Animal cell culture formulas

X is the viable cell concentration (cells/mL), X_0 its value at the start of the exponential phase, and μ the specific growth rate (per hour); valid only in the exponential phase.

X in cells/mL and t in hours, so μ is in per hour; both points must lie in the exponential phase.

Convention used here: t_d = ln 2/μ, in the same time unit as μ; exponential phase only.

For exponential growth from X_0 with no lag, n doublings take n × t_d. For a cell line, the population doubling level adds n at each subculture (cells harvested over cells seeded); the passage number counts subcultures only.

S is the limiting substrate concentration (for animal cells often glucose or glutamine), μ_max the maximum specific growth rate and K_s the substrate concentration at which μ = μ_max/2. When S is much larger than K_s, μ ≈ μ_max.

In the standard chamber one large square is 1 mm × 1 mm with depth 0.1 mm, so its volume is 0.1 mm³ = 10^-4 mL. Cells on two agreed sides of a square are counted, those on the other two are not. The dilution factor includes the stain: a 1:1 mix with trypan blue gives 2.

Live cells with intact membranes exclude the dye; dead cells with damaged membranes take it up and look blue.