And 22

1
Growth - Overview
Microbial Growth Overview of terms exponential
growth u td productivity Substrate limitation of
metabolism Link between metabolism and growth
2
Growth - Overview

• Microbial Growth I
• Energy metabolism overview glycolysis, TCA
  cycle, respiration chain, ATP synthase
• Growth medium components, energy, carbon,
  nitrogen, phosphorus sources , minerals, trace
  elements, buffer
• Growth rate, specific growth rate, exponential
  growth, semilog plot, maximum and total
  productivity, lag phase

3
Growth - Overview

• Microbial Growth II
• Substrate limitation
• Michaelis Menten model of substrate dependent
  substrate uptake rate vmax, km
• The yield coefficient connects the Michaelis
  Menten Model to the Monod model of substrate
  dependent growth rate, umax, ks
• Yield coefficient measurements
• Yield coefficient is not constant
• Maintenance coefficient
• Pirt model contains 4 growth constants, ms, Ymax

4
Growth - Overview

• Microbial Growth III
• Maintenance coefficient
• Microbial Growth IV
• Growth in batch culture
• Microbial Growth V
• Chemostat
• Microbial Growth VI
• Determining growth constants
• Biomass retention

5

• 1 Growth Medium Ingredients
• 1.1 The rationale of media recipes
• Bacterial cells typically grow by cell division
  into two daughter cells. To do this they require
  a suitable growth medium. Growth media recipes in
  the literature vary widely and it can be
  confusing to students to discriminate between
  essential ingredients and replaceable ones.
  Rather than blindly following recipes, it would
  be more useful for microbiologists to be able to
  design own media, or to modify or optimise
  exiting media. For this it is useful to
  understand the generic microbial growth
  requirements. The ingredients of a typical growth
  medium satisfy a number of principal needs of
  growing cells by providing a source of Energy,
  carbon, nitrogen, phosphate, sulfur, minerals,
  trace elements, vitamins, growth factors, buffer
  capacity.
• 1.2 Energy source
• Microbial growth (assimilation) is an endergonic
  process and requires energy input for the
  conversion of ingredients from the growth medium
  into biomass. This energy is derived from the
  energy source component of the growth medium.
  Typically an energy source consists of a suitable
  electron donor and electron acceptor. It is the
  transfer of electrons from the electron donor (a
  redox couple that of a more negative potential
  than that of the electron accepting redox couple)
  to the acceptor that liberates energy which is
  conserved as ATP. The ATP is typically generated
  during this electron transfer via electron
  transport phosphorylation (electron carriers,
  electron transport chain, proton gradient, ATP
  synthase).
• For most bacteria the electron donor is an
  organic compound being oxidised to CO2 and the
  electron acceptor is oxygen, which is supplied by
  allowing air access to the growht container (e.g.
  petri dishes or shake flasks). However many
  bacteria use inorganic reduced chemical species
  as the electron donor, such as ferrous iron,
  sulfide, ammonia, or hydrogen gas which supply
  electrons by being oxidised to ferric iron,
  sulfate, nitrite or protons, respectively.
  Electron accepting species alternative to oxygen
  are can be ferric iron, nitrate, sulfate, CO2,
  etc. which accept electrons by being reduced to
  ferrous iron, N2, sulfide and methane
  respectively. When supplying specific electron
  acceptors it needs to be considered that the
  presence of multiple potential electron acceptors
  can cause mutual inhibition. For example the
  presence of oxygen inhibits the reduction of
  nitrate, sulfate and CO2 while the presence of
  nitrate inhibits the reduction of sulfate and
  CO2. The use of external electron acceptors other
  than oxygen is still a respiration (anaerobic
  respiration).
• If a suitable electron donor and electron
  acceptor is provided this enables the bacteria to
  generate ATP by harnessing the energy liberated
  from the flux of electrons from electron donor to
  electron acceptor.

6

• 1.3 Carbon source
• The carbon source for microbial growth is
  typically an organic compound and is often
  identical to the electron donor. For example an
  aerobic bacterium growing by oxidising sugar to
  CO2 for ATP generation will also use the same
  sugar as a starting material for biomass
  synthesis. The sugar may be partly degraded via
  glycolysis to pyruvate or even to Acetyl-CoA to
  use parts of the TCA cycle for biomass synthesis
  purposes (compare to pathway of glutamate
  formation later in this text). The ratio of
  carbon that is used as energy source (catabolism,
  dissimilation) or as carbon source for biomass
  synthesis (anabolism, assimilation) determines
  the bacterial yield coefficient. Aerobic bacteria
  degrading a sugar use about 40 to 50 of the
  carbon for assimilation and the rest for energy
  generation. Hence a yield coefficient of 0.4 to
  0.5 (g of microbial cells formed per g or carbon
  source used) is commonly observed.
• In rare but interesting cases no formal carbon
  source needs to be provided to the growth medium.
  This is the case for autotrophic bacteria.
  Similar to plants and algae, autotrophic bacteria
  use CO2 as the carbon source which can be
  obtained from the air supply. However the
  additional supply of CO2 via a bicarbonate buffer
  (HCO3- H ? H2CO3 ? CO2 H2O) helps the
  growth of autotrophs by minimising CO2 limiting
  conditions. Examples of autotrophic bacteria with
  industrial and environmental significance
  include nitrifying bacteria that use NH3 as
  electron acceptor and Fe2 and sulfur oxidising
  bacteria. These bacteria of the genera
  Nitrosomonas and Thiobacillus are used for
  nitrogen removal from wastewater and bioleaching
  of ores respectively.
• 1.4 Nitrogen source
• Nitrogen is next to carbon, hydrogen and oxygen
  (the latter two are sourced from water) the
  quantitative most important element. Nitrogen is
  needed for the synthesis of enzymes and other
  proteins. In minimal media it is typically
  supplied as ammonium or nitrate salts, in rich
  media it is supplied as an organic nitrogen
  source (e.g. part of yeast extract or peptone
  based media). With nitrate as the nitrogen source
  the bacteria need to first reduce the nitrate to
  ammonia (assimilative nitrate reduction) followed
  by ammonia assimilation into biomass.
• Some bacteria are capable of using the relatively
  inert (triple bond) N2 from air as the nitrogen
  source. Hence selective media for such nitrogen
  fixing bacteria do not include any nitrogen
  source.

7

• 1.3 Phosphate source
• The next most important element for microbial
  growth is phosphorous. In contrast to the other
  elements in biomass, phosphorus does not undergo
  oxidation or reduction and stays in its phosphate
  status (hence phosphate source). Phosphate needs
  to be present in all microbial growth media,
  without it growth cannot occur. Phospholipids and
  ATP are two examples of essential phosphate
  containing cell components. Rich media produced
  from biomass hydrolysates (e.g. yeast extract or
  peptone) contain organic phosphate compounds.
• Many media use manifold more phosphate than
  necessary for biosynthetic purposes (e.g. about
  50 mM). Here phosphate serves as the buffer
  species for pH control. While phosphate buffers
  are typically recommended to be added in two
  components, the more acidic phosphate (KH2PO4)
  and the more basic phosphate (K2HPO4) to result
  in a precise pH of the final media, it can also
  be provided by other phosphate sources followed
  by adjustment of the pH to a precise setpoint by
  any suitable acid or base. This pH adjustment
  will result in producing the same ratio of
  hydrogen and dihydrogen phosphate as suggested by
  the original recipe.
• 1.4 Sulfur source
• Sulfur is needed for protein synthesis and hence
  essential to all growth media. For aerobic media
  sulfur is added as sulfate, which the bacteria
  reduce (assimilatory sulfate reduction) to
  sulfide prior to assimilation into amino acids.
  Alternative sulfur sources are sulfide (for
  anaeroboic media) or organic sulfur sources such
  as yeast extract or cysteine.

8
OUR- Growth medium for microbes
Components of Growth Medium Energy source
(electron donor and acceptor) C-source (e.g.
sugar) N-source (e.g. NaNO3) P-source (e.g.
KH2PO4) other minerals (e.g. NaMg, SO42-, Trace
elements (e.g. Co, Mn, Fe, etc) Vitamins (e.g.
cyanocobalamin) Buffer (e.g. carbonate or
phosphate buffer)
9
Growth- Overview of Energy Metabolism Dissimilati
on simplifying FAD and ATP genration in TCA
glucose
TCA cycle
glucolysis
1 ATP ? 3 H
ATP synthase
2 ATP 12 NADH
Cell
Overall 38 ATP allowing growth
ETC
each NADH ? 9 H
O2
10
Growth- Simplified Scheme of Energy preservation
as ATP
Important Quantities ATP-synthase 3H ? 1
ATP ETC 1 NADH ? 33 9 H 2 NADH reduce 1 O2 1
NADH 2 electron equivalents 1 O2 accepts 4
electron equivalents glycolysis 1 glucose ? 12
NADH 1 glucose ? 129108 H 36 ATP 2 ATP
from glycolysis via substrate level
phosphorylation 38 ATP
11
Growth- Simplified Scheme of Energy preservation
as ATP
Minor corrections not needed for exams During
TCA cycle not only NADH is produced but also FAD.
FAD translocates only 2 H rather than 3 ?
hence 2 less ATP. However TCA also generates 2
ATP not mentioned in simplified balance.
12
Growth- Exponential
Multiplication by binary fission
0 min
30 min
60 min
1, 2, 4, 8, 16, 32 ? exponential
13
Growth- Exponential (split split split )
The resulting seqeunce in numbers is exponential
( 2, 4, 8, 16, 32)
14
Growth- Exponential (split split split )

• The resulting sequence in numbers is exponential
  ( 1,2, 4, 8, 16, 32).
• Not only the biomass (X) increases exponentially
  but also the rate at which it is produced
  (calculate from above)
• growth rate is NOT constant in batch culture
  (similar to OTR not being constant)
• needed a constant that describes the speed of
  binary fission (similar to kLa in oxygen
  transfer)
• Plotting the growth rate as a function of time
  will reveal

15
Growth- Exponential (split split split )
Not only biomass (X) increases exponentially, but
also the rate at which it is produced.
The proportionality factor is µ the specific
growth rate
dX/dt µ X
(g/L.h)
(h-1)
(g/L)
16
not examinable dX/dt µ X dx u n X
dt dx/X u dt ?dx/x ? udt ?1/x dx ?
udt lnx ut c x e utc x e ut ec for t
0 xxo xo e ut ec Hence x e ut xo
17
Growth- Estimation of u from single interval
0.023 min-1
1.3847 h-1
Doubling time
0.5 h
18
Growth- Estimation of doubling time from semilog
plot
When plotting the log of cell mass versus time a
straight line is obtained. The slope of the line
reveals the doubling time. The specific growth
rate can be calculated from the doubling time
by Advantage of plot averaging out, avoiding
outliers
19
Growth- Limitation and growth phases

• Growth in batch culture can not continue forever
• Typical industrial growth curve incl.
• preparation time (clean, sterilise, fill)
• lag phase
• log phase
• stationary phase
• decay phase

X (g/L)
Time (h)
20
Growth- Limitation and growth phases
log
lag
21
Growth- Productivity in industrial batch cultures
Most important to industryproductivity of the
process (g.L-1.h-1). Productivity is the overall
product (here biomass X) concentration produced
per time required. The process can be stopped
for maximum productivity or maximum product
concentration (total productivity) Choice
depends on cost of operation and product
maximum productivity
X (g/L)
total productivity
Time (h)
22
Growth- Substrate Limitation
In most environmental and many industrial
bioprocesses (e.g. chemostat), the growth rate is
limited by substrate availability. Substrate
uptake rate at different substrate concentrations
is important (limitation and saturation of
substrate)
substrate saturation
Substrate (g/L)
substrate limitation
Time (h)
23
Growth- Substrate Limitation
Substrate uptake rate at different substrate
concentrations is important
substrate saturation
v (g/L/h)
substrate limitation
Substrate (g/L)
24
What is the relationship between substrate
concentration (S) and its uptake rate (v) ?
Growth- Michaelis Menten model
vmax (h-1)
v (h-1)
substrate limitation
Described by Michaelis-Menten kinetics (standard
biochemistry knowledge)
S (g/L)
kM
Growth- Michaelis Menten model
25
Growth- Relationship between Michaelis Menten
kinetics and and Monod kinetics
Michalis Menten Model predicts substrate uptake
fromsubstrate concentration Monod Model
predicts specific growth rate from substrate
concentration Under substrate limitation ?
Substrate concentration ? ? Substrate uptake
rate (SUR) ? ? ATP production rate ? ? rate of
producing new cells (u)
Growth- Michaelis Menten model
26
End of Lec1 on Growth
27
Growth- Relationship between Michaelis Menten
kinetics and and Monod kinetics
Michalis Menten Model predicts substrate uptake
fromsubstrate concentration Monod Model
predicts specific growth rate from substrate
concentration Under substrate limitation ?
Substrate concentration ? ? Substrate uptake
rate (SUR) ? ? ATP production rate ? ? rate of
producing new cells (u)
Growth- Michaelis Menten model
28
What is the relationship between substrate
concentration (S) and its uptake rate (v) ?
Growth- Michaelis Menten model
µ (h-1)
Described by Michaelis-Menten kinetics (standard
biochemistry knowledge)
Growth- Michaelis Menten model
29
Growth- Relationship between Michaelis Menten
kinetics and and Monod kinetics

• What is the relationship between specific growth
  rate (µ) and specific substrate uptake rate (v)
• Relationship is given by the
• yield coefficient Y (g of X formed
• per g of S degraded).
• v substrate uptake rate (SUR)
• but can also be OUR
• Note unlike µmax and kS, Y is
• not a true growth constant.
• kS and kM are equivalent

µ Y v
S
µ Y vmax --------
kS
S
Growth- Michaelis Menten model
30
Substrate limitation of microbial growth
The two curves are described by two
properties The maximum specific growth rate
obtained with no substrate limitation (umax
(h-1)) and the half saturation constant
(Michaelis Menten constat), giving the substrate
concentratation at which half of the maximum u is
reached (ks (g/L)).
Growth- Michaelis Menten model
31
Substrate limitation of microbial growth
Typically there are low and high substrate
specialists and ecological substrate niches
for the specialists to outcompete each other
µ (h-1)
Substrate (g/L)
kS
kS
Growth- Michaelis Menten model
32
Substrate limitation of microbial growth
To be most competitive against other microbes a
low ks value and a high umax value are
important. This simplified growth model only
uses 2 out of 4 growth constants.
Growth- Michaelis Menten model
33
Substrate limitation of microbial growth
There is also room for medium substrate
allround specialists
µ (h-1)
Substrate (g/L)
kS
kS
Growth- Michaelis Menten model
34
Substrate limitation of microbial growth
With the same ks the organism with a higher µmax
will always win.
µ (h-1)
Substrate (g/L)
kS
Growth- Michaelis Menten model
35
Substrate limitation of microbial growth
With the same same umax the organism with a lower
ks will always win.
µ (h-1)
Substrate (g/L)
kS
Growth- Michaelis Menten model
36
Conclusions substrate limitation

• Substrate limitation slows down metabolism
• Slowed metabolism slows growth (how? via Y!)
• The limitation effect can be quantified
  (S/(SkS))
• The quantifier term has values between 0 and 1
• e.g. if SkS then u is half of umax
• different microbes have different kS
• competition between microbes is determined by kS
  and umax
• What is missing -- maintenance, death, Ymax

Growth- Michaelis Menten model
37
Microbial Growth
Comparison of µmax and kS for competition
under Substrate limitation
Which of the two growth constants influences to a
larger extent The growth of an organism under
substrate limitation (substrate Concentration
approaches zero)
Approach 1.
For S approaching zero the µmax term approaches
zero. Thus it appears that µ would be mainly
influenced by kS (Textbook explanation).
Growth- Michaelis Menten model
38
Microbial Growth
Comparison of µmax and kS for competition
under Substrate limitation
Approach 2.
Question is doubling of µmax (strain A) or
halving of kS (strain B) having a larger effect
on µ?
µmax(B) S
µmax(A) S
µ(B)
µ(A)
ks(B) S
ks(A) S
To compare growth rate of strain A and B µ(A)
µ(B)
µmax(A) S
µmax(B) S

ks(A) S
ks(B) S
µmax(A)
µmax(B)

ks(A) S
ks(B) S
Growth- Michaelis Menten model
39
2
1

1 0.1
0.5 0.1
1.82 gt 1.67
At all substrate concentrations µmax is more
important than kS
Growth- Michaelis Menten model
40
Microbial Growth
Dependence of Biomass concentration on substrate
used (Yield Coefficient) - Intro
Final X in several batch cultures with increasing
S
X (g/L)
Substrate Concentration (g/L)
Substrate inhibition
Growth ceased because of endproduct inhibition
Growth ceased because of lack of substrate
Growth- Yield Coefficient
41
Microbial Growth
Dependence of Biomass concentration on substrate
used (Yield Coefficient) - Intro
In the absence of inhibition the biomass formed
is correlated to the substrate used (X)
X (g/L)
The correlation factor is the Yield Coefficent
(dimensionless, X/S)
S (g/L)
Typical Y for aerobes on glucose 0.4 to 0.5
Growth- Yield Coefficient
42
Microbial Growth- Yield Coefficient Y
Microbial processes not only turn substrate to
products Because of Y there will be new biomass
formed Resulting for aerobic processes in the
following E.g. Substrate Oxygen ? Products
Biomass An empirical formula for biomass can be
given as CH1.8O0.5N0.2 Formula just an
approximation and varies with different
microbes. Formula is useful to establish carbon
or electron balance for bioprocesses (e.g.
BioProSim)
Growth- Yield Coefficient
43
E.g. Gluconate degradation by Klebsiella
Ideal biocatalyst
a. By resting Cells (non growing)
1 gluconate ? 1.5 acetate 0.5 ethanol 2
formate
b. By growing cells
1 gluconate 0.174 NH3 0.04 H2O ? 1.4 acetate
0.3 ethanol 1.7 formate 0.87 CH1.8O0.5N0.2
Thus Growing cells incorporate 14.5 of carbon
from Gluconate into cell growth resulting in
increased acetate/ethanol ratio.
Growth- Yield Coefficient
44
Microbial Growth
Significance of Special Yield Coefficients
X (g/L)

• Only works for same substrate, pathway

YS
S (g/L)
X (g/L)
Molar yield coefficient
S (mol/L)

• Works only for aerobes and for same
• ATP/O2

X (g/L)
YO2
O2 (mol/L)
works for unknown or complex substrates (e.g.
cornsteep liquor, wastes
Growth- Yield Coefficient
45
Microbial Growth
Significance of Special Yield Coefficients
Similar to YO2 but works also for other
electron acceptors
X (g/L)
Ye
Mole of reducing equivalents respired
Works also for fermenting Bacteria, and
unknown Substrates and pathways
X (g/L)
YkJ
kJ of heat of combustion
For scientific purposes under N or P limitation
X (g/L)
YN, YP
Mole of N or P
Growth- Yield Coefficient
46
Microbial Growth
YATP
X (g/L)
YATP
Mole of ATP

• completely comparable between different
  physiological types
• can compare efficiency of growth for aerobes
  and anaerobes
• requires knowledge about how much ATP is gained
• Note Moles of ATP generated can be estimated
• for many pathways
• e.g. glycolysis to pyruvate 2 ATP
• consumption of 1 mole of O2 2 NADH 4
  electrons ? 6 ATP
• For rich media where all cell building blocks are
  provided
• (e.g. Yeast Extract) YATP 10.5 g/mol

Growth- Yield Coefficient
47
Microbial Growth
YATP
Comparison of YS and YATP for glucose fermenting
bacteria
YATP gX/ mol ATP
ATP Yield (mol ATP/ mol substance)
YS
Organism
Streptococcus lactis
19.5
2
9.8
Lactobacillus plantarum
18.5
2
9.4
Saccharomyces cerevisiae
18.5
2
9.4
Zymomonas mobilis
9
1
9
Aerobacter aerogenes
29
3
9.6
E. coli
26
3
8.6
The literature valuefor YATP is given as 10.5 g
biomass/ mol ATP (Baushop and Elsden 1960)
Growth- Yield Coefficient
48
Microbial Growth
Calculation and Inconsistencies of YATP

• ATP gained per mole of substrate can be estimated
  for
• bacteria growing in rich media from Ys if the
  YATP is known
• (e.g. 10.5 g/ATP)
• E.g. If Ys 21 g/mole of substrate ? about 2
  mole of ATP
• generated per mol of substrate
• Although the YATP is more consistent than any
  other way of
• expressing the yield coefficient it can also
  vary
• Not constant for all microbes (4.7 to 21) in rich
  media
• Experimental YATP lt theoretical YATP (30 g/mol
  ATP)
• Low YATP on minimal media
• YATP dependent on growth conditions (ease of
  life)
• ? temperature ? ? YATP (thermal denaturation of
  proteins)
• Unsuitable growth conditions ? ? YATP
• Likely Reason for less cells formed Higher ATP
  usage for cell maintenance rather than cell
  growth ? Maintenance coefficient

Growth- Yield Coefficient
49
Microbial Growth
Maintenance Coefficient

• 1 mole of ATP generated during catabolism allows
• theoretically ? synthesis of 32 g cells
• in praxis ? 10.5 g cells
• The maintenance coefficient (ms) is the reason
  for
• 2/3 being wasted
• Substrate transport into cell (e.g. against
  diffusion gradient)
• Osmotic work
• Motility
• Intracellular pH
• Replacement of thermally denatured proteins (? T
  ? ? ms)
• Leakage of H ions across membrane (uncoupling)
• ms influences Y, µ and the metabolic activity of
  the cells and
• is thus important to be considered in
  bioprocesses.

Growth- maintenenace
50
Effect of Maintenance Coefficient on Growth Rate
What is maintenance coefficient? The energy
supply rate needed to maintain the life functions
of a non growing cell. Units? strictly speaking
mol ATP/ cell/ h mostly used g substrate / g
biomass / h (h-1)
Growth- maintenenace
51
Effect of Maintenance Coefficient on Growth Rate

• What does the maintenance coefficient (mS)
  affect?
• ms is the reason for Y not being constant.
• ms ? ? Y hence
• ms ? ? u (compare slide)
• Why? Because some substrate is taken up just for
  maintenance, not for growth.
• Effect is more apparent in slow growing cultures
  than in fast growing cultures.
• Slow growing cultures can have a very low Y .
• mS (gS/gX/h) Ymax (gX/gS) Decay rate (h-1)

Growth- maintenenace
52
Effect of maintenance coefficient on growth rate
Effect of mS on Y? Y is the observed yield
coefficient. The maximum yield coefficient Ymax
is approached only when u umax Ymax is one of
four growth constants
Ymax
Y (gX/ gS))
Specific Growth rate u (h-1)
Growth- maintenenace
53
Effect of maintenance coefficient on growth rate

• mS and Ymax can be combined
• mS (gS/gX/h) Ymax (gX/gS) Decay rate (h-1)
• The Pirt equation of growth includes all four
  growth constants

Growth- maintenenace
54
Effect of maintenance coefficient on growth rate
ms the respiration activity used to just stay
alive
u (v mS) Ymax
S
u ( vmax -------- - mS) Ymax
S kS
S
µ Ymax vmax -------- - mS Ymax
S kS
substrate uptake
Growth- maintenenace
55
Effect of Maintenance Coefficient (mS) on growth
Rate
ignoring mS
µ (h-1)
0
including mS
S(g/L)
56
Effect of Maintenance Coefficient (mS) on growth
Rate
Sm critical substrate concentration ? growth is
zero
µ (h-1)
mS.kS.Ymax
sm ------------------
umax- ms.Ymax
0
S(g/L)
Sm
Growth- maintenenace
57
Effect of Maintenance Coefficient (mS) on growth
Rate
The negative specific growth rate (µ) observed in
the absence of substrate (when S 0) (cells are
starving, causing loss of biomass over time) is
the decay rate mSYmax
µ (h-1)
0
S(g/L)
- mSYmax
58
Points about ms

• ?ms ? more heat produced (e.g. uncoupler)
• when S 0 and u is negative (decay rate) then any
  oxygen uptake is via endogenous respiration.

Growth- maintenenace