Microbial growth records, counts and optical signals

What you’ll learn

• Calculate doubling time from supplied exponential-growth data.
• Interpret the strengths and limitations of count and turbidity methods.

Understand the idea

Core practical 13 concerns the rate of growth of microorganisms in a liquid culture. This lesson uses supplied measurements from approved non-pathogenic classroom material and gives no culturing procedure. During an exponential phase, equal time intervals can give equal multiplication factors. A graph of the logarithm of population size against time is then approximately straight. A lag phase, stationary phase or declining phase does not satisfy the same constant exponential-rate assumption.

Different measurements describe different aspects of a population. A direct microscopic count may include both living and dead cells. A viable count estimates colony-forming units rather than guaranteeing one colony for every individual cell, because cells may occur in groups. Turbidity measures light scattering and can be affected by dead cells, debris, cell size and instrument range. Calibration is needed before interpreting an optical signal as a cell concentration.

State the growth constant's definition and time units. The natural-log constant in $N=N_0e^{\mu t}$ differs numerically from the number of generations per unit time, although both can describe the same dataset. Aseptic practice protects the work and its surroundings from contamination, but actual handling and disposal remain governed by trained supervision and the institution's approved procedures.

Key formulae

$$N=N_0\,2^{t/g}$$

$$g=\frac{t\ln2}{\ln(N/N_0)}$$

$$\mu=\frac{\ln N_2-\ln N_1}{t_2-t_1}$$

Worked example

In a supplied exponential-phase record, a measured population rises from $4.0\times10^6$ to $3.2\times10^7$ cells in $90\ \mathrm{min}$. Find the number of doublings and the doubling time.

1. The multiplication factor is $(3.2\times10^7)/(4.0\times10^6)=8$.
2. Since $8=2^3$, the record contains three doublings.
3. The doubling time is $90/3=30\ \mathrm{min}$, assuming the exponential model applies throughout the interval.

Answer: Three doublings; doubling time 30 minutes.