1. Chapter 3 Objectives
The fastest known doubling time for a bacterium and under what conditions this occurs
The slowest estimated doubling time for a bacterium and under what conditions this occurs
Calculate a growth rate, u, from the slope of a growth curve
Compare and contrast growth in pure culture with growth in the environment
The growth curve and the parts of the curve
A mathematical equation for each part of the curve as well as the Monod equation
At least two electron acceptors that can be used under anaerobic conditions in place of oxygen
Whether aerobic or anaerobic metabolism yields more energy and why
The mass balance equation for aerobic metabolism

2. Lecture 3 – Growth
What are the differences between growth in a flask in pure culture and growth in the environment (e.g. soil, water, skin surfaces, leaf surfaces)?

3. Growth Curve
Log CFU/ml
Optical Density
Lag

4. Lag phase Three causes for lag: physiological lag low initial numbers
appropriate gene(s) absent
growth approx. = (dX/dt = 0)

5. Exponential phase
Nutrients and conditions are not limiting
growth = 2n or X = 2nX0
Where X0 = initial number of cells
X = final number of cells
n = number of generations 20 21 22 23 24 2n 20 21 22 23 24 2n 20 21 22 23 24 2n 20 21 22 23 24 2n 20 21 22 23 24 2n 20 21 22 23 24 2n

6. This is an increase is 5 orders of magnitude!!
Example: An experiment was performed in a lab flask growing cells on 0.1% salicylate and starting with 2.2 x 104 cells. As the experiment below shows, at the end there were 3.8 x 109 cells.
This is an increase is 5 orders of magnitude!!
How many doublings or generations occurred?
Cells grown on salicylate, 0.1%
X = 2nX0
3.8 x 109 = 2n(2.2 x 104)
1.73 x 105 = 2n
log(1.73 x 105) = nlog2
17.4 = n

7. How does this compare to growth in the soil?
Response of culturable microbial community to addition of a carbon source.
Soil
Unamended
CFU/g soil
1% Glucose
Log Increase
Pima
Brazito
Clover Springs
Mt. Lemmon
5.6 x 105
1.1 x 106
1.4 x 107
1.4 x 106
4.6 x 107
1.1 x 108
1.9 x 108
8.3 x 107
1.9
2.0
1.1
1.7
Only a 1 to 2 order of increase!!

8. Now compare how environmental conditions can impact metabolism in soil
Degradation of straw under different conditions
Residue
Half-life
Days u
Days-1
Relative rate
Wheat straw, laboratory
Rye straw, Nigeria
Rye straw, England
Wheat straw, Saskatoon 9 17 75
160
0.008
0.04
0.01
0.003 1
0.5
0.125
0.05
Nigeria hot all year round with a rainy season and a dry season
England is a warm summer and cold winter and plenty of rainfall
Saskatoon cold winters and summers in the high 60s. Plenty of rainfall

9. Calculating growth rate during exponential growth
dX/dt = uX
where u = specific growth rate (h-1)
Calculating growth rate during exponential growth
dX/dt = uX where u = specific growth rate (h-1)
Rearrange: dX/X = udt
Integrate: lnX = ut + C, where C = lnX0
lnX = ut + ln X0 or X = X0eut
y = mx + b (equation for a straight line)
Note that u, the growth rate, is the slope of this straight line

10. Calculating growth rate during exponential growth
dX/dt = uX where u = specific growth rate (h-1)
Rearrange: dX/X = udt
Integrate: lnX = ut + C, where C = lnX0
lnX = ut + ln X0 or X = X0eut
y = mx + b (equation for a straight line)
Note that u, the growth rate, is the slope of this straight line

11. Find the slope of this growth curve
lnX = ut + ln X0 or u = lnX – lnX0
t – t0
u = ln 5.5 x 108 – ln 1.7 x 105
= 2 hr-1

12. What is fastest known doubling time? Slowest?
Now calculate the doubling time
If you know the growth rate, u, you can calculate the doubling time for the culture.
lnX = ut + ln X0
For X to be doubled: X/X0 = 2
or: 2 = eut
From the previous problem, u = 2 hr-1,
2 = e2(t)
t = hr = min
What is fastest known doubling time? Slowest?

13. How can you change the growth rate???
When under ideal, nonlimiting conditions, the growth rate can only be changed by changing the temperature (growth increases with increasing temp.). Otherwise to change the growth rate, you must obtain a different microbe or use a different substrate.
In the environment (non-ideal conditions), the growth rate can be changed by figuring out what the limiting condition in that environment is.
Question: Is exponential growth a frequent occurrence in the environment?

14. Growth Curve
Stationary

15. Stationary phase Death phase
nutrients become limiting and/or toxic waste products accumulate
growth = death (dX/dt = 0)
death > growth (dX/dt = -kdX)
Death phase

16. Monod Equation
The exponential growth equation describes only a part of the growth curve as shown in the graph below.
The Monod equation describes the dependence of the growth rate on the substrate concentration:
u = um S
Ks + S .
u = specific growth rate (h-1)
um = maximal growth rate (h-1)
S = substrate concentration (mg L-1)
Ks = half saturation constant (mg L-1)

17. Combining the Monod equation and the exponential growth equation allows expression of an equation that describes the increase in cell mass through the lag, exponential, and stationary phases of growth:
dX/dt = uX
u = dX/Xdt
u = um S
Ks + S .
Monod equation
Exponential growth equation
dX/dt = um S X
Ks + S .
Does not describe death phase!

18. Ks . There are two special cases for the Monod growth equation
At high substrate concentration when S>>Ks, the Monod equation
simplifies to:
dX/dt = umX
growth will occur at the maximal growth rate. Ks
2. At low substrate concentration
when S<< Ks, the Monod equation
simplifies to:
dX/dt = um S X Ks .
growth will have a first order dependence on substrate concentration (growth rate is very sensitive to S).
Which of the above two cases is the norm for environmental samples?

19. Growth in terms of substrate loss
In this case the growth equation must be expressed in terms of substrate concentration. The equations for cell increase and substrate loss can be related by the cell yield:
dS/dt = -1/Y (dX/dt) where Y = cell yield
Y = g cell mass produced
g substrate consumed
Glucose (C6H12O6) Pentachlorophenol (C6Cl5OH) Octadecane (C18H38)
0.4
0.05
1.49

20. Growth in terms of substrate loss
dS/dt = -1/Y (dX/dt)
dS/dt = -1/Y (dX/dt)
Combine with: dX/dt = um S X
Ks + S .
Combine with: dX/dt = um S X
Ks + S . .
dS/dt = - um (S X)
Y (Ks + S)
Which parts of this curve does the equation describe?

21. Aerobic vs. anaerobic metabolism

22. Examples of when this knowledge is important??
Aerobic metabolism
General equation:
(C6H12O6) + 6(O2) (CO2) + 6(H2O)
Mass balance equation:
a(C6H12O6) + b(NH3) + c(O2) d(C5H7 NO2) + e(CO2) + f(H2O)
cell mass
The mass balance equation illustrates that some of the carbon in the substrate is used to build new cell mass and some is oxidized completely to CO2 to provide energy for the cell.
Using the mass balance equation and the cell yield, one can calculate the % of the substrate carbon that is used to build new cell mass and the % that is evolved as CO2
Examples of when this knowledge is important??

23. Anaerobic metabolism
Under anaerobic conditions, the substrate undergoes disproportionation, whereby some of the carbon is oxidized completely to CO2 and some is reduced to CH4 (because CO2) acts as a terminal electron acceptor.
General equation:
C6H12O6 + alternate TEA CO2 + CH4 + H2O
Some Typical Terminal Electron Acceptors