1. Chapter Six: How Cells Grow

2. Cell Growth Growth is autocatalytic reaction
Characterized by specific growth rate, μ
Net specific growth rate is:

3. Batch Growth In batch growth:
Cells are placed in a vessel (Bioreactor) with an initial charge of growth medium.
The growth medium is not altered by further addition or removal of nutrient.

4. Quantifying Cell Concentration
Cell concentration can be measured directly and/or indirectly.
Direct: based on cell number or mass.
Indirect: based on substrate consumption and/or product formation

5. Counting Cells Cell number counting using: Hemocytometer Plate counts
Particle counts.

6. Counting Cells: Hemocytometer
Counting is achieved using microscope.
Advantages: accurate
Disadvantages: time consuming, not suitable for mold cells, stains are used to distinguish between viable (live) and dead cells (stains
might be carcinogenic).

7. 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: takes days.

8. 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, expensive, complicated.

9. Mass Concentration
Obtained by centrifuging sample, drying and weighing.
Advantages: Simple, low technical requirement method.
Disadvantages: Presence of solids makes it inaccurate, difficult to accurately measure low cell (biomass) concentrations.

10. Indirect Concentration Measurements
Turbidometer or spectrometer (most common).
Substrate uptake or product evolution.
Luciferin/ATP fluorescence.
Protein or DNA/RNA concentration measurements.

11. Optical Density Measured with a Spectrometer
Optical density is the 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.

12. Growth Patterns and Kinetics in Batch Culture
Fixed amount of substrate (growth medium) present at beginning.
Batch is seeded with an inoculum (small amount of live cells to start growth).
5 phases of growth: lag phase, exponential growth phase, deceleration phase, stationary phase, and death phase.

14. Lag Phase Adaptation of cells to new environment
Inoculum cells adjust their enzyme systems to new environment (repression of unneeded enzymes, induction of useful enzymes).
The lag phase is extended by low temperature, small inoculum, radical substrate/temperature changes, low nutrient levels, inoculum age.
Inoculum size should be large (5% to 10% by volume) and from exponential phase culture.
Multiple lag phases can exist with multiple growth substrates (diauxic growth).

15. Exponential Growth Phase
In this phase, cells has already adjusted to the new environment and started producing growth-related products (primary metabolites).
Cell numbers and mass increase exponentially with time.
Growth is balanced (all components of a cell grow at the same rate).
Since nutrient concentrations are large in this phase, the growth is independent of nutrient concentrations (growing at intrinsic maximum growth rate).
Growth rate is a 1st order with respect to cell concentration, 0th order with respect to substrate concentration.
The time required to double the microbial mass is:

16. Doubling Times

17. Deceleration Phase End of exponential phase.
Caused by either build-up of toxic products or depletion of nutrients.
Cell physiology changes to favor survival over growth.

18. Stationary phase Net growth rate is zero.
Cells produce secondary metabolites (nongrowth-related products).
Many products important to the biotechnology industry are produced during this phase (such as hormones and antibiotics).
Cells begin to lose ability to reproduce.
Cells begin to lyse, cryptic growth occurs.
Although net growth ceases in this phase, energy and maintenance requirements still exist.
S= Sbiomass +Sextra cell prod +Senergy + Smaintenance

19. Death Phase Death becomes dominant.
Commonly modeled as a 1st order process with respect to cell mass (biomass).
During death phase cell may or may not lyse
Lysed cells may serve as nutrients for viable cells.
Some portion of cells may remain viable for a long time, but are altered.

20. Growth Yield and Yield Coefficients
Growth yield coefficient = microorganisms produced per unit substrate utilized.
Other yield coefficients.

21. Typical Yield Coefficients

22. Microbial Products
Growth-associated products: Produced simultaneously with microbial growth.
Nongrowth-associated products: products formed during the stationary phase when the net growth rate is zero.
Mixed-growth-associated products: products formed during deceleration and stationary phases.

23. Example 6.1
A strain of mold was grown in a batch culture on glucose and the following data were obtained:
Calculate the maximum net specific growth rate
Calculate the apparent growth yield coefficient
What maximum cell concentration could one expect if 150 g of glucose were used with the same size inoculum?
Time (h)
Cell Concentration (g/l)
Glucose Concentration (g/l)
1.25
100 9
2.45 97 16
5.1
90.4 23
10.5
76.9 30 22
48.1 34 33
20.6 36
37.5
9.38 40 41
0.63

24. Solution a) A plot of ln X versus t has a slope of
(the maximum specific growth rate).
Therefore, from the plot = h-1 b)
The apparent growth yield coefficient is: c)
The maximum cell concentration could one expect if 150 g of glucose were used with the same size inoculum:

25. How Environmental Conditions Affect Growth Kinetics
The patterns of microbial growth and product formation are affected by:
Temperature of the medium
pH of the medium
Dissolved oxygen concentration

26. Effects of Temperature
Microorganisms can be classified (according to their temperature optima) to:
Psychrophiles (Topt<20 °C)
Mesophiles (20<Topt<50 °C)
Thermophiles (Topt>50 °C)
When the temperature increased, the growth rate also increased until we reach the optimal temperature. Any further increase in the temperature above the optimal temperature will cause cell death.

27. Effects of Temperature
The net growth rate above the optimal temperature can be expressed as:
and vary with temperature as follows:
What is the net effect of the two functions of T?

28. Biological reaction rate is similarly affected relative to diffusion.
At high T:
Rate determining mechanism may shift with T.

29. Effects of pH
Affects microbial growth through influencing growth enzyme activity.
pH optima: bacteria 3-8, yeast 3-6, molds 3-7, plant cells 5-6, animal cells
pH varies significantly during fermentation if pH of the system is not controlled well.
CO2 evolution and ammonium consumption as nitrogen source both lower pH.
Nitrate utilization raises pH.

30. Dissolved Oxygen (DO) Requirements
DO can become limiting substrate.
At high DO concentration, growth is independent of [O2].
O2 saturated concentration in pure water ~7 ppm (at 25 C and 1 atm).
Bacteria and yeast require ~10% of saturation for [O2] independent growth, while mold requires 10-50%.

31. Dissolved Oxygen Requirements
O2 introduced to cells by pumping air through the growth medium.
Rate of O2 transfer usually limited by stagnant liquid film around bubbles.
When O2 transfer is limiting, OTR=OUR (oxygen transfer rate = oxygen uptake rate), so …

32. Quantifying Growth Kinetics
Structured versus unstructured (cell composition does not change with time).
Segregated versus unsegregated (all cells are identical).
There are four different combinations (structured segregated model, structured unsegregated model, unstructured segregated model, and unstructured unsegregated model)

33. Using Unstructured Unsegregated Models to Predict Specific Growth Rate
These models assume:
Fixed cell composition (balanced growth)
No variations in cell concentration and growth rate throughout the cell growth medium (culture)

34. Monod Equation Single substrate controls growth.
Analogous to Michaelis-Menten enzyme kinetics.
Mechanistic if only one enzyme system controls growth.

35. Monod Equation

36. Other Models for Cell Growth
There are other unsegregated unstructured models for cell growth such as:
Blackman Equation:
Tessier Equation:
Moser Equation:
Contois Equation:

37. Models with Growth Inhibitors
Inhibitory kinetic expressions are not typically mechanistic, but are selected to fit data.
Expressions are analogous to inhibited enzyme kinetics.

38. 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.

39. Growth Inhibition by Product
Competitive
Noncompetitive

40. Growth Inhibition by Toxic Compounds
Competitive
Noncompetitive
Uncompetitive

41. How Cells Grow in Continuous Culture
CO2 and air out
Substrate
Cells
Substrate
Products
Chemostat (constant chemical environment) or continuous flow stirred tank reactor (CSTR)
Air or oxygen

42. Instrumentation pH probe and controller DO probe and controller
Antifoam probe and controller
Level probe and controller
Nutrient addition pump
Agitation rate controller

43. The Ideal Chemostat Let: 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 (usually =0)
S0= substrate concentration in the feed
P0= product concentration in the feed (usually =0)

44. Cell Mass Balance Mass balance on cells: Define: So: accum
in out + growth - death =
(1)
(2)
(3)

45. Steady-state operation
For kd<<µg, dX/dt=0, and X0=0
For Monod kinetics:
(4)
Can use to find µm and Ks
(5)
Or:
(6)
If D> μm, the culture cannot reproduce quickly enough to maintain itself
and therefore it is washed out of the reactor.

46. 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)

47. Equation for Cell (Biomass) Concentration (when kd=0)
Since µg=D, at steady state (for kd=0):
(9)
Using the equation for substrate concentration based on cell mass balance at s.s. (Eq. 6):
(10)

48. Allowing for endogenous metabolism (kd > 0):
Recall:
(3)
Assume s.s. and X0=0, but allow for significant endogenous metabolism:
(11)

49. Equation for Cell (Biomass) Concentration (when kd>0)
Subst. Eq. (11) into Eq. (8):
(12)
(13)
or:
Compare to Eq. (9) when kd=0, which is:
(9)

50. Finding the True Yield Coefficient
Rearranging equation (13) gives:
(14)
or:
(15)
Where:

51. Determining True Yield Coefficient
(16)
or:
(17)
Where:
(maintenance coefficient)

52. Figure 6.19

53. Product Generation Product mass balance: (18)
At steady state and letting F/VR=D:
(19)
From Eq. (11) and Eq. (7) at s. s.:
(20)

54. Cell Productivity with Endogenous Metabolism (kd>0)
For substrate balance accounting for nonzero kd, Eq. (6) becomes:
(21)
Solving Eq. (20) for X, the cell (biomass) concentration:
(22)

55. Cell Productivity with Endogenous Metabolism (kd>0)
Substituting S from Eq. (21) into Eq. (22):
(23)
Combining Eq. (22) and Eq. (19):
(24)
where PrP is the product productivity in g. product/liter/hour

56. Productivity with Endogenous Metabolism (kd>0)
Or substituting S from Eq. (21) into Eq. (24):
(25)

57. Example 6.4
A new strain of yeast is being considered for biomass production. The following data were obtained using a chemostat. An influent substrate concentration (S0) of 800 mg/l and an excess of oxygen were used at pH 5.5 and T=35 C. Using the following data, calculate , , , , and , assuming
Dilution rate, D, (h-1)
Carbon substrate concentration, S, (mg/ml)
Cell concentration, X, (mg/l)
0.1
16.7
366
0.2
33.5
407
0.3
59.4
408
0.4
101
404
0.5
169
371
0.6
298
299
0.7
702 59

58. Example 6.4: Solution Using Eq. (17) and from the plot of versus .
is calculated from X/(S0-S) D
S (mg/ml)
1/D
0.1
16.7 10
0.2
33.5 5
0.3
59.4
0.4
101
2.5
0.5
169 2
0.6
298
0.7
702
S0=800 mg/l
From the plot, y-intercept= 1/ = , therefore = g X/g S
From the plot, Slope= =
But = / , therefore = = h-1

59. Example 6.4: Solution (Cont.)
To find and , we use:
From the plot of versus , the slope is and the y-intercept is . D S
1/(D+kd)
1/S
0.1
16.7
0.2
33.5
0.3
59.4
0.4
101
0.5
169
0.6
298
0.7
702
= h-1
From the plot, y-intercept= = , therefore = h-1
From the plot, Slope= = , therefore =Slope = 83.0 mg/l

60. Example 6.5
The specific growth rate for inhibited growth is given by the following equation:
Where: , , ,
, , ,
Determine X and S as a function of D when I=0
With inhibitor added to a chemostat, determine the effluent substrate concentration (S) and X as a function of D
Determine cell productivity, DX, as a function of D.

61. Example 6.5: Solution Determine X and S as a function of D when I=0
b) With inhibitor added to a chemostat, determine the effluent substrate concentration (S) and X as a function of D
c) Determine cell productivity, DX, as a function of D.

62. Assignment Three
6.11
6.17
9.4
9.11
Due date 18/12/2011 during lecture. LATE SUBMISSION WILL NOT BE ACCEPTED.
There will be Quiz (Chapters 6 and 9) on the same day

63. End of Chapter Six