The growth curve

Bacteria multiply by binary fission: one cell divides into two, two into four, then 8, 16 and so on. So their numbers rise exponentially. Because the numbers become huge, they are plotted as the logarithm of the number of living cells against time. This growth curve has four phases:

• Lag phase: the number does not rise yet. The cells are adjusting to the new medium and making the components they need. The lag is long if the inoculum was old or refrigerated, short if it was young and active.
• Exponential (log) phase: cells divide at the maximum, constant rate, and the number doubles every doubling time (for E. coli, about 20 minutes). The cells are healthy and uniform, so this is the best phase for studying them.
• Stationary phase: the number stays level. Cells still divide, but new cells balance those that die, usually because a nutrient has run out.
• Death phase: nutrients are exhausted and toxic wastes build up (for example, the acids made by Streptococcus). The number of living cells falls, usually logarithmically.

Two numbers describe the speed of growth:

• The specific growth rate, µ = 2.303 (log Xₜ − log X₀) / t, where X₀ is the starting number of cells and Xₜ the number after time t.
• The doubling time, t_d = 0.693 / µ. It can also be found as t_d = t / n, where n is the number of generations in time t.

The larger µ, the shorter the doubling time. µ depends on the temperature, pH, medium, and the amount of dissolved oxygen.

A worked example: if a culture grows from 10⁴ to 10⁸ cells per mL in 2 hours, then µ = 2.303 × (8 − 4) / 2 = 4.606 per hour, and t_d = 0.693 / 4.606 = 0.15 hours, about 9 minutes.