This document discusses cellular engineering and modeling of cell growth kinetics, including: - Cell metabolism involves hundreds of enzyme-catalyzed reactions, and growth can be modeled based on limiting substrates. - The Monod model relates specific growth rate to limiting substrate concentration. - Continuous culture systems like chemostats operate at steady-state with dilution rate equal to specific growth rate. - Critical dilution rate marks the point where cells are "washed out" of the system faster than they can grow.

1. Cellular Engineering
UPIIG - IPN
Author: Guillermo Garibay Benítez University: Instituto Politécnico Nacional
Mexico

2.  The rates of consumption or production of all
other substrates and products are based on
the empirical relation between specific
growth rate and the key-indepent variables.
 The characteristic feature is that rates of
formation or consumption of all reactants,
except the key reactant are proportional to
the key reaction rate.

4.  Cell metabolism is made up of hundreds of
sequential, branched and parallel biological
reactions that are normally catalysed by enzymes.
 We can assume that growth is the result of
hundreds of such enzyme-catalyzed reactions.

6.  The relationship between specific growth rate and
limiting substrate concentration proposed by Monod
states that:
 µ and µmax :specific and maximun specific growth rate
respectively
 S : limiting substrate concentration
 Ks : saturation constant

7.  When substrate concentration is not limited,
when S>>Ks numerically, Ks can be ignored
 Specific growth rate approaches umax, and
growth rate becomes independent of S and
only proportional to cell concentration.
 µ=µmax

9.  The dilution rate (D) describes the
relationship between the flow of medium into
the bioreactor (F) and culture volume within
the bioreactor (V):
 D=F/V

10.  The change on cell concentration over a
period of time, can be expressed as:
• During stationary conditions, cell
concetration remains constant, so dx/dt = 0
then:

11.  In stationary state, specific
growth rate is controlled by
dilution rate (D), which is an
experimental variable
 Continuos culture must be
operated ath dilution rates
below specific growth rates
 Dilution rate can be used for
controlling growth of the
cultrue

12.  Cell growth depends on growht limiting
subrate, therefore, growth is expressed as:
 In stationary condictions: μ = D, therefore:

13.  A quimiostat is operating in stationary state
which has a dilution rate of 0.30 h-1 with a
limiting substrate concentration of 0.06 mM
L-1. Determine Monod constant if the umax
for the organism is 0.25 h-1.

14. Constant
biomass
concentration Low glycerol
concentration

15.  From measurements of the residual glucose
concentration in a steady-state chemostat at various
dilution rates, you can find the following results:
 Calculate by linear regression the parameters in the
Monod Model. Are any of the data points suspect?
D (h-1) s (mg L-1)
0.13 11
0.19 14
0.23 18
0.36 38
0.67 85
0.73 513

16.  The outlet limiting substrate concentration is
independent of the input limiting substrate
concentration.
 At a fixed dilution rate, called the critical dilution
rate, the cell concentration drops to the constraint :
 And the limiting substrate concentration reaches
the upper constraint:
xv0 = concentración de
celulas viables inicial

17.  Después de esta velocidad de dilución crítica,
se dice que las células están siendo lavadas
(wash out), ya que están saliendo del
bioreactor a una velocidad mayor que el
crecimiento
 Asumiendo que el crecimiento se comporte
de acuerdo a la cinética de Monod, la
velocidad de dilución crítica se encuentra
usando la serie de condiciones de lavado:

18.  Then, in monod expression:
 Since Si is usually very much greater than Ks,
Dcrit is approximately equal to μmax

20.  Check the value of μmax increasing the dilution rate in the
chemostat to D=1.1 h-1.
 The result of the change in dilution rate is a decrease in the biomass
concentration, and during the wash-out you measure the biomass
concentration as a function of time, and obtain the following results:
 Determine μmax from this experiment
Time (h) x (g L-1)
0 5.1
0.5 4.5
1.0 3.7
2.0 2.8
3.0 2.1
4.0 1.4