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Difference between revisions of "Cell count and normalization in HRR"

From Bioblast
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| O<sub>2</sub> flow per cell || ''I''<sub>O<sub>2</sub>/ce</sub> || = || ''J''<sub>''V'',O<sub>2</sub></sub>/''C''<sub>ce</sub> || amol·s<sup>-1</sup>·x<sup>-1</sup> || extensive quantity
| O<sub>2</sub> flow per cell || ''I''<sub>O<sub>2</sub>/ce</sub> || = || ''J''<sub>''V'',O<sub>2</sub></sub>/''C''<sub>ce</sub> || amol·s<sup>-1</sup>·x<sup>-1</sup> || extensive quantity
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| volume-specific O<sub>2</sub> flux, per ''V''<sub>ce</sub> || ''J''<sub>O<sub>2</sub>(''V''<sub>ce</sub></sub> || = || ''I''<sub>O<sub>2</sub>/ce</sub>/''V''<sub>ce</sub> || amol·s<sup>-1</sup>·pL<sup>-1</sup> || size-specific quantity of the cell
| volume-specific O<sub>2</sub> flux, per ''V''<sub>ce</sub> || ''J''<sub>O<sub>2</sub>/''V''<sub>ce</sub></sub> || = || ''I''<sub>O<sub>2</sub>/ce</sub>/''V''<sub>ce</sub> || amol·s<sup>-1</sup>·pL<sup>-1</sup> || size-specific quantity of the cell
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Revision as of 00:31, 11 October 2020


high-resolution terminology - matching measurements at high-resolution


Cell count and normalization in HRR

Description

The cell count Nce is the number of cells, expressed in the abstract unit [x] (1 Mx = 106 x). The elementary entity cell Uce [x] is the real unit, the 'single individual cell'. A cell count is the multitude or number N of cells, Nce = N·Uce (Gnaiger MitoFit Preprint Arch 2020.4). Normalization of respiratory rate by cell count yields oxygen flow IO2 expressed in units [amol·s-1·x-1] (=10-18 mol·s-1·x-1).

Abbreviation: Nce

Reference: Gnaiger 2020 MitoPathways, Gnaiger MitoFit Preprint Arch 2020.4

Communicated by Gnaiger Erich (2020-09-18) last update 2020-10-10
Contributions by Cardoso Luiza HD, Schmitt Sabine, Sobotka Ondrej, Zdrazilova Lucie

Cell count and cell concentration

Figure 1. Stoppers removed from the O2k-chamber are placed into dry Falcon tubes on the Tube Rack preventing contamination.
Cells are frequently pipetted into the O2k-chamber, which is opened after closing and siphoning off any medium from the receptacle of the stopper. During opening, the medium in the stopper capillary is drawn into the chamber. Then the experimental chamber volume V containing respiration medium of 0.5 mL or 2.0 mL in the two types of O2k-chambers is automatically increased by the dead volume Vstc of the stopper capillaries, corresponding to 0.04 mL or 0.085 mL medium, respectively. If the volume of the stopper capillary is ignored in the calculation of cell-count concentration, then the final cell-count concentration in the respirometric chamber is underestimated by 7 % and 4 %, respectively. V´ including the volume of the stopper capillary is 7 % and 4 % larger than the calibrated experimental volume of V=0.5 mL or 2.0 mL using the 0.5-mL and 2.0-mL chamber, respectively. The corresponding corrections, however, depend on the technical details of the procedures used when adding cell suspensions into the open chamber when the stoppers are removed (Figure 1), as summarized in the following section.


Cell concentration from cell suspension to experimental chamber

Figure 2a. Volume balance in the 2-mL O2k chamber when the stopper is removed for addition of a cell suspension with complete volume replacement CVR.
Figure 2b. Volume balance in the 2-mL O2k chamber when the stopper is removed for addition of a cell suspension with partial volume replacement PVR.
When a cell suspension is added to the open O2k-chamber, the volume balance in the O2k-chamber depends on complete or partial volume replacement (CVR or PVR; Figure 2). After the O2k-chamber filled with experimental respiration medium is closed with the stopper in the volume-calibrated position, any excess medium is siphoned off the receptacle of the stopper (1). Then the stopper is gently removed from the chamber (2) and placed into an empty 50-mL Falcon on the Tube Rack (Figure 1). The aqueous medium in the stopper capillary is sucked out of the capillary when moving the stopper up to the edge of the glass chamber, by the negative pressure exerted when moving the stopper upwards. The stopper must not be dried. A volume VJ.i of respiration medium is pipetted off the chamber and discharged (3). The same or larger volume VJ.i of stock cell suspension J is pipetted into the chamber (4). The stirrer may be switched off during this time to avoid foam formation. The stirrer is switched on before taking any subsample from the cell suspension (5). Any drop remaining on to the lower conical surface or up to the lower O-ring is returned to the chamber volume when closing the chamber. Thus the effective dilution by the aqueous content of the stopper capillary is the same, whether the stopper is removed with or without a drop on the lower end of the stopper. When the chamber is closed with the stopper, the experimental volume is V, the stopper capillary is full with experimental medium, if no drops are lost from the removed stopper and no medium is lost by evaporation, and any excess volume of cell suspension Vexc is siphoned off the stopper receptacle (6). If any aqueous medium is lost from the stopper while it is removed, then the capillary would not be re-filled completely, and the dilution would be less. Or you would even see a gas bubble remaining after closing the chamber. Addition of medium to replace the gas bubble would dilute the sample as if the entire drop of medium would have been returned with the stopper.


The harvest of cultured cells typically includes first a centrifugation step to separate the cells from the culture medium, after which the pellet is taken up by adding a defined volume ΔVσ of experimental medium to yield a harvested cell suspension with total volume Vσ. Since the volume of the pellet is not known accurately, the total volume Vσ is more accurate when ΔVσ is very larger compared to the volume of the pellet, which in addition leads to a higher dilution of any remaining aqueous medium in the pellet. Subsamples of Vσ are used for cell counting (N), additional assays, and respirometry (J), either directly (suspension J is equal to suspension σ) or after further dilution from σ to J. Subsamples are transferred from the stock cell suspension J into the O2k-chamber in a variety of ways, selection of which depends on the optimum treatment of the specific cell suspension and practical considerations on the accuracy of titrations:

1. Complete volume replacement CVR

The stock cell-count concentration Cce,J is equal to the initial cell-count concentration Cce in the experimental chamber (Figure 3a (b) and (e)). The stopper is removed from the O2k-chamber and placed into an empty 50-mL Falcon on the Tube Rack (Figure 1). Aqueous medium is siphoned off from the chamber and discharged. No drops remain in the chamber (V´´ = 0 mL; Figure 3b (3)). When a surplus of cell suspension is available, a small volume (0.1 mL) may be used for an initial wash. A volume VJ.i = V# (equal or higher than the experimental chamber volume V plus volume of stopper capillary) is added into the empty chamber. The stirrer may be left on, but is switched off if this helps to avoid foam formation. The stirrer must be switched on before taking subsamples from the chamber, and before closing the chamber with the stopper, which must have a dry conical plate and dry capillary, but wet O-rings. In the example shown in Figure 3, the volume V# is 2.10 mL, leaving a small excess volume Vexc = 0.015 mL as a safety margin for avoiding any bubbles and completely filling the stopper capillary when closing the chamber. The small excess volume of suspension is siphoned off from the receptacle. The cell-count concentration Cce calculated from the initially determined Cce,σ (4) can be compared with the median of the finally determined cell-count concentrations Cce.i (14) for quality control of cell counting and dilution. Experimental evidence indicates, that the accuracy and reproducibility of IO2/ce in high-resolution respirometry is limited by the accuracy and reproducibility of cell counting.
» Download Excel template: File:O2k-2 mL Cell count.xlsx

2. Partial volume replacement PVR with Vout

Figure 4a and 5a show the work flow from cell harvest to filling the respirometric chamber, whereas Figure 4b and 5b zoom into the details of the volume balance in the 2.0-mL and 0.5-mL O2k-chamber, respectively, from opening to closing the chamber.
» Download Excel template: File:O2k-2 mL Cell count.xlsx
» Download Excel template: File:O2k-0.5 mL Cell count.xlsx

3. Partial volume replacement PVR with variable titration volume

» Download Excel template: File:O2k-0.5 mL Cell count.xlsx

4. Partial volume replacement PVR without Vout

Figure 7a shows the work flow from cell harvest to filling the respirometric chamber, whereas Figure 7b zooms into the details of the volume balance in the 2.0-mL O2k-chamber from opening to closing the chamber. After the O2k-chamber filled with experimental respiration medium is closed with the stopper in the volume-calibrated position, any excess medium is siphoned off the receptacle of the stopper. Then the stopper is gently removed from the chamber and placed into an empty 50-mL Falcon on the Tube Rack (Figure 1). A volume VJ.i of concentrated stock cell suspension VJ is pipetted into the open chamber. Then the total volume is V# = V+VStopper capillary+VJ.i. A sufficiently large volume of cell suspension is available for taking subsample(s) from the chamber. When the chamber is closed with the stopper, the experimental volume is V, and the stopper capillary is full with experimental medium. An excess volume is siphoned off the receptacle of the stopper. In this way more cells are lost compared to the previous procedure, but an excess volume is available that may be helpful in case of having to remove any trapped gas bubble from the chamber.
» Download Excel template: File:O2k-2 mL Cell count.xlsx

5. Titration into closed chamber V

After the O2k-chamber filled with experimental respiration medium is closed with the stopper in the volume-calibrated position, a volume VJ.i of concentrated stock cell suspension VJ is titrated into the chamber, identical to adding a suspension of isolated mitochondria. This approach is well tested for yeast cells, but is not recommended for mammalian cells which may loose viability due to the high shear stress in a Hamilton syringe. When the titration is performed fast into the O2k-chamber, a volume VJ.i of pure medium is extruded through the stopper, before mixing of cells into the chamber volume, such that no cells are lost from the experimental chamber into the stopper capillary. The dilution of the cell stock concentration in the experimental chamber is then calculated with reference to the chamber volume V. Slow titrations, however, entail an escape of cells into the stopper capillary leading to an inaccurately calculated cell-count concentration Cce. During subsequent titrations in a SUIT protocol, the cell suspension is diluted and excess cell suspension filles the volume of the stopper capillary. When opening the chamber for reoxygenation or decreasing the oxygen level with a gas phase, the cell suspension is pulled back into the open chamber. However, if the chamber is opened without prior SUIT steps, the medium in the stopper capillary does not contain cells and dilutes the cell-number concentration in the chamber.


Normalization of respiratory rate by cell count

Oxygen flow IO2 [amol·s-1·x-1], normalized for the cell count Nce [x], is as inaccurate and irreproducible as the quantification of cell count. In technical respirometric repeats with the same volume of cells sampled from the same stock, reproducibility of volume-specific oxygen flux JO2 [pmol·s-1·mL-1] depends on the homogeneity of the cell stock and reproducibility of titration of the cell suspension into the experimental chamber. If cell counts are taken for subsamples obtained from each experimental chamber separately, the variability of IO2 and JO2 can be compared to assess the reproducibility of the respirometric measurement versus cell counting.
A population of living cells includes a majority of viable cells vce, but is characterized by a small fraction of dead cells dce. As a rule, the cell viability index VIce should be equal or higher than 0.95 in a healthy reference cell population. Normalization for the cell count of the total of living cells Nce underestimates mitochondrial function in 'intact' cells, if dead cells have lost all mitochondrial respiratory capacity. On the other hand, normalization for the cell count of only the viable fraction of living cells, Nvce = VIce·Nce, overestimates mitochondrial respiratory function, if mitochondria of dead cells contribute to some extent to oxygen flux. This source of uncertainty of normalization increases with decreasing cell viability index (Gnaiger 1997 Transplant Proc, Steinlechner-Maran 1997 Transplantation, Gnaiger 2000 Transpl Int, Stadlmann 2002 Transplantation, Stadlmann 2006 Cell Biochem Biophys).


Definition of terms, symbols and units

Table 1. Definition of terms, symbols and units.
Term Symbol = Definition Unit Comment
Cell suspension σ σ
volume of cell suspension σ Vσ mL The symbol σ is used for 'suspension', distinguished from the symbol s for 'sample'. Cell suspension σ is the first suspension obtained upon harvesting the cells. Frequently the sediment of cells obtained from centrifugation, with Vs, is re-suspended in the experimental medium (e.g. MiR05 plus pyruvate) to obtain Vσ = Vs + ΔVσ.
cell count in Vσ Nce,σ = Cce,σVσ Mx The total cell harvest available for respirometry and additional analyses of this sample of cells.
cell-count concentration in cell suspension Vσ Cce,σ = Nce,σ/Vσ Mx/mL
subsample from Vσ for cell counting Vσ→N mL For a reliable cell count and normalization of respiration, Vσ→N should be equal or larger than 0.05 mL. Smaller volumes are taken as a subsample for counting, if the aim is merely to define a procedure of dilutions, with final subsamples taken after dilutions for cell-counting.
subsample from Vσ for respirometry J Vσ→J = Vσ-Vσ→N mL For high accuracy and reproducibility of technical repeats of respiration, Vσ→J should be equal or larger than 0.05 mL.
cell count in cell-count subsample from σ Nce,σ→N = Cce,σVσ→N Mx These cells are not available for respirometry, but only a fraction is required for addition into cell counters, hence several technical repeats of cell counting are feasible, or remaing cells may be used for additional characterization of the cell sample.
Respirometric stock J J
Volume added to Vσ→J ΔVJ = VJ-Vσ→J mL Volume added for dilution of Cce,σ to Cce,J.
volume of respirometric stock J VJ = Nce,J/Cce,J mL The respirometric stock is the cell suspension diluted from Vσ to VJ for further subsampling of cells to be added into the respirometric chamber for measurement of flux J. VJ = Vs→J + ΔVJ
cell count in VJ Nce,J = Cce,σVσ→J = Nce,σ-Nce,σ→N Mx The cell count available for respirometry.
cell-count concentration respirometric stock VJ Cce,J = Mx/mL If cells are pipetted into the O2k-chamber opened after closing and siphoning off any medium from the receptacle of the stopper, then Cce,J is adjusted according to Cce·V'/VJ.i.
subsample volume of stock VJ titrated into respirometer chamber VJ.i mL i = 1 to n, where n is the number of technical respirometric repeats. For a reliable cell count and normalization of respiration, VJ.i should be equal or larger than 0.05 mL.
maximum number of technical JO2 repeats n = VJ/VJ.i
Volume balance and cell suspension in respirometric chamber
experimental chamber volume V mL Effectively mixed aqueous volume in the experimental system, which is the closed chamber with the stopper in a volume-calibrated position (2.0 mL or 0.5 mL). When the closed chamber contains respiration medium without sample, a measurement is obtained of instrumental O2 background flux JV,O2° [state (1) in Figure 3b]. Volume-specific respiratory flux JV,O2 of the sample in the closed chamber is the total oxygen flux corrected for instrumental background [state (6) in Figure 3b].
experimental chamber volume plus dead volume in stopper capillary V´ = V + Vstc mL When the stopper is removed from a closed chamber with a completely filled stopper capillary but without any aqueous medium in the receptacle of the stopper, the chamber is said to be 'open'. The volume Vstc in the stopper capillary is drawn into the chamber [state (2) in Figure 3b].
reduced volume in open chamber V´´ = V´ + Vout mL The volume of respiration medium is reduced by Vout (which has a negative value when medium is removed from the chamber) in the open chamber before adding the cell suspension, avoiding a large excess volume leading to loss of cells upon closing the chamber [state (3) in Figure 3b].
total volume in open chamber after addition of cells V# = V + Vstc + Vout + VJ,i mL The minimum V# is 0.54 mL or 2.085 mL in the 0.5-mL or 2.0-mL chamber, respectively [state (4) in Figure 3b]. The volume of the stopper capillary does not mix with V in the closed chamber. Therefore, only V is the experimental volume and VStopper capillary is considered as a 'dead volume' outside of the experimental chamber volume.
volume in open chamber after subsampling cell suspension from chamber V´´´ = V# - ΣVij mL The minimum V´´´ is 0.54 mL or 2.085 mL in the 0.5-mL or 2.0-mL chamber, respectively [state (5) in Figure 3b].
volume of stopper capillary Vstc mL Vstc = 0.04 mL and 0.085 mL in the 0.5-mL and 2.0-mL O2k-chamber, respectively.
volume of respiration medium removed from open chamber Vout = VJ.i - ΣVij - Vexc mL The stirrer may be stopped when removing medium from the chamber. Removal of medium minimizes excell volume of cell suspension Vexc.
sum of volumes sampled from chamber i before closing ΣVij mL For various assays j a volume of cell suspension is sampled from the open chamber i before closing the chamber.
excess volume of cell suspension Vexc mL Vexc is wasted in the stopper receptacle upon closing the chamber.
cell-count in experimental chamber Nce = N·Uce Mx 106 x = 1 Mx
cell-count concentration in experimental chamber Cce = Nce/V Mx/mL 106 x/mL = 1 Mx/mL = 109 x/L = 1 Gx/L
cell-count in V# Nce# = Cce·V# Mx
Respirometry JO2
O2 flow of the cells in the chamber IO2 pmol·s-1 extensive quantity
volume-specific O2 flux, per V JV,O2 = IO2/V pmol·s-1·mL-1 size-specific quantity of experimental system
O2 flow per cell IO2/ce = JV,O2/Cce amol·s-1·x-1 extensive quantity
volume-specific O2 flux, per Vce JO2/Vce = IO2/ce/Vce amol·s-1·pL-1 size-specific quantity of the cell

Keywords


MitoPedia methods: Respirometry 


MitoPedia O2k and high-resolution respirometry: DatLab, Oroboros QM, O2k-Respirometry, O2k-FluoRespirometry