Quantitation of Microbial Growth - Comprehensive Notes

Recommended Reading

• 'Brock Biology of Microorganisms’ by Madigan et al. (15th ed): Ch5 paras 1-8.

• Access e-textbooks via Canvas or IFIND.

• Use textbooks as primary sources and lectures as secondary sources.

• Improve scientific reading skills for advanced research papers.

• Contact subject librarians at medlib@Swansea.ac.uk for help.

Learning Objectives

• Understand microbial growth principles.

• Quantify microbial growth parameters.

• Apply understanding of culturing techniques.

• Appreciate differences between batch and chemostat culturing.

Principles of Microbial Growth

• Microbial growth results from cell division (binary fission).

• Growth is an increase in cell number, measured per volume unit in liquid culture.

• Filamentous microbes use different parameters.

• Diversity in division styles:

  • Binary fission (most common)

  • Budding

  • Hyphal growth and sporulation

Growth, Cell Generation, and Generation Time

• Microbes grow in suspension or attached to surfaces:

  • Planktonic growth: cells in liquid.

  • Sessile growth: cells on surfaces (biofilms, colonies).

• Generation time $g$ or $t_d$: time for cells to double.

• Time to divide depends on genetics, nutrition, and physical factors.

• Example: Escherichia coli doubles every 20 minutes.

Quantitative Aspects of Microbial Growth

Methods for Culturing Microbes in Liquid Media

• Batch and continuous methods exist.

• An inoculum is added to sterile media to start a culture.

• Cells start dividing after adjustment.

Growth Phases in Batch Culture

• Lag phase

• Log phase: cell numbers double at a fixed growth rate.

• Stationary phase

• Death phase

Cell Number Doubling

• $N = N_0 \times 2^n$ Eq (1)

  • $N$: Total cell number

  • $N_0$: Starting cell number

  • $n$: Number of generations

Exponential Growth Example

• $t_d$ is 30min

• Exponential growth from the start (no lag phase)

Identifying Exponential Growth

• Exponential growth appears as a straight line on a log-scale graph.

Doubling Time

• Doubling time $t_d$ (=mean generation time $g$) is:-

• $t*d = \frac{\Delta t}{n}$

• $t*d = \frac{t - t_0}{n}$ (in Brock: $g = \frac{t}{n}$ ) Eq (2)

  • $\Delta t$: duration of exponential growth

  • $n$: number of doublings

  • $g$: mean generation time

  • $\Delta t = t - t_0$- $t$: endpoint of exponential growth.

    • $t_0$: start point of exponential growth.

• Doubling time depends on the environment (nutrients, temperature, pH).

• It is not a fixed characteristic.

Growth Curve Slope

• Faster $g$ leads to a steeper slope on a log-scale growth curve.

• Slope = $log{10}(N-N0) / \Delta t$

• Longer log phase for cultures with slower doubling times if the maximum is the same.

Determining Doubling Time Practically

• $t*d = \frac{0.301 \cdot (t - t0)}{log{10}(\frac{N}{N0})}$ Eq (3)

  • $\Delta t$: exponential growth interval

  • $N_0$: starting cell number

  • $N$: cell number after exponential growth

• See also Ch36 Practical Skills Textbook.

Growth Rate

• Growth rate $\mu$: rate of population growth (per time).

• Brock: $\mu$ is the instantaneous growth rate constant, $k$

• $\mu$ is constant during log phase.

• $\mu$ allows comparison of microbes, strains, and growth conditions.

• $\mu_{max}$: maximum growth rate under optimal conditions.

• $\mu = \frac{2.303 \cdot log{10}(\frac{N}{N0})}{t - t_0}$ Eq (4)

Relationship Between Growth Rate and Doubling Time

• $\mu = \frac{ln2}{t_d}$

• $\mu = \frac{0.693}{t_d}$

• $t_d = \frac{0.693}{\mu}$

• Eq (5)

• $\Delta t$ is not the doubling time $t_d$!

Critical Parameters in Microbial Growth

• Log phase

• Doubling time $t_d$ (also $g$)

• Growth rate $\mu$

• $\mu$ is constant during log phase

• $\mu_{max}$ is the maximum microbial growth rate

Real World Aspects of Microbial Growth

Batch Culture

• Batch culture: closed-system, fixed volume.

• Typical growth curve:

  • Lag phase

  • Log or exponential phase

  • Stationary phase

  • Decline or death phase

• Gene expression changes affect growth rates.

Computing Growth Rate

• Growth curves may not be 'clear'.

• Use semi-log scale to set $t$ and $t_0$

Culturing and Quantifying Microbes

• Considerations:

  • Appropriate culture medium

  • Pure 'axenic' culture (aseptic techniques)

  • Counting cell numbers

  • Turbidity or biomass as proxies

Culture Media

• Defined media: exact composition known.

• Complex media: digests of biological products.

• Enriched media: complex media + nutritious materials for fastidious microbes.

• Selective media: inhibit some microbes.

• Differential media: detect metabolic reactions.

Counting Cells

Total Cell Count

• Light Microscopy: counts all cells in a known volume.

• Bacterial counting chamber: grid with squares and fixed volume.

• Different grids: Helber, Thoma, Improved Neubauer, Petroff-Hauser.

• Depths: 0.01-0.2mm.

• Limitations: counts live+dead cells, requires dilution.

Viable Cell Count

• Viable cell count: living, reproducing population.

• Each viable cell forms one colony.

• Spread-plate method is common.

• Dilute sample in 10-fold steps.

• For accurate results:

  • 30–300 colonies per plate

  • Measured as colony-forming units (CFU)

Reporting Cell Density

• Cell density: cell number or CFU per volume (ml-1).

• Compare/graph same properties for growth curves.

• Viable counts are reliable on selective media.

• CFU is typically lower than total count in active growth.

Viable Count Anomaly

• Organisms have different growth characteristics.

• Viable But Not Culturable (VBNC) cells exist.

• Dead cells are counted in total count.

Counting Cells by Proxy: Turbidity or Biomass

Turbidity or Optical Density (OD)

• Growth curves: OD vs time.

• OD is measured at a specific wavelength (e.g., 600nm).

• OD is proportional to cell number within limits.

• Establish a standard curve.

• OD underestimates at high values; dilute culture.

Biomass

• OD is poor for multicellular/clumping cells.

• Other proxies: Biomass (wet/dry weight), DNA, Total protein.

• More laborious.

Microbial Growth in Continuous Culture

Continuous Culture

• Continuous culture: open system, fixed volume.

• Chemostat: common continuous culture device.

• Steady state: cell density and substrate concentration are constant.

Controlling Growth

• Control growth rate and population density independently:-

  • Dilution rate $D$ controls growth rate $\mu$

  • Limiting nutrient determines cell density

Experimental Uses

• Chemostat maintains exponential growth for weeks/months.

• Used for studying physiology, ecology, evolution.

Simulator of Human Intestinal Microbial Ecosystem (SHIME)

• Animals and humans maintain continuous cultures.

• Diarrhea: effluent rate exceeds inflow rate.

• Series of chemostats can mimic the human GI tract.

Summary of Quantification of Microbial Growth

• Batch growth shows phases due to changing conditions.

• Exponential growth parameters:

  • Growth rate $\mu$

  • Doubling time $t_d$ (mean generation time $g$)

  • Generations $n$

• Methods to count cells directly/indirectly.

• Continuous culturing studies microbes under defined conditions.

Equations of Microbial Growth

• $N = N_0 \times 2^n$ Eq (1)

• Eq 1: Relationship between $N_0$ and $N$ after exponential growth with $n$ doublings

Calculating Number of Doublings

• $n = 3.3 \times (log{10} N – log{10} N_0)$ Eq (1b)

• $n = 3.3 \times (log{10} (\frac{N}{N0}))$ Eq (1c)

Determining Doubling Time Practically

• $t*d = \frac{(t - t0)}{n}$ Eq (2)

• $n = 3.3 \times (log{10} (\frac{N}{N0}))$ Eq (1c)

• $t*d = \frac{(t - t0)}{3.3 \times (log{10} (\frac{N}{N0}))}$

• $t*d = \frac{0.301 \times (t - t0)}{(log{10} (\frac{N}{N0}))}$ Eq (3)

• Eq 3: Doubling time as a relationship between $\Delta t$, $N_0$, and $N$

Summary of Equations

• $N = N_0 \times 2^n$ Eq (1)

• $n = 3.3 \times (log{10} N – log{10} N_0)$ Eq (1b)

• $n = 3.3 \times (log{10} (\frac{N}{N0}))$ Eq (1c)

• $t*d = \frac{(t - t0)}{n}$ Eq (2)

• $t*d = \frac{0.301 \times (t - t0)}{(log{10} (\frac{N}{N0}))}$ Eq (3)

• $\mu = \frac{2.303 \times (log{10} N – log{10} N0)}{(t - t0)}$ Eq (4)

• $\mu = \frac{2.303 \times (log{10} (\frac{N}{N0}))}{(t - t_0)}$ Eq (4b)

• $\mu = \frac{ln2}{t_d}$

• $$\mu = \frac{0.6