Unit 7: Microbial growth-curve determination

I. Orientation — quantitative study of bacterial multiplication

Microbial growth-curve determination describes the change in the number or biomass of microorganisms in a closed liquid culture over time. In a batch culture of Escherichia coli, nutrients are initially abundant, while oxygen, space, and usable substrates progressively become limiting. Turbidity provides an indirect estimate of biomass because suspended cells scatter light.

• Governing principle: Cell multiplication changes culture density, and increasing density generally increases optical turbidity.
• Growth measurement: Growth may be expressed as viable cell number, total cell number, dry mass, or optical density (OD); this unit uses OD as the primary measurement.
• Closed-system assumption: A fixed volume of nutrient broth is inoculated once, with no continuous addition of nutrients and no removal of cells.
• Growth-curve convention: Time is plotted on the horizontal axis, while OD or biomass is plotted on the vertical axis.
• Four phases: A standard batch culture passes through lag, exponential or log, stationary, and death or decline phases.
• Turbidity limitation: OD measures light scattering by both living and dead cells; it is therefore not identical to viable-cell concentration.
• Aseptic requirement: Contamination can alter turbidity and growth rate, so sterile media, instruments, and handling are essential.

II. Microbial growth-curve determination — phases and mathematical description

Microbial growth-curve determination is the construction of a time-dependent profile showing how a bacterial population changes under defined laboratory conditions.

A. Definition and purpose

The purpose of a growth curve is to identify the physiological phases of a culture and estimate parameters such as generation time and specific growth rate from sequential measurements.

• Population variable: Let (N) represent cell number or let (X) represent biomass concentration; the measured OD is used as a practical proxy for (X).
• Exponential model: During balanced log-phase growth, the population follows:

N_t = N_0 × 2^n

• (N_t): Population at time (t).
• (N_0): Initial population.
• (n): Number of generations during the interval.
  • Generation number: The number of doublings is calculated as:

n = (log10 N_t − log10 N_0) / log10 2

• Meaning: Since (\log_{10}2 \approx 0.301), two doublings correspond to (n=2).
  • Generation time: The average time for one doubling is:

g = t / n

• (g): Generation time, usually in minutes.
• (t): Duration of the exponential-growth interval.

B. Phases of the microbial growth curve

Each phase reflects a characteristic balance between cell adaptation, multiplication, nutrient use, and cell injury.

• Lag phase: Cells adapt to the new medium without an immediate increase in cell number.
  • Cell activity: Enzyme synthesis, repair, adjustment of membrane transport, and preparation for division occur.
  • Curve appearance: OD remains nearly constant or rises slowly after inoculation.
• Log phase: Cells divide at approximately a constant maximum rate under the available conditions.
  • Curve appearance: On a semilogarithmic plot of OD against time, the log phase appears approximately linear.
  • Physiology: Cells are metabolically active and relatively uniform, making this phase useful for physiological experiments.
• Stationary phase: Net population growth approaches zero because growth and death rates become approximately equal.
  • Limiting factors: Nutrient depletion, oxygen limitation, toxic metabolites, pH change, or crowding may contribute.
  • Curve appearance: OD reaches a plateau, although cells may continue to metabolize.
• Death or decline phase: Loss of viable cells exceeds formation of new cells.
  • Important distinction: OD may decline slowly or remain high because dead cells and cell debris can continue scattering light.
• Phase transitions: The exact duration of each phase depends on inoculum age, nutrient composition, temperature, aeration, and initial cell density.

C. Plotting and interpretation

Plotting the measurements correctly reveals the growth phases and prevents conclusions based on a single reading.

• Arithmetic plot: Plot time on the x-axis and OD on the y-axis.
  • Use: This plot displays the overall sigmoid shape and makes the stationary plateau visually clear.
• Semilog plot: Plot time on the x-axis and (\log_{10}(\text{OD})) on the y-axis.
  • Use: Exponential growth becomes approximately a straight line, allowing growth-rate estimation.
• Specific growth rate: During exponential growth:

μ = [ln(X_2) − ln(X_1)] / (t_2 − t_1)

• (\mu): Specific growth rate, commonly expressed as time(^{-1}).
• (X_1, X_2): Biomass proxies, such as OD values at times (t_1) and (t_2).
  • Doubling-time relationship: When growth is exponential:

g = ln(2) / μ

• Interpretation: A larger (\mu) gives a shorter generation time.
  • Worked example: If OD increases from 0.10 to 0.40 in 60 minutes, the culture undergoes two doublings because (0.10 \rightarrow 0.20 \rightarrow 0.40); therefore (g=60/2=30) minutes.

III. Escherichia coli — organism used for the experiment

Escherichia coli is a Gram-negative, facultatively anaerobic, rod-shaped bacterium commonly used to demonstrate rapid growth in laboratory media.

A. Biological characteristics relevant to growth measurement

The properties of E. coli make its growth pattern measurable within a typical laboratory session.

• Cell morphology: E. coli cells are small rods, generally about 1–3 µm long; suspended cells scatter incident light and produce measurable turbidity.
• Metabolism: It can grow by aerobic respiration when oxygen is available and can use alternative pathways under oxygen-limited conditions.
• Nutritional response: In a nutrient-rich broth, cells can pass rapidly from lag into exponential growth after adapting to the medium.
• Temperature: Many laboratory strains grow well near 37°C, although the actual incubation temperature must remain constant throughout the experiment.
• Culture uniformity: A well-mixed suspension distributes cells throughout the cuvette, making OD readings more reproducible.
• Inoculum effect: An old, stressed, or very dense inoculum can lengthen the apparent lag phase or reduce the time available to observe exponential growth.

B. Culture conditions and sampling design

Reliable growth-curve data depend on keeping biological and sampling conditions constant.

• Medium: Nutrient broth supplies carbon, nitrogen, minerals, and other requirements; the same medium should be used for blanking and culturing.
• Inoculation: A measured volume of an actively growing starter culture is transferred aseptically into sterile broth.
• Aeration: Shaking improves oxygen transfer and keeps cells suspended; flask volume should leave adequate headspace.
• Sampling interval: Early readings may be taken at shorter intervals because the culture can change rapidly during log phase.
• Replicates: Duplicate or triplicate cultures help distinguish biological variation from instrument error.
• Asepsis: Sterile pipette tips, capped vessels, and disinfected work surfaces reduce contamination by other microorganisms.
• Biosafety: Laboratory strains must be handled according to institutional biosafety rules, with proper decontamination of cultures and disposables.

IV. Turbidimetric method — optical estimation of biomass

The turbidimetric method estimates microbial biomass from the reduction in transmitted light or increase in light scattering produced by cells suspended in broth.

A. To study and plot the growth curve of Escherichia coli by turbidimetric method

This experiment measures OD at successive time points and plots the resulting values to identify the phases of E. coli growth.

• Materials: Use sterile nutrient broth, an E. coli culture, sterile culture tubes or flasks, pipettes, a spectrophotometer, cuvettes, a shaker or incubator, and disinfectant.
• Blank preparation: Fill a clean cuvette with uninoculated sterile broth.
  • Purpose: The blank corrects for light absorbed or scattered by the medium and cuvette.
• Instrument setting: A wavelength near 600 nm, commonly designated OD600, is widely used for bacterial suspensions.
  • Meaning: OD600 is an optical-density reading at 600 nanometres; it is dimensionless.
• Inoculation: Add the measured E. coli inoculum to sterile broth, mix gently, and record this as time zero.
• Sampling: At fixed intervals, mix the culture uniformly and transfer a sample to a clean cuvette.
  • Consistency: Use the same cuvette orientation, sample volume, mixing method, and measurement wavelength each time.
• Data record: Record elapsed time and OD in a table.

Time (h) | OD600
---------|------
0.0      | ...
0.5      | ...
1.0      | ...
1.5      | ...

• Plot construction: Plot time in hours on the x-axis and OD600 on the y-axis for the arithmetic growth curve.
• Phase identification: Mark the initial lag region, steep log-phase region, plateau stationary region, and any later decline.
• Exponential analysis: Plot (\log{10}(\text{OD}{600})) against time when estimating the slope of the log phase.
• Interpretation: A steadily increasing OD indicates increasing suspended biomass, but it does not by itself prove that every measured cell is viable.

B. Instrumental precautions and data quality

Careful technique is necessary because turbidity readings are sensitive to both biological and physical variation.

• Cuvette cleanliness: Fingerprints, droplets, scratches, or bubbles can scatter light and produce falsely high OD values.
• Range limitation: Very dense cultures may exceed the reliable linear range of the spectrophotometer.
  • Correction: Dilute the sample with sterile broth, record the dilution factor, and calculate:

OD_corrected = OD_measured × dilution factor

• Symbol definition: The dilution factor is the reciprocal of the fraction of original culture present in the measured sample.
  • Mixing error: Settled cells give a nonrepresentative sample; mix consistently without creating foam.
  • Blank drift: Recheck the blank if the experiment is long or if the medium changes visibly.
  • Temperature control: Temperature variation changes metabolic rate and therefore changes the apparent slope of the growth curve.
  • Sampling disturbance: If repeated samples are removed from one flask, the volume and aeration gradually change; parallel sacrificial tubes can reduce this effect.
  • OD versus viable count: A plate count measures colony-forming units, whereas OD measures light scattering from total suspended material; the two methods should not be treated as interchangeable.

C. Applications and limitations

The turbidimetric growth curve is useful for comparing growth conditions, but its results require biological interpretation.

• Applications: It can compare media, temperatures, aeration conditions, antimicrobial effects, or mutant strains by changes in lag duration, log-phase slope, or final OD.
• Calibration need: To convert OD into cells per millilitre or dry mass, prepare a calibration curve relating OD to an independent measurement such as viable count or dry weight.
• Nonlinearity: At high cell concentrations, multiple scattering makes OD no longer proportional to biomass; dilution is required.
• Dead-cell contribution: Cells killed by heat or antibiotics may still scatter light, causing OD to remain high while viable counts fall.
• Clumping: Aggregates scatter light differently from evenly dispersed cells and can produce poor repeatability.
• Reporting standard: State the organism, medium, temperature, wavelength, sampling interval, dilution, replicate number, and plotting scale so that the curve can be interpreted accurately.
• Overall significance: The method provides a rapid, non-destructive estimate of culture density and a practical way to visualize the transition from adaptation through active multiplication to nutrient-limited growth.