Flux / Slope

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Flux / Slope


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

Abbreviation: J

Contributed by Cardoso Luiza HD, Iglesias-Gonzalez Javier & Gnaiger Erich 2020-03-04

Slope configuration menu

Slope configuration in DatLab 7


In an ideally closed chamber the external fluxes are zero, thus 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 2020).
 Eq(1):  X Slope neg = dcX/dt · νX-1 · SF  | Units: [pmol/(s·mL)]
For the oxygen channel, X=O2, cO2 is the oxygen concentration [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).
A Savitzky-Golay smoothing filter is used in DatLab as a basis of calculating the time derivative (Flux / Slope) of the signal (oxygen, fluorescence, ..).
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=-log(cX/c°) and then transformed to cX. The slope is calculated as the change of concentration over time, dcX/dt [nmol· s-1· mL-1]. 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. Oxygen is consumed in aerobic respiration and νX=-1 when expressing respiration as 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)]

O2 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 Instrumental background oxygen flux 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.

Copy from file

If you did not apply an instrumental O2 background correction to your experimental DatLab file, you have the option to load the instrumental O2 background test parameters directly from the Instrumental O2 background.DLP by clicking on the Copy from file button in the Slope configuration window. Select your previously evaluated instrumental O2 background test file and load the parameters (i.e., intercept and slope) in DatLab.


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 2020).
Eq(3a): IX = JV,X/(106 cells/mL)  |  Units: [pmol/(s·106 cells)] = [amol/(s·cell)] 
Eq(3b): IX(bc) = (JV,X - JV,0)/(106 cells/mL)  |  Units: [pmol/(s·106 cells)] = [amol/(s·cell)]
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 Ratio

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 2020),
Eq(5a): FCR = JV,X/JV,1
Eq(5b): FCR(bc) = (JV,X - JV,0)/(JV,1 - JV,0)

Smoothing, noise, and sample stability

Recorded data: The default data recording interval is 2 s, applied with most SUIT protocols. The larger the data recording interval, the lower is the time resolution and the larger is the smoothing of flux.
Smoothing in Flux / Slope: The default setting of Slope smoothing is 40 data points, i.e., 40 data points or an interval of 80 s at a data recording interval of 2 s are used for calculation of a non-linear fit, from which the slope is calculated for the current data point. 40 is used for O2 calibration and instrumental O2 background tests. 20 is recommended for data recording and analysis in typical SUIT experiments. When a larger noise is observed particularly in experiments with permeabilized muscle fibres, and increase to 25 displays more representative traces.
Flux may decline over time, due to (1) loss of respiratory capacity within a respiratory state when the properties of the sample are not stable, (2) reversible oxygen limitation in the closed chamber, (3) an overshoot directly after re-oxygenation, or (4) a slow response to an inhibitor. Flux may increase over time due to (1) a slow response to the addition of ADP or a fuel substrate, or (2) an undershoot observed in rare cases after re-oxygenation. An extended time interval is required for recording flux in a particular respiratory state, if (1) flux increases over time (this may take >30 min, with a mark set at the final steady-state), and (2) flux shows high levels of noise (then 10 min may be required for setting a mark).

Flux analysis

In a SUIT protocol each titration can be considered as a transition between a background state and a reference state, expressed as a flux control efficiency. A sequence of steady-state states can be analysed in terms of flux control ratios, FCR, corrected for a common baseline, and normalized for flux in a common reference state. If a steady-state (constant) flux is not reached between sequential respiratory states induced by titrations, corrections for dynamic changes of flux as a function of time may be applied, else the conditions for steady-state analysis break down. In such cases, step analysis with continuous evaluation of a change of flux (second-time derivative) may provide the only reliable information. In reality, some noise or bias is included in steady-state analysis above a threshold level, below which such data sets would be excluded from the steady-state analysis.


How to Analyse with DatLab 7.4

» Bioblast pdf MiPNet24.06_Oxygen_flux_analysis_-_DatLab_7.4

Previous versions of DatLab

Look for MiPNets and take information from DatLab-Analysis templates


Further information about hydrogen peroxide detection using Amplex UltraRed assay could be found under the page Amplex UltraRed

How to Analyse with DatLab 7.4

  • Instruction to the Excel template for H2O2 flux analysis using Amplex UltraRed assay in MiR05-Kit: MiPNet24.10 Hydrogen peroxide flux analysis
  • The calculations applied in the Excel template are provided here complying with Oroboros transparency policy and can be applied for measurements carried out in MiR05-Kit supplemented with DTPA:
1. Calculation of the theoretical chemical fluorescence background of the Amplex UltraRed assay using MiR05-Kit supplemented with the iron chelator DTPA

Theoretical chemical fluorescence background is the calculated chemical fluorescence background slope using Amplex UltraRed (AmR) assay without any biological sample. There is a linear relationship between the chemical fluorescence background slope of the AmR assay and the raw chemical fluorescence signal without any biological sample, therefore:

 Eq(1):dAmpraw,BG,t/dtBG,t =0.0119·Ampraw,ch + 0.1046


· dAmpraw,BG,t/dtBG,t: theoretical chemical fluorescence background slope [mV/s]

· Ampraw,ch: raw chemical fluorescence signal with AmR assay [V] in the biological experiment

Using this equation, the theoretical chemical fluorescence background slope can be calculated for your own measurement without measuring the chemical fluorescence background slope using AmR assay in the absence of biological sample in MiR05-Kit supplemented with DTPA over the experimental time.

2.   Theoretical chemical background fluorescence slope corrected for oxygen concentration

The chemical fluorescence background slope of the AmR assay is linearly dependent on the oxygen concentration in the O2k-Chamber in MiR05-Kit with or without DTPA. The following equation shows/expresses the relationship between these above-mentioned parameters:

 Eq(2):dAmpraw,BG/dtBG =0.000176·[O2] + 0.07116


· dAmpraw,BG/dtBG: chemical fluorescence background slope [mV/s] in the absence of biological sample

· [O2]: oxygen concentration in the O2k-Chamber [µM]

Based on this, an oxygen correction factor (FO2) can be calculated:

Eq(3):FO2=(0.000176* [O2]a+0.07116)/(0.000176 *[O2]r+0.07116) 


· [O2]a: actual oxygen concentration in the experiment

· [O2]r: reference oxygen concentration, usually before the sample addition

Knowing the oxygen concentration at a given time point in your biological experiment allows you to normalize/correct the theoretical chemical fluorescence background slope for the oxygen concentration in the O2k-Chamber.

Having the FO2, theoretical chemical fluorescence background slope can be corrected for the oxygen concentration:

 Eq(4):dAmpraw,BG,O2,t/dtBG,O2,t= dAmpraw,BG,t/dtBG,t · FO2


· dAmpraw,BG,O2,t/dtBG,O2,t: theoretical chemical fluorescence background slope is corrected for the oxygen concentration [mV/s]

· dAmpraw,BG,t/dtBG,t: theoretical chemical fluorescence background fluorescence slope [mV/s]

· FO2: oxygen correction factor

3.   Raw fluorescence slope corrected with the theoretical chemical fluorescence background slope

The theoretical chemical fluorescence background slope is subtracted from the raw fluorescence slope (not calibrated for H2O2) using AmR assay with biological sample.

  (Eg.5) dAmpraw/dtcorr=dAmpraw/dt-dAmpraw,BG,O2,t/dtBG,O2,t


· dAmpraw/dtcorr: raw fluorescence slope with biological sample corrected with the theoretical chemical fluorescence background slope

· dAmpraw/dt: raw fluorescence slope with biological sample from the experimental DatLab file

· dAmpraw,BG,O2,t/dtBG,O2,t: theoretical chemical background slope is corrected for the oxygen concentration [mV/s]

4.   H2O2 calibration of the raw fluorescence signal

Corrected raw fluorescence slope normalized previously with the theoretical background is calibrated with H2O2 concentration using sensitivity values over the whole experiment.



· J H2O2/BG: H2O2 flux [pmol·s-1·x-1] corrected for oxygen corrected theoretical chemical fluorescence background slope; background-corrected H2O2 flux

· dAmpraw/dtcorr: fluorescence slope with biological sample corrected for the theoretical chemical fluorescence background slope

Sensitivity refers to the response obtained for a given amount of analyte and is often denoted by two factors: the limit of detection and the limit of quantification. Sensitivity is expressed in [V/µM] and calculated in DatLab 7.4 in the ‘Amp calibration’ window after H2O2 calibration was performed: open menu [Calibration] and ‘A: or B: Amperometric,Amp’ .

5.   Specific H2O2 flux [pmol·s-1·x-1] 

Specific H2O2 flux is the flux corrected by the sample concentration. When using the Excel analysis template to calculate the H2O2 fluxes, be sure to check accordingly the following options: ‘ Titration volume correction’ and ‘Known sample concentration’. The specific H2O2 flux is given in the following unit [pmol·s-1·x-1], taking in consideration that the sample concentration is [x·mL-1]. The unit x can be substituted by the unit used in your project, e.g., a mg of protein or a million of cell.

Eq(7):JH2O2/X= JV,H2O2/(SCF·CX0)

Where: · JH2O2/X: Specific H2O2 flux [pmol·s-1·x-1]

· JV,H2O2: H2O2 flux [pmol·s-1·mL-1] corrected for theoretical background normalized for oxygen concentration and sensitivity declin

· SCF: sample concentration correction factor

· CX0: initial sample concentration in the chamber [x·mL-1]

- If ‘titration volume correction’ option is not enabled: sample concentration correction factor = 1

- If ‘Known sample concentration’ is unchecked: [sample] = 1 [x·mL-1]

- The calculation of the sample concentration correction factor is the same used for the calculation of the specific oxygen flux (See: MiPNet24.06 Oxygen flux analysis with DatLab7.4

6.  Specific H2O2 flux baseline corrected (bc) [pmol·s-1·x-1]

The baseline state is pre-set for each SUIT protocol available at the template.


Where: · JH2O2/X(bc): Specific H2O2 flux baseline corrected [pmol·s-1·x-1]

· JH2O2/X: Specific H2O2 flux [pmol·s-1·x-1]

· JH2O2/X(baseline): Specific flux of the baseline state [pmol·s-1·x-1]

7.   Specific H2O2 flux/Specific O2 flux ratio

The H2O2 flux/O2 flux ratio gives us information about the relative contribution of H2O2 production relating to the respiration, or other words, how much oxygen of total oxygen turned over is consumed for H2O2 generation.


Where: · JH2O2/X: Specific H2O2 flux [pmol·s-1·x-1]

· JO2/X: Specific O2 flux [pmol·s-1·x-1]

The specific fluxes corrected for the baseline are not used for this ratio, because the baseline state for H2O2 flux and O2 flux calculations might be different depending on the protocol.


  • Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - »Bioblast link«
  • Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun:112 pp. - »Bioblast link«
  • Press WH, Teukolsky SA (1990) Savitzky-Golay smoothing filters. Computers in Physics Nov/Dec 1990:669-72. - »Bioblast link«

Further links

DatLab links to this page from

MitoPedia methods: Respirometry, Fluorometry 

MitoPedia O2k and high-resolution respirometry: DatLab