GROWTH OF CULTURE Population growth

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GROWTH OF CULTUREPopulation growth
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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

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Unrestricted growth

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

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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

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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

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Growth equations (1)

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

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Growth equations (2)

• tg(td) ln2 /µ 0.693 /µ
  tg generation time or
  doubling time
• ? 1 / tg
  ? the growth-rate
  constant for a batch culture (doublings per
  hour),
  µ 0.693?

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Measurement of growth (1)

• Cell mass Dry weight / Turbidity
  Light scattering Nephelometer
  Spectrophotometer Lambert-Beers law
  Absorbance (A)
  log(I0/I) elc
  Optical density (OD)
  Relationship, Fig. 1

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Measurement of growth (2)

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

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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

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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)

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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.

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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)

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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

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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

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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

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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

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Study questions

1. 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
2. How to increase the steady-state cell density in
   the growth vessel of a glucose-limited chemostat?
   
   Ans increase cr or decreas D

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Study questions

1. 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)
2. Show the profiles of dilution rate vs. cell
   concentration in a chemostat using glucose,
   phosphate or ammonium as limiting nutrient.