Microbial Growth – Overview of terms: exponential growth u td productivity

Microbial Growth –Overview of terms:exponential growthutdproductivitySubstrate limitation of metabolismLink between metabolism and growth

Growth - Overview

And 11

Microbial Growth I

1) Energy metabolism overview: glycolysis, TCA cycle, respiration chain, ATP synthase

2) Growth medium components, energy, carbon, nitrogen, phosphorus sources , minerals, trace elements, buffer

3) Growth rate, specific growth rate, exponential growth, semilog plot, maximum and total productivity, lag phase

Growth - Overview

And 22

Microbial Growth II –

1) Substrate limitation

2) Michaelis Menten model of substrate dependent substrate uptake rate vmax, km

3) The yield coefficient connects the Michaelis Menten Model to the Monod model of substrate dependent growth rate, umax, ks

4) Yield coefficient measurements

5) Yield coefficient is not constant

6) Maintenance coefficient

7) Pirt model contains 4 growth constants, ms, Ymax

Growth - Overview

And 33

Microbial Growth III –Maintenance coefficient

Microbial Growth IVGrowth in batch culture

Microbial Growth VChemostat

Microbial Growth VIDetermining growth constantsBiomass retention

Growth - Overview

And 44

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.

And 55

1.3 Carbon sourceThe 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 sourceNitrogen 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.

And 66

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.

And 77

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. Na+Mg+, SO42-,Trace elements (e.g. Co, Mn, Fe, etc)Vitamins (e.g. cyanocobalamin)Buffer (e.g. carbonate or phosphate buffer)

OUR- Growth medium for microbes

And 88

glucose

TCA cycle

ETC

ATPsynthase

1 ATP 3 H+

glucolysis

2 ATP + 12 NADH

each NADH 9 H+

Overall:38 ATPallowing growth

Cell

O2

Growth- Overview of Energy Metabolism=Dissimilation

simplifying FAD and ATP genration in TCA

And 99

Important Quantities:

ATP-synthase: 3H+ 1 ATP

ETC: 1 NADH 3*3 = 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 12*9=108 H+ = 36 ATP

+ 2 ATP from glycolysis via substrate level phosphorylation = 38 ATP

Growth- Simplified Scheme of Energy preservation as ATP

And 1010

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.

Growth- Simplified Scheme of Energy preservation as ATP

And 1111

Multiplication by binary fission:

0 min

30 min

60 min

1, 2, 4, 8, 16, 32 → exponential

Growth- Exponential

And 1212

The resulting seqeunce in numbers is exponential ( 2, 4, 8, 16, 32)

Growth- Exponential(split… split… split )

And 1313

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


And 1414

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)

Thus: dX/dt X , dX/dt = factor • X˜

Xt = XoeμtIntegration gives

Take ln of both sides

μ indicates how much more biomass is producedper biomass present (g/h/g) = (h-1)

ln(Xt) = ln(Xo) + μt

μ = (In(Xt) – In(Xo))t


And 1515

not examinable:dX/dt = μ * Xdx = u *n X * dtdx/X = u * dt∫dx/x = ∫ udt∫1/x * dx = ∫ udtlnx = ut +cx = e ut+c

x = e ut *ec

for t= 0: x=xo

xo = e ut *ec

Hence:x = e ut *xo 16

Growth- Estimation of u from single interval

= 0.023 min-1

= 1.3847 h-1

μ =InXt – ln Xo

t

=In 8 – In 2

90 min

=2.77 – 0.693

90 min

=90 min

2.077

Doubling time = =In 2

μ 0.69

1.38 h-1

= 0.5 hAnd 1717

When plotting the log of cell mass versus timea straight line is obtained.

The slope of the line revealsthe doubling time.

The specific growth ratecan be calculated from thedoubling time by:

Advantage of plot: averagingout, avoiding outliers

Growth- Estimation of doubling time from semilog plot

And 1818

Growth in batch culture can not continue forever

Typical industrial growth curve incl.:

preparation time (clean, sterilise, fill)lag phaselog phasestationary phasedecay phase

X(g/L)

Time (h)

Growth- Limitation and growth phases

And 1919

loglag

Growth- Limitation and growth phases

And 2020

Most important to industry:productivity 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

X(g/L)

Time (h)

maximum productivity

total productivity

Growth- Productivity in industrial batch cultures

And 2121

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(g/L)

Time (h)

substrate saturation

substrate limitation

Growth- Substrate Limitation

And 2222

Substrate uptake rate at different substrate concentrations is important

v(g/L/h)

Substrate (g/L)

substrate saturation

substratelimitation

Growth- Substrate Limitation

And 2323

What is the relationship between substrate concentration (S) and its uptake rate (v) ?

Described by Michaelis-Menten kinetics (standard biochemistry knowledge)

v = vmax -------kMS +S

v(h-1)

S (g/L)

substratelimitation

kM

vmax(h-1)

Growth- Michaelis Menten model


And 2424

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- Relationship between Michaelis Menten kinetics and and Monod kinetics


And 2525

End of Lec1 on Growth

And 2626

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)



And 2727

What is the relationship between substrate concentration (S) and its uptake rate (v) ?

Described by Michaelis-Menten kinetics (standard biochemistry knowledge)


µ(h-1)



S (g/L)

substratelimitation

kS

µmax(h-1)

And 2828

µ = Y * vmax --------kSS +S

•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




And 2929

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)).

Substrate limitation of microbial growth


And 3030

S (g/L)

substratelimitation

kS

µmax(h-1)


µ = µmax * ----------kSS +S

µ(h-1)

Substrate (g/L)kS

Typically there are low and high substrate specialists and

ecological “substrate niches” for the specialists to outcompete each other

kS


And 3131


µ = µmax * ----------kSS +S

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.


And 3232

S (g/L)

substratelimitation

kS

µmax(h-1)


µ = µmax * ----------kSS +S

µ(h-1)

Substrate (g/L)kS

There is also room for medium substrate “allround” specialists

kS


And 3333


µ = µmax * ----------kSS +S

µ(h-1)

Substrate (g/L)kS

With the same ks the organism with a higher µmax will always win.


And 3434


µ = µmax * ----------kSS +S

µ(h-1)

Substrate (g/L)kS

With the same same umax the organism with a lower ks will always win.


And 3535

Conclusions – substrate limitation

• Substrate limitation slows down metabolism• Slowed metabolism slows growth (how? via Y!)• The limitation effect can be quantified (S/(S+kS))• The quantifier term has values between 0 and 1• e.g. if S=kS 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


And 3636

Microbial GrowthComparison of μmax and kS for competition under

Substrate limitation

Which of the two growth constants influences to a larger extentThe growth of an organism under substrate limitation (substrateConcentration approaches zero)

Approach 1.

μ =μmax • Sks + S

For S approaching zero the μmax term approaches zero.Thus it appears that μ would be mainly influenced by kS(Textbook explanation).


And 3737

Microbial GrowthComparison 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?

μ(A) =μmax(A) • Sks(A) + S

μ(B) =μmax(B) • Sks(B) + S

To compare growth rate of strain A and B: μ(A) = μ(B)

μmax(A) • Sks(A) + S

μmax(B) • Sks(B) + S

=

μmax(A)

ks(A) + Sμmax(B)

ks(B) + S=


And 3838

21 + 0.1

10.5 + 0.1

=

1.82 > 1.67

At all substrate concentrations μmax is more important than kS


And 3939

Microbial GrowthDependence 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)

Growth ceasedbecause of lackof substrate

Growth ceasedbecause ofendproductinhibition

Substrateinhibition

Growth- Yield Coefficient

And 4040

Microbial GrowthDependence of Biomass concentration on substrate used

(Yield Coefficient) - Intro

X (g/L)

[S] (g/L)

In the absence of inhibition thebiomass formed is correlated tothe substrate used (X)

The correlation factor is theYield Coefficent (dimensionless, X/S)

Typical Y for aerobes on glucose: 0.4 to 0.5


And 4141

Microbial Growth- Yield Coefficient Y Microbial processes not only turn substrate to productsBecause 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)


And 4242

E.g. Gluconate degradation by Klebsiella

a. By resting Cells (non growing): Ideal biocatalyst

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 fromGluconate into cell growth resulting in increasedacetate/ethanol ratio.


And 4343

YS =X (g/L)S (g/L)

X (g/L)S (mol/L)

YO2 =X (g/L)

O2 (mol/L)

Microbial GrowthSignificance of Special Yield Coefficients

- Only works for same substrate, pathway

Molar yield coefficient

-Works only for aerobes and for sameATP/O2

+ works for unknown or complex substrates(e.g. cornsteep liquor, wastes


And 4444

YN, YP =X (g/L)Mole of N or P

YkJ =X (g/L)kJ of heat of combustion

Ye =X (g/L)

Mole of reducingequivalents respired

Microbial GrowthSignificance of Special Yield Coefficients

Similar to YO2 but worksalso for other electronacceptors

Works also for fermentingBacteria, and unknownSubstrates and pathways

For scientific purposes underN or P limitation


And 4545

Microbial GrowthYATP

YATP =X (g/L)

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 ATPconsumption 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


And 4646

Comparison of YS and YATP for glucose fermenting bacteria

Microbial GrowthYATP

Organism YS ATP Yield(mol ATP/mol substance)

YATPgX/mol ATP

Streptococcus lactisLactobacillus plantarum

Saccharomyces cerevisiaeZymomonas mobilis

Aerobacter aerogenesE. coli

19.518.5

18.59

2926

22

21

33

9.89.4

9

8.69.6

9.4

The literature valuefor YATP is given as 10.5 g biomass/ molATP (Baushop and Elsden 1960)


And 4747

Microbial GrowthCalculation and Inconsistencies of YATP

ATP gained per mole of substrate can be estimated forbacteria 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 ofexpressing the yield coefficient it can also vary:1.Not constant for all microbes (4.7 to 21) in rich media2.Experimental YATP < theoretical YATP (30 g/mol ATP)3.Low YATP on minimal media4.YATP dependent on growth conditions (ease of life)5.↑ temperature → ↓ YATP (thermal denaturation of proteins)6.Unsuitable growth conditions → ↓ YATP

7.Likely Reason for less cells formed: Higher ATP usage for cell maintenance rather than cell growth Maintenance coefficient


And 4848

Microbial GrowthMaintenance Coefficient

1 mole of ATP generated during catabolism allows• theoretically → synthesis of 32 g cells• in praxis → 10.5 g cellsThe maintenance coefficient (ms) is the reason for2/3 being “wasted”1.Substrate transport into cell (e.g. against diffusion gradient)2.Osmotic work3.Motility4.Intracellular pH5.Replacement of thermally denatured proteins (↑ T → ↑ ms)6.Leakage of H+ ions across membrane (uncoupling)

ms influences Y, μ and the metabolic activity of the cells andis thus important to be considered in bioprocesses.

ms =S (mg)

X (mg) • time (h)

Growth- maintenenace

And 4949

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/ hmostly used: g substrate / g biomass / h = (h-1)


And 5050

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)


Effect of Maintenance Coefficient on Growth Rate

And 5151

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

Y(gX/gS))

Specific Growth rate u (h-1)

Ymax


And 5252


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:

µ = µmax * -------- - mS *YmaxS + kS

S


And 5353


µ = Ymax * vmax * -------- - mS *YmaxS + kS

S


u = ( vmax * -------- - mS) * Ymax S + kS

S

u = (v – mS) *Ymax

substrate uptake

µ = µmax * -------- - mS *YmaxS + kS

S

ms the respiration activity used to just stay alive

And 5454

Effect of Maintenance Coefficient (mS) on growth Rate

µ = µmax * ----------kSS +Sµ

(h-1)

S(g/L) including mS0

µ = µmax * -------- - mS *YmaxS + kS

S

ignoring mS

And 5555

µ(h-1)

S(g/L)

Sm = critical substrate concentration growth is zero

Sm

0

sm= ------------------umax- ms.Ymax

mS.kS.Ymax



And 5656

µ(h-1)

S(g/L)

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 mS*Ymax

- mS*Ymax

0


And 5757

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.


And 5858

Documents

Microbial Growth – Overview of terms: exponential growth u td productivity