CHAPTER 6 : CELL GROWTH KINETICS: BATCH & CONTINUOUS CULTURES - - PowerPoint PPT Presentation

CHAPTER 6 : CELL GROWTH KINETICS:

BATCH & CONTINUOUS CULTURES

By: Puan Nurul Ain Harmiza

1

PTT203: BIOCHEMICAL ENGINEERING SEMESTER 1 (2014/2015)

[Page 133] Shuler, M. L. and Kargi. (2002). Bioprocess Engineering: Basic Concept. 2nd Ed. Upper Saddle River, NJ: Prentice Hall PTR

CHAPTER 6 : CELL GROWTH KINETICS:

BATCH & CONTINUOUS CULTURES

COURSE OUTCOME 2: Ability to categorize the metabolic pathways in microorganisms and analyze the growth kinetics in both batch and continuous reactors

Content

• Introduction
• Batch Culture
• Quantifying Growth Kinetics
• Continuous Culture

INTRODUCTION

Cell growth

• Microbial growth is an autocatalytic reaction.
• The rate of growth is directly related to cell

concentration.

 

      nX P X S Cells More Products lar Extracellu Cells Substrate

S: substrate concentration (g/L); X: cell mass concentration (g/L); P: product concentration (g/L); n: increased number of biomass.

Cell growth

• Characterized by the net specific growth rate:
• (1/time)
• t: the time

dt dX X

net

1  

Cell growth

• Net specific growth rate (1/time):
• Endogenous metabolism: during the stationary

phase, the cell catabolizes cellular reserves for new building blocks and for energy-producing monomers.

d k g    net

: g 

Gross specific growth rate (1/time)

: d k

The rate of loss of cell mass due to cell death

• r endogenous metabolism

Cell growth

• Microbial growth can also be described in terms of cell

number concentration, N.

• So, the net specific replication rate (1/time):

dt dN N 1

R 



:

' R



Gross specific replication rate (1/time)

: d k

The rate of cell death (1/time)

d k  

' R R

 

N : Cell number concentration (cell number /L)

BATCH CULTURE

• QUANTIFYING CELL CONCENTRATION
• GROWTH PATTERNS AND KINETICS
• HOW ENVIRONMENTAL CONDITIONS AFFECT

GROWTH KINETICS

• HEAT GENERATION BY MICROBIAL GROWTH

Batch growth

• Refers to culturing cells in a vessels with an

initial charge of medium that is not altered by further nutrient addition or removal.

Quantifying Cell Concentration

• Either cell mass or cell number can be quantified.
• Purpose :
• For determination of the kinetics and stoichiometry of microbial

growth.

• Two categories:
• Direct – not feasible due to the presence of suspended solids or
• ther interfering compounds in the medium.
• Indirect

Quantifying Cell Concentration

DETERMINING CELL NUMBER DENSITY

1.

Hemocytometer

• Direct microscopic count
• Counts all cells present (viable and non-viable)
• Immediate result

2.

Agar plates

• Counts only living cells
• Delayed result
• Assumption: each viable cell will yield 1 colony
• Results expressed in CFUs(colony-forming units)

3.

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

Viable Cell Count

Coulter Particle Counter

Quantifying Cell Concentration

DETERMINING CELL MASS CONCENTRATION: DIRECT

• 1. 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

• 2. Packed cell volume
• Like wet cell weight, but measures cell pellet volume
• 3. Optical density (OD)
• Turbidity –based on the absorption of light by suspended cells in

culture media

Quantifying Cell Concentration

DETERMINING CELL MASS CONCENTRATION: INDIRECT

• When direct method is inapplicable. (mold solid state

fermentation)

• Indirect methods are therefore employed, based on the

measurement of substrate consumption and/or product formation.

• Cell mass can be determined by measurement of

protein, DNA or ATP. e.g. 1mg ATP/g dry weight bacterial cell.

• If 100 mg ATP/L is measured, then the cell mass:
• 100 mg (ATP/L)/1 mg ATP/g dry cells=100 (g dry weight cells/L)

Growth Patterns and Kinetics

Growth Patterns and Kinetics

Growth Phases

1.

Lag

2.

Exponential

3.

Deceleration

4.

Stationary

5.

Death/Decline

L a g Exponential Stationary Death Turbidity (optical density) 9.0 8.0 7.0 6.0 5.0 4.0 Time Optical density Log CFU/ml

10

Log CFU/ml Optical Density Lag

Growth Patterns and Kinetics

Lag Phase

• Occurs immediately after inoculation and is a period
• f 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: 5-10% by volume), 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

• rganism

 The concentration of Mg2+

in the medium is indirectly proportional to the duration

• f the lag phase

Log/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:

t net net

net

e X X t X X t X X X dt dX



 

• r

ln at where     

Log/Exponential Growth Phase

• 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:

• The doubling time based on cell number is expressed as:

max max

693 . 2 ln     

d R d

  2 ln

' 

Nutrients and conditions are not limiting

Exponential phase 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

growth = 2n or X = 2nX0 Where X0 = initial number of cells X = final number of cells n = number of generations

Log/Exponential Growth Phase

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 growth = death (dX/dt = 0)

Stationary Phase

• 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

• 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:

t k SO d

d

e X X t k dt dX



  

• r

Death Phase

1.

Cell lysis (spillage) may occur

2.

Rate of cell decline is first-order where: –kd = 1st order death rate constant, Xs = conc. of cell at end of stationary phase

3.

Growth can be re-established by transferring to fresh media

Summary: Batch Culture Growth Patterns

• Lag Phase – Period of no net growth after inoculation during which the
• rganism adapts to the new environment. The length of this phase varies

with organism and cultivation conditions. This phase is unproductive in terms of biomass/product accumulation and should be as short as

• possible. It is often negligible, due to culture transfer between identical

media.

• Exponential or Logarithmic Growth Phase – Cell mass and cell

number increase exponentially with time. Cell population doubles at regular intervals of time (td – doubling time).

• Deceleration Phase – essential nutrient in culture begins to run out. This

nutrient is often referred to as the growth limiting substrate. Media are

• ften designed in a way that this nutrient is generally the carbon source

(i.e. glucose or other carbohydrate)

• Stationary Phase – Cell growth rate = Cell death Rate. The length of the

stationary phase is often dependant on the organism. Yeast and higher fungi have long stationary phases where cells are in stasis. This is due to storage carbohydrate (glycogen) accumulation. In general bacteria and actinomycetes have short stationary phases.

• Death/Decay/Decline Phase – Death rate > Growth rate.

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:
• 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

S X Y

S X

   

/

Aerobic and Anerobic Growth Yields of S. faecalis on Glucose

Anaerobic growth is less efficient and the yield coefficient is reduced substantially.

Yield Coefficients

• At the end of a batch growth period, there is an apparent
• r observed growth yield:
• 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

energy maintence energy growth product lar extracellu an into

• n

assimilati biomass into

• n

assimilati

S S S S S         

Yield Coefficients

• Yield coefficients can also be defined for other substrates or

for product formation:

• 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)

S P Y O X Y

S P O X

       

/ 2 /

2

Summary of Yield Factors for Aerobic Growth

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:

• 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

g X P p

Y dt dP X q 

/

1  

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:
• Many secondary metabolites, such as most antibiotics

(e.g. penicillin), are non-growth-associated products

constant   

p

q

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:

• 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

   

g p

q

Product Yield Coefficients (cont…)

a) Growth-associated product formation b) Non-growth-associated product formation c) Mixed-growth-associated product formation

Example 6.1

• A strain of mold was grown in a

batch culture on glucose and the following data were obtained:

• Answer the following:
• Calculate the maximum net specific

growth rate.

• Calculate the apparent growth yield.
• What maximum cell concentration

could one expect if 150g of glucose were used with the same size of inoculum?

Time (h) Cell conc. (g/L) Glucose conc. (g/L) 1.25 100 9 2.45 97 16 5.1 90.4 23 10.5 76.9 30 22 48.1 34 33 20.6 36 37.5 9.38 40 41 0.63

Environmental Factors

• Patterns of microbial growth and product formation

are influenced by environmental factors such as:

• 1. Temperature
• 2. pH
• 3. Dissolved oxygen concentration (D.O.)

• 1. Effects of Temperature

Affect the performance of cells.

• Microorganisms can be classified by their optimum growth

temperatures, T

• pt
• Psychrophiles: (T
• pt< 20°C)
• Mesophiles: (20°C < T
• pt< 50°C)
• Thermophiles: (T
• pt> 50o°C)

Affect product formation.

• Yield coefficient is critical.

Affect the rate-limiting step in fermentation process.

• At high T, the rate of bioreaction higher than the diffusion

rate.

Optimum Growth Temperature

Effects of Temperature

As the temperature increases towards Topt, the growth rate doubles every ~10°C Above Topt the growth rate decreases and thermal death may occur.

• 2. Effect of pH
• 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
• f 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

 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

• 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-
• rder rate dependence on DO (oxygen is a limiting

substrate)

• Above a critical concentration, the growth rate becomes

independent of DO (oxygen is non-limiting))

• 3. Effect of Dissolved O2

• 3. Effect of Dissolved O2

Obligate aerobic cells

Saturation kinetics

Facultative aerobic cells

Saturation kinetics

• 3. Effect of Dissolved O2
• 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)

• 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,

• smotic pressure):

where : Ci = molar concentration of ion i Zi = ion charge

Other Effects on Cell Growth

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

• rganisms; ammonium, 5 g/l; phosphate, 10 g/l; nitrate, 5 g/l

HEAT GENERATION BY MICROBIAL GROWTH

Heat Generation by Microbial 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

• f Substrate

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

Heat Generation by Microbial Growth

For substrates:

The oxidation state of S has a large effect on 1/ YH

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

QUANTIFYING GROWTH KINETICS

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

Quantifying Growth Kinetics

• Substrate-limited growth
• Monod model
• Models with growth inhibitors
• Substrate inhibition
• Product inhibition
• Inhibition by toxic compound
• The logistic equation
• Growth models for filamentous organisms

• 1. MONOD EQUATION
• Monod equation: unstructured and nonsegregation model.
• Unstructured model: assuming fixed cell composition.
• Applicable to balanced-growth condition:
• exponential growth phase in batch culture
• single-stage, steady state continuous culture
• cell response is fast compared to external changes
• the magnitude of the external changes is not too large

(e.g. 10%-20% variation from initial conditions).

• Nonsegregation model: assuming all cells are the same in the

culture.

• 1. MONOD EQUATION

• 2. Growth Models for Filamentous Organisms
• Fungi growth:
• On solid surface

= mat-like biomass

• In liquid media

= pellet/ball-like biomass

• Pellet or colony radial growth rate:

CONTINUOUS CULTURE

INTRODUCTION

• In batch, product formation and substrate utilization

terminate after a certain time of interval.

• But in continuous:
• Fresh nutrient is continually supplied,
• Products and cells are simultaneously withdrawn
• Growth and product formation can be maintained for a prolonged

periods.

• After some time, the system reaches a steady state – all conc

remain constant.

• Benefit of continuous:
• To produce products under optimal environmental conditions.

INTRODUCTION

Type of culture;

 Batch;  varies during culture cycle  Fed-batch;  is controlled or regulated after a certain time  Continuous;  is controlled

• µ reflects the physiological state or intracellular

environment.

• So, control µ  control intracellular environment
• Continuous culture methods enable constant cell numbers

to be maintained in a constant chemical environment at specified growth rates for prolonged periods of time

DEVICES FOR CONTINUOUS CULTURE

Method of control;  Chemostat - regulated by control of concentration of limiting nutrient  Turbidostat - regulated by biomass using optical density (photoelectric cell)

DEVICES FOR CONTINUOUS CULTURE

• 1. CHEMOSTAT
• Cellular growth is limited by ONE essential nutrients and
• ther nutrients are in excess.
• Chemostat refers to constant chemical environment.

Schematic of Chemostat

medium Products, cells

DEVICES FOR CONTINUOUS CULTURE

• 2. TURBIDOSTAT
• Cell conc in the culture vessel is maintained constant by:
• monitoring the OD of the culture
• controlling the feed flowrate
• When OD>setpoint, fresh medium is added by pump.
• Volume is kept constant by removing an equal amount of

culture fluid.

• It is more complex than chemostat, less used.

Schematic of Turbidostat

• Ideal chemostat = CSTR
• Control elements:
• pH
• Dissolve oxygen (DO)
• Temperature
• Feeding and Removal at same rate.
• Completely mixed (stirred) and aerated (if required).
• Volume kept constant.
• Material balance:

THE IDEAL CHEMOSTAT

Simplified schematic of a chemostat

 dt dS

 dt dX

Control: 1. Concentration of a limiting nutrient 2. Dilution rate

• > both influences X

and P

Fin = Fout ≠ 0 V = const.

Cell Number Time in Hours Steady State

The development of growth in a chemostat

Inoculation

max

Population density increases Nutrient limitation causes decrease in  Growth rate equals loss of cell biomass

A material balance on the cell and substrate concentration around the chemostat yields,

dt dX R V X d k R V X g R V FX FX      F is the volumetric flowrate of nutrient solution (l/h); VR is the culture volume (l) (constant); X is the cell concentration (g/l); P is the extracellular product (g/l); µg and kd are growth rate and endogenous rate constant, respectively (h-1). Subscript 0 denotes the parameters at the feed medium.

dt dS R V s p Y X p q R V Y X g R V FS FS

M S X

    / 1 1

/



qp is the specific rate of extracellular product formation (g P/g cells-h) Yp/s is the product yield coefficient (g P/g S).

Cell Growth in Ideal Chemostat

dt dX R V X d k R V X g R V FX FX     

dt dS R V s p Y X p q R V Y X g R V FS FS

M S X

    / 1 1

/



At steady state, X0=0, kd ≈ 0, qp=0 , Monod equation applied,

S K S

S m g

   

Cell Growth in Ideal Chemostat

At steady state, X0=0, kd ≈ 0, qp=0 , Monod equation applied,

) ( ) (

/ /

D m D s K S Y S S Y X

M S X M S X

     

S S K S m D g     

D m D K S

S

  

Cell Productivity: DX D=F/VR, is dilution rate (1/time), the reciprocal of residence time.

• Assign. Q 6.13, qo2
• pt

D dD DX d   0 ) (

) ) ( ( ) 1 (

/

s s s

• pt

s s m

• pt

K S K K S Y X S K K D

M S X

       

Cell Growth in Ideal Chemostat

Study Example 6.4 (pg 198)

Batch versus Chemostat

Exponential phase Chemostat

• f batch culture
• perating in

steady-state Growth rate of culture Specific growth rate of culture Biomass Available nutrients Culture volume Toxic metabolites Constant, Variable, Increasing, Decreasing Increasing Constant Increasing Decreasing Constant Increasing Constant Constant Constant Constant Constant Constant

APPLICATION OF CONTINUOUS CULTURE

INDUSTRY;

• Waste-treatment
• Single-cell protein
• Continuous beer production
• Continuous amino acids, organic acids production
• Continuous ethanol
• Continuous bakers yeast

ADVANTAGES / DISADVANTAGES OF CC

Advantages

• Uniformity of operation
• Process demands are constant

i.e. continuous cycle of sterilisation, fermentation, harvesting, extraction

• Once in steady-state demands re process control are constant

i.e. oxygen demand

Disadvantages

• Susceptibility to contamination
• Duration of run is longer  increased chance of contamination
• Strain degeneration arising from large number of generations
• Contamination with "fitter" competitor e.g. lower Ks

Chemostat as Tool

THANK YOU