What is doubling time?
When 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.
μ, Td and generations: how they relate
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.
The four phases of growth
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).
- •Lag. Cells adapt to the new medium: synthesising enzymes, repairing DNA, adjusting metabolism. No net increase in viable count.
- •Log (exponential). Every cell divides at the maximum rate nutrients and temperature allow; μ is constant and equal to μmax. This is the only phase where Td is defined.
- •Stationary. Nutrient depletion or waste build-up halts growth; division equals death and μ ≈ 0.
- •Death. Death outpaces division and the population falls exponentially. Some species sporulate or produce secondary metabolites at this stage.
Assumptions and limitations
The model is simple and robust, but it rests on several conditions:
- •Exponential phase only: outside log phase the formula does not apply. Confirm the culture is growing logarithmically before estimating μ.
- •Homogeneous, well-mixed culture: gradients in oxygen, pH or nutrients (common in large bioreactors or biofilms) produce heterogeneous μ values.
- •Asynchronous population: synchronised cultures (e.g. after cell sorting) grow in steps, not along the smooth exponential curve.
- •Extreme ratios: an Nt/N0 ratio above 100 (more than ~6.6 generations) in a single window is biologically implausible without intermediate readings — a sign the culture has already left log phase.
Measuring growth: OD₆₀₀
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.
- •Linear range: ~0.1–0.6 with a 1 cm path length. Beyond ~0.6 the Beer–Lambert law breaks down: readings underestimate true density, so dilute before measuring.
- •Typical inoculation: start at 0.05–0.1 and harvest at 0.4–0.6 to stay in log phase and within the detector’s linear range.
- •Conversion: 1 OD₆₀₀ ≈ 8×10⁸ cells/mL for E. coli, but the factor is species- and instrument-dependent. Calibrate with direct counts (haemocytometer or flow cytometry) for your strain.
On counting methods, see Koch (1994), Growth Measurement (ASM Press).
Reference doubling times
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.).
Beyond exponential: Monod kinetics
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.