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

Screenshot 2018-11-07 06.51.56

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

Screenshot 2018-11-07 09.40.58

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.

Screenshot 2018-11-07 10.00.30

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)