A batch culture passes through four phases: lag (adaptation, little or no increase), log or exponential (constant doubling time, highest viability; the best time for experiments, freezing or infection), stationary or plateau (growth slows and stops because of nutrient depletion, waste build-up or, for adherent normal cells, density limitation; the viable count stays roughly constant), and decline (death exceeds division). Animal cells divide much more slowly than bacteria; doubling times of cultured mammalian cells are commonly about 12-48 hours.
NUMBER OF DOUBLINGS
n=log2X0X≈3.32log10X0XX=X02t/td
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.
MONOD MODEL (SUBSTRATE-LIMITED GROWTH)
μ=Ks+SμmaxS
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.
HAEMOCYTOMETER COUNT
cells/mL=mean count per large square×dilution factor×104
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.
VIABILITY BY TRYPAN BLUE EXCLUSION
Viability(%)=total cells countedunstained (live) cells×100
Live cells with intact membranes exclude the dye; dead cells with damaged membranes take it up and look blue.