrically related to the changes of all other substrates and products involved in the reaction. If the stoichiometry of the reaction is normalized for substance X, then its stoichiometric coefficient is unity and ''ν''<sub>X</sub> equals 1 if the substance is a product formed in the reaction, but ''ν''<sub>X</sub> equals -1 if the substance is a substrate consumed in the reaction. Oxygen is formed in photosynthesis and ''ν''<sub>X</sub>=1 when expressing photosynthesis as oxygen flux. Oxyygen is consumed in aerobic respiration and ''ν''<sub>X</sub>=-1 when expressing respiration as oxygen flux.
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{{MitoPedia methods
{{MitoPedia methods

Revision as of 08:12, 25 July 2016


high-resolution terminology - matching measurements at high-resolution


Flux / Slope

Description

Flux / Slope is the pull-down menu in DatLab for (1) normalization of flux (chamber volume-specific flux, sample-specific flux or flow, or flux control ratios), (2) flux baseline correction, (3) background correction, and (4) flux smoothing, selection of the scaling factor, and stoichiometric normalization using a stoichiometric coefficient.

For each signal channel, the signal for the measured substance X is typically calibrated as an amount of substance concentration, cX [µM = nmol/ml]. The signal of the potentiometric channel, however, is primarily expressed logarithmically as pX=-logcX and then transformed to cX. The slope is calculated as the change of concentration over time, dcX/dt [nmol/(s · ml)]. In a chemical reaction, the change of substance X is stoichiometrically related to the changes of all other substrates and products involved in the reaction. If the stoichiometry of the reaction is normalized for substance X, then its stoichiometric coefficient is unity and νX equals 1 if the substance is a product formed in the reaction, but νX equals -1 if the substance is a substrate consumed in the reaction. Oxygen is formed in photosynthesis and νX=1 when expressing photosynthesis as oxygen flux. Oxyygen is consumed in aerobic respiration and νX=-1 when expressing respiration as oxygen flux.

Abbreviation: J


MitoPedia methods: Respirometry, Fluorometry 


MitoPedia O2k and high-resolution respirometry: DatLab 

Corrections and normalization

Contributed by Gnaiger Erich 2016-03-16
Slope configuration in DatLab 7

Slope

In an ideally closed chamber, the external fluxes are zero, thus that the concentration changes are exclusively due to (internal) transformations, which are chemical reactions. Then respiratory flux expressed per unit of chamber volume can be calculated from the slope of oxygen concentration over time (Gnaiger 2014),
 Eq(1):  X Slope neg = dcX/dt · νX-1 · SF  | Units: [pmol/(s·ml)]
For the oxygen channel, X=O2, cO2 is the oxygen conentration [nmol/ml = µmol/l = µM], dcO2/dt is the (positive) slope of oxygen concentration over time [nmol/(s · ml)], νO2-1 = -1 is the stoichiometric coefficient for the reaction of oxygen consumption (oxygen is removed in the chemical reaction, thus the stoichiometric coefficient is negative, expressing oxygen flux as the negative slope; Gnaiger 1993), and SF=1,000 is the scaling factor (converting units for the amount of oxygen from nmol to pmol).


Background correction

In an experimentally closed chamber, external fluxes due to diffusion or convection into or out of the chamber are minimized, ideally to zero. Unavoidable external fluxes are corrected for, as are side reactions due to the measuring system, such as oxygen consumption by the oxygen sensor or chemical background effects due to autoxidation of chemical components added to the medium. These external fluxes and side reactions of the experimental system are lumped together in the background flux, J°V,X. A background correction is applied to the total slope, to obtain the metabolic flux, JV,X, describing the experimental reaction under investigation:
Eq(2a):  JV,X = dcX/dt · νX-1 · SF - J°V,X  | Units: [pmol/(s·ml)]
J°V,O2 is the volume-specific background oxygen flux.


Flux baseline correction

If the sample itself introduces a constant flux in a baseline state (indicated as subscript 0), which is not considered to represent the metabolic reaction, then a flux baseline correction (bc) may be applied by subtracting the baseline flux, JV,0, from the total flux:
Eq(2b):  JV,X(bc) = JV,X - JV,0  |  Units: [pmol/(s·ml)]

Normalization

Eqs(1) and (2) describe the dynamics of X per unit volume.
Eq(2a):  JV,X = X Slope neg - J°V,X  |  Units: [pmol/(s·ml)] 
Eq(2b):  JV,X(bc) = JV,X - JV,0  |  Units: [pmol/(s·ml)]
Normalization for the amount or concentration of sample yields metabolic flow per number of cells, IX, or specific metabolic flux per mass, Jm,X (unstructured analysis), or per mt-content (per mt-marker) in structured analysis (Gnaiger 2014).
Eq(3a): IX = JV,X/(cells/ml)  |  Units: [pmol/(s·106 cells)]
Eq(3b): IX(bc) = (JV,X - JV,0)/(cells/ml)  |  Units: [pmol/(s·106 cells)]
Eq(4a): Jm,X = JV,X/(mg/ml)  |  Units: [pmol/(s·mg)]
Eq(4b): Jm,X(bc) = (JV,X - JV,0)/(mg/ml)  |  Units: [pmol/(s·mg)]
Flux control ratios are dimensionless, using a reference flux for normalization. The reference flux is determined in a metabolic reference state (1) as internal mt-marker (Gnaiger 2014),
Eq(5a): FCR = JV,X/JV,1
Eq(5b): FCR(bc) = (JV,X - JV,0)/(JV,1 - JV,0)


References

  • Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - »Bioblast link«
  • Gnaiger E (2014) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 4th ed. Mitochondr Physiol Network 19.12. OROBOROS MiPNet Publications, Innsbruck:80 pp. - »Bioblast link«