growthkinetics
Introduction
Microbial growth results from cell division and changes in cell size.
Influenced by a variety of physical, chemical, and nutritional conditions.
Nutrients are converted into biological compounds for energy production and biosynthesis.
Serves as a good example of an autocatalytic reaction.
Microbial Batch Growth
Growth Phases:
Decelerating Growth Phase
Exponential Growth Phase
Initial Lag Phase
Phases of Growth
Lag Phase
No increase in cell number; period of adaptation to a new environment.
Increase in mass without change in number.
Multiple lag phases may occur in the presence of more than one carbon source (Diauxic growth).
Length influenced by microbial species characteristics and media conditions.
Log Phase
Higher growth rate during this phase.
Increase in cell mass and number exponentially over time.
Characterized by a straight-line manifestation in growth projection; hence known as the Exponential phase.
Represents balanced growth where all cellular components grow at the same rate, maintaining constant biomass composition.
Exponential Growth Rate
First-order reaction characterized by the equation:
( \frac{dX}{dt} = \mu \cdot X )
Integration yields:
( ln(\frac{X}{X0}) = \mu t )
( X = X0 e^{\mu t} )
Generating a Growth Curve
Bacterial growth defined as cell replication (binary fission).
For example, one cell becomes two, then four, and so forth, doubling efficiently under favorable conditions.
Steady growth leads to population doubling; significant scaling leads to high cell counts over time.
Phases of Growth (Continued)
Deceleration Phase
Occurs post-exponential phase; characterized by unbalanced growth.
Growth decelerates due to nutrient depletion or toxin accumulation.
Stationary Phase
Initiates when net growth rate becomes zero (growth rate = death rate).
Cells remain metabolically active, producing secondary metabolites.
Death Phase
Number of new cells equals the number of dying cells.
Cell death follows first-order kinetics:
( r_d = K_d N )
Rate of cell death corresponds to viable cell numbers and the specific death constant.
Effect of Substrate Concentration in Batch Culture
Specific growth rate dependent on three parameters:
Concentration of growth-limiting substrate ( S )
Maximum specific growth rate ( \mu_{max} )
Substrate-specific constant ( K_s )
Monod equation states:
( \mu = \frac{\mu_{max}}{K_s + S} )
Commuting this equation provides a linear relation when plotted with 1/( \mu ) against 1/( S ).
Continuous Culturing
Characterized by a continuous feeding process where conditions and substrate concentrations are stable.
Continuous Growth Kinetics
Actual growth rates are dependent on the volumetric flow rate and dilution rate ( D ):
( D = \frac{F}{V} )
Net change in cell concentration defined as:
( \frac{dX}{dt} = \text{rate of growth} - \text{rate of loss (}\mu X - DX) )
At steady state:
( \frac{dX}{dt} = 0 )
Thus, ( \mu = D ) under these conditions.
Steady State Substrate Concentration
Used to predict residual substrate concentration through the Monod equation with substitution.
Operational Considerations
Advantages
Versatility for different reactions.
Sterilization capabilities.
Low labor costs at steady state.
Disadvantages
High skilled labor costs.
Risks of infection and mutation.
Potential for unfulfilled continuous production promises.
Problem Statement
Context involving a wastewater treatment facility:
Batch reactor for biodegradable pollutant treatment with specifics given on pollutant concentration, treatment stages (coagulation, sedimentation, biological treatment), and biomass yield from degradation.
Questions to analyze treatment stages and biomass generation as well as assessing the effect of altering coagulant doses on efficacy.