Initial population count (OD600)
Final population count (OD600)
Start of the measurement interval (h)
End of the measurement interval (h)
2.321
h0.2986
1/h2.585
divWhen a population grows by binary fission, every cell splits in two and the total count doubles at regular intervals. The doubling time (Td) is exactly that: how long the population takes to become twice as large. It is the microbial counterpart of a radioactive material’s “half-life”, only reversed — instead of decaying, the population grows.
While nutrients are plentiful, that growth is exponential: the more cells there are, the faster the total climbs. The continuous model is:
where N0 is the population at time t0 (measured in OD₆₀₀ or cells/mL) and μ is the specific growth rate, which sets how fast it accelerates. It was formalised by Monod (1949) and remains the foundation of culture microbiology.
The rate μ comes from two population measurements separated in time: it is the slope of ln N versus t during the exponential phase.
It is a net balance between division and death: μ = μmax − kd, where kd is the specific death rate. To go from μ to the doubling time, require the population to reach double, N(t0 + Td) = 2N0, and solve:
μ and Td are the same information in two languages: high μ ↔ short Td. The same measurements yield a third quantity, the number of generations — the division cycles that occurred:
The base-2 logarithm reflects the binary nature of division. Non-integer values are normal: they represent the average across an asynchronous population, where not all cells divide at once.
In a batch culture, the population follows a stereotyped trajectory with four distinct phases. The exponential model — and therefore Td — only makes sense in one of them, the log phase (Brock, ch. 6).
The model is simple and robust, but it rests on several conditions:
Optical density at 600 nm (OD₆₀₀) is the standard proxy for bacterial biomass. It is not absorbance in the strict sense but light scattering, so it reflects cell number and size rather than pigmentation.
On counting methods, see Koch (1994), Growth Measurement (ASM Press).
Typical values under optimal conditions — handy to sanity-check your results.
| Organism | Td | Conditions |
|---|---|---|
| E. coli | ~20 min | LB, 37 °C, aerated |
| B. subtilis | ~25 min | LB, 37 °C |
| S. cerevisiae | 90–120 min | YPD, 30 °C |
| CHO (hamster ovary) | 18–24 h | DMEM/F12, 37 °C |
| HeLa (human) | 24–30 h | DMEM + 10 % FBS, 37 °C |
| M. tuberculosis | ~18 h | 7H9 medium, 37 °C |
Typical values from Madigan et al., Brock Biology of Microorganisms (16th ed.).
μ is not constant forever. It depends on substrate concentration [S] through the Monod equation, analogous to Michaelis–Menten kinetics:
Ks is the half-saturation constant (the [S] at which μ = μmax/2). When [S] ≫ Ks (nutrient excess) μ ≈ μmax and the exponential approximation holds; as [S] falls, μ decreases and the culture transitions to stationary phase. It is the bridge between exponential growth and the substrate-limited regime.
Open reading: LibreTexts — Microbial Growth.