Immortalized cell lines, which are cells that can live and proliferate semi-indefinitely in vitro, are an extremely valuable tool for scientists. Because they divide rapidly and can be genetically manipulated, cell lines can be used to ask and answer many questions about the structure and function of cells, proteins, and genes.
When working with cultured cells, it’s important to know the general rate of proliferation and be able to calculate density and cell number so you can time and standardize your experiments by using the same number and density of cells for each condition or treatment. Cell density also affects cell growth and proliferation, so making sure your cells are happy and growing well requires being able to determine their density.
Although it’s critical to know the approximate number of cells you’re using in a given experiment, you don’t have to count each cell. That would be impossible! Instead, counting one or more random subsets of a larger sample will give you a good estimate of cell numbers. Random sampling and estimation are important techniques in almost every aspect of scientific research.
A sample solution to the calculations in this Snack:
Q: Find the area of an image, or field of view, by using the scale bar to estimate its length and width. The result will be the same for all three images.
A: You can fit approximately 6 scale bars across the image, and approximately 4.5 scale bars down. So the image measures about 300 µm wide, and about 225 µm tall. Therefore, the area of the image is about 300 µm x 225 µm = 67,500 µm2.
Q: Convert the area in µm2 to mm2.
A: To convert your estimate to mm2, multiply by 10-6. In this case, the area is about 0.068 mm2.
Q: Choose any of the three images and use the scale bar to estimate the diameter of one HeLa cell. Estimate the diameter of at least three cells in your sample and calculate an average diameter.
A: Answers will vary depending on which cells you choose to measure, where and how you measure them, and how close your estimate is. Between 20 and 30 µm is a reasonable estimate for the average diameter of one cell.
Q: Try estimating the area of one HeLa cell. You can assume the cells are circular.
A: Answers will vary based on your estimate of the average diameter of a cell. Reasonable estimates for the area of one cell are between 300 µm2 and 700 µm2.
Q: Next, using all three images, determine the average number of cells in a field of view. Count the cells in each of the three fields of view, add them together, and divide by 3.
A: Answers will vary depending on how accurate your method of counting is and whether you choose to count cells on the edges of the image that are only partially visible. A reasonable estimate of the average number of cells in one field of view is about 150 cells.
Q: Density is expressed as number of cells/mm2. Calculate the average density of the cells on the coverslip by dividing the average number of cells in a field of view by the area of the field of view.
A: A reasonable estimate of the density of the cells on the coverslip is 2,200 cells/mm2.
Q: The coverslip used for these images measures 22 mm by 22 mm. Calculate the area of the coverslip. Then calculate the total number of cells on the coverslip by multiplying the density of the cells by the area of the coverslip.
A: The area of the coverslip is 484 mm2. An estimate of the total number of cells on the coverslip based on a density of 2,200 cells/mm2 is 1,064,800 cells.
Q: Calculate the number of cells there would be after one day, or 24 hours, given the generation doubling time of 16.2 hours.
A: Answers will vary depending on how many cells you calculate as your starting number. The calculations below are based on using 1,064,800 for N0.
After 24 hours, there would be about 2.97 x 106 cells, or 2,970,000 cells.
Q: Calculate the area these cells would cover in mm2, assuming that they have the same density that you calculated above.
A: After 24 hours, these cells would cover about 1.35 x 103 mm2, or 1,350 mm2.
Q: Calculate the number of cells there would be after one week (168 hours), and the area they would cover.
A: After 1 week, there would be about 1.41 x 109 cells, or 1,410,000,000 cells. These cells would cover about 641,000 mm2, or 0.641 m2.
Q: Calculate the number of cells there would be after three weeks (504 hours), and the area they would cover.
A: After three weeks, there would be about 2.47 x 1015 cells, or 2.47 quadrillion cells. These cells would cover about 1.12 x 1012 mm2, or 1.12 km2.
Q: Calculate the number of cells there would be after four weeks (672 hours), and the area they would cover. Convert mm2 to square kilometers (km2).
A: After four weeks, there would be about 3.25 x 1018 cells, or 3.25 quintillion cells. These cells would cover about 1.48 x 1015 mm2, or 1,480 km2.
Q: The city of San Francisco is approximately 10 km by 10 km. How many HeLa cells would it take to cover the city? About when do you think the cells on the coverslip would grow to cover the city?
A: San Francisco is approximately 100 km2. It would take approximately 2.2 x 1017 cells to cover the city. Based on the time points calculated above, it would take between three and four weeks for the cells on the coverslip to grow to cover the city.