CEN 551: Biochemical Engineering

1
CEN 551 Biochemical Engineering

• Instructor Dr. Christine Kelly

2
Cell Growth

• Growth is autocatalytic
• Characterized by specific growth rate, µ

3
Measuring Cell Concentration

• Cell concentration can be measured directly
  and/or indirectly.
• Direct mass or cell number basis.
• Cell number counting hemocytometer, plate counts
  and particle counts.

4
Counting Cells Hemocytometer

• Counting Cells Hemocytometer.
• Advantage accurate, typically low noise in
  measurement.
• Disadvantage time consuming, carcinogenic,
  mutagenic stains.

5
Counting Cells Plate Counts

• petri dish or dilution plate counts count
  colonies (CFUs colony forming units) formed by
  individual cells (dilute sample).
• Advantages counts viable cells, fairly
  accurate.
• Disadvantages noisy, takes days.

6
Counting Cells Particle Counters

• Particle counters (Coulter counter) measure
  particle size distributions.
• Advantages very quick, obtain a size
  distribution in addition to a count.
• Disadvantages solutions must be particle free
  for accurate count, finicky hardware, expensive,
  complicated.

7
Mass Concentration

• Most common units to report biomass.
• Obtained by centrifuging sample, drying and
  weighing.
• Advantages Mass concentration is typical
  variable in models, simple, low tech method.
• Disadvantages Presence of solids makes
  inaccurate, difficult to measure low biomass
  concentrations.

8
Indirect Concentration Measurements

• Turbidometer or spectrophotometer (most common).
• Substrate uptake or product evolution.
• Luciferin/ATP fluorescence.
• Protein or DNA/RNA concentration measurements.

9
Optical Density measured with a Spectrophotometer

• Optical density is the a measure of the amount of
  light that passes through a turbid sample.
• Reported with the wavelength of the light used in
  the measurement. For example OD600 optical
  density at 600 nm.
• Biomass is often measured in OD and converted to
  mass per volume with a standard curve.

10
Batch Cultures

• Fixed amount of substrate (growth medium) present
  at beginning.
• Batch is seeded with an innoculum (small amount
  of live cells to start growth).
• 5 phases of growth lag, exponential,
  deceleration, stationary, death.

11
(No Transcript)
12
Lag Phase

• Adaptation as innoculum cells adjust enzyme
  systems to new environment (repression of
  unneeded systems, induction of useful enzyme
  systems).
• Growth is suppressed, duration 1-10 hours.
• Extended by low temperature, small innoculum,
  radical substrate/temperature changes, low
  nutrient levels, innoculum age.
• Innoculum should be 5 volume and from
  exponential phase culture.
• Multiple lag phases can exist with multiple
  growth substrates (diauxic growth).

13
Exponential Growth Phase

• Growth is balanced (intercellular concentrations
  remain constant).
• No dependence on substrate concentration (growing
  at intrinsic maximum growth rate).
• Primary metabolites (growth associated) produced.
• Growth rate is 1st order with respect to cell
  concentration, 0th order with respect to
  substrate concentration.

14
Doubling Times
15
Deceleration Phase

• End of exponential phase.
• Caused by either build-up of toxic products or
  depletion of substrate.
• Cell physiology changes to favor survival over
  growth.

16
Stationary phase

• Net growth rate is zero.
• Cells produce secondary metabolites (not growth
  associated).
• Many products important to the biotechnology
  industry are produced during this phase.
• Cells begin to lose ability to reproduce.
• Cells begin to lyse, cryptic growth occurs.
• Cells catabolize energy reserves (eg PHB) in
  endogenous metabolism.
• Although growth slows or ceases, maintenance
  requirements still exist.

17
Death Phase

• Death is relative to the population, death always
  occurs.
• Commonly modeled as a 1st order process with
  respect to biomass.
• Some portion of cells remain viable for a long
  time, but are altered.

18
Growth Yield, Yield Coefficient

• Growth yield microorganisms produced per unit
  substrate utilized.
• Other yield coefficients.

19
Typical Yield Coefficients
20
Effects of Temperature

• What is the net effect of the two functions of T?

21

• Biological reaction rate is similarly affected
  relative to diffusion.
• Rate determining mechanism may shift at high T.

22
Effects of Temperature
23
Effects of pH

• pH optima bacteria 3-8, yeast 3-6.
• pH varies significantly during fermentation if
  system is not buffered or controlled for pH.
• CO2 evolution and ammonium as nitrogen source
  both lower pH.
• Nitrate utilization raises pH.

24
Dissolved Oxygen Requirements

• DO can become limiting substrate.
• At high DO concentration, growth is independent
  of O2.
• O2 solubility in water 7 ppm.
• Bacteria require 10 of saturation for O2
  independent growth, yeast 10-50.

25
Dissolved Oxygen Requirements

• Rate of O2 transfer usually limited by stagnant
  liquid around bubbles.
• When O2 transfer is limiting OTROUR (oxygen
  transfer rate oxygen uptake rate), so

26
Models for Growth Kinetics

• Structured versus unstructured (cell composition
  does not change with time).
• Segregated versus unsegregated (all cells are
  identical).
• Monod equation is unstructured, unsegregated
  model.

27
Monod Equation

• Single substrate controls growth.
• Analogous to Michaelis-Menten enzyme kinetics and
  the Langmuir isotherm.
• Mechanistic if one enzyme system controlled
  growth.

28
Example Problem

• Find
• Maximum growth rate
• yield on substrate
• doubling time
• saturation constant
• specific growth rate at 12 hr

29
stat. death
30
Example Problem Solution ?max
? is constant when ? ? max.
Integrate ln(X) ln(Xo) ?t plot ln(X) vs.
T Slope (largest) ?max , intercept ln(X)
31
(No Transcript)
32
Example Problem Solution YX/S
Overall yield for the entire batch growth period.
33
Example Problem Solution td
Maximum doubling time will occur in exponential
growth, when ? ?max
34
Example Problem Solution KS

• Lag phase 0 4 hr ? ?0
• Exponential phase 4-14 hr ? ? ?max
• Deceleration phase 14 hr ? ? f (S)
• Apply Monod Kinetics in the deceleration phase.
• Draw tangents to the time versus X curve at the
  thre time points in the deceleration phase.
• Calculate the slope of the tangents.
  Slope dX/dt, ?(1/X)(dX/dt)

35
Slope 0.01
Slope 0.47
Slope 0.146
stat. death
36
Example Problem Solution KS
?
37
(No Transcript)
38
Example Problem Solution doubling time at 10 hr

• ?max at 10 hr,
• So,
• doubling time maximum doubling time
• td 0.237 hr

39
Yield

• ?S ?Sbiomass ?Sextra cell prod ?Senergy
  ?Smaintenance
• Maintenance energy expenditures for repair,
  transport, motility
• Endogenous metabolism consumption of storage
  polymers for energy

40
Monod Equation

• Single substrate, S, controls growth.
• Analogous to Michaelis-Menten enzyme kinetics and
  the Langmuir isotherm.
• Mechanistic if one enzyme system controlled
  growth.

41
Monod Equation
42
Other Models for Cell Growth

• There are other nonsegregated, unstructured
  models for cell growth (see Shuler, pp. 170-171)
  but the difference is not worth the work.

43
Modeling Growth Inhibition

• Inhibitory kinetic expressions are not typically
  mechanistic, but are selected to fit data.
• Expressions are analogous to inhibited enzyme
  kinetics.

44
Growth Inhibition by Substrate
Competitive Noncompetitive If a substrate is
inhibiting cell growth of a batch culture, the
substrate should be added in a fed-batch mode.
45
Growth Inhibition by Product
Competitive Noncompetitive If a product were
inhibiting cell growth of a batch culture, the
product recovery will be expensive.
46
Growth Inhibition by Other Compounds
If a product were inhibiting cell growth of a
batch culture, the product recovery will be
expensive. Competitive Noncompetitive
47
Growth Inhibition by Other Compounds
Uncompetitive
48
Continuous Culture
CO2 and air out
Substrate
Cells Substrate Products
Chemostat or continuous flow stirred tank reactor
(CSTR)
Air or oxygen
49
(No Transcript)
50
(No Transcript)
51
Instrumentation

• pH probe and controller
• DO probe and controller
• Antifoam probe and controller
• Level probe and controller
• Nutrient addition pump
• Agitation rate controller

52
Modeling an Ideal Chemostat
X cell mass concentration in the chemostat S
substrate concentration in the chemostat F
volumetric feed rate P product concentration in
the chemostat VR volume of fluid in reactor
vessel

• Let

X0 cell mass concentration in the feed (usu.
0) S0 substrate concentration in the feed P0
product concentration in the feed (usu. 0)
53
Modeling an Ideal Chemostat

• Mass balance on cells
• Define
• So

accum
in - out growth - death
(1)
(2)
(3)
54
Steady-state operation

• For kdltltµ, dX/dt0, and X00
• For Monod kinetics

Can use to find µmax and Ks
Or
55
Substrate Mass Balance
in - out consumption due to X and P
accum
(7)
where qp is the specific product formation rate
(g P/g cells hr)
For negligible product formation rate and steady
state
(8)
56
Equation for Cell Density
Since µD at steady state
(9)
Using the equation for substrate concentration
based on cell mass balance at s.s. (Eq. 6)
(10)
57
Allowing for endogenous metabolism (kd gt 0)
Recall
(3)
Assume s.s. and X00, but allow for significant
endogenous metabolism
(11)
58
Cell density with endogenous metabolism
Subst. Eq. (11) into Eq. (8)
(12)
or
(13)
Compare to Eq. (9).
59
What does kd represent?

• Shuler uses kd to represent changes in cell mass
  due to endogenous respiration and kd for changes
  in cell mass due to cell death and lysis.
• Endogenous respiration catabolism of cellular
  reserves for continued maintenance and energy.

60
Recall
kd small
kd not small
61
Finding the True Yield Coefficient

• Rearranging what was equation (13)

(1)
or
(2)
62
Definitions of Yield

• Where

63
Determining True Yield
(3)
or
(4)
where
(maintenance coefficient)
64
Figure 6.19
65
Product Generation
Product mass balance
(5)
At steady state and letting F/VRD
(6)
The steady state substrate balance is
(7)
66
Optimizing Productivity
A biomass balance accounting for nonzero kd gives
(8)
Solving Eq. (7) for X, the biomass concentration
(9)
67
or, using Eq. (8) for S in Eq. (7)
(10)
Combining Eq. (9) and Eq. (6)
(11)
where PrP is the product productivity in g.
product/liter/hour
68
Productivity with Endogenous Metabolism
or, using Eq. (8) for S in Eq. (11)
(12)
69
Stoichiometry

• WWWebsters Dictionary 2.b) the quantitative
  relationship between two or more substances
  especially in processes involving physical or
  chemical change
• If cells have a characteristic molecular
  composition (i.e. CHaObNc) then yield
  coefficients can be determined through
  stoichiometry. In practice, these will be
  estimates.

70
Stoichiometry of Biomass Formation
aerobic growth on a carbohydrate
carbon balance
hydrogen balance
oxygen balance
nitrogen balance
71

• 4 equations, 5 unknowns (assuming we have a
  molecular formula for biomass).
• Experimental data needs to be used to close the
  system.
• We define the respiratory (or respiration)
  quotient to be moles CO2 evolved/mole O2 consumed

72
Yield Coefficients

• The system is determinate and we can form the
  yield coefficients
• from the stoichiometric coefficients and formula
  weights.