#2_Fundamentals of Microbial Growth StoichiometryL

Quantification of Microbial Rates Consumption or Production Micro-organism

N-source

Biomass Product Heat

Substrate O2

H2O #1_Rates

H+

HCO3-

Marc Deront (Sirous Ebrahimi)

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Fundamentals of microbial growth stoichiometry • Composition of biomass • Anabolism • Maintenance • Catabolism • Coupled anabolism + Maintenance / catabolism • Microbial growth stoichiometry using conservation principles • Degree of reduction • Stoichiometric calculations in undefined chemical systems #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Biomass Composition Molecules

Elements

Proteins

30-60%

C

40-50%

Carbohydrates

5-30%

H

7-10%

Lipids

5-10%

O

20-30%

DNA

1%

N

5-10%

RNA

5-15%

P

1- 3%

Ash

3-10%

Ash (P, K+, Mg2+, etc)

Typical biomass composition formula (CHON :49% 7% 33% 11%)

MW =1∗12+1.8∗1+0.5∗16+0.2∗14 =24.6

C1H1.8O0.5N0.2P0.01 MW =24.6 gr/C-mole

1 kg dry biomass contains e.g. 5% ash  950 gr organic matter = 950 gr / (24.6 gr/C-mole) = 38.62 C-mole biomass #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Anabolism From C-source (e.g. glucose) + (…)

Σ of all reactions …

Amino acids  Proteins  Sugars  Carbohydrates  Fatty acids  Lipids  Nucleotides  DNA RNA ______________________________

gives the  Anabolic reaction

(..) C-source + (..) N-source + (..) P-source + (..) Energy 

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C1H1.8O0.5N0.2P0.01 + (..) H2O + (..) H+ + (..) HCO3-

For Anabolism, Thermodynamic Energy is needed for biomass growth and synthesis. #2_Stoichio

Marc Deront (Sirous Ebrahimi)

Note: No electron acceptor is required, only energy!

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Maintenance Micro-organism (Self) Restoration of : • Leakage processes • Degradation processes

Protein degraded

Thermodynamic Energy is required for Maintenance.

Pump out

Leakage of ions, etc.

Energy Membrane

#2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Catabolism Catabolism generates the energy required for Anabolism & Maintenance Catabolic reaction consists of a red/ox reaction, between 2 couples • electron donor couple • electron acceptor couple 1 glucose + (..) O2  (..) HCO3– +(..) H+ + (..) H2O • e_donor couple: glucose / HCO3–(soluble CO2) Oxidation: “C” Oxid. nb (0) (+4) • e_acceptor couple: O2 / H2O

C6H12O6 + 6 O2  6 CO2 + 6 H2O + Energy Reduction: “O” Oxid. nb (0)  (-2)

1 glucose  (..) ethanol + (..) HCO3– +(..) H+ + (..) H2O • e_donor couple: glucose / HCO3– • e_acceptor couple: HCO3– / ethanol  Gibbs Energy (kJ) produced − ΔGCat.reaction #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Anabolism/Catabolism coupling Growth system definition electron donor (D) + electron acceptor (A)

Catabolism oxidized donor + reduced acceptor

Biomass (X) C1H1.8O0.5N0.2

Energetically Coupled

Maintenance

Anabolism • • • • •

C-source N-source H2O HCO3− H+

Catabolism provides energy to Anabolism and Maintenance Note: C-source and electron donor are often the same compound (but not always) #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Coupled Anabolism/Catabolism C-source (Anabolism) and electron-donor (Catabolism) are often the same (e.g. organic substrate) Only a fraction of the substrate, used as C-source, ends in biomass. The other part is catabolized as electron donor to provide Energy for Anabolism and Maintenance requirements  Concept of Yield of Biomass on Substrate YSX

YSX =

produced biomass (X) ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶ ̶̶ ̶ ̶ ̶ consumed substrate (S)

YSX is the result of anabolic/catabolic coupling #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Global growth equation As Catabolism provides energy to Anabolism and Maintenance YSX is the result of anabolic/catabolic coupling The global growth equation is the result of the catabolic reaction (Energy) and anabolic reaction (Biomass). −

1 YSX

Substrate + (..) electron acceptor + (..) N-source(e.g.NH4+)

+ (..) H2O + (..) HCO3− + (..) H+ + 1 C1H1.8O0.5N0.2 + (..) oxidized substrate + (..) reduced acceptor Note: A + B  C + D ≈ – A –B + C +D (= 0) #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Stoichiometry of general growth equation 1 − YSX

Substrate + (..) electron acceptor + (..) N-source(e.g.NH4+)

+ (..) H2O + (..) HCO3− + (..) H+ + 1 C1H1.8O0.5N0.2 + (..) oxidized substrate + (..) reduced acceptor • N-source, and Biomass are always present with H2O, HCO3-, H+ are partner elements (from medium) • Substrate often acts as electron-donor and C-source • Only substrate and electron-acceptor are case specific • Most often only 1 measured yield is available e.g. biomass yield on substrate YSX YSX unit [C-mole of biomass /mole consumed substrat ]

What about the stoichiometric coefficients ? #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Stoichiometry of global growth equation 1 − YSX

Substrate + (..) electron acceptor + (..) N-source(e.g.NH4+)

+ (..) H2O + (..) HCO3− + (..) H+ + 1 C1H1.8O0.5N0.2 + (..) oxidized substrate + (..) reduced acceptor • By convention Biomass stoichiometric coefficient is always 1 • Often catabolic reaction end products are H2O, CO2 which are taken into account through partner elements … • If YSX unit [C-mole of biomass / mole substrate] is available  Only 5 coefficients are required to determine the global growth equation With Conservation principles - Balances These coefficients can be determined over atomic element (C, H, O and N) balances and charge (+, −) balance #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Example global growth stoichiometry Aerobic growth on oxalate 1/3

Establish the global growth equation for aerobic growth of Pseudomonas oxalaticus on oxalate (C2O42-, 88 g/mole), and NH4+ as N-source. The measured biomass yield is 0.0506 gram TSS biomass per gram oxalate (C2O42− ). Biomass has 5% ash. C-source: N-source for biomass: Catabolism: • Electron donor couple: • Electron acceptor couple:

Oxalate NH4+ Oxalate / CO2 O2 / H2 O

1- Convert Biomass yield YSX 0.0506 [gTSS. gOxal.-1] in [C-mole X / mole oxalate] Note: 1 C_mole X = 24.6 g Biomass [VSS]

0.95 gVSS 1 C-mole X 88 g oxal. YSX = 0.0506 [gTSS/g oxal.] × ———— × ————— × ———— gTSS 24.6 gVSS mole oxal. C-mole X YSX = 0.172 —————  Observed growth yield of Biomass over substrate mole oxal. #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Example global growth stoichiometry Aerobic growth on oxalate 2/3

2- Set up the global stoichiometric growth equation

f C2O42−+ a NH4++ b H+ + c O2 + d H2O + 1 C1H1.8O0.5N0.2 + e HCO3a.

Use YSX value to calculate f coefficient:

-1 -1 mole oxal. f = —— = ——— = - 5.815 ———— Ysx 0.172 C-mole X

b. How many unknown coeff. and how many conservation equations? 5 unknowns (a, b, c, d, e) 5 conservation balances (C, H, O, N, charge) c. Set up the conservation balances C 2.f + 1 + e = 0 H 4.a + b +2.d + 1.8 + e = 0 O 4.f + 2.c + d + 0.5 + 3.e = 0 N a + 0.2 = 0 d. Solve for a, e, b, d, c (with f = -5.815) Charge -2.f +a + b – e = 0

- 5.81 C2O42− - 0.2 NH4+ - 1.86 O2 - 0.8 H+ − 5.41 H2O + 1 C1H1.8O0.5N0.2 + 10.63 HCO3#2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Example global growth stoichiometry Aerobic growth on oxalate 3/3

Global Growth reaction - 5.81 C2O42− - 0.2 NH4+ - 1.86 O2 - 0.8 H+ − 5.41 H2O + 1 C1H1.8O0.5N0.2 + 10.63 HCO3Catabolic reaction to provide Energy Catabolism of growth consumes: 1.86 mole O2 and 3.71 mole Oxal.

− 1 C2O42− − 0.5 O2 − H2O + 2 HCO3− (for 1 mole oxalate) − 3.71 C2O42− − 1.86 O2 − 3.71 H2O + 7.43 HCO3−

Anabolic reaction = Global Growth reaction – Catabolic reaction For substrate : 5.81 Global_Growth - 3.71 Catabolisme  2.1 mole available/used for Anabolism 2−

+

+

- 2.1 C2O4 - 0.2NH4 - 0.8 H -1.7 H2O + 1 C1H1.8O0.5N0.2 + 3.2 HCO3 3.71 Catabolism fraction: —— = 64% 5.81 #2_Stoichio

−

Note: No electron acceptor is required, only energy!

2.1 Anabolism fraction: —— = 36% 5.81

Marc Deront (Sirous Ebrahimi)

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Example global growth stoichiometry Anaerobic growth on glucose 1/3

Establish the global growth reaction for anaerobic growth on glucose C6H1206 with ethanol C2H60 as product and NH4+ as N-source. The measured biomass yield is YSX = 0.123 g VSS biomass / g glucose C-source: N-source for biomass: Catabolism: • Electron donor couple: • Electron acceptor couple:

Glucose NH4+ Glucose / CO2 CO2 / Ethanol

1- Convert Biomass yield YSX 0.123[gVSS. gGlucose.-1] in [C-mole X / mole Glucose] Note: 1 mole Glucose = 180 g

1 C-mole X 180 g Glucose YSX = 0.123 [gVSS/g glucose] × ————— × —————— 24.6 gVSS mole Glucose. C-mole X YSX = 0.9 ——————  Observed growth yield of Biomass over substrate mole Glucose #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Example global growth stoichiometry Anaerobic growth on glucose 2/3

2- Set up the global stoichiometric growth equation

f C6H12O6+ a NH4++ b H+ + c H2O + d C2H6O+ e HCO3- + 1 C1H1.8O0.5N0.2 a.

Use YSX value to calculate f coefficient:

-1 -1 mole Glucose f = —— = ——— = - 1.11 ———— Ysx 0.9 C-mole X

b. How many unknown coeff. and how many conservation equations? 5 unknowns (a, b, c, d, e) 5 conservation balances (C, H, O, N, charge) c. Set up the conservation balances C 6.f + 2.d + e + 1 = 0 H 12.f + 4.a + b + 2.c + 6.d + e + 1.8 = 0 O 6.f + c + d + 3.e + 0.5 = 0 N a + 0.2 = 0 d. Solve for a, e, b, d, c (with f = -1.11) Charge a + b – e = 0

-1.11 C6H12O6 -0.2 NH4++ 2.12 H+ -1.47 H2O +1.87 C2H6O +1.92 HCO3- + 1 C1H1.8O0.5N0.2 #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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Example global growth stoichiometry Anaerobic growth on glucose 3/3

Global Growth reaction -1.11 C6H12O6 - 0.2 NH4++ 2.12 H+ -1.47 H2O +1.87 C2H6O +1.92 HCO3- + 1 C1H1.8O0.5N0.2 Catabolic reaction to provide Energy

− 1C6H12O6 + 2C2H6O + 2HCO3- + 2H+ − 2H2O (for 1mole glucose)

Catabolism of growth − 0.93C6H12O6 +1.87C2H6O +1.87 HCO3- +1.87 H+ −1.87 H2O consumes: 0.93 mole Glucose produces: 1.87 mole Ethanol. Anabolic reaction = Global Growth reaction – Catabolic reaction For substrate : 1.11 Global_Growth – 0.93 Catabolisme  0.18 mole available/used for Anabolism - 0.18 C6H12O6 - 0.2 NH4+ + 1 C1H1.8O0.5N0.2 + 0.05 HCO3- + 0.25 H+ +0.40 H2O 0.93 Catabolism fraction: —— = 84% 1.11 #2_Stoichio

0.18 Anabolism fraction: —— = 16% 1.11

Marc Deront (Sirous Ebrahimi)

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Stoichiometry of general growth equation −

1 YSX

Substrate + (..) electron acceptor + (..) N-source(e.g.NH4+)

+ (..) H2O + (..) HCO3− + (..) H+ + 1 C1H1.8O0.5N0.2 + (..) oxidized substrate + (..) reduced acceptor • Energetic coupling of Catabolism / Anabolism determine YSX Biomass yield over substrate [C_mole X / mole S] • If YSX is known coefficients are given from C, H, O, N and Charges conservative balances ! • As Global

Growth = Anabolism + Catabolism

• Catabolic and Anabolic substrate fractions are given by the electron acceptor stoichiometry of Global Growth Reaction #2_Stoichio

Marc Deront (Sirous Ebrahimi)

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