Cell Growth

•Cell Growth
Cells and Substrate Cells and Extracellular Product
+ S +S +P
•Autocatalytic reaction
•Rate of microbial growth is characterized by the specific growth rate (m (h-1))
X – cell mass (g cells/L)
t – time (h)
•Determination of Cell Growth
•Direct counting – hemacytometer
•Counting by diluting and plating the cells on solid medium
•Particle counters
•Dry cell weight
•Cell volume by centrifugation
•Turbidity or optical density – 560 – 600 nm
•Measure amount of product formed or amount of substrate consumed
•Measure amount of cellular protein or DNA
•Mycelial growth or extracellular polysaccharide formation – viscosity
•Follow pH
•Typical Batch Cell Growth
•Lag Phase
•Immediately after inoculation – period of adaptation
•Reorganize their molecular constituents
•Depending on the nutrients may have to synthesize new enzymes or repress some enzymes
•Cell mass may increase a little, without an increase in cell number
•Age of inoculum effects lag and amount
•Rule of thumb to minimize lag phase – 5% by volume, young cells
•Exponential Growth Phase
•Logarithmic growth
•Cells are adjusted to their environment
•Cell mass & number increase exponentially with time.
•Balanced growth – when all components of a cell grow with the same rate. The average composition of the cell remains constant with time
•First order growth
•Growth decelerates due to depletion of one or more essential nutrients.
•Accumulation of toxic by-products
•Phase is short, changes occur over a short period of time – unbalanced growth
•Cell changes to increase the prospects of cellular survival
•Stationary Phase
•Net growth is zero, no cell division or death rate = growth rate
•Cells still produce secondary metabolites (non-growth related products)
•Production of certain metabolites is enhanced during stationary phase (antibiotics) due to metabolic deregulation
•Cell catabolizes cellular reserves for new building blocks and for energy-producing monomers. Endogenous metabolism
•Stationary Phase – cont.
•The following can occur
–Cell mass concentration may stay constant but number of viable cells may decrease
– Cell lysis may occur and viable cell mass may drop. A second growth phase may occur and cells may grow on lysis products of lysed cells (cryptic growth)
–Cells may not be growing but may have active metabolism to produce secondary metabolites. Cellular regulation changes when concentrations of certain metabolites (C,N,P) are low.
•Cell must use energy to maintain an energized membrane and transport nutrients for essential functions like motility and repair of cellular structures.
•Energy expenditure is maintenance energy
•Death Phase
•Decline phase
•Clear demarcation between stationary and death may be difficult
•Cells usually lyse
XS = Cell concentration at end of stationary phase
kd = first order death constant
•Transfer cells to fresh medium could have cells grow
•Distribution of cells in medium
•Using old inoculum may elect for variants of the strain with altered metabolic capabilities.
•Yield Coefficients
•Defined based on the amount of consumption of another material
•Growth yield
DS = DSassimulation into biomass + DSsimulated into extracellular product + DSgrowth energy + DSmaintenance energy
•Other yield coefficients may be defined such as
•Yield Coefficients – cont
•Aerobic growth
–YX/S is usually 0.4 to 0.6 g cells/g substrate for yeast and bacteria – Glucose
–YX/O2 = 0.9 to 1.4 g/g – Oxygen
•Anaerobic bacterial growth is less efficient
–YX/S = 0.2 to 0.4 g/g – glucose
–YX/S = 0.6 to 1 g/g – methane
•Maintenance Coefficient
•Rate of uptake of a substrate for cellular maintenance
•Stationary Phase – endogenous metabolism of biomass components
•Energy expenditure to
–repair damaged cellular components
– transfer nutrients and products in and out of cells
– motility
– adjust osmolarity of cells interior volume
•Product Formation
•Growth-associated products – produced simultaneously to growth (exponential, decline)
–Constitutive Expressed Enzyme
–Substrate Utilization enzymes
•Non growth associated – takes place during stationary phase
qp= constant
–RDX degradation
•Product Formation – cont
•Luedeking-Piret Equation
–a = 0 non-growth associated
– b = 0 only growth associated
–a = YP/X
–Lactic acid fermentation
–Xanthan gum production
•Temperature Effects
•Optimum temperature for cell growth
–psychrophiles (T<20)
–mesophiles (20<T<50) – thermophiles (T>50)
•Above optimum temperature the growth rate decreases and thermal death results
•Both m and kd vary according to the Arrhenius Equation
m = Ae-Ea/RT, kd = A’e-Ed/RT
•Activation energy for cell growth 10-20 kcal/mol
•Activation energy for thermal death 60-80 kcal/mol
•Thermal death is more sensitive than growth.
•Temperature Effects – cont.
•Temperature affects product formation,
–Optimum for growth not necessarily optimum for product formation.
–Temperature sensitive promoter product
–Yield coefficient effected.
•Maintenance coefficient increases with increasing temperature
• Decreasing the yield coefficient.
•Reaction rate may be greater than the diffusion rate at high temperatures.
–Usually assume things are reaction limited
–Molecular diffusion activation energy = 6 kcal/mol
–Bioreactions = 10 kcal/mol.
–Increase rate lowering activation energy diffusion limited.
•pH Effects
H+ concentration enzyme activity growth rate
•Optimal for growth not necessarily optimum for product formation.
–3 to 8 – bacteria
–3 to 6 – yeast
–3 to 7 – molds
–5 to 6 – plants
–6.5 to 7.4- animal cells
•pH Effects – cont.
•Most cells can control intracellular pH in the presence of fluctuations in external pH changes.
–Nitrogen source – ammonia – decrease in pH add base
–Nitrogen source – Nitrate – reduce to ammonia increase in pH add acid
–Production of either acids or bases change pH adapt to higher or lower pH.
•Dissolved Oxygen
•Limiting in aerobic cultivation since it is sparingly soluble in water
–Saturation 25 C 1 atm 7 ppm
–Salts alter solubility
–High temperatures decreases oxygen solubility
•Sparge oxygen throughout fermentation.
•Oxygen Transfer Rate
•Oxygen transfer is limited by dissolving oxygen in liquid cell medium, then can diffuse to cells
•Oxygen transfer from gas to liquid
NO2 = kl a (C* – CL) = OTR
–kl oxygen transfer coefficient (cm/h)
–a gas-liquid interfacial are (cm2/cm3)
–kla volumetric oxygen transfer coefficient (h-1)
– C* saturated DO concentration (mg/l)
–Cl actual DO concentration in the broth (mg/l)
– NO2 rate of oxygen transfer (mgO2/lh)
•Oxygen Uptake Rate (OUR)
–QO2 – specific rate of oxygen consumption (mg O2/l h)
–YX/O2 – oxygen yield coefficient (g dw cells / g O2)
–X cell concentration (g dw cells/l)
•If oxygen transport is limiting then rate of oxygen cons = rate of oxygen transfer or OUR = OTR
•Oxygen Limitation
•Growth rate varies linearly with dissolved oxygen concentration under oxygen limitation conditions.
•Overcome oxygen limitation
–sparge reactor continuously
–oxygen enriched air,
–work under higher pressure – 1 to 2 atm.
•Redox Potential
•Influences the rate of oxidative-reductive reactions
•Function of DO pH, ion concentrations
•Electrochemical potential of a fermentation, Eh
–E0 – constant
–F – Faraday constant
–R – gas constant
–PO2 – partial pressure of oxygen (atm)
–measured in millivolts
•Reduce Redox potential by
–purging with nitrogen
–addition of reducing agents like cysteine HCl or Na2S
•Dissolved CO2
•Performance of cells
•High concentration may be toxic
•Some DCO2 required for metabolic functions of cells,
•Controlled by changing amount in air supply or changing the agitation speed.
•Ionic Strength
•Effects transport of nutrients in and out of cells, metabolic functions of cells, and the solubility of certain nutrients
–Ci – ion concentration
–Zi – ion charge
–Glucose – above 200 g/l ethanol fermentations – reduction in water activity
–NaCl – above 40 g/l high osmotic pressure
•Inhibition can be overcome by intermittent feeding of substrate – Fed batch reactor
•Heat Generation during Microbial Growth QGR
•VL – reactor volume
• X cell concentration (g/l)
•1/YH – metabolic heat evolved per gram of cell mass produced (kJ/g cells)
•mnet – net growth rate
•Aerobic fermentation – rate of heat evolution can be roughly correlated to the rate of oxygen uptake
QGR = 0.12 QO2
•YH Determination – Thermo
•DHs – heat of combustion of substrate (kJ/g substrate) – combusting substrate
•YX/S – substrate yield coefficient (g cell/g substrate)
•DHc – heat of combustion of cells (kJ/g cells) – combusting cells ( 20 to 25 kJ/g cells)
•1/YH – metabolic heat evolved per gram of cell mass produced (kJ/g cells)
•YH Determination – Thermo
•Rearrange Heat Equation to Solve for YH
•Example Values for YH values for
–glucose 0.42 g/kcal
–acetate 0.3 g/kcal
–ethanol 0.18 g/kcal
–methane 0.061 g/kcal

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