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CHAPTER 3 MICROBIAL GROWTH KINETICS (CONTINUOUS CULTURE (Definition: if…
CHAPTER 3
MICROBIAL GROWTH KINETICS
BATCH CULTURE
closed culture system
Substance @ the initial time = limit
growth curve
lag phase
: no growth appears
a time of adaptation
In a commercial
process: should be reduced = suitable inoculum (chap 6)
log phase
(exponential)
constant cell growth rate = max. growth rate
μ.x= dx/dt
:red_flag:
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
1 more item...
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
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
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
:!:
deceleration phase
stationary phase
growth rate is reaching 0
but, phase = max. population phase =>
biomass production
produces
secondary metabolites
=
non-growth linked product
In general, it is used for producing
biomass
by supporting the maximum cell
population
primary metabolites
by extending the
exponential phase accompanied by product excretion
secondary metabolites
extend the
exponential phase accompanied by product excretion
decreasing growth rate in the log phase
CONTINUOUS CULTURE
Multistage systems
Feedback systems
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 = μ.x -
D.x
with
dx/dt = 0
SO: μ.x = D.x AND μ = D :red_flag:
REMINDER:
Monod equation
:
μ = (μ max . s)/(Ks+s)
:!!:
Therefore, dx/dt = x ((μ max . s)/(Ks+s) - D) :red_flag:
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) :red_flag: explain how D control μ (READ it on P. 8)
x̄: steady-state cell concentration
s with bar: steady-state residual substrate concentration
dx/dt = growth - output = μ.x -
D.x
:red_flag:
TYPES
chemostat
growth rate of the culture is controlled by its chemical environment
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
critical dilution rate Dcrit = (μ max . S R) / (Ks + S R)
GRAPH
Dcrit = dilution rate at which x equals zero (cells are washed out)
Y: affects steady-state biomass concentration
turbidostat = biostat
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
FED-BATCH CULTURE
mode of operations = type of products
