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