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**PTT 203 Biochemical Engineering**

Kinetics MICROBIAL GROWTH IN BATCH CULTURE WEEK 9-10 By: MADAM NOORULNAJWA DIYANA YAACOB

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**Lecture Outline Introduction Batch Growth Characteristics**

Growth Stages, Effects of Environmental Conditions, Product Formation, Mathematical Models

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**Cell growth Microbial growth is an autocatalytic reaction**

The rate of growth is directly related to cell concentration Characterized by the net specific growth rate:

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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): Microbial growth can also be described in terms of cell number, N: where μR is the net specific replication rate (h-1)

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**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 Suitable for discrete cells in a particulate-free medium Can distinguish between cells of different sizes

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Hemocytometer

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**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.

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Viable Cell Count

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**Coulter Particle Counter**

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**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

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**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

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**Time-Dependent Changes in Cell Composition and Cell Size**

Azotobacter vinelandii Growth in Batch Culture

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Batch Growth

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**Batch Growth Curve Growth Phases Lag Exponential Deceleration**

Stationary Death/Decline

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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

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**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

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**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:

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

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**Exponential Growth Phase (cont…)**

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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

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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

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**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

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**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:

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Death Phase The death or decline phase is characterized by the expression: 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’

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**Death Phase Cell lysis (spillage) may occur**

Rate of cell decline is first-order where: –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

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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

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**Aerobic and Anerobic Growth Yields of S. faecalis on Glucose**

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Yield Coefficients At the end of a batch growth period, there is an apparent or 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

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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)

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**Summary of Yield Factors for Aerobic Growth**

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**The Maintenance Coefficient**

The maintenance coefficient is used to describe the specific rate of substrate uptake for cellular maintenance: 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

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Microbial Products Microbial products can be classified into three major categories Growth-associated products Non-growth-associated products Mixed-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

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**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

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**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

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**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

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**Product Yield Coefficients (cont…)**

Growth-associated product formation Non-growth-associated product formation Mixed-growth-associated product formation

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**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

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**Optimum Growth Temperature**

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**Optimum Growth Temperature**

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**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: Both and vary with temperature according to the Arrhenius equation: Where: Ea =activation energy for growth ≈ kcal/mol Ed =activation energy for death ≈ kcal/mol

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**Arrhenius Plot of Growth Rate of E. Coli**

Legend: (●) Growth on rich, complex medium (○) Growth on glucose-mineral salts medium

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**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

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**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

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**Effect of pH on Cell Growth (cont…)**

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**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 non-limiting))

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**Effect of Dissolved O2 on Cell Growth (cont…)**

Obligate aerobic cells Saturation kinetics Facultative aerobic cells Saturation kinetics

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**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)

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**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

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**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

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**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)

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**Energy Balance on Microbial Utilization of Substrate**

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**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 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, g/kcal Clearly, the degree of oxidation of the substrate has a strong effect on the amount of heat released

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**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

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**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

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**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

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**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

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MONOD EQUATION

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**Batch Culture Growth Model**

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**Batch Culture Growth Model (cont.)**

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**Batch Growth Data and Monod Parameters**

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**Cooling coils and Water Jacketed Fermenter**

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