PTT 203
Biochemical Engineering
KINETICS MICROBIAL
GROWTH IN BATCH
CULTURE
WEEK 9-10
BY:
MADAM NOORULNAJWA DIYANA YAACOB
Lecture Outline
 Introduction
 Batch Growth Characteristics
 Growth Stages, Effects of Environmental Conditions, Product
Formation, Mathematical Models
Cell growth
Substrate  Cells  Extracellu lar Products  More Cells
 S  X   P  nX
 Microbial growth is an autocatalytic reaction
 The rate of growth is directly related to cell concentration
 Characterized by the net specific growth rate:
 net
1 dX

X dt
Cell growth
 The net specific growth rate is the difference between
a gross specific growth rate (μg, h-1) and the rate of
loss of cell mass due to cell death (kd, h-1):
net   g  kd
 Microbial growth can also be described in terms of
cell number, N:
1 dN
R 
N dt
where μR is the net specific replication rate (h-1)
Batch Growth –Determining Cell
Number Density
 Hemocytometer
 Direct microscopic count
 Counts all cells present (viable and non-viable)
 Immediate result
 Agar plates
 Counts only living cells
 Delayed result
 Assumption: each viable cell will yield 1 colony
 Results expressed in CFUs(colony-forming units)
 Particle counters
 Counts all cells present (viable and non-viable)
 Suitable for discrete cells in a particulate-free medium
 Can distinguish between cells of different sizes
Hemocytometer
 The 4 outer squares,
marked 1- 4, each cover a
volume of 10 4 mL.
 The inner square, marked
as 5, also covers a volume
of 10 4 mL, but is further
subdivided into 25 smaller
squares.
 Each of the 25 smaller
squares is further divided
into 16 squares, which are
the smallest gradations on
the hemocytometer.
Viable Cell Count
Coulter Particle Counter
Determining Cell Mass Concentration –
Direct Methods
 Dry cell weight (DCW)
 A sample of fermentation broth is centrifuged, washed, and
dried at 80°C for 24hrs
 Off-line measurement; wet cell weights (WCW) can performed
in-process
 Packed cell volume
 Like wet cell weight, but measures cell pellet volume
 Optical density (OD)
 Turbidity –based on the absorption of light by suspended cells
in culture media
Determining Cell Mass Concentration –
Indirect Methods
 In many fermentation processes, particularly with
moulds, direct methods cannot be used
 Indirect methods are therefore employed, based on
the measurement of substrate consumption and/or
product formation


Intracellular components of cells such as RNA, DNA and
protein can be measured as indirect indicators of cell growth
Concentration of RNA/cell weight varies significantly during a
batch growth cycle, while DNA and protein concentrations per
cell weight remain fairly constant, and can therefore be used as
reasonable measures of cell growth
Time-Dependent Changes in Cell
Composition and Cell Size
Azotobacter vinelandii Growth in Batch Culture
Batch Growth
Batch Growth Curve
Growth Phases
1. Lag
2. Exponential
3. Deceleration
4. Stationary
5. Death/Decline
Lag Phase
 Occurs immediately after inoculation and is a period
of adaptation for the cells to their new environment




New enzymes are synthesized, synthesis of other enzymes is
repressed
Intracellular machinery adapts to the new conditions
May be a slight increase in cell mass and volume, but no
increase in cell number
The lag phase can be shortened by high inoculum volume,
good inoculum condition (high % of living cells), age of
inoculum, nutrient-rich medium
Influence of [Mg2+] on Lag Phase
Duration in E. aerogenes Culture
 E. aerogenes requires Mg2+
to activate the enzyme
phosphatase, which is
required for energy
generation by the organism
 The concentration of Mg2+
in the medium is indirectly
proportional to the
duration of the lag phase
Exponential Growth Phase
 In this phase, the cells have adjusted to their new
environment




At this point the cells multiply rapidly (exponentially)
Balanced growth –all components of a cell grow at the same
rate
Growth rate is independent of nutrient concentration, as
nutrients are in excess
The first order exponential growth rate expression is:
dX
  net X where X  X 0 at t  0
dt
X
ln
  net t or X  X 0 e  nett
X0
Exponential Growth Phase (cont’d)
 An important parameter in the exponential phase is
the doubling time (time required to double the
microbial mass)
 A graph of ln X versus t produces a straight line on a
semi-logarithmic plot:
d 
ln 2
 max

0.693
 max
 The doubling time based on cell number is expressed
as:
 
'
d
ln 2
R
Exponential Growth Phase (cont…)
t
Deceleration Phase
 Very short phase, during which growth decelerates
due to either:


Depletion of one or more essential nutrients, or,
The accumulation of toxic by-products of growth (e.g. Ethanol
in yeast fermentations)
 Period of unbalanced growth: td=td’
 Cells undergo internal restructuring to increase their
chances of survival
 Followed quickly by the Stationary Phase
Stationary Phase
 Starts at the end of the Deceleration Phase, when the
net growth rate is zero (no cell division, or growth
rate is equal to death rate)
 Cells are still metabolically active, and can produce
secondary metabolites



Primary metabolites are growth-related products, while
secondary metabolites are non-growth-related
Many antibiotics and some hormones are produced as
secondary metabolites
Secondary metabolites are produced as a result of metabolite
deregulation
Stationary Phase (cont’d)
 During this phase, one or more of the following
phenomena may occur:



Total cell mass concentration may stay constant, but the
number of viable cells may decrease
Cell lysis may occur, and viable cell mass may drop. A second
growth phase may occur as cells grow on lysis products from
the dead cells (cryptic growth)
Cells may not be growing, but may have active metabolism to
produce secondary metabolites
Stationary Phase (cont’d)
 During the stationary phase, the cell catabolizes
cellular reserves for new building blocks and for
energy-producing monomers

This is called endogenous metabolism
 The cell must expend maintenance energy in order to
stay alive

The equation that describes the conversion of cellular mass
into energy, or the loss of cell mass due to lysis during the
stationary phase is:
dX
kd t
 k d t or X  X SOe
dt
Death Phase
 The death or decline phase is characterized by the
expression:
dN
 k d' t
'
 k d t or N  N S e
dt
 Where Ns is the concentration of cells at the end of
the stationary phase, and is the first-order death-rate
constant
 A plot of ln N versus t yields a line of slope –kd’
Death Phase
1.
2.
Cell lysis (spillage) may occur
Rate of cell decline is first-order
where:
3.
–kd = 1st order death rate constant,
Xs = conc. of cell at end of stationary phase
Growth can be re-established by transferring to fresh
media
Yield Coefficients
 Growth kinetics are generally further described by
defining stoichiometrically related parameters
 Yield coefficients are defined based on the amount of
consumption of a given material

For example, the growth yield coefficient is:
YX / S

X

S
For organisms growing aerobically on glucose, Yx/s is typically
0.4 to 0.6 g/g, for most yeast and bacteria; anaerobic growth is
much less efficient
Aerobic and Anerobic Growth Yields
of S. faecalis on Glucose
Yield Coefficients
 At the end of a batch growth period, there is an
apparent or observed growth yield:
S  S assimilation  S assimilation  S growth  S maintence
into biomass
into an
extracellular
product
energy
energy
 The apparent yield is not a true constant for
compounds that can be used as both a carbon and
energy source, but the true growth yield (YX/S) is
constant ΔS
Yield Coefficients
 Yield coefficients can also be defined for other
substrates or for product formation:
YX / O2
YP / S
X

O2
P

S
 YX/O2 is typically 0.9 to 1.4 g/g for most yeast and
bacteria, but is much lower for highly reduced
substrates (e.g. methane, CH4)
Summary of Yield Factors for
Aerobic Growth
The Maintenance Coefficient
 The maintenance coefficient is used to describe the
specific rate of substrate uptake for cellular maintenance:

dS / dt m
m
X
 However, during the Stationary Phase, where little
external substrate is available, endogenous metabolism
of biomass components is used for maintenance energy
 Maintenance energy is the energy required to repair
damaged cellular components, to transfer nutrients and
products in and out of cells, for motility, and to adjust the
osmolarity of the cells’ interior volume
Microbial Products
 Microbial products can be classified into three major
categories



Growth-associated products
Non-growth-associated products
Mixed-growth-associated products
 Growth-associated products
 These products are produced simultaneously with microbial
growth
 Specific rate of product formation is proportional to the
specific growth rate, μg
 Note that μg is not equal to μnet, the net specific growth rate,
when endogenous metabolism is occurring
Growth-Associated Products
 The rate expression for product formation in growth-
associated production is:
1 dP
qp 
 YP / X  g
X dt
 Where qp is the rate of product formation (h-1)
 The production of a constitutive (continuously
produced, as opposed to inducible) enzyme is an
example of a growth-associated product
Non-Growth-Associated Products
 Non-growth-associated product formation takes
place during the Stationary Phase, when the growth
rate is zero
 Specific rate of product formation is constant:
q p    constant
 Many secondary metabolites, such as most
antibiotics (e.g. penicillin), are non-growthassociated products
Mixed-Growth-Associated Products
 Mixed-growth-associated product formation takes place
during the Deceleration (slow growth) and Stationary
Phases
 The specific rate of product formation is given by the
Luedeking-Piret equation:
q p  g  
 If α= 0, the product is completely non-growth associated;
If β= 0, the product is completely growth-associated
 Examples: lactic acid fermentation, production of
xanthan gum, some secondary metabolites
Product Yield Coefficients (cont…)
a) Growth-associated product formation
b) Non-growth-associated product formation
c) Mixed-growth-associated product formation
Environmental Factors
 Patterns of microbial growth and product formation
are influenced by environmental factors such as
temperature, pH and dissolved oxygen concentration
(D.O.)
 Microorganisms can be classified by their optimum
growth temperatures, Topt
Psychrophiles: (Topt< 20°C)
 Mesophiles: (20°C < Topt< 50°C)
 Thermophiles: (Topt> 50o°C)

 As the temperature increases towards Topt, the
growth rate doubles every ~10°C
Optimum Growth Temperature
Optimum Growth Temperature
Effect of Temperature on Cell Growth
 Above Topt the growth rate decreases and thermal
death may occur

The net specific replication rate for temperatures above Topt is
expressed by:
dN
'
'
 Both 
'
R
'
d
dt


  R  kd N
and k vary with temperature according to
the Arrhenius equation:
  Ae
'
R
 Ea / RT
k   Ae
'
d
 Ea / RT
 Where:
 Ea =activation energy for growth ≈ 10-20 kcal/mol
 Ed =activation energy for death ≈ 60-80 kcal/mol
Arrhenius Plot of Growth Rate of E. Coli
Legend:
(●) Growth on
rich, complex
medium
(○) Growth on
glucose-mineral
salts medium
Effect of pH on Cell Growth
 pH affects the activity of enzymes, and therefore the
microbial growth rate
 Acceptable pH’s for growth are typically within 1 or 2
pH units of the optimum pH
 pH range varies by organism:




bacteria (most) pH = 3 to 8
yeast pH = 3 to 6
plants pH = 5 to 6
animals pH = 6.5 to 7.5
Effect of pH on Cell Growth
 The optimal pH for growth may be different from the
optimal pH for product formation (e.g. Pichia
pastoris)
 Microorganism have the ability to control pH inside
the cell, but this requires maintenance energy
 pH can change due to:


Utilization of substrates; NH4+ releases H+, NO3- consumes
H+
Production of organic acids, amino acids, CO2, bases
Effect of pH on Cell Growth (cont…)
Effect of Dissolved O2 on Cell Growth
 At high cell concentrations, the rate of oxygen
consumption may exceed the rate of O2 supply

When oxygen is the rate-limiting factor, specific growth rate
varies with [DO] according to saturation (Michaelis-Menten)
kinetics
 Below a critical concentration, growth approaches a
first-order rate dependence on DO (oxygen is a
limiting substrate)
 Above a critical concentration, the growth rate
becomes independent of DO (oxygen is nonlimiting))
Effect of Dissolved O2 on Cell Growth (cont…)
Obligate aerobic cells
Saturation kinetics
Facultative aerobic cells
Saturation kinetics
Effect of Dissolved O2 on Cell Growth
 The saturated DO concentration for water at 25°C
and 1 atm is ~7 ppm


The presence of dissolved salts and organics can alter the
saturation value
Increasing temperatures decrease the saturation value
 The critical oxygen concentration is about 5%-10% of
the saturated DO concentration for bacteria and
yeast, and about 10%-50% of [DO]sat for moulds,
since they grow as large spheres in suspended
culture (diffusion issues)
Other Effects on Cell Growth
 Dissolved CO2 can have a profound effect on the
performance of microorganisms


Very high DCO2 concentrations can be toxic to some cells
On the other hand, cells require a certain minimum DCO2 level for
proper metabolic function
 Ionic strength (I); too high dissolved salts is inhibitory to
membrane function (membrane transport of nutrients,
osmotic pressure):
where :
Ci = molar concentration of ion i
Zi = ion charge
Other Effects on Cell Growth
 The redox potential is an important parameter that affects
the rate and extent of many oxidative-reductive reactions

In fermentation media, the redox potential is a complex
function of DO, pH, and other ion concentrations, such as
reducing and oxidizing agents
 Substrate concentrations significantly above stoichiometric
requirements are inhibitory to cellular functions


Inhibitory levels of substrates vary depending on cell type and
substrate
Typical maximum non-inhibitory concentrations of some
nutrients are –glucose, 100 g/l; ethanol, 50 g/l for yeast, much
less for other organisms; ammonium, 5 g/l; phosphate, 10 g/l;
nitrate, 5 g/l
Heat Generation by Growth
 About 40% to 50% of the energy stored in a carbon and
energy source is converted to biological energy (ATP)
during aerobic metabolism, and the rest of the energy is
released as heat



For actively growing cells, the maintenance requirement is low, and
heat evolution is directly related to growth
The heat of combustion of the substrate is equal to the sum of the
metabolic heat and the heat of combustion of the cellular material:
Where ΔHS is the heat of combustion of the substrate (kJ/g
substrate), ΔHC is the heat of combustion of cells, and 1/YH is the
metabolic heat evolved per gram of cell mass produced (kJ/g cells)
Energy Balance on Microbial
Utilization of Substrate
Heat Generation by Growth
 The above equation in heat generation can be
rearranged to become:
 ΔHS and ΔHC can be determined from the
combustion of substrate and cells



Typical ΔHC values for bacterial cells are 20-25 kJ/g cells
Typical values of YH are: glucose, 0.4 g/kcal; malate, 0.3
g/kcal; acetate, 0.21 g/kcal; ethanol, 0.18 g/kcal; methanol,
0.12 g/kcal; and methane, 0.061 g/kcal
Clearly, the degree of oxidation of the substrate has a strong
effect on the amount of heat released
Heat Generation by Growth (cont…)
For substrates:
Substrate, S
∆Hs (kJ/g S)
YH (g dcw/kJ)
Glucose
15.64
0.072
Methanol
22.68
0.029
Ethanol
29.67
0.043
n-Decane
47.64
0.038
Methane
55.51
0.015
The oxidation state of S has a large effect on 1/ YH
Rate of Heat Generation by Growth, QGr
 The total rate of heat evolution in a batch
fermentation is:
where: VL = liquid volume
 In aerobic fermentations, the rate of metabolic heat
evolution can roughly be correlated to the rate of
oxygen uptake:

where: QGR is in kcal/h, and QO2 is in mM of O2/h
Heat Generation by Microbial Growth
 Metabolic heat released during a fermentation can
be removed by circulating cooling water through a
cooling coil within the fermenter, or a cooling jacket
surrounding the fermenter
 Temperature control is a critical limitation on
reactor design
 The ability to estimate heat removal is essential to
proper reactor design
MODELLING CELL GROWTH
 1. STRUCTURED MODELS:
Model divides cell mass into components ( by molecule
or by element) and predicts how these components
change as a result of growth. This models are very
complex and not used very often
 2. UNSTRUCTURED MODELS:
Model assumes balanced growth where cell
components do not change in time. Much less
complex and much more commonly used. Valid for
batch growth during exponential growth stage and
also for continuous culture during steady-state
operation
MONOD EQUATION
Batch Culture Growth Model
Batch Culture Growth Model (cont.)
Batch Growth Data and Monod Parameters
Cooling coils and Water Jacketed Fermenter