Question

For cell culture, various laboratories use different volumes of culture medium in their culture flasks according to their conventions. However, many do not consider how this might affect the diffusion time of O2 from the gas/liquid interface to the cells attached to the bottom of the flask. To address this, it is useful to have an understanding of how the O2 diffusion time might be influences by the volume of medium added. A typical cell culture flask has a surface area available for cell attachment of 75 cm2 , therefore the height of medium, thus the diffusion distance will be a function of the volume of culture medium added. Cell culture is typically done at a temperature of 37 ºC. a) Calculate the diffusion time for O2 through culture medium from the gas/liquid interface if the height of medium (distance from the gas/liquid interface to the bottom of the culture dish) is 4 mm. Use the Einstein's approximation equation to determine your answer and cite the reference for the O2 diffusivity value you used in your calculations. b) Produce a plot of the O2 diffusion time as a function of culture medium volume for volumes in the range of 7 to 15 ml. c) If you wanted to standardize your laboratory’s practice in cell culture by keeping the height of culture medium the same (at 1.2 mm) for whatever vessels you use to culture cells, what volumes would be required for: - Standard round cell culture dishes with 35, 60, and 100 mm diameter. - For flasks, standard surface areas are 25, 75, and 175 cm2 . Show calculations for one of the conditions and present your results for all of the conditions in a table

Answer 1

Ans. a) Here O₂ is used as solute for the diffusion process, in cell culture. We are supposed to calculate the diffusion time for O₂ through culture medium in the gas liquid interface.

Given the height of medium = 4 mm.

In diffusion process, diffusing solute moves in all the three dimensions, down a concentration gradient. Einstein's approximation equation is used to approximate the time taken in diffusion. It is given as:

;......................................................... (i)

Here, x = distance of diffusion (in cm)

D = diffusion coefficient of a solute in a free solution, D is for Oxygen, it is taken in cm²/S, D is dependent on both physical properties of solute and the medium. Diffusion coefficient always varies with temperature and under standard conditions of 37 ^oC, the value for diffusion coefficient of oxygen is given as:

. This is the standard value of diffusion coefficient of oxygen at 37 ^oC.

t = time required for the given length of diffusion, in seconds.

Here x = 4 mm (given) = the height of medium

we know 1 mm = 0.1 cm

Hence:  

Now we will substitute this value of x and D in equation (i) and we get the value for time as:

Diffusion time required for oxygen through culture medium is 3809.52 sec.

................................................................................................................................................................

b) We are supposed to plot for the oxygen diffusion time as a function of culture medium volume in the range of 7ml to 15 ml volume.

We are given the available area for cell culture = 75 cm².

D = diffusion coefficient for oxygen is dependent on both physical properties of solute and the medium. Diffusion coefficient under standard conditions of 37 ^oC, for oxygen is given as:

.

This is the standard value of diffusion coefficient of oxygen at 37 ^oC.

t = time required for the given length of diffusion, in seconds.

We are supposed to develop a plot for the diffusion time of oxygen versus the volume. For this we are required to assume a range of height of the medium so that we get the volume in the range of 7 ml to 15 ml. And for those heights we will calculate the time for diffusion using Einstein's approximation and then will plot for the given range.

Height of the medium considered (assumed) for the plot are:

x = 1 mm, 1.2 mm, 1.4 mm, 1.6 mm, 1.8 mm, 2 mm. (we assumed these values so that we will get the volume in the range of 7 ml to 15 ml as per the given conditions, for an area of 75 cm².

we will convert these assumed lengths (x) from millimeter to centimeter as

Here x = 1 mm (assumed) = the height of medium

we know 1 mm = 0.1 cm

Here x = 1.2 mm (assumed) = the height of medium

we know 1.2 mm = 0.12 cm

Hence we will all x as:

x = 0.1 cm, 0.12 cm, 0.14 cm, 0.16 cm, 0.18 cm, 0.2 cm.

Now we will substitute this value of x and D in equation (i) and we get the value for time as:

, for

Volume V (cm³) = x (cm) * Area (75 cm²)

as ,

Similarly:

,

Volume V (cm³) = x (cm)  * Area (75 cm²)

as ,

Similarly

,

Volume V (cm³) = x (cm)  * Area (75 cm²)

as ,

similarly

,

Volume V (cm³) = x (cm)  * Area (75 cm²)

as ,

similarly

,

Volume V (cm³) = x (cm)  * Area (75 cm²)

as ,

similarly

, for

Volume V (cm³) = x (cm)  * Area (75 cm²)

as ,

Hence the plot will be:

........................................................................................................................................................................................................

c) Here we are supposed to keep the height of culture medium same as 1.2 mm for all kind of vessels, we need to calculate the volume required:

for round cell culture dishes the volume required will be calculated as:

Volume (V)(cm³) = area of vessel (cm²) x the height of the medium (cm)

area of vessel (cm²) = A, is calculated as:

here, the diameter of dish = d, given 35 mm, 60 mm and 100 mm.

we know 1 mm = 0.1 cm,

hence the diameter of dish = d, will be given is cm as: 3 .5 cm, 6.0 cm and 10.0 cm.

So,

for round cell culture dishes the volume required will be calculated as:

Volume (V)(cm³) = area of vessel, A (cm²) x the height of the medium (x) (cm)

height of culture medium same as 1.2 mm

we know 1 mm = 0.1 cm,

Hence, height of culture medium same as 0.12 cm.

thus,

,

.......................................................................

similarly we calculate the volume for flasks as:

Given area as: 25 cm ², 75 cm ² and 175 cm ²

For  A = 25 cm ²,

For the vessel of 25 cm ² area volume is 3 cm ³,

The table for volume of all vessels with given conditions is:

Vessels with given conditions of diameter of area.	Volume (cm3) or (ml)
35 mm	1.154
60 mm	3.39
100 mm	9.424
25 cm2	3
75 cm2	9
175 cm2	21

......................................................................................................................................................................................................

Here x = 1 mm (assumed) = the height of medium

we know 1 mm = 0.1 cm