Correcting for Oxygen Diffusion in Respiration Measurements

Determining instantaneous oxygen consumption rate in OxoDishes® applied as closed-system respirometers

E. T. Polymeropoulos1,2, N. G. Elliott2, S. J. Wotherspoon3, P. B. Frappell1,3
1School of Zoology, University of Tasmania, AU
2Commonwealth Scientific and Industrial Research Organisation (CSIRO), National Food Futures Flagship, CSIRO Marine and Atmospheric Research, AU
3Institute for Marine and Antarctic Studies, University of Tasmania, AU

When using multiwell plates made of polysytrene - like the PreSens OxoDishes® - as closed-system respirometers, one has to take oxygen diffusion through the well material into consideration, as polystyrene is permeable for oxygen. Here an equation is provided to account for the empirically determined rate of oxygen diffusion through polystyrene when calculating the instantaneous rate of oxygen consumption. Oxygen diffusion out of the wells of an OxoDish® was experimentally determined at different temperatures with the SDR SensorDish® Reader. The gathered data could be used to predict the diffusion constant k for the OxoDishes®.

Multiwell plates or vials with integrated chemical optical sensors (optodes) are increasingly used for aquatic respirometry in small animals. They are inexpensive, their volume is ideal for this kind of study, and their application allows simultaneous measurements of replicates. In recent years the application of chemical optical sensors is preferred over formerly used Clark-type electrodes, because the optodes do not consume oxygen, require low maintenance, and provide more stable measurements. The SDR SensorDish® Reader is such an optical oxygen measurement system often applied in respirometry studies. With this reader the sensors at the bottom of each well in an OxoDish® - a polystyrene multiwell plate with integrated optodes - can be read out. Ideally, a respirometer chamber is non-diffusible for gasses. However, polystyrene is oxygen permable, so when using an OxoDish®, O2 will diffuse across the walls of the well if the pO2 within is reduced below the pO2 of the surrounding. To make precise measurements of the rate of oxygen consumption R (in mmol min-1) of cells, or whole animals inside the OxoDishes®, diffusion into the sealed wells needs to be accounted for.

Instantaneous Rate of O2 Consumption

R is derived from changes in oxygen concentration, which is the product of the capacitance coefficient for oxygen ßO2 (in mmol L-1 kPa-1, which is dependent on temperature) and its partial pressure pO2 (in kPa). The organism in the respirometer consumes O2 at an instantaneous rate R(t). In the infinitesimal time interval (t, t + Δt), the organism consumes a number of moles of O2, R(t)Δt. We assume that the media inside and outside the well are thoroughly mixed, and PW(t) is the pO2 inside the well at time t and PA is the constant pO2 outside the well. By Fick´s law, the diffusive flux is proportional to the gradient (PA - PW(t)) across the surface, and conservation of O2 requires that the change in moles of O2 in the well balances the moles of O2 replenished or lost through diffusion and the moles of
O2 consumed:

Here V is the volume of the well and k is the diffusion constant. This differential equation has the solution:

τ is a dummy variable of integration and e-k(t-τ) is an integrating factor. In the absence of the organism R(t) = 0 and

so that

k can be determined from the slope of a plot of log(IPW(t) - PAI) against time. Monitoring PW(t) and dPW/dt, R(t) can be estimated as

According to equation 5 dPW/dt is used to determine R. During data acquisition, there needs to be a balance between signal noise and sampling frequency to obtain appropriate resolution and simultaneously overcome noise magnification. An alternative would be to fit a relationship to the data of pO2 against time, from which a differential can then be calculated at any point in time - effectively smoothing noise from the data.

Oxygen Diffusion across the Walls of Polystyrene Wells

Each well of an OxoDish® has about 3.3 mL volume and an optode integrated at the bottom. When using it as multiple closed-system respirometer, the medium inside each well has to be thoroughly mixed; therefore, we put a stainless steel ball (2mm diameter) in each well, which moves around the perimeter and the oxygen sensor when the OxoDish® is put on an orbital shaker. The investigated organism is separated from the oxygen sensor and the steel ball by a mesh. Then each well is sealed individually with a glass cover slip (Fig. 1). In order to evaluate the oxygen diffusion across the surface of the polystyrene wells of an OxoDish®, we filled 12 wells with air-equilibrated pure water (pO2 = 21 kPa). Another four wells were filled with oxygen-free medium (1 % soldium sulfite solution, pO2 = 0), as a control for oxygen sensor drift. Each well was sealed under exclusion of air bubbles and the OxoDish® was positioned on the SDR SensorDish® Reader. The whole system was then placed on an orbital shaker (75 rpm) in an anoxic (nitrogen flushed) and temperature-controlled environment. Oxygen measurements were taken at an interval of 1 minute at 8 °, 22.5 °, and 37 °C, respectively, until a pO2 of about 5 kPa was reached. As a control, where no oxygen diffusion takes place, a custom-built 24-well plate made of aluminum with glass bottoms and a sensor spot (SP-PSt5,  PreSens) integrated in each well, was used to repeat the  measurements in the same set-up. O2 diffused across the walls of the OxoDish® and the pO2 in the water inside the wells decreased exponentially over time. The change in pO2 over time was greater at increased temperature, as can be seen in Fig. 2. In the non-diffusible aluminum plate, on the other hand, the oxygen content inside the wells remained constant over the same time period. A plot of log (IPW(t) - PAI) against time, where in this case PA = 0 shows straight lines and slopes that are the k values for each temperature. A linear relationship exists between k and temperature, so at a given temperature, k can be predicted for the polystyrene OxoDishes®.


Plastic multiwell plates with integrated oxygen sensors, like the OxoDishes® by PreSens, can be reliably used as small closed-system respirometers, provided that diffusion of O2 across the walls of the chambers is accounted for. With the method provided here, the data can be accurately adjusted for this error. Furthermore, with the relationship between the diffusion constant k and the temperature this method can be applied to different experimental conditions.

Application Note adapted from:
E. T. Polymeropoulos, et al.: Respirometry: Correcting for Diffusion and Validating the Use of Plastic Multiwell Plates with Integrated Optodes; Physiological and Biochemical Zoology 86 (5), 588 - 592, 2013


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