You can use this formula to calculate he plating cell volume based on doubling time.

"PDT = 3.32 (log Xe - log Xb) + S"

PDT=Population doubling time

Xb = cell number at the beginning of the incubation time

Xe = cell number at the end of the incubation time

S = starting PDT

3.32 = is a constant cell proliferation rate for all cells

(or)

The proper calculation of PDT should be done by counting cells on daily basis for e.g. 7 days using 6-wells, T-25 or similar culture vessels. Next, draw a growth curve from the data (number of cells versus time) and calculate the PDT from the linear part of the curve using this equation:

"Plating cell volume using PDT = (t2 - t1)/3.32 x (log n2 - log n1)"

where t is time and n number of cells

t2 = cell numbers at end of incubation period

t1 = cell numbers at start of incubation period

Hi Bargavi,

Thank you for your input.

For an example, If I start with 0.5 million cells A then I see that its getting doubled (1million) in 24 hrs. With the second formula you mentioned,

Plating cell volume PDT= 24 hrs/ 3.32* log 1million- log 0.5million

= 1.26

What does this value 1.26 mean exactly?

For my project, I need to know the appropriate cell volume of different cell lines plate on different culture vessels to do the culture for 24, 48, 72 or 96 hours? Do you know how to calculate it?

Thank you for your time.

Hi Venkatesh,

The idea of using a single formula to calculate optimal seeding density across different cell lines sounds interesting, so I made an attempt at it. I assume you work with attached cells which grow in a 2D-plane, so that the available area (cm2) is the main restriction for cell growth. I also assume that the cell number increases exponentially. This means we can use an exponential function, find the slope of the function, and use this to calculate optimal seeding number.

Note that an exponential function will not take into account cell-cell contact inhibition, nutrient depletion, waste accumulation or other factors which alter the growth conditions of your cells during culture (alter proliferation rates over time). It is more likely I think, that cell growth follows a sigmoid curve (4PL), including a slower “lag phase” where cells attach and a reduced growth phase near confluence. But for this case let's say the cells grow exponentially, as it makes the equation much simpler (but still usable, hopefully!).

Starting at the base exponential function:

y = y0ax

In our scenario, y is the number of cells at the end of the experiment, y0 is the starting number of cells, a is the slope and x the duration of the experiment in hours.

To find a, or the slope, we need to know the doubling time of the cell line. You can calculate this if you have experimentally determined the number of cells at two time-points, in any given vessel. Let’s say we seed out 5000 cells on day 0 in a 96-well plate. We measure the same well again after 72 hours, and find the number of cells to be 40’000.

This gives us the values:

X1 = 0, Y1 = 5000, X2 = 72, Y2 = 40000

To find a:

a = (y2/y1)(1/(x2-x1)) = (40000/5000)(1/(72-0) = 1.0293

This is the slope of our exponential function. We now have this function describing the growth of our cell line:

y = y0 * 1.0293t

If however you already know the doubling time of a cell line, we can use a simplified function: a = (2/1)(1/t) where t in this case is the doubling time in hours.

For a cell line with a doubling time of 48 hours: a = (2/1)(1/48) = 1.01454 , making the equation:

y = y0 * 1.01454t

If I need to find the seeding number for a cell line which has a doubling time of 48 hours, I input the duration of the experiment (say 72 hours), and the number of cells I want the well/flask to contain at the end of the experiment (say 1 million cells):

1’000’000 = y0 * 1.0145472 = 353’687 cells per well/flask

If I understand you correctly, you want a formula which gives you a seeding density which accounts for controls reaching confluence, i.e. you want to avoid fully confluent wells at the end of the experiment.

There is a table for the area of common plates/wells on ThermoFisher’s website (here: https://www.thermofisher.com/no/en/home/references/gibco-cell-culture-basics/cell-culture-protocols/cell-culture-useful-numbers.html). The 96-well plate, for example, has an area of 0.32 cm2. The table also lists the number of cells in a fully confluent well to be 40’000 cells. Like doubling time, this value is definitely cell-line specific and should be determined experimentally. But let’s use the listed value here.

40’000 cells at 100% confluence. I want 85% confluence so

40000*0.85 = 34000. 34’000 cells/0.32cm2 = 106’250 cells/cm2.

This “optimal” cell density can then be used to calculate the number of cells I want my control well to contain at the end of an experiment, for any given plate/well. For a 6-well plate, with an area of 9.6 cm2, I want the controls to contain a maximum number of:

9.6 cm2 * 106’250 cells/cm2 = 1 million cells

So for an experiment with a cell line which divides once every 48 hours, where we seed a 6 well plate in an experiment which lasts 96 hours, the formula says we need to plate:

y = y0 * 1.01454t

1’000’000 = y0*1.0145496 = 250’126 cells

Hope this helps, let me know if it works!

Regards,

Theodor M.

Hi Theodor,

You exactly answered my question. The formula you mentioned will serve my needs. Thank you so much for your time.

Best regards,

Venkatesh.

Hi Theodor,

I have a small doubt about the determination of 'a' value if we know the doubling time already.

a = (2/1) to the power of 1/doubling time.

What does 2/1 mean exactly?

Thank you so much for your time.

Best,

Venkatesh Murugasan

Hi Venkatesh,

My mistake, (2/1) simply means 2, making:

a = 2 to the power of (1 / doubling time)

The number 2 in this function describes how the population grows (i.e. a "doubling"). If we say instead that only half of the cells are able to divide each time, we could write:

a = 1.5 ^ (1/doubling time)

With "(1/doubling time)" we can use the units we like (day, hours, etc), to determine the number of times the population divides over a given period. For instance, if we have a cell line which doubles every 24 hours, after 72 hours the cells will have divided (72 h / 24 h) = 3 times. And "a" would simply be:

a = 2^3 = 8

This could also be written as:

a = 2^(1/24) = 1.0293^t, and at 72 hours: a = 1.0293^72 = 8

Let me know if you have further questions!

Best regards,

Theodor M.