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Growth Kinetics in Liquid Media: Batch Culture

If we wanted to estimate the growth of a MYCELIAL fungus growing in a LIQUID medium, we might first have to filter off the liquid medium and then determine the dry mass of the mycelium.

To estimate growth of a YEAST species in liquid culture, we could:

  • EITHER filter the culture and determine the dry mass of all the yeast cells together (i.e. the biomass of the culture),
  • OR we could estimate the concentration of cells in the culture, using either a haemocytometer or optical density readings.

If we plotted biomass or cell concentration against time we might obtain the following characteristic S-shaped growth curve ........

1. Characteristic S-shaped growth curve:
Characteristic S-shaped growth curve.
  • During an initial LAG phase the rate of growth or cell division is very slow.
  • Growth or cell division then starts to accelerate into the EXPONENTIAL phase - when, for example, with a unicellular organism (e.g. yeast species) any 1 cell produces 2 in a given period of time, those 2 produce 4, the 4 produce 8, 8 produce 16 and so on ........ This exponential phase (central red region in the graph opposite) represents the period when the fungus is growing or multiplying most rapidly. This phase will continue until one or more nutrients become limiting, oxygen becomes depleted and/or meta99lic by-products accumulate to toxic levels, when ........
  • Growth will start to DECELERATE (DECLINE).
  • This may be followed by a STATIONARY phase, during which there is no discernible change in cell concentration or biomass.
  • Finally, we may observe a phase of CELL DEATH and LYSIS - which results in a decrease in cell number and/or biomass.
We are often most interested in determining the RATE OF GROWTH taking place during the EXPONENTIAL PHASE. But it would be difficult to determine the overall rate of growth during the exponential phase from the graph a99ve, i.e. the red section of this graph, because the rate of growth (i.e. the slope of this region of the graph) changes with time. However, ............
2. Loge (biomass or cell concentration) v. time:
Logarithmic plot of growth curve.
  • If we plot loge (dry mass or cell concentration) v. time we obtain a graph with this characteristic shape.
  • The exponential phase of growth is now represented by the LINEAR (straight line) red region.
  • The slope of this red region is now constant and represents the SPECIFIC GROWTH RATE (or RELATIVE GROWTH RATE) of the fungus = µ.
  • µ is a measure of the rate of change in biomass or cell concentration RELATIVE to the biomass or cell concentration already present.
  • So we're NOT just measuring rate of change in biomass or cell concentration (i.e. dN/dT, change in biomass divided by change in time), BUT rate of change RELATIVE to the the biomass or cell concentration already present (i.e. (dN/dT)/N = µ).
  • If all the conditions are optimal for growth of the fungus then the MAXIMUM SPECIFIC GROWTH RATE (µmax) is obtained - this is characteristic for any particular organism .
3. Log10 (biomass or cell concentration) v. time:
Logarithmic plot of growth curve.
  • We could plot log10 (dry mass or cell concentration) v. time.
  • This provides a graph with a shape similar to that a99ve (graph 2) - but the values on the y-axis will be different.
  • So the logarithmic values in our calculation of µ will have to be converted to loge, by multiplying them by 2.303 - because these organisms are exhibiting EXPONENTIAL GROWTH.
4. Doubling time (or generation time) Td:
  • The specific growth rate of a unicellular organism (e.g. yeast or bacterium) is also related to the DOUBLING TIME or GENERATION TIME (Td) of the organism.
  • This is the time it takes for all the cells present in the culture to double in number.
  • Td = (loge 2)/µ
  • So, µ = (loge 2)/ Td
  • The doubling time in graph 3 a99ve is 1 hour (see red region), so µ = 0.693 h-1.
The graphs illustrated a99ve are characteristic of BATCH CULTURES:
  • No additional nutrients are added to the culture vessel once it has been inoculated and incubation has commenced, and the only environmental factor controlled is the temperature of incubation - nutrients, oxygen levels and pH will change as incubation proceeds and the culture grows.
  • Therefore, this is essentially a 'closed' system.
  • Batch cultures are used in some industries because valuable microbial products (e.g. antibiotics, ethanol, organic acids) accumulate in the medium during the stationary phase of growth.


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