Microbial Growth Kinetics describe how the microbe grows in the fermenter.

This information is important to determine optimal batch times.

The growth of microbes in a fermenter can be broken down into four stages: Lag Phase

Exponential Phase

Stationary Phase

Death Phase

Apparatus

Bioreactor

pH meter

Sampling

device

Mixer

Temperature

sensor

YSI 2700

Biochemistry

Analyzer

pH probe

D-oxygen

probe

Using Biochemistry Analyzer and Spectrophotometer to measure and make calibration curves for sugar and yeast cell concentrations

Reactant initial concentration

dextrose/or sucrose 25 g/L

yeast 3 g/L

volume reactant solution 2 L

Lag Phase

This is the first phase in the fermentation process

The cells have just been injected into a new environment and they need time to adjust accordingly

Cell growth is minimal in this phase.

Exponential Phase

The second phase in the fermentation process

The cells have adjusted to their environment and rapid growth takes place

Cell growth rate is highest in this phase

Stationary phase

This is the third phase in the fermentation process

The cell growth rate has leveled off and become constant

The number of cells multiplying equals the number of cells dying

Death phase

The fourth phase in the fermentation process

The number of cells dying is greater than the number of cells multiplying

Growth Can be represented by:

Considering primary constituents:

Generalized substrate consumption and biomass growth with time.

Experimental observation ; Cell mass is proportional to available substrate

Concept : Cell Yield

Xdt

dX

• Growth rate to population size

• units are 1/t (i.e. h-1 1/h)

Cell Growth - Kinetics

X = concentration of

microorganisms at time t (g/l) t = time (h) = proportionality constant or specific growth rate, [h-1] dX/dt = microbial growth rate, [mass/volume time]

Generation time or doubling time is the time

required for the population to double.

The calculation is: td = ln(2)/

Doubling Time

Classified based on the relationship between product synthesis and energy generation in the cell

Growth associated

Non-growth associated

Mixed-growth associated

Growth-associated produced at the same time as cell growth

▪ metabolic intermediates ▪ pyruvate, citrate, acetate

Non-growth-associated takes place during the stationary phase (=0)

▪ secondary metabolites ▪ antibiotics

Mixed - growth associated takes place during growth and stationary phases

▪ metabolic byproducts ▪ lactate, ethanol

▪ secondary metabolites

Growth-associated Non growth-associated Mixed-growth-associated

Rate per microbe, which depends on

Species

Substrates

Environmental factors

Total numbers of microbes

Product yield is defined as:

dS

dXY s/x

Cell Yield is:

ConsumedSubstrate

MassCellinChangeY s/x

dS

dPY S/P

Batch Growth Kinetics

Growth Yield, Yield Coefficient

• Growth yield = microorganisms

produced per unit substrate utilized.

• Other yield coefficients.

ΔS

ΔXYX/S

YP / S

P

SYX / O2

X

O2

time (hr) X (g/L) S (g/L)

0 0.34 19.38

2 0.36 19.34

4 0.52 19.05

8 1.67 16.86

10 3.01 14.28

12 5.44 9.66

14 9.52 1.93

16 10.46 0.16

18 10.54 0.00

Find…

•Maximum growth rate

• Yield on substrate

• doubling time

•specific growth rate at

12 hr

Example Problem Solution

max

Integrate

ln(X) – ln(Xo) = t

plot ln(X) vs. t

Slope (largest) = max

1

X

dX

dtXdt

dX

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20

Time (hr)

ln(X

)

experimental data

regression

slope=u max=0.292

Maximum doubling time will occur in

exponential growth, when = max

td = ln 2/

substrategcellg

0.52

Lsubstrateg

19.38)(0

Lcellg

0.34)(10.54

ΔS

ΔXYX/S

Example Problem Solution

YP/S

Temperature

effects

on growth

rate.

Classifications of microbes according to temperature optima.

Classification

of microbes

according

to tolerance

of pH

extremes

Classification

of microbes

according to

their oxygen

responses.

a. Aerobic

b. Anaerobic

c. Facultative

d. Microaerobic

e. Aerotolerant