Slide 1

GROWTH OF CULTURE

Population growth


Slide 2

Growth curve of culture
• Semi-log plot

• Growth phases:
lag, exponential, and stationary
• Real lag phase:
spores germination,
physiological readjustment
• Apparent lag phase: turbidometric measurement of
growth when inoculum consists of living and dead
cells


Slide 3

Unrestricted growth
• Culture grow at a characteristic rate
• No limiting concentration of nutrients and no
effective level of toxic compounds
• Balanced growth
• Exponential phase


Slide 4

Balanced growth
• All cell constituents begin to increase by the same
proportion over the same interval
• The mean cell size remain constant
• Balanced growth refers to the average behavior of
cells in a population, not to that of individual cells
(bacteria do not usually grow and divide
synchronously)
• Usually unbalanced for most bacteria under natural
conditions


Slide 5

Practical advantages in working with
balanced growth cultures
• It can be approximated for a considerable time in
the laboratory
• Samples of different time are identical except cell
number
• The relative rate of synthesis of any cellular
component becomes known just by measuring the
growth rate
• The most reproducible physiological state of a
bacterial culture


Slide 6

Growth equations (1)
• dx / dt = μx
cell number or some specific cellular
component per unit volume,
instantaneous growth-rate constant or specific
growth-rate constant.
• lnx2 – lnx1 = μ(t2 – t1)
x) dx =μdt, ∫(1/ x) dx =∫μdt then, lnx =μt
• μ = 2.303 (logx2 – logx1) / (t2 – t1),
= logex = logx / loge = logx / log2.718..
= logx / 0.4343.. = 2.303 logx

x:
μ:

(1/
lnx


Slide 7

Growth equations (2)
• tg(td) = ln2 /μ = 0.693 /μ
tg: generation time or doubling time
• κ = 1 / tg
κ: the growth-rate constant for a batch culture
(doublings per hour),
μ = 0.693κ


Slide 8

Measurement of growth (1)
• Cell mass: Dry weight / Turbidity
Light scattering: Nephelometer & Spectrophotometer
Lambert-Beer’s law:
Absorbance (A) = log(I0/I) = εlc
Optical density (OD)
Relationship, Fig. 1


Slide 9


Slide 10

Measurement of growth (2)
• Cell number
Viable count:
(1)operational errors: bacterial clumps, true sampling
time etc.
(2)sampling errors: (X±√X)
Total count:
(1)Bacterial counting chamber / Hemocytometer
(2)Electronic counting / Flow cytometer (measure the
size distribution and the number)
• Cellular constituent: Protein or ATP …


Slide 11

Growth yield
• Yield coefficient: unitless parameter, dry weight
produced per unit weight of limiting nutrient
• Yglucose: usually about 0.5 for aerobes / may be 100
times greater for a required amino acid or vitamin
• Used in bioassay of vitamin or biosynthetic
intermediates
• Measurement of YATP is restricted to culture that
generate ATP by fermentation


Slide 12

Specific oxygen consumption (1)
• Andersen and von Meyenburg (1980) found that the
specific oxygen consumption QO2 (mmole h-1 g-1 dry
weight) in cultures of E. coli does not vary
significantly with the growth rate.
• QO2 is about 20 in cultures grown in a mineral salts
medium with various carbon sources. (μ is 0.3 in
acetate, 0.9 in glucose, 1.2 in glucose and casein
hydrolysate)


Slide 13

Specific oxygen consumption (2)
• If ATP generated per mole of oxygen consumed does
not vary with the growth rate, then the total energy
available for doubling the cell mass decreases in
proportion to the growth rate. How can we interpret
the finding?
• At low growth rates, the cells must make their own
building blocks, a demand requiring extra energy.


Slide 14

Effect of concentration of nutrients on the
growth rate
• Monod equation: μ = μmaxc / (Ks + c)
• Michaelis-Menten equation: V = VmaxS / (Km + S)
• Double reciprocal plot (1/μ vs. 1/c)


Slide 15

Continuous culture
• Turbidostat (growth rate is determined internally)
• Chemostat (growth rate is determined externally,
vigorous mixing)
Useful in studies of bacterial physiology, mutagenesis
and evolution


Slide 16

Equations in chemostat culture
• Mean resident time, MRT = V / f
Dilution rate, D = f / V
• μ= D (dx / dt =μx – xf / V =μx – Dx = 0 in the
chemostat)
• c = KsD / (μmax – D) (solving Monod equation for c
gives the relationship between nutrient concentration
in the growth vessel and the dilution rate)
• Y = x / (cr – c), cr: nutrient conc. in the reservoir
dc / dt = Dcr – Dc, dc / dt = (dx / dt) (dc / dx),
dx / dt = μx, dc / dx = 1/Y, μx / Y = Dcr – Dc,
D
=μ


Slide 17

Lower limit to the dilution rate in chemostat
culture
• If the limiting nutrient is the source of energy, growth
ceases at low dilutions and the cells are washed out.
• If the limiting nutrient is an amino acid or other
precursor in macromolecular synthesis, chemostat
can be operated at dilution rates leading to a mean
residence time of several days or weeks


Slide 18

Maintenance energy
• A certain amount of energy used for essential
processes other than those leading to increase in
mass: (1)the maintenance of a potential across the
cytoplasmic membrane, (2)the transport of certain
solutes, (3)the constant hydrolysis and resynthesis of
certain macromolecules – termed turnover, (4)cell
motility, etc.
• dx /dt = Y‧dc / dt - ax a: the specific maintenance
rate, 0.02-0.03 hr-1 for E. coli growing at 37℃
• Maintenance coefficient m = a / Yg


Slide 19

Study questions
1.

2.

Calculate the doubling time of a culture if it contains
103 cells at t1 and 108 cells 6 hours later
Ans: μ = (8-3) x 2.303 / 6 = 1.92 hr-1,
tg = 0.693 / 1.92 = 0.36 hr = 21.7 min
How to increase the steady-state cell density in the
growth vessel of a glucose-limited chemostat?
Ans: increase cr or decreas D


Slide 20

Study questions
3. A technician has isolated a mutant of E. coli that has
lost a certain function. When mixed with its parent
and grown at low dilution in a glucose-limited
chemostat, the mutant persists and the parent
disappears. How could this phenomenon be
explained?
Ans: the mutant blocked a function that contributed
to maintenance energy (lowered maintenance
energy requirement)
4. Show the profiles of dilution rate vs. cell
concentration in a chemostat using glucose,
phosphate or ammonium as limiting nutrient.