Microbial Lifestyles and Metabolism (Dr. Kreft): Exponential Growth Flashcards
What is the definition of growth?
- forming two cells from 1
- increase in both mass and number
- absolutely necessary for survival
- application of growth = stop growth of microbes or exploit it
Describe some E. coli growth facts!
- 20 min generation time of cell under optimal conditions
- 40 min DNA replication
- 20 min from end of replication to cell division
- They have to start replication 60 min before division, every 20 min, so that several rounds of replication are running simultaneously. Bacteria usually have one chromosome with one origin of replication
- generation time in colon = 12 hours or more
In terms of number of cells and generation describe what the following numbers mean:
2^0 -> 2^1 -> 2^2 -> 2^3 –> 2^4
- 1 cell, generation 0
- 2 cells, generation 1
- 4 cells, generation 2
- 8 cells, generation 3
- 16 cells, generation 4
Describe N= N0 * 2^n
- Number of cells after n generations (general)
- N= number of cells
- N0= number of cells at the beginning (time 0)
- n= number of generations
- generation time = time/number of generations (g=t/n)
- t= time (since t0)
How many offspring from a single E. coli cell in 2 days?
- generation time = 20 min
- 3 generations per hour
- 2 days = 48 hours
- 3x48= 144 generations
- N= 2^144= 2.2 x10^43 cells in 2 days
**estimated 10^30 prokaryote cells on earth….so this is unlikely
Mass: one cell 10^-12 g… 2.2x10^43 cells * 10^-15kg/cell = 2.2 10^28kg = ~ 4,000 times the mass of the earth (6x10^24kg)
Explain why exponential growth does not go on forever!
- run out of nutrients (just a single nutrient lacking will stop growth)
- waste products can be toxic( acetic acid, ethanol..)
- predation/phages( in nature, not in lab batch culture)
- space ( usually not the first resource to run out)
Why does exponential growth occur?
- because growth is proportional to the current cell number (low numbers = continuous growth is possible)
Examples of exponential growth?
- microbes (not with mycelium)
- animal/plant cells in tissue culture –> cancer
What is specific growth rate?
- growth rate per biomass
- growth rate/ biomass
Growth of ___, not ___
biomass
number
**growth rate (slope) increases exponentially and so does biomass on a graph with x= time and y= biomass
**growth rate is proportional to the current biomass
** twice as much biomass grows twice as fast. In other words, growth rate is proportional to biomass . Specific growth rate is growth rate per biomass
For animal/human populations, the specific growth rate is called?
per capita growth rate
Explain the change of biomass per time
dX/dt= u*X
- x is biomass, t is time, dX, dt are change of X, t, u is specific growth rate
- the specific growth rate is the proportionality constant
- that is a differential equation expressing rate of change
- growth rate= specific growth rate *biomass
What is the solution for the change of biomass per time differential equation?
dX/dt= u*X
- X= X0 exp(ut) or X= X0 e^ut
-x = biomass - X0= biomass at t0
- u = specific growth rate (dimension per time)
t= time - e = euler’s number = 2.71828
**inverse of the natural logarithm ln(x)= 1, ln(e^x)= x
Explain balanced growth!
- all components of the cell increase in proportion
- biomass, protein, number of cells, all increase at the same rate
- the composition of the cell does not change
- this is characteristic for exponential growth phases
Cell number based measures/concepts:
- generation time?
- division rate?
- g
- v= 1/g
