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Chapter 6 Environmental factors affecting cell growth
Outlines
• Temperature
• pH
• Dissolved Oxygen
• Other factors
Temperature Effects
• Enhance cell growth when T is less than the optimal temperature;
• Inhibit cell growth when T is higher than the optimal temperature;
• Kill cells when it is higher than the tolerable temperature range;
• May change the product formation;
• May affect the rate-limiting step in a fermentation process
Temperature Effects
• Net growth rate:
g and kd vary with temperature according to the Arrhenius equation:
RTaEAe
RTE
dbeAk
'
• Ea activation energy for growth 10 to 20 kcal/mol • Eb activation energy for endogenous metabolism, 15 to 20 kcal/mol In the textbook (will discuss in detail in sterilization): • Ed activation energy for thermal death, 60 to 80 kcal/mol. • Thermal death is more sensitive to temperature changes than microbial growth)
Xkdt
dXdg )(
Other Effects of Temperature
• Temperature also affects product formation: when temperature is increased past the optimum temperature, maintenance coefficient increases with increasing temperature, which may result in a decrease in the yield coefficient of target product.
• Temperature may also affect the rate-limiting step in a fermentation process: – Activation energy of diffusion is about 6 kcal/mol and more than 10
kcal/mol for growth; – Cell growth more sensible to temperature change; – at high temperatures, the rate of bioreaction might become higher than
the diffusion rate (diffusion becomes the rate-limiting step, e.g. immobilized systems);
Typical Variation of Growth Rate with Temperature
Change from reaction limiting to diffusion limiting
The range where the Ahrinious equation applies
pH Effects
• Optimal pH for growth may be different from that for product formation; • In general, acceptable pH range varies around the optimum by +0.5 to 2
pH units; • Different organisms have different pH optima:
bacteria pH = 3 to 8 yeast pH = 3 to 6 molds pH = 3 to 7
plant cells pH = 5 to 6 animal cells pH = 6.5 to 7.5
• Organisms have mechanisms to maintain a constant intracellular pH in presence of fluctuations in exterior environmental pH
• If environmental pH differs from the optimal value, the maintenance energy requirements increase, resulting in decrease of biomass and/or product yield.
Variation of Specific Growth Rate with pH
Possible Sources of pH Variation in Medium
• When ammonium is used as nitrogen source, hydrogen ions are released as a result of the utilization of ammonia, resulting in a decrease in pH;
• When nitrate is used as nitrogen source, pH increases when nitrate is consumed;
• pH can change because of the production of organic acids, the utilization of acids (particularly amino acids), or the production of biochemical bases;
• Evolution or supply of CO2 can alter pH greatly in some systems (especially at basic conditions);
• pH control: buffering and active pH control system.
Effects of Dissolved Oxygen (DO)
• Molecular oxygen serves as electron receptor;
• DO might be the limiting substrate (O2 is sparingly soluble in water with a solubility of 8 -11 mg/L);
• Below a critical oxygen concentration, growth follows a first-order rate dependence on the oxygen concentration (e.g. Monod kinetics).
• Above the critical oxygen concentration, the growth rate becomes independent of the DO concentration (zero order ).
Oxygen Transfer
• Oxygen transfer from gas bubbles to cells is usually limited by oxygen transfer through the liquid film surrounding the gas bubbles;
• The rate of oxygen transfer from the gas to liquid phase is given by
OTRCCakN LLO )*(2
Oxygen Consumption
2
2OX
OY
XXqOUR
2
2
OX
OY
q
Effects of Oxygen Transfer on Cell Growth
• When DO is above the critical value, no effect;
• When DO is below the critical DO, the rate of oxygen transfer and the rate of oxygen consumption equal to each other at steady state;
• Further assume that the demand for oxygen for maintenance is negligible. Then
)*(
2
LLOX
CCakY
X
)*(2 LLOX CCakY
dt
dXx
Methods to Overcome DO Limitations
• Increased agitation to increase O2 transfer: increasing
______;
• Use of enriched air or pure oxygen to increase ____;
• Higher operating pressure (2 to 3 atm): increasing ______;
• Use of surfactants to increase O2 transfer: increasing ______ (be careful).
)*(2 LLOX CCakY
dt
dX
Other Environmental Factors
• Dissolved Carbon Dioxide (DCO2) – High DCO2 concentration may be toxic to some cells. – Cells require a certain DCO2 level for proper metabolic functions. – Can be controlled by changing the CO2 content of the air supply and
the agitation speed.
• High Substrate/Salt Concentrations
– High substrate concentrations significantly above stoichiometric requirements could be inhibitory;
– Inhibitory levels vary depending on the type of cells and substrates; – Substrate inhibition can be overcome by intermittent addition of the
substrate to the medium (fed-batch).
Heat Generation by Microbial Growth
• 40-50% of the energy in a carbon energy source is converted to biological energy (ATP) during aerobic metabolism; the rest of the energy is released as heat;
• Heat evolution is directly related to growth;
• Estimation of heat-removal requirements essential to reactor design;
• Heat released can be removed by a cooling coil or cooling jacket;
• Temperature control (adequate heat removal) can limit bioreactor design.
Enthalpy Balance for Microbial Utilization of
Substrate
Calculation of Heat Generation During Cell Growth
Heat of the Combustion of Substrate = Heat of Metabolism + Heat of the Combustion of Cells + Heat of the Combustion of Products
Ht
S = HtC + Ht
P + Qm Let 1/YH be the metabolic heat generated by unit biomass, then HS S = HC SYx/s + SYP/sHP + SYx/s/YH
Assume Yp/s = 0 and divide both sides of the equation by SYx/s, then
HC
SX
S
YH
Y
H 1
/
Specific Metabolic Heat
• Equation can be re-arranged to give:
HC
SX
S
YH
Y
H 1
/
HS heat of combustion of substrate (kJ/g substrate), YX/S substrate yield coefficient (g cell/g substrate), HC heat of combustion of cells (kJ/g cells) 1/YH metabolic heat evolved per gram of cell mass produced (kJ/g cells).
Rate of Heat Generation
• The total rate of heat evolution in a batch fermentation is:
• In aerobic fermentation, the rate of metabolic heat evolution can roughly be correlated to the rate of oxygen uptake:
QGR (Kcal/h)= 0.12 QO2 (mmoles of O2/h)
where QGR is the total rate of heat generation, VL the volume of the culture, and QO2 the rate of oxygen consumption.
H
netGR
1
YXVQ L
Cell Growth Kinetics
Characteristics of Unstructured Models
• Assume constant cell composition (balanced growth).
• Simple and applicable to situations of practical interest.
• Limitations: – Valid at steady-state continuous culture and the
exponential phase of batch culture – Fails during any transient condition. – Acceptable when deviation less than 10-20%
Unstructured Models
• Substrate-Limited growth (Monod kinetics)
• Derivatives of Monod kinetics
• Other kinetic equations
• Models with Growth Inhibitors
• Determination of Kinetic Constants and Ki in Batch System
• Logistic equation
Substrate-Limited Growth
• A single chemical species, S, is growth rate limiting (the limiting substrate);
• Changes in other nutrient concentrations have no effect on cell growth;
• the Monod Equation
SK
S
S
m
g
Kinetic Equation of Fast Growing Cells
• Monod equation describes the substrate limited growth only when the growth is slow and the population density is low.
• For fast growing cells, the production of toxic product is more likely and at high cell density, the inhibition by toxic by-products becomes more important:
S0 Initial substrate concentration
KSO A dimensionless constant
KS1 Saturation constant
Effects of initial substrate
concentration counted.
Other Kinetic Equations
Models with Growth Inhibitors
• Substrate inhibition
• Product inhibition
• Inhibition by toxic compounds
Models with Substrate Inhibition
• Microbial growth rate is inhibited by high substrate concentrations (fed-batch fermentation)
• If a single-substrate enzyme reaction is rate-limiting, then inhibition of enzyme activity results in inhibition of microbial growth by the same pattern:
where KI is the inhibition coefficient
Product Inhibition
• High concentration of product can be inhibitory for microbial growth
• Feed back inhibition and feedback repression to essential enzyme
• Unknown mechanism
• Some examples:
Inhibition of Ethanol
• Ethanol fermentation from glucose by yeasts is an example of non-competitive product inhibition (6.43).
• Ethanol is the inhibitor at concentrations above about 5%
• Examples of other rate expression used for ethanol inhibition are:
Inhibition of Toxic Compounds
In analog to inhibited enzymatic kinetics:
If the toxic compound results in inactivation (of death) of cells,
then:
where K’d is the death rate constant (h-1)
Logistic Equation
• The maximum attainable cell density is equivalent to the ecological concept of carrying capacity;
• Logistic equations are a set of equations that characterize cell growth in terms of carrying capacity. For example, specific growth rate can be related to the amount of unused carrying capacity:
Integration gives:
Controversies Surrounding the Logistic Equation
• Disapproval – The equation does not include substrate concentration and may
predict growth beyond zero substrate; – It does not discriminate different phases
• Approval – Only in deceleration phase, a relatively short period of growth phase
in a typical batch growth profiles, cell growth is actually substrate dependant;
– When the maximum biomass concentration, which corresponds to the “carrying capacity” of a particular system, is accurately predicted, logistic equation provides satisfactory prediction for many studied cases;
– Logistic equation eliminates the requirement of accurately determining the transit between different physiological phases, which is usually very difficult to achieve in practice.
Summary
See the outline