CHAPTER 3
MICROBIAL GROWTH KINETICS
BATCH CULTURE
CONTINUOUS CULTURE
FED-BATCH CULTURE
Multistage systems
Feedback systems
mode of operations = type of products
closed culture system
Substance @ the initial time = limit
growth curve
lag phase: no growth appears
log phase (exponential)
deceleration phase
stationary phase
a time of adaptation
In a commercial
process: should be reduced = suitable inoculum (chap 6)
constant cell growth rate = max. growth rate
μ.x= dx/dt 🚩
x: concentration of microbial biomass
μ: specific growth rate (h-1)
t: time (hour)
On integration: x t = x 0 . e^ (μ.t)
x 0: original biomass concentration
x t: biomass concentration after t time interval
t (hours)
e: base of natural logarithm
ln x t = ln x 0 + (μ.t) ❗
plot = a line with a slope = μ
HOWEVER
growth rate of the culture decreases
- substrate limitation: depletion of some essential nutrient
- toxin limitation: accumulation of some autotoxic product
substrate limitation: plot Biomass concentration at the onset of stationary phase vs. initial substrate concentration
zone A to B = substrate limitation
x= Y (S R - s)
x: concentration of biomass produced
Y: yield factor (a dimensionless constant)
S R: original substrate concentration
s: residual substrate concentration, and s = 0 at the point of cessation of growth ❗
zone B to C: the transition between substrate and toxin limitation zones
zone C to D: toxin limitation
the decrease in growth rate and the cessation of growth, due to the depletion of substrate:
Monod equation: μ = (μ max . s)/(Ks+s) ‼
Ks: substrate utilization constant and Ks = S R when μ = 1/2 μ max
also, as a measure of the affinity of the organism for it substrate.
plot: specific growth rate (μ) vs. residual limiting substrate concentration
zone A to B = exponential phase
zone A to C = deceleration phase
if Ks = very low = high affinity: deceleration phase is short
B/c: growth rate will not be affected
until the substrate concentration has declined to a very low level
Ks = high values = low affinity: deceleration phase is long
growth rate is reaching 0
but, phase = max. population phase => biomass production
produces secondary metabolites = non-growth linked product
produces primary metabolites = growth-linked products
dp/dt = q p . x OR q p = Yp!r . μ
p: concentration of product
q p: specific rate of product formation
Yp!r: yield of product in terms of substrate consumed
dp/dx = Yp!r
Yp!r: yield of product in terms of substrate consumed
if multiply with dx/dt, so: dp/dt = Yp!r . (dx/dt)
OR dp/dt = Yp!r . (μ.x)
REMINDER: μ.x= dx/dt ❗
q p = Yp!r . μ
meaning: when product formation is growth associated the
specific rate of product formation increases with specific growth rate
non-growth associated product; the q p = constant over different growth rates or varied in a complex manner
In general, it is used for producing
biomass
primary metabolites
secondary metabolites
by supporting the maximum cell
population
by extending the
exponential phase accompanied by product excretion
extend the
exponential phase accompanied by product excretion
decreasing growth rate in the log phase
Prolongation of exponential growth = addition of fress medium
applied in batch culture as well as continuous culture 🚩 (SEE CONTINOUS CULTURE)
Definition: if the added medium were to displace an equal volume of culture from the vessel then a
continuous production of cells could be achieved
fed medium is added at a suitable rate => a steady state
D = F / V
D: the flow of medium (h -1)/ dilution rate
F: flow rate
V: volume
dx/dt = growth - output = μ.x - D.x 🚩
dx/dt = μ.x - D.x with dx/dt = 0
SO: μ.x = D.x AND μ = D 🚩
REMINDER: Monod equation: μ = (μ max . s)/(Ks+s) ‼
Therefore, dx/dt = x ((μ max . s)/(Ks+s) - D) 🚩
net change in the residual growth limiting substrate concentration ds/dt = Input of substrate - output of substrate - consumption by cells
ds/dt = D.S R - D.s - μ max (x/Y) (s/(Ks + s))
steady state: ds/dt = 0
dx/dt = 0 ‼
x̄ = Y (S R - s with bar)
s with bar = (Ks.D)/ (μ max - D) 🚩 explain how D control μ (READ it on P. 8)
x̄: steady-state cell concentration
s with bar: steady-state residual substrate concentration
TYPES
chemostat
turbidostat = biostat
growth rate of the culture is controlled by its chemical environment
concentration of cells in the culture is kept constant by controlling the flow
of medium such that the turbidity of the culture is kept within certain, narrow limits
C02 concentration
Kinetic characteristics: Y, μ max, and Ks
μ max affects maximum dilution rate
Ks affects the residual substrate concentration (then biomass concentration)
Effect of D on steady-state biomass and residual substrate concentration
Y: affects steady-state biomass concentration
critical dilution rate Dcrit = (μ max . S R) / (Ks + S R)
GRAPH
Dcrit = dilution rate at which x equals zero (cells are washed out)