Experiment 05Growth Kinetics • B.Sc. / M.Sc.
Bacterial Growth Curve Kinetics by Spectrophotometric Turbidimetry (OD600)
🎯 Aim: To monitor the population dynamics of Escherichia coli growing in batch culture over a 6-hour period by measuring optical density at $600,text{nm}$ ($text{OD}_{600}$), construct the growth curve, and determine the generation time ($g$) and specific growth rate constant ($mu$).
🔬 Theoretical Principle & Population Mathematics
In a closed batch culture system with finite nutrient resources, unicellular bacteria undergoing binary fission exhibit four classic physiological growth phases:
- 1. Lag Phase: Period of physiological adaptation. No net increase in cell number; cells synthesize essential metabolic enzymes, cofactors, transport systems, and ribosomal machinery required for the new medium.
- 2. Exponential (Log) Phase: Unrestricted balanced growth where population doubles at a constant maximal rate. Cell mass and cell numbers increase logarithmically according to first-order kinetics:
$$frac{dN}{dt} = mu N implies ln left(frac{N_t}{N_0}right) = mu (t – t_0)$$
Where $mu$ is the specific growth rate ($text{h}^{-1}$). The generation / doubling time ($g$) is:
$$g = frac{ln 2}{mu} = frac{0.693}{mu}$$ - 3. Stationary Phase: Exhaustion of essential carbon/energy sources, limitation of dissolved oxygen, and accumulation of toxic metabolic end-products (organic acids) cause growth rate to balance death rate ($dN/dt = 0$). Cells express RpoS general stress response sigma factors.
- 4. Death (Decline) Phase: Viable cell count declines exponentially as cellular energy reserves (ATP, proton motive force) collapse.
Figure 5.1: Bacterial Growth Curve (OD600 Turbidimetry) & Generation Time Kinetics
📊 Representative Growth Kinetics Data Matrix
| Time t (min) | Measured OD600 | log10 (OD600) | Viable Count (CFU/mL) | Observed Growth Phase |
|---|---|---|---|---|
| 0 min | 0.050 | −1.301 | $2.5 times 10^6$ | Inoculation / Lag Phase |
| 30 min | 0.065 | −1.187 | $3.2 times 10^6$ | Lag Phase adaptation |
| 60 min | 0.120 | −0.921 | $6.4 times 10^6$ | Early Exponential Phase |
| 90 min | 0.245 | −0.611 | $1.3 times 10^7$ | Mid-Exponential Phase (Doubling) |
| 120 min | 0.485 | −0.314 | $2.6 times 10^7$ | Mid-Exponential Phase (Doubling) |
| 180 min | 0.980 | −0.009 | $1.0 times 10^8$ | Late Exponential Phase |
| 240 min | 1.450 | +0.161 | $1.8 times 10^8$ | Transition to Stationary Phase |
| 300 min | 1.480 | +0.170 | $1.8 times 10^8$ | Stationary Phase Plateau |
Calculation of Generation Time ($g$):
Between $t_1 = 60,text{min}$ ($text{OD} = 0.120$) and $t_2 = 180,text{min}$ ($text{OD} = 0.980$):
$$n = frac{log_{10}(0.980) – log_{10}(0.120)}{0.301} = frac{-0.009 – (-0.921)}{0.301} = frac{0.912}{0.301} = 3.03text{ generations}$$
$$g = frac{t_2 – t_1}{n} = frac{120,text{min}}{3.03} = 39.6,text{minutes}$$
$$mu = frac{0.693}{g} = frac{0.693}{0.66,text{h}} = 1.05,text{h}^{-1}$$
Between $t_1 = 60,text{min}$ ($text{OD} = 0.120$) and $t_2 = 180,text{min}$ ($text{OD} = 0.980$):
$$n = frac{log_{10}(0.980) – log_{10}(0.120)}{0.301} = frac{-0.009 – (-0.921)}{0.301} = frac{0.912}{0.301} = 3.03text{ generations}$$
$$g = frac{t_2 – t_1}{n} = frac{120,text{min}}{3.03} = 39.6,text{minutes}$$
$$mu = frac{0.693}{g} = frac{0.693}{0.66,text{h}} = 1.05,text{h}^{-1}$$
💬 Viva-Voce Questions & Model Answers
Q1: Why is optical density at 600 nm referred to as “turbidimetry” rather than true light absorbance?
Bacterial cells do not contain chromophores that genuinely absorb 600 nm photons. Instead, whole bacterial bodies act as microscopic colloidal particulate scatterers (Rayleigh and Mie scattering) that deflect incident light away from the spectrophotometer’s photodetector. The apparent “absorbance” reading is actually an optical light-scattering index proportional to cell biomass.
Q2: Why does the OD600 curve fail to show a sharp drop during the death phase?
Spectrophotometric turbidimetry cannot distinguish between living and dead bacteria. Even after cells lose reproductive viability and die, intact cell walls, ghost envelopes, and debris remain suspended in the medium and continue scattering light. To detect the true death phase, viable plate counts (CFU/mL) must be measured.
Q3: What factor determines the duration of the lag phase?
The physiological state of the inoculum and the difference between the pre-culture and new media. Inoculating stationary-phase cells into fresh medium results in a long lag phase because cells must rebuild depleted ribosomes and cofactors. Inoculating actively growing exponential-phase cells into identical fresh medium produces zero lag phase.
