week 4 - how microbes grow Flashcards
what is growth
- Definition of Growth: forming 2 cells from 1
o Increase in both Mass and Number
o absolutely essential for survival
o looks simple but is complex
o application of this: stop growthof micorbes, or exploit it
o 20min generation time of cell under optimal conditions
- E. Coli growth facts
o 40min DNA replication
o 20min from end of replication to cell division
o 20min generation time in LB: how is this possible?
Note the generation time in the colon is 12 hrs or more
measurement growth
1. measurment of biomass
- Protein assay (50% of biomass is protein, doesn’t change much with conditions)
- Dry mass (wash cells, dry and weigh them)
- Optical density (OD)
o Particles scatter light (quick and easy)
o Bacteria are particles
o OD is a measure of biomass concentration rather than cell numbers per volume
Measure of cell number only so far as numbers correlate with mass (balanced growth)
measurement of growth
2. measurement of cell number
- Total count
o Count cells in known volume under the microscope (counting chamber)
Cells.mL - Viable count – CFU (colony forming units)
o Spread 0.1mL of (diluted) culture on agar plant and count number of colonies forming
CFU/mL
opitical density (OD)
if OD too high have to dilute sample as response no longer linear
OD proportional to biomass per volume as brock figure implies
cell number correlates with biomass only in balanced growth but not in stationary phase
growth in numbers
number of cells
1 –> 2 –> 4 –> 8 –> 16 –>
generations
0 –> 1 –> 2 –> 3 —> 4 —-> n
number of cells more elegantly
2^0 -> 2^1 -> 2^2 -> 2^3 -> 2^4 -> 2^n
number of cells after n generations (general)
EQUATION: N = N0 x 2^n
N: number of cells
N0= number of cells at the beginning T0
n: number of generations
- generation time = time / number of generations
g = t / n
t: time (since t0)
consequences
how many offspring from a single E. Coli cell in 2 days
Generation time 20mins
- 3 generations per hour
- 2 days = 48hrs
- So 3 x 48 = 144 generation
N= N0 x 2^n
- N = 2^144
- 2.2 x 10^43 cells in 2 days
Mass
- One cell is 10^-12 g
- 2.2 x 10^43 cells x 10^-15kg.cell = 2.2x10^28kg
- ~4000 times mass of earth
Why does this not happen??
Exponential growth stops because
- What limits growth?
o Not enough food for that many cells
- Limit of resources
o This is the most common reason
o Also bacteria produces waste that can be toxic to growth
o So start to die
o Therefore limiting growth
examples of exponential growth
- Microbes (both population of cells and individual cells
- Animal/plant tissue in culture
- Cancer cells in body
- Constant interest rate, wealth (exponential growth does not mean fast growth)
- Nuclear chain reaction
growth of biomass
- Biomass increases exponentially
- Growth rate (=slope of biomass increase) also increases exponentially
o Since growth rate is propotional to current biomass - So specific growth rate (growth rate per biomass) is constant
The slope is dX/dt
Rate of population growth proportional to current size of population
dX / dt = u X
Can solve this to show exponential growth
- Can plot x / t
Can get specific growth rate
By slope divided by current population
So:
(dX/dt) / X = u
Allows us to predict population size at any time
- As long as conditions remain constant
growth of biomass
- Explain specific growth rte
o Specific growth rate = growth rate / biomass
see notes for table
- Recall twice as much biomass grows twice as fast
- In other words, growth rate is proportional to biomass
- Think of ‘specific growth rate’ as ‘growth rate per biomass’
For animal/human population the specific growth rate is called “per capita growth rate”
In brock (textbook) it is called “instantaneous growth rate constant”
change of biomass per time
- dX / dt = u x X
o X is biomass
o t is time
o dX is change of X
o dt is change of t
o u is specific growth rate - so the specific growth rate is the proportionality constant
- this is a differential equation expressing rate of change
- the equation in words is simply this
o growth rate = specific growth rate x biomass
biomass as a function of time
- X = X0 x exp(u x t) OR X = X0 e^ut
o This is the solution to the differential equation above - X is biomass
- X0 is biomass at t0
- u is specific growth rate (dimension: per time)
- t is time
exponential function recap
- exp(x) is also written as e^x
- e is Euler’s number, e = 2.71828…
- inverse of the natural logarithm ln(x): ln(e) = 1, ln(e^x) = x
