Notes on Time Resolution
Titrations and Plots of Oxygen Flux
A disturbance of the traces of flux are caused by titrations titration of chemicals into the chamber. These disturbances are increasingly pronounced as the level of dissolved oygen declines, when oxygen is added with the solvent. Oxygen is highly soluble in ethanol, hence the effect is higher with the same volume of ethanol than water. An increase in oxygen concentration would correspond to a negative flux. The trace of flux, therefore, shows a sharp negative peak after the titration. Since 40 data points are used for the calculation of flux, the peak is smoothed and extends over a prolonged period of time, depending on the selected data sampling interval.
Oxygen Flux and Time Resolution
Q: Upon rapid changes in oxygen concentration (as seen by switching the stirrer on and off), oxygen flux (the negative time derivative) seems to lag behind and even stretches to a much longer time span than the duration of the oxygen changes themselves would suggest. Can this problem be avoided for (kinetic) applications which require a high time-resolution?
A: High time-resolution is necessary in various kinetic studies. Most common applications of high-resolution respirometry, however, require only information on respiratory flux over a period of time when metabolic activity is constant. Standard settings in DatLab 4 are optimized for such applications (O2k Manual O2k.E). DatLab 4 offers a simple on-line solution for improving the time-resolution, by reducing the data recording interval (standard is 2 seconds) to the minimum of 0.2 s (setting in the Oxygraph Control window; see O2k-Manual O2k.A, page 13). As the data recording interval is reduced, the flux appears more noisy, but represents transitions more accurately and reduces the apparent time-delay. Most routine applications aim at obtaining average flux over short periods of time (some minutes), for which application the high smoothing effect of the standard DatLab 4 settings are suitable.
Off-line, DatLab 2 offers numerous options for optimizing analyses between the opposite demands on high time-resolution versus low noise of flux. While the on-line filter in DatLab 4 is fixed (Savitzky-Golay smoothing filter applied on the 40 preceeding data points), off-line options are many.
(1) A deconvolution is possible on the raw signal, applying a calibrated first-order exponential time constant (simply applying the 'stirrer test'; see O2k-Manual O2k.G).
(2) Subsequent to time correction (signal deconvolution), 'mild' polynomial smoothing or 'strong' arithmetic smoothing may be applied on the oxygen signal, with variable number of data points (the more data points, the stronger the smoothing effect).
(3) The slope can then be calculated over a variable number of data points, not merely selecting the only on-line option for preceding data points, but including leading data points (symmetrical fit) which avoids the apparent delay in the trace of flux.
(4) For the specific application of oxygen kinetics, an elaborate script (macro) applies an optimized strategy for high time-resolution combined with sufficient filtering of noise (O2k-Manual O2k.H).
Q: Does the time constant of the polarographic oxygen sensor change when measurements are performed at low or high oxygen pressures?
A: The time constant should be independent of the absolute oxygen pressure. In the scientific literature, it has been argued that at very low oxygen the time constant increases - without any evidence, and without theoretical basis. Experimental tests in the Oxygraph-2k revealed no difference of the exponential time constant of the POS measured close to air saturation or close to zero oxygen levels.
|Oxygraph-2k: High Time Resolution|
A standard stirrer test is applied under experimental conditions for calibration of the time constant. Does the oxygen sensor respond sufficiently fast for resolving rapid changes?
DatLab yields the answer and displays the time-corrected signal. Sensors respond with a time delay to changes of oxygen (blue line), characterized by the exponential time constant. This is the basis for the time correction of OROBOROS® Oxygraph-2k recordings in high-resolution respirometry (red line), particularly in kinetic studies.